{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Room impulse responses\n", "======================\n", "\n", "- - - \n", "
\n", "![RIR Measurement Session](files/echoes.png)\n", "\n", "*Photos from one of the measurement sessions in the Lausanne cathedral. A huge set of audio-visual measurements is available [here](http://lcav.epfl.ch/eCathedral). Among other things, these measurements were used to [hear the shape of a room](http://www.pnas.org/content/110/30/12186.full).*\n", "\n", "
\n", "- - -\n", "- - -\n", "\n", "\n", "\n", "\n", "The *mother of all* tool to do acoustics is of course the linear acoustic wave equation. In room acoustics, sound levels are low enough so that the acoustics are indeed linear, and we can use this convenient model. But one thing we know about linear systems is that they are completely described by their *impulse response*. Since the wave equation depends on both space and time (it's a *partial* differential equation), better than using the term *impulse response*, we can talk about its *Green's function*. That's basically the same thing, except that the Green's function explicitely depends on the location of the sound source, and on the location of the receiver (microphone).\n", "\n", "**Room impulse response** (RIR) is then exactly what the phrase says. For a source (S) and a receiver (R) at fixed locations inside the room, the RIR describes the acoustic (linear, time-shift invariant) channel between S and R. So it's a Green's function for some particular choice of the source and receiver locations. Put simply, an RIR is what we would record at R if we fired a pulse of sound at S.\n", "\n", "The set of all RIRs in a room (for all possible S and R) is the complete description of the room's acoustics. Actually we don't need all of them. For example, an RIR from S to R is the same as the RIR from R to S because of the property called *duality*.\n", "\n", "Let's load some RIRs to see how they look like and hear how they sound like! The first RIR is from an emptied classroom at EPFL, the infamous BC329 room for LCAV seminars." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline\n", "from scipy import io\n", "\n", "mat = io.loadmat('BC-329.mat')\n", "fs = mat.get('fs') # Sampling frequency\n", "h1 = array(mat.get('h')) # Room impulse response\n", "\n", "n1 = arange(0, fs);\n", "nEarly = arange(0, fs/15);\n", "\n", "# Plot the first second of the impulse response\n", "subplot(2, 1, 1)\n", "plot(n1/double(fs)*1e3, h1[n1])\n", "ylabel('$h(t)$')\n", "\n", "subplot(2, 1, 2)\n", "plot(nEarly/double(fs)*1e3, h1[nEarly])\n", "xlabel('Time in [ms]')\n", "ylabel('$h(t)$')" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 1, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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oEBkhxJwkt1XWVQYmPT1dY56oqCiMGTMGAwYMQEVFBXbt2mXuMAkhhBgguRaM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\n8L755hskJydj48aNAIBt27Y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"text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we plotted the first second of the RIR, and we also zoomed in to the first 70 milliseconds. In this zoomed-in figure we can see some distinct peaks that are in fact echoes. More on this in the subsection on the *Structure of RIRs* (further down).\n", "\n", "Now we'll load and plot a room impulse response from the Lausanne cathedral!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "mat = io.loadmat('Cathedral.mat')\n", "fs = mat.get('fs') # Sampling frequency\n", "h2 = array(mat.get('h')) # Room impulse response\n", "\n", "n5 = arange(0, 5*fs);\n", "\n", "# Plot the first second of the impulse response\n", "subplot(2, 1, 1)\n", "plot(n5/double(fs)*1e3, h2[n5])\n", "ylabel('$h(t)$')\n", "\n", "# Plot the early part of the impulse response\n", "subplot(2, 1, 2)\n", "plot(nEarly/double(fs)*1e3, h2[nEarly])\n", "xlabel('Time in [ms]')\n", "ylabel('$h(t)$')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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BAwEAISEhSE5Ohp2dnV62z+ySip+fHzIyMpCVlYWKigrs2rULwcHBxg5LL+q7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\nu2mTiBUgev/95sW0eTORjY1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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see how the spectrograms of these two RIRs look like. Spectrogram represents the spectral distribution of energy over time. It tells us which frequencies will be amplified and which attenuated by different portions of an RIR. In the figures below we can notice that high frequencies are much more pronounced in BC329, perhaps thanking to flat, very reflective surfaces (glass walls for example)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figure()\n", "\n", "subplot(2, 1, 1)\n", "specgram(h1[n1,0], NFFT=1024, noverlap=4);\n", "subplot(2, 1, 2)\n", "specgram(h2[n1,0], NFFT=1024, noverlap=4);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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EBqltzjjQtp1Kr/UuMUeNvRHX2ISv3MShl+ATNDe5uL8ugas81INqdRA1MCrQ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\n7xJ6AZ8dtqkYC/eHgM8xWPWbEq+OozQhTPsr0mxhnTWs4SX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JuIDENGkM4A7ezIt5Rfa8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peZ45XqHn74bvjv7h62TTyP3L5a4Ag4VCTbK+B6RddFuj7ejwP1nQO1fQDsb6AlcHoDyfk0mWvX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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is a very good idea to listen to room impulse responses. By doing that, we can really appreaciate the difference between various acoustic spaces." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from Audio import *\n", "\n", "Audio(h1[0:3*int(fs)],rate=fs) # Play the BC329 impulse response (3 seconds)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "Audio(h2[0:5*int(fs)],rate=fs) # Play the cathedral impulse response (5 seconds)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another good exercise is to slow these responses down by stretching them in time. This is equivalent to playing them at the lower sampling rate... of course this will also pitch shift them so they'll sound deeper." ] }, { "cell_type": "code", "collapsed": false, "input": [ "R=14;\n", "Audio(h1[0:3*int(fs)],rate=fs/R) # Play the BC329 impulse response at a lower sampling rate" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 16, "text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This seems quite neat. What do you observe? What can you hear? Compare this with the cathedral's RIR slowed down." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Audio(h2[0:5*int(fs)],rate=fs/R) # Play the cathedral impulse at a lower sampling rate" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Please note that some audio players may have problems with the value we divide the sampling rate by (the variable `R` above). In those cases you may change `R` for the playback to work." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Structure of RIRs\n", "-----------------\n", "\n", "How is an RIR constructed? Well, an impulse fired somewhere in the room travels to the microphone. But together with this direct path impulse, echoes from the walls also arrive at the microphone. Echoes generate new echoes from other walls that we call higher-generation echoes, and this goes on and on until the energy is absorbed. Every time an echo bounces off a wall, the wall absorbs a fraction of the sound energy (we increase the heat of the walls). Additionally, different materials absorb energy differently in different frequency bands, so the walls also *filter* the impulse (if we look at the wall as a filter, its impulse response is not a Dirac---it has some finite, non-infinitesimal duration). This means that with every reflection, what once was a perfect impulse becomes more and more spread in time.\n", "\n", "Next important effects are diffuse reflections. For most of the frequencies of interest, and most of the common materials, the walls are essentially *mirrors*. That is, in order to hear a reflection of a point source of sound from a particular wall, we must be listening in exactly the right spot, so that the incident angle of the sound waves with respect to wall's normal equals the outgoing angle. Check out the following figure that explains the image source model. Image source model says that these echoes (which BTW we call *specular*, again in analogy to light), can be modeled as virtual image sources of the original source.\n", "\n", "- - -\n", "\"Image\n", "- - -\n", "\n", "But also similarly to light (typically in a much smaller proportion), some sound energy is scattered around this *ideal* direction. Even if this energy is very small, and difficult to even measure for a single reflection, it is quite important for the perception of sound in a room. \n", "\n", "Another important effect not modeled as an echo is diffraction. Diffraction is essentially *bending* of the sound around edges and corners. It's the reason why we can hear someone talking around the corner, even if there are no walls around. Again, these contributions are really important for the listening experience.\n", "\n", "All these effects together are reflected in the structure of an RIR. Take a look again at the RIRs we plotted earlier. We observe that the early part of a room impulse response contains more or less isolated, well pronounced peaks that correspond to individual echoes. But non-flat fading, diffusivity of reflections, and the diffractions all unite in the latter part of a RIR to create noise-like exponential decay (of course, an equally important contribution is from the fact that echoes get denser and denser as the time passes). In fact, that's how modern auralization software models the tail of the room impulse response---as noise multiplied by an exponential decay. The rate of the decay varies wildly between different rooms, and is linked to *reverberation time*. $T_{60}$ is defined as the time for reflections of a direct signal to decay 60 dB. It varies from around 1 second in speech-only lecture halls, to around 2 seconds for generale-purpose auditoria, to for example more than 8 seconds in the Notre-Dame cathedral in Paris, and then some, as in the [world's longest echo](http://www.bbc.com/news/uk-scotland-highlands-islands-25757937)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Measuring RIRs\n", "==============\n", "\n", "An important practical question is how to measure RIRs. As they are \"responses to an impulse\", the first idea is to simply use an impulsive source of sound, and record the room reponse with a microphone. There are numerous drawbacks of this simple idea:\n", "\n", "* RIR is a response to an idealized impulse, a Dirac delta function. Realistic impulsive sources are only approximations of the Dirac, and usually not very good ones. Even if we might think that popping a balloon or firing a starter pistol generates a very good impulse, this is not very true (see Figures ??),\n", "* Repeatability is an issue: popping different balloons generates different sounds,\n", "* Sound level is an issue: most sources are not loud enough (even if we could think they are) to yield sufficient signal-to-noise ratio (SNR) in the recorded response,\n", "* Directivity: balloons and starter pistols are not omnidirectional sources (most loudspeakers are not omnidirectional either, but we know their directivity patterns).\n", "\n", "A very good way to measure RIRs is to use a loudspeaker. Again, we could try to reproduce a sound impulse through the loudspeaker, but the energy we would require in order to get resonable SNRs would destroy the loudspeaker. That is why in practice we spread this energy over time. We play a known sound through the loudspeaker, and then deconvolve in the spectral domain. Denote the room impulse response by $h(t)$, and the sound that we play by $x(t)$. Then the microphone measures their convolution,\n", "\n", "\\begin{equation}\n", " y(t) = [x \\ast h](t).\n", "\\end{equation}\n", "\n", "In the frequency domain, convolution becomes multiplication\n", "\n", "\\begin{equation}\n", " Y(\\omega) = X(\\omega) H(\\omega),\n", "\\end{equation}\n", "\n", "and we can estimate the RIR $h(t)$ by spectral division as\n", "\n", "\\begin{equation}\n", " h(t) = \\mathcal{F}^{-1} \\bigg\\{ \\frac{Y(\\omega)}{X(\\omega)} \\bigg\\}.\n", "\\end{equation}\n", "\n", "This formula suggests that we want to pick $X(\\omega)$ which is flat across frequencies. Two common choices are maximum length sequences (MLS) and sine sweeps. We will look a bit more closely into using sine sweeps for RIR measurements.\n", "\n", "Sweeped sine signals\n", "--------------------\n", "\n", "We always measure the RIR in a certain range of frequencies. That is, even if in the ideal case we fire a true Dirac delta function with infinite bandwidth, we can't do in practice, because loudspeakers and microphones have finite bandwidths. Dirac is one extreme---the other extreme is a sinusoid $x_0(t) = A \\sin(\\omega_0 t) = A \\sin(2 \\pi f_0 t)$. A sinusoid contains only a single frequency (in this case $f_0$).\n", "\n", "The idea is then to cover the desired frequency range $[f_1, f_2]$ by *sweeping* the sinusoid's frequency through it. The test signal has a general form\n", "\n", "\\begin{equation}\n", " x(t) = A \\sin (2 \\pi f(t)).\n", "\\end{equation}\n", "\n", "We call $f(t)$ *instantaneous phase*, and its derivative $df(t) / dt$ is *instantaneous frequency*. \n", "We can choose how to vary the instantanous frequency from $f_1$ to $f_2$. A known acoustician Angelo Farina suggests to use exponential sweeps, where\n", "\n", "\\begin{equation}\n", " x(t) = \\sin \\left[ \\frac{\\omega_1 T}{\\ln(\\omega_2 / \\omega_1)} \\left( e^{\\frac{t}{T} \\ln(\\omega_2 / \\omega_1)} - 1 \\right) \\right].\n", "\\end{equation}\n", "\n", "Here, $\\omega_1$ is the start frequency, $\\omega_2$ is the end frequency, and $T$ is the total duration of the sweep.\n", "\n", "Sure enough, we need a discrete version of this signal, as we want to generate it using a computer. Denote the sampling frequency by $f_s$ and the corresponding sampling period by $T_s = 1/f_s$. Then the duration of the pulse in samples is $N = \\lfloor T/T_s \\rfloor$. We obtain the following formula for discrete $x$,\n", "\n", "\\begin{equation}\n", " x[n] = \\sin \\left[ \\frac{\\omega_1 N T_s}{\\ln(\\omega_2 / \\omega_1)} \\left( e^{\\frac{n}{N} \\ln(\\omega_2 / \\omega_1)} - 1 \\right) \\right].\n", "\\end{equation}\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "f1 = 50. # Start frequency in [Hz]\n", "f2 = 10000. # End frequency in [Hz]\n", "T = 5. # Pulse duration in [s]\n", "fs = 44100. # Sampling frequency in [Hz]\n", "Ts = 1./fs # Sampling period in [s]\n", "N = floor(T / Ts) # Pulse duration in samples\n", "n = arange(0, N) # Sample index\n", "\n", "om1 = 2*pi*f1\n", "om2 = 2*pi*f2\n", "\n", "x_exp = sin(om1*N*Ts / log(om2/om1) * (exp(n/N*log(om2/om1)) - 1))\n", "\n", "subplot(2, 1, 1)\n", "plot(n[0:int(fs)], x_exp[0:int(fs)])\n", "xlabel('$n$ [samples]')\n", "ylabel('$x_{exp}[n]$')\n", "\n", "subplot(2, 1, 2)\n", "plot(abs(fft.fftshift(fft.fft(x_exp))))\n", "xlabel('Frequency bin $k$')\n", "ylabel('$X_{exp}[k]$');\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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MCoiXlQqoEOaC4i6ZHnnkEafFQYHw8wjXXnttR/qUc2hzQKRy6HiuXG2ZKiCq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\niMfjGDBgAI4cOYKpU6di/vz5+M1vfoOTTjoJt99+OxYvXoz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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "specgram(x_exp, NFFT=1024, noverlap=4);\n", "ylabel('Normalized frequency (1 is $f_s/2$)')\n", "xlabel('n [samples]')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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5udP92R4xgwKGG8R6kJblYjG5dRcBCxFuS5ifhiIsRmHBYhoO0SfbLe1f18v/\na4HEDBHGtXWY9U5tHBbAmglrJj/LYFS5GtRWY/Ryj9bkRWHhuZsiFrgCvdZ8Lrweg1F2CjLSz75m\nkcp1hzE8ZVnBNYY/9czZiq2hP7q/rFC0qm9LrUJtZVlkrRm93st+SxFeTdMiRofWRTgXel+K3O47\n+KaDy3UILMblQh4Q+152ox9myrAs1HUdrrzySjznOc/B/v378bCHPQwPfehDsX//fjz72c/Ghz70\nIcR4D02OZjJsDmttzBI62mqQ+xpVn9ZcWTvXdWhrxmJcfN8S5j1FzIimYDG2xFD5nRkPf2bIxxq/\nhsV0H7SGqqEbqZfrB93D5bzxmfur27QElJRnC4afl15PU5q7LsfrZwmsxvVZa8F6jhbTtCyBJW1b\nY7S+rwOzWePgYIap+2QdiFJm+TBrgqGGLsxBqKED+ICji4Pva+cCc4Bv6rCYQ0TIZqxHd98VLgcO\nHMAXvvAFXHrppfjWt76F//7v/8b//M//4Fvf+hYuvfRS/PM//zOe8pSnHO6+TpOlVU6VZW10auG5\nShlmYLo9Wfx6k9cEHDBktNxHTRpTn3uC1gas3TenyWnBXRMuPF59ne8vEAT9vmRFsmWlBQyPb4rR\n8LO35t0SllqwWvdYCkRNQMk4rD7W5kELfw2/Tq1jbRXrsfHzq/WXhbVW2pasRz0OLYR4vgKGL+Rb\nMi4f64rAUr5Q6skMfwoW8/m8iraQjfLO5zDlnbLu7+W0CBb727/9WxMC29zcxBOe8AQ84QlPwN13\n373jnVtMzKRY+2EtkmPurZBB3iz6lPkS4vun3j9h/a43WFDXWDA59WcxGA2z1Hwd0pY1Rr5nbjMw\n9MfMS99b07atzaitTrZsdLvaotRt1ITaEmJBxr/VSASDToiphanFoK2yVj+sPknbc+tWW4I1iIvL\n6XHUyLqmLTfNhKUtbSHLHGjLZema9ACaCDQtsFLSmv2u5jtWllPKF5ZefzyAyPIzkMOSPmchbfOD\n3o2WiqZFrHNzcxPXXHMNrrzyStx4443l909/+tP42te+VsrcIyTrpgYn1Ex5zbinyjHcsa7WwZvL\nguhqcNy6xNbSXD90W974DPqsfQ7WPEwxNh67hpGs/ur6a9r6lNDUY+Q6p+bC6otluc4x8hqMNcec\nLSWB+8pzYQkG/Rytdab7qa9tZ53X+iHfl1g1vIalfIs+6oyF0lKoUeqVsqbfJ/tFfG8iOZctl3yf\n9x1CWBXNROuAAAAgAElEQVQB4lxEaFaD8ysIgG9SFmT42Fs1o+6kQ5M+a7rp8300ceXv//7v4z/+\n4z/w8Ic/HO9+97tx/vnn4zWveQ2e8pSn4OSTT8b3v//9w93POlmQlNYypyyXWp01KEgzcE5c6VUZ\nvbn0OY4pqo2jtqmWwC7M5HXaftD/tblhwSNtWX3ScJA1F5rYAtEn9NexHqdgIQ35zAkNhtd4LViC\nFUbdPGa2aLhPS5QJvQanxrh0rqTfnLuLIxktuJD3ErcnfztxyJyfidQ556cJEePkXapOhtlq63sw\nzx2cd4is1MyR5X/j6n1EQIvdeBrfokXC5YQTTsAVV1xRvl999dV4y1vegte+9rXwfp3VfJhIwwSa\noU3dw9j7HJxgXWMGooWc1Cmbg0ORmWlp7ZJhMas9ywJaCoXM4dfWb3MMkIWn5QvRjL1W/5RQsywN\nnjdmeNIWn2vSAoSVgdrYtFWnBZJOBa9pyse0XcvAskp0/5bAuVqbB+qWZO1+FgK8nmuJR+W7ts70\nvuFxbAE4uHAsTiCuJgkbXlfacrSsKQek1xe76l7vc4N5tK1PZ1l8hw5h/IzvBazxnqRFwuWoo47C\nrbfeissvvxwvfOELceDAAZxzzjl4xzvega2trfkKflKk4SvehEstlznYZYpkwdY0LW0JWdc1nMCw\n1BK4Qgta+a1WrgaZaEhmarM49f8S0oLUwvZZiFrCiZ+15SNgBqX7WuvT3BiFZK1pYa0tlClFR681\naUesBnlZWE0J0X0XRWaJUsLQWk0gLPEFWVQrp32dVrv6GW5hOF4PwGUBsMQACG1uw3iwE2MZyN3c\n1+InsSySph2tT48WoXKStIfF0uewC62ZRazzpS99KT7xiU/gpptuKpbKSSedhEsuuQRvfetb1270\nqquuwllnnYUzzjgDb3vb20bXb7nlFlxwwQV4zGMeg0c96lF43/veV69MNiJDEku0L0v7rW1KC0bR\nZTWjY6etV/cKzeH2mub6yFDGFESkIQ8Wagx9yTUL9tLf5/B9bR1OMamp66xdT41RE8/RlK+LLRW+\nxn4AS/vldVKz9rRiwfdwfUvqsBg4r72lCpKeQ71+oerQVoh+VrwHdP848ovb1RYeP6ctAIcaK6T7\nqA5SD/KESTc8+WByGHIgp72ceRk48UMSNN5F89nJIUrHuchatxszvwBYYLlce+218N7j+c9//uia\ncw4ve9nL1mqwbVtccskl+NSnPoX9+/fjcY97HJ7xjGfg7LPPLmUuu+wynHvuuXjrW9+KW265BWee\neSZe8IIXoGmM7s5pU8wARBMU62WKLMczMxGmqayvXN56299cvzXVGGpN4GnnvKWp6jrmEj4yzTFA\nhmnYorDqlrKdKmtZLOwT0f3j5637pOuIsPtTE0JTc289A2aUMu+amc4RC1TuQy3Sq2ZlaWI4UfrH\nr4SeUihQKXeojFK3cxfGyWgH7UegWQFObRa2GB0S3DU32b4FAi1yj+zPmbhFYDEXcnsRzrBCAroM\nnHiknGK7PyvyrN73iEc8Av/1X/+Fd7zjHXjnO9+Jf/mXfzmkBj//+c/j9NNPx2mnnYaNjQ0873nP\nw4c//OFBmQc/+MH44Q9/CAD44Q9/iJNOOskWLDyKqSgZ3nSuUo61vKXmv0WWViukNUI9hqDK6evs\nz1jH5zLnj7F8PNY8TdWh57xmqVkWw1Tduk/6mgU76XKsGNSERo2kj/o51vqrn+OclTa3zqas3Q36\nPGXtTLVbs8CtMWoLj63z2nO0LMGadcbPp7qu40T/cgJKZ8BX0lYtV5n+qTY/NXJZvhGE6X2HBi0a\nJUwAgcVE+4mj67uBZi2Xpmnw1Kc+FU996lMBJOHwzne+E13X4cwzz8SBAwemGb+iG2+8Eaeeemr5\nfsopp+Caa64ZlHnJS16C888/Hw95yEPwox/9CB/84AfrFbIWbmn6vJhFS51aMMwU13HKsTYt33nj\nAeO0LczwLE2W61zq2lrCYKS9qXIMAx0q8caeKqPHzs+B+6OZmSU0uMy6bsG5NcJltqtw8rpkAcEK\nkfZH6H7V+BEzOcu6sYQ8+0K00JgaQ22e9LXtrqVNAPu43giELnPyec7vXETUkyDwnJxzCR2cG74t\n0vkOzrm0ZUML17TltL3LIcoxuvI9+BR+PFBgVfdc9q3sRkFi0XKpkOnxj388Hv/4xwNIkNmf/umf\n4uDBg9i/fz+e9rSn4dhjj528302FDGb6gz/4AzzmMY/B1VdfjW9+85v45V/+ZXz5y1/G8ccfPy78\nvjemhfK/AJ50AHj0Ads6kE0j0JiOJKph4bzBlmL8tXKWNaItq7k9Y9XNDIOZq8OY2WpGy5qi9Zpd\nYXi6D9o5K79NWSEssHWdc5ATfz9Ugafb0gzVgs/4z7JOeexcP0N11pqzGLRT5YXmFB69Vtlp38G+\nX/q6JOW+da22HmUtTgXOeIyFM1u/DYBjkCy0dckD8BEuRKBT3Rid+k8+lc63gG+qe1DyhHWdR8x8\nLPg2CzAHeMC7nOF4QkHR6V7YuX+46Oqrr8bVV199WNvQtLZwYTrzzDNx5plnAgC++93v4mMf+xh+\n67d+a/Ke/fv344Ybbijfb7jhBpxyyimDMv/wD/+A17/+9QASLPewhz0M1157Lc4777xxhS9+Y9oY\n3wbwwEqjgi3r0FGGE5bCE1rrA4ZJKTVpy8XSJK3FXIOQpuAjC9bS9TL2vw6xENK/y7zU/Dg1v4Ue\nO1s4WqBY5fR8WBAZX5N7OGlkpHuYaVrwWY2ssVvPQ8otXXNs/S6F8YD6Oqn1RzJSONTT5LPFuBQq\nkvt4zfA6lnqmBNkmeuHCypPs6QKFGRWUZ9kCQWlJFrTmgGr6mBq5bB2V+lKCSzSAdx0kSWVHA05F\nOzTo1mrqUOjAgQM4cOBA+f6mN73psLe5E6AHAOAhD3nIrGABgPPOOw/XXXcdrr/+ehw8eBCXX345\nnvGMZwzKnHXWWfjUpz4FALjppptw7bXX4uEPf/iyjjATYU1T/67hK73o191E+h5r8U5F8dR8H9xH\nPUbWEKee5FKIQsNz3N85+MMZ9+j5tJieBWlN9Yn/B+rWn57b7a50ay0ww59SCqZ8bFzXFE35XALs\n9a7JUoim+jPnB+M69d5aZ55re4bHomExUM4vq8q5+ZRIMf3aDUUhdPmkfTo74wkWsylOjt+j7n/Z\nrXRIlgsAXHnllfj2t7+Ns846CxdccMF8g02Dyy67DE972tPQti1e/OIX4+yzz8a73vUuAMDFF1+M\n173udXjRi16ERz/60ei6Dn/4h3+I+9///naFenEvJVnYGhbTzGFdpiT3MMQkm9CyXHSf2ArQfZQy\nrPGxdstCUgsT2bQcDTQFsyyDtBPxnO1UFgsNVVlCVDvqLcFlQYFTzHZKO9dzNucT4d+t71Z966w5\nC8LjdWDBTrrcEj43pVhYwo8VtXXRHj2Hsm4HbXZV2MqFDjH7RJxHCieOIVkWlefqHEqqls6Rh8bF\nJFxmyIldYimqC+g+nf5liu68807ccssteNCDHrT4ngsvvBAXXnjh4LeLL764fH7AAx6Aj370o8sq\nW8IABf5oMe9Yljq1xbNd0sKAyXKs17BaC07QtK6GyoyowAyV8kuZXo3Js+9H91cz4CmSeyxGoeub\ns4SWkLYONTNnwaDnkzVyWXdWUAlDVNx36xXAzLSmnPXSVxEgouxoa0rKWD4Xbo8h4XUt+nXu0Vaw\nRMRpKopFhG+69MqPkbBPSSVjSxcknYw6juBzAspB2n2k+p3KOwag+F+CW8GjQ+s8kM+4+Ax3SYhx\npxZcOjTZZoGye62YRdvsr//6r3H99deb1377t38bb37zm3HdddftZL+WE1stLAx4kQppWIU37JxZ\nb5nsDGPN4dE1gbHORq2RpSnVfCR6nBbDqEFwGvpiC28JfMb1TfkFNLauITMW1kuEKTNUDWnVrD3d\n1nafFQs5XceclcRr2hr/VH/WLVMLWpDrLKy2Mw8jayQCwWCs/LwdknDZjkN/UGeKCAPQB6JItLLP\niSYV1MavKBYYy+VDkCGMITKHOLakXQoxDhkK48+lLysH2IbYEU+LhMtnPvMZ3HLLLQAwOpPinINz\nDs95znN2vneHQqxp8WKVa0udtVyfBXlo2IrLa0HEzE2TZpQWQ2GBYEUFTdES62DOV1HTyGsWBP9N\n9Wu0KWf6KW1wHfLbnG9HWxdW/yy/xpyVZMGqljBZ13Ka8rnoumuWhWWxZM1+UsBrC8lS1jz9P6Uw\naKtPXwPsQ69qn8qbHrebIh9A9R0xKWeYWC9xdM3KcAwkCyW4juYs1zGxjkXY9FmRd98hykWAz6//\n+q/jLW95C+666y7ceeed+PrXv45zzjkH55xzDvbv33+4+7icZAHPOY712rHglDlNfKoPFswAjIVF\nTWu2mB1DHZ7K6c8WgxZIZh2mZsGCU/fz/DIDZ0YODMfG2rD1vLSw0AJaW5BWHdrnMqV5c/+Z5LvF\npKGuaYbP45d1x7/XYLYlpOen9vx3Si1mYeKQLA/vKkrIghPxXIdWEHgvWvNhCPyUBr9FdED0HRBW\n8KFFjLToLFjMIb1zJXTwIaJTdcspfIs80on8CD/sq0c6O5OveXQpXBkowmS3O/YXCZfzzz8f559/\nPgDgj/7oj3Deeefha1/7Gj7ykY/gu9/9Lk455RS88pWvLGHJP1HyGKZfWbqRGAqwmBLXv2SWWKhZ\nJ4AFQ69pgdwnbRlMQXVWXXNzIPO0nQgfi4ThzqVGX+d369o6kMyURbfU2qv1Sf40xm/1j4VizUci\nz6GWdLJWn9W3QP/LuhWfy6Cc4EJZw25dX/9OrAsWnpa1W7NiavOH3GcW9ACcA0LTovXRnF/n4niq\nZD708+NmJTCg8iKx/iVgFE7sAIcOwbVAs4JzYpHkrMmAKVTu05YL06te9SoAGLzW+C/+4i/wkY98\nBK9+9at3rmdLqcakWROSz7WsyFpL6jC/0JdSMD7zobalG3iOsbJWLcSCscb8uJw+RCn16VxsU4Ji\nSvPWEOU6dbJlWWN+teejmVutnRrDttrj+fQYKw1LBWHtebCw5nEvWS9L5lL/3sTEqbUQYislIFkZ\nh4MkRFjalfFuYNmYx0jWkOQ5iuWyZmSey074Dm50ELz4Ulj4zZBHBx/b2ZDoI5kOOVoMAPbt24ez\nzjprJ6pan7R2JBuIr00lqmSoiRmQ1g4HsJOKPtHvf7D8JcJMBS3g+mrWU83fwVqpbELr4KG2ZoSx\nePRMZM7a4/nkAAFHvzHz19YLC4OV+p3ngWEz7tNU/yzhLPNmKRwiKNnXIifr9ZqR+mvKhDxTURKs\nbAW6Pp5HFkxzQq3m++LfgipvjV+35TskDMnogIZga3Vsx18mbYcItOxQwRh2VH2QcGMXgMh9G736\noANCkiKpfJceCWdEVjzB+xbeDxewA+BDm2GxfPrepU/jgiAelOoK6NCqsk4xJHkz5W6jHREuv/Eb\nv7ET1WyfLE1R1qwwEz6hL896LrR3CWlGJEJENgpDEi21Z70HxBJImtbRiNkC4fYsDVzKST/X8Tfp\nPhUtO6ZomKnylhBdR5PzyEzKDa1PaUN8LrrNqXlkK8GpzzUGalkWLMw5FLlGc5aftLMOE5d7RsKG\nDiOycLHm0BIoDb2YS1fuIhBW6Zp3dS7D5aIbavEsXAcKYyy5vUbV5VcPt/msigMQQofIUohfmwyk\nd7GENvlqYk2TqJNAWi28uaYcIhq0aJFSxIggcUq47EbaEeFyjxL7OETLkQWpnfa8wfU1FhJ6YS+d\nJdaOLWJYTN9nlZO2BSKxtFG+h/uurZZaf+eYlNQ3d8aLYQctLHQfLbKgGg5iaJCgG3H+MlSlBcBc\nP6euLblf+nWoPEFDfOsqrzrwhNc+Q5ojgU3+luj6/4W08J1bS5aF56QdN+4rC2FLKZQxbGGIKph6\nShIoHftFGCHQ9zD8FvM/luHmuzIlzuU/sOyL8BRi7JGsKe87eLdK74exfDW5Bo8OTezgVlnO70IB\nc6iu3HsP1aCQOS3QYlA7TZrhM4NibdgSDFD3LGXWwNDnYjlWGR6yiK/NafpTSt/UuOZoBM1Mh3iW\nPVqD2rTfZ6otoF9DFsxozb1T15jh833WWtWWFX+W+/iZaAWJLVC5x4oc8zFDRkjwEb0Uq5Tl+mK+\n5uO4vimBHtyy/SRldMCLNe88hkpIsSiQFnOfsh6D7/IbJVfZQurgm3SuJbh2Grqi5+oQ80vDbEe9\nwzDIwMU9h/69k2TxTQkX0Qo745512gnA6ASvvs5MQH6H8Vk0/HUZbs1pz1lva8TMdZTEM0NLhXmr\njjHjFbjPmgqLQeu+Wv6xKeJxCWOBG7fFwnQd0gKen2P5Y65HZUUhsXwumglzIIcev1O/e4xP1ev7\nLD/M3PM3BWhMDLUNea6dsZfk/Ifhayh9ypalXltLYDyZG7ZcDOGSorRydNhEnc7FlDYfOarLd8n4\nXqF/dfKaxsIQ4krzILBYhzCYC++7HKkWSyAAAIScdr8/ob97aS09/YMf/GB5ideb3/xmPOtZz8IX\nv/jFw9KxtUhv4trBvqVRRpamXTZ93oiDPyNKhBmPpZFOjcHqk1U30xqRL2sRzwV/ZphjyvLTgqFW\nv/7j4IWpubVI94kFPj+LJtatGG6LP5sWT+zrqvXJUjosq2JJoIful76u15kW6qWtdqwssfCy7lli\ngXIIL/eF4c2GTs0DdWWFBWZo4YINNwEoJ+hH1x36hJZbSAKGxuWQ7/O9HypBXvkd9003fAVy6bB8\n7xCwApokxELlTZSjd7lkf6yPuzO32Frs6M1vfjPud7/74e///u/x6U9/Gi9+8YvXfs3xjpNmekJL\nIaM5KGwgrBaoOlMMVMMbzERChJkOw6pjCfH4WavV9w82LwnJddrSgtCjd/j6btz3mtCoUU0oOyQG\nFVZ1i3JUHsPosKlyNR/WUgokdLSCYSkuS0gLKGsOGe7cjnW8qB9ZQBzKSXkWQuILYWtlwf4sAsUQ\nks6nvGMlAEB8h5XXCoiFY15TZ1HEihkIixwkkfq0qkJp4qfZjX4WprWESwhpVX/sYx/DS17yEvza\nr/0aDh48eFg6tpimBIpmJoxZ18ox41mHAbJ2qKEarq+24a1xsCBawgy1oLU0dtDvcyRzwmNbck+t\nbgvSm7LOBlBVHAordvYXixK9Rcdj3Emrbk4wLhEU+lnNWU5z1lBDY1/k34n9PBa4S92zdM7K+qww\nSnl2orjU6uyQrApB3qYEqEO/FnQ/pEg+5Dhi4HcBOIgyT95H+Gb7CSRL5JdDntNkgvkQB7AYO/6H\nJ/Tlt90naNbacvv378dLX/pSXH755Xj605+Ou+66C113L3NEsaXBG503msXYNfPdrrYqfVjCiJkE\no9ftauYwsDQwzZxqjKkwpcp9mpasksMxZxYjz6+lLc+stifXsQaE5uZT99fy79Tmdl1FpRZIwde2\nzY8oDFkEjTiyQzfcJ0Xx6vIf7Ggv8ds0nf0ca4JOqGa5aJ9LDh3ettZ/J4C7QX00EkoiwViNTyHK\noUmWkVVOhEM6RNnC+RbBdcmZ78Z+FavfrvL7kU5rCZcrrrgCF1xwAT75yU/ixBNPxG233Ya3v/3t\nh6tvy2mOsVm/L4XFhGSDhW1go7p/wiCs0MwlddTGuwRa00yuMI7VkNEsqUPan4sqk7kWxqFx/CWM\nfMDw4/D3KbJgQLbCnPqz+t2gZ65a8MyFQ9eUHd321HosEFGc9sdI2ZqfqlgR8tvMWrE+L6aKEyUL\nIdes4MTn4pDgqrsxDiFeqqgFwDUpt9jA5+KQDkHmA5W4GwPLhQcn+cUsYlhMXvzVWyRqOefXAHjq\nh74/OfSlrd0JkS2KrXnyk5+Mz33uc3jgAx84Tn3gXHHy3yNUokaoX7JRJeyQI0NqGrJDH+XCGr/W\nuFzEMH23z4zHAw2rWOgZkbTNGuecwbeO9TOnFXJ9NUZqlZe65T5mysU3E1G8pRacUt6R4cYQB0Mw\nGgZZ0r8pYeDRRx8xAy/POAvS4IHg1rc0B+0KHKK2k468K1YA9WnddmvWqLa6eLyD9dv/7306YBg7\nY7L5WVl8L0djWYf7nYtwTboWdbi0NV6f25DDrl79r9t3SHvOd3CdIVCQxhZyGHHH49sEcDTqflSd\nT8yhz5Zsdr3PbuxCB6gcZ8naWSHm9wYMfC35+Qt8tttokXD53Oc+BwC4/fbbD2tntkWyMIXmoCBr\nwVrXGBqYxNeFg2USQWalD59MQ5PhiDluU8Ot9W+sYesMtVUGlTstp92bif5qGqhv2cILHbAyxsMC\nS1swLACQ+6DfJMmMR4REOzFvge6RqQjImL2StNovt66hKvPa5vq9m7dKpa0lIbxaq6+uTfJxRLd8\nHFMoAPXJOaQXcXEffYfRu+zFEm7Hg0lCqEWUtz/qx6GFkfUyL6GlQvo49KHIEwqMJ8vLu/oLV8SP\nEp1L73nJZUNoEYz0L2KtlASXO+kPvJfRkX/OBSDYAMNFUHtowpjYYS00YsrA5Cq0+mLdwhtGrCT5\nTcMpDNk0sRdYjRufn7Dat05s12gnFrcwY060KFqhfG6wHqOWsbPF07To3yULspQy3u/pYda0ZLZi\nrTYH/ae+C/PX1sdcPAs/hyUWq753LphDmDenWlkQYeWyIuFcBziH2PqkDMTcqIIPnU8We7SsXp9h\n1ZmzJ33I9hpRZoP2kpM+BMMBz89VUupbtAngKAz2hUR+dZ7f2aIsoRxu7PKE6LdLilPfueyX0ZbU\nKOV+b73sZUU+kkgWJGupQJ/by8rr5TDOQruddjUF4/MUc1vXKc6O5ak+a1gMWMbwZf7meIH0Xad/\n0X3gsQ0sECwbN2vkIyaHZc74Gk1ZAnP1sxCS77VyWnBphYjXr/695ptZqiRwTjH5SSyIdodiljKM\nFB1pQqEFfL8ZBGqKgqsFJLiKX2usIW3V5+EPSQCGDGk515UQ5QGSfzSSQrCR7vE+IoQ5y6Q/8yK/\nic9kEAQQVkk4OZTT+VJmK5vN4qfx2XJxGyjBAruNdp9BNgdjWQ5Xa2Hp3wOyQ7WyCKZ8JDWIY46Z\n1Yg12sFYMkS05D7uK4em+uy4LuGVRl/nNNQp0kLOqz9NmolKX5f4ZWrCWo+rVo9o2gE5isqY27lg\nDGsOpwSg5bdy6J+t24aGy236yji4LRmzqSzF4ZxV5s+HfCadfRhkSbv8fvtCDZJFoefSWhcOcEES\nWGafi/RZlfNZyATxk+5Dsl42KuMrzcYU7TVxaDOVS875YGhp9lmW9HIxhzwfG5JJYM9yufeRMMKm\nGWqEAf27G0T7mcuKLIxIa4w8S3LQygExCpzQYuAv4XvYGpJrAotxP2pauJAwSu0PGtw31kpnqfgX\nItCqzb7COJtyMwzDTOGnAWh9P9fMDLyErza9JWk5aLUgX6oAGIxn5MOwrEe9VjSUaPWv6i+LPdMv\nPpcc+BF8/yw1LDZg+rD9S4N+UPCEtDuYa4yj2wAghhR4oqL0gm/R1Rz6vL7YUszfXUjnQ6KPiLlP\n5QVbQutYkSJcuD0ORlhiOU9ej/3c7IP5nphkaciGHb9krHfON7BS7jehRfArBKwyhGYLjHLexbXA\nxsIDwEcgHbLl8t73vncn+nF4iH0OGk7QzMsKTa2RYLUujrOf6vvYSpiCLgy4Yq79wfeRhg/SgrPF\nNef0lGgXq+51rAR5l4bxLvJSthYu24ifZmY+nPHHiRVrwrkw1xnsfwrWAqaFUK2+2u9TL5nSVqYF\nb0q5Q93NPOdcdxUyMr5MzUGeM9kz8lriwvgFFmNo0RhXid6aGL/P52H6MvnDvvyn1nRQ0Fd/V0Qo\nocfijAdc8cHQaXsn12K5T6yagBUatMNT/dmqC66vezfRIQuXN7zhDTvRj50h2XjraEw1QROQNv1S\nhi/MxmIUFhw3up8gtwHDlMirinNEb2ZhorLZChRC41gCKWlal3k5pBPSU1qZFv4aqgttD9FowZl/\ncz6mMwxWnqyJvplj4XkJFIzAsFZtfbmJ3/X6Mg9qGn2vPSfuk5yw13m8JkhSpsgzCk1bzni4IIcp\naR1H9I50PxXyiLE15eL0GuCxTkWpZWvJBXnXfUdKnUvXm4jgOzkkD2RLY/ByLmnHeP4OgM8vI/Ou\nDlU5csiLteORosPSq4+TYKn5UYrQcS3CvlV6SdkuFC6LYLFzzjmneu3mm2/esc5sm4rmLtqMWqHJ\nlzb8zlpRzex2HNJ1iOQxzHIrVYvTUhhDiEBw/bsmSjI910dkOXXPUqavxzwXCDDlR7LK8cvQrHYF\nFls3vDdbMr5pER1tWYtxW0JIa7iA/VhrzFmvkTntXMOW1vxK33T/WDEoZ3IkKwFbyCz86DBi8Q2q\nPsUIdG6saEh1PiK2M2u9+OYGKn/qHwkdfmmXg0vnYRpkiDB1zIcOznfo2hyZtg/KoR9T5FqHPoTf\nOG/igOS4byTSDdMh/xsYWC5y4j/VldLkuxwQ0E/fgmgul8bEjnyPPomlxWKci2iaLXh/CBkH7sW0\nSLjcfPPNuOqqq3DiiSeOrj3pSU/a8U4dMlnaPPs6NFpT9WFgCH8sZeLMbAehzfl/y+cgF6bgE2ZI\n+triaKGZyzlVeOc2hnXPKVYirGrymGGTmoa/gJzvgODskFirHmmvRkEsxnzj4HnLYmnSAblOPTpW\naiY7jfVCkXls5X/SvK3541DwUk/2+0SX/C5iVSyxxpV/ZnTND69LksiOI8SMcUlE18hJPmW5VEn5\ndwxEF0gQmQQYRD5+oGCxsZelL8OpX5ItJGXTq4+9hB9T+XK4Mt8b4YYwmVuh2VjB71KfyyLh8qu/\n+qu4/fbbce65546uPeUpT9nxTq1FjdqxDF2IEJmEo4zrwgzU786nd3GXRRSTU79AE3pDNvRZBJtu\ne6pfS6yGwT0dBulftPZc0dqd7+CaFl1LHdLv5ih1Ze3V50qatmijdp8yg7NI+iWM1xIYc8J0Cjaq\n7a0QCGIAACAASURBVNl1rT0+UT+AyCLQupyqvUvvdCcV1YcWsckMjesbKT+Z6XtjMPzcgsx77oTv\nAH7nO5eVHGzVcSUIqYsOsaPJcOgRAGsNZkbofAcfVimcuN5KfSyaAnp/S7HEXP/8V9K9mCPAVumd\nLj03zww9KQQuC5Tqeqr0QywIl8fYGNFi4pCXFDDpfS4+p9tvUXKNzc2MS2HQsy8iO0JpkXB5z3ve\nU732gQ98YMc6s20qGmTl+nZhMaspF0f5h1ad67VXL+b5KBRlyEBb+q0wyRm1bQCVUP+rna1c5/kI\nSDAckDWoCDOnh0eOfsrMzHrveg0W43IiZEuUmlGuWBM0jikhwt/ZoR+Na4X5IlsjIQmFpUELcwJt\nbi05oGRMKP4XOck/pwnROOTz6HrEKGPwQpJ13XparLk9F7qc3kTBczNC2vkuvce+G5+hkRd/ORfT\nM9gAPfuYYLSRNQb1bpWh1eDRJTS7S9catOlFXkJiuVjKI4UO8xkWzgWWgD4NfVA/Rvelg5dy6LIX\nPh0alxNj+nY9g+0IoUXCJcY4yim2nTL3GM1pqnJNmN52rdQSbaMYr9TPsBhPlTC6UGnad+l0vjW9\n7CBmX0ox/bPl0ElhgyQBVA2qWBMWcyEdygu+RdsC0YXeOpmsIwJhBXQBJZprNc1wnesKzNKFxpSL\ngz6SoEpat4JWPFJHJUBgzg+hSZ6BTv8jb/qcm8c5ISfWY7Malpt6RiJocooc73o/gxdLFEj+D66v\nR37ye+SNB2jAYM5HNKHFysdhl7LT3TctQrOCc+hTo9QE/AIL3iEO9+3UOqsGVMyTWCzJZe8Gv/d/\ngIQs64OXck8p6/oMz/dSznlItAgcOHDgAN7+9rfj61//+ujatddei7e97W33PDwGoBwAnIo6sUJ2\n5U+fOWhEU8OAKZmk77fOU8xSFk58UK2hKChpYzubo4yJxlI+3wuW9pQvoRGmlKPPhFlzIk2L+HmP\noKiJfmgYzAoKoLcWVtutQUtzxNmtBabiZIrclKdweKOtUcjughDv8T2qPvO25MR3TUzpxVSb3nqh\nF5NHfqY5Wq3pRoEJIXTl9cGhSQEBg/tp7N71GY4LRAaMgihKgkuXzqZ48qaUdvPvo/Hm0GKxchgm\nG4YwD0OWywl9tGiwhQYr3GffRPnJT34SJ510El7xilfgwQ9+MH7mZ34GZ5xxBh784Afjkksuwckn\nn4xPfepTh7uvNjGj1BEyFefdgNHOMWn24WyXBwsUUgRXHPcJQAm/Pdy8XsFDzGycizb8MQXBMTOc\ngsUclWXGO3WPgiB8hllmiS1G+RzpuzzP2sl7ACUKSgsWYfgWRDQYhxpUYaCrvt45RcgKw5bvlqDI\nColr2iR0io8wtetCHx7uvRF9Jc9fhSJLey50SYCEDKM6ZJ9dJWxXQsVZWJsFrWtxpBQ4RLiYoSc5\nJI10r/MJikIbJ6w4GPt5LPSGEWIOrnwXwTC0Sti/IoJF/9ZHkfUvD2OBtNtoESy2ubmJiy66CBdd\ndBHatsUtt9wCAHjAAx5Q3k55j9EUIwOyT6N3wJs3CBRinVTmKv3Y3zLZLzkrU2CxSH0CaaVuvLEY\nW+fvNQUnAC4khhf1PVN+ANePq+t8z2wkw61zqd88NyUsdrDr+3JK03VNhzj1psJJ4bIGSbqWiOTD\nGIH86OGpdavOL9Ea3Jrn12cteqUd+r5Dx6HTJmXYUmcTrlFNuCyBLrkahxxu6wsq6jNUNvBRVO/P\nb3oM7XIUeQoBEJ9LsfSzotVBzY3FyNvy7hQGrORaq30uIrhnjIVyHqg4+Ts4NTciMCQSjN/ZkiyY\nNMcMi0ldyXIRa2lphMmRQ2unfwkh4OSTTz4cfdkWuZxvacBQOfEdE0cmzTldjVQwCUGKZRPG6NC1\nPjHmEAnvJ0iDN8vIITANT5ikNVkN4yypw2rOGXmQChOT7xm2SDcAyGdPVqEqtwewYKTP1jikrPg7\nykFKXVfW/rtga8ILxj1wyjr1p+sSS2sJF2Wfi0safoF7Wj+hwMShMmBVHbqUbgXRzi6wHQgOva90\n8O4VbXTlQ5aV18+nW+Qcikfxg42mzOU0KU0KzW0lQlGEy0ayuhyATqLYVF9kD3oOgGCfSwu4LtpQ\nE1vMW7ksUCyN4FbZH9SvjcYNX/TFznm9ZzhSLFkryTpp0UB8MQlKi5BT/gl2uxdA0ztMu0NczsEL\nGh8v8BRQklHKxm4I4plr1lHMfrm/HddR4K7cD+sQm3FAjO+fSp43LIsh3OeSRuoaClMeCD2UVeAJ\nMjHrrQo8iiLL8+1dlzPSqnnQMNLAOsvXHQnxhXvO7LtYKiLIGApskHB7fnb8N9vujO+iurPoPlYM\nJBODBXPJKXfp62yEViz9T6ny87t1qA/OdXAOJU1KyCG3LvsgHM9BhpYH6123iRRWy20j19/kDABO\n3oIpfXPpGjPyEXmY+8XowLK1wlDsZDGGxXohwfBW33SykIZCpc+ILPWJg7/3uXRF0OxGOvITVzIV\nfDxzEfEnlPBgWdUYLkRh+J2h9gmzFijrUIjDeBv0J5ALpEVMJ6Z++SadV4hwPaTDPiOORNOQjaWF\nc/TXEkZa4ImwuJzL0W/pTYcuz29L1lv1kEFigq02maqN5kN5qxTpJAxavzisWCVkQUxXC+QzTYiu\nNzhZAWli3R8D1KE+GaMkBh1ckHpyvW2yzFxA77yuCRfR3F0SKOJrSanvfUooGTr4nCF49uAea/hW\nWzK+0A2tMV535PdyWsGz6txAn+0YLq8nmfQ0puB1rFbfrnM5HLiNBfLySOswyLMa+BpTv4LvIGdk\nNKO3hAkTw2Ku+FOkvljuW6EpFlKfSXmF/lDl7vO5rMUu/+RP/gS33Xbb4erL9kifhyhOU2UhyEuV\nrPMwTiAS0qAawDXd8D3f2+ofafVzVM4oxO23t5SmND0JAy7a8lKraQrmi/3/YUXf0Ud+Wc8ltEDT\n5fejJ8jCN6v8LLu6VjtxUG5YruLQz+NOGQFWfZnqnMGeUw4emIStpubYvuZ8l8N6KaV9kO4Y1q6L\ng3etVYlhy0rZkjZFR5ZNUQ5FDo2KHKO25BxZsVrpMKiMSdLoC5Qb0PZWUQTQAr7riqUxgK5YMSsk\nAkSfcxmvCxYefRRYR5FmUlebf2vLffr9L2zx3GejxYRuuukmPO5xj8Nzn/tcXHXVVYhxIdNRdNVV\nV+Gss87CGWecgbe97W1mmauvvhrnnnsuHvWoR+HAgQPzlZoLfGLVyyYbHDg7BI6u4/SFaQqDbmgj\nrgNxaVp6wFD6VBhbRcip+xO2nrFknYRwcB/DO3QafNQfYnJ8T40Z7wQVZaFCfgL6HPUpfZF5GZXN\nqee9OH5z3Q4Zjiwas5FYM68ZL8xWmLqllqu+m+HCDiiwm7bMDbhNXqYlFEKHpmkRwkrBmehDdpvV\nSGi5cq0t72kpAi8//5FvwnfD4Bhj/4zGWJmScv8SbsbPNx+2nL+lDx3uz6TEck2qCwSFsWBL9wGu\nWCxtCWOuhT/vBlpLuLzlLW/B17/+dVx00UV43/vehzPOOAOve93r8M1vfnNxHW3b4pJLLsFVV12F\nf/u3f8MHPvAB/Pu///ugzA9+8AO84hWvwEc/+lF89atfxV/+5V/WB+BTzHtxug4okgAxsP5yFiVm\nqKKbnBHZRBJrX6rLEFD/Q4WRi28itBTP39ra7GizkN9m0Kl+LL7ZXpiuC9FkGqn+DP8USyb7N/Jf\nr4XmciqTdImwEwtBpxbZSa+fWKehZ2x9n6hMTbiXrAG8lipWg/hB1iTzNQ1mwdj77oxnXkKMhfIz\ndQF9xuAc0TWVndpxGcsvCcxEGnaTYxlktJiy3LJV45uu7CeXo9HMNDYRfSiyQNY+w1ArAG3l7Y5l\n74+vafhL/FFD30lv5aQpGJ53CRSm7LOvptaOTiGz22jtre29x4Me9CCcfPLJCCHgtttuw7Of/Wy8\n+tWvXnT/5z//eZx++uk47bTTsLGxgec973n48Ic/PCjz/ve/H7/5m7+JU045BUAKeV7ewS6fXhaY\ngLRr42AWgKE1UeAzsTKgBFcsr0ZtmnbokARKttf+h2hvjlH7M+Oas3iEmYpfhTTASUf9HDkUwdyf\nWbCEkJSrWQQz8AkL+5BynSXoI9fL700XBk1WZ4oeUvMsgpHnVwIGEPu3DGqtWY+LoUpZF1DWg4aS\nOILvUKL1xS9AlsFU2YFgB7LlpCwNCbF1vZB02hqeCg8npWDgwAeqFoQ8HxE2EuwxCoiRPlXg2KL9\n0/MOEP9Seq5YRbgWkPQryXJo+743GersIlzXWxMsjGp+Fj4I2ah7Bq88zgKDIbIAHUnWt32fFy5/\n/Md/jMc+9rF4zWtegyc/+cn46le/ine+8534whe+gCuvvHJRHTfeeCNOPfXU8v2UU07BjTfeOChz\n3XXX4dZbb8Uv/dIv4bzzzsOf//mfT4yAHspSuInLyyn8yXIYw1G1ctbPWlsV+ILIh3Z0hsY5FEw9\nsCU0xQyFlFVQXqvKBzjV/QXGORTKEEqTIZR1Mr5a82T2SQl6LeABjH0uMnaBCAm2qZEXYTrqaEVQ\nKh9B+a0Iw05Fx2EIgxUma9RROtUVQTuClqS4G8N4Mre+WdljmqK8ZkbRXQupCA+GaUeFUIR++p4U\nuDJvk9mn43C9r6DOsFAAgECirr8VxSqxBYonKKsXIHF0LahyOmJM/pfwYy6/G4XLWtFit956K668\n8ko89KEPHfzuvcdHP/rRRXUsyT+2tbWFL37xi/j0pz+NH//4x3jiE5+IJzzhCTjjjDMqlSYIweXD\nfeXVwzlO3jdteiWxPL8S6SLafkpZoZduCCnaadFWHGycLIg0RC/vFY8OnUSKDXZa0iDjlKYbJAsx\nFWINvdYnKYNA48c48AGJObkmzV+MKSIrTsBJzqfI/xgdoq8nTZTgiNhKf9zwDMgkxXwifAKCycKg\nmzgMq89euGxplt+y5Zv8IJUN7xcoJFXKz5iCR3xI7bfRAVhh7j1CDrG3GLKW7wJSRJj4zKh/khcs\nqnNWzsc+szfIwo1I76TnIbo4ECri0C81sg8nW0ZiFaV090qZypGEJRN3Xo+SdwxQ2ZoBBB+LsjJK\nHilCPHZwK8DVYLE8FvgO6GLd0NaBAPS7r6TntxJfioXT5nv4vEw687IFryyg3UJrCZf//M//xE/9\n1E+V77feeisuvfRSvOc978HP/uzPLqpj//79uOGGG8r3G264ocBfQqeeeioe8IAH4Oijj8bRRx+N\nX/zFX8SXv/xlU7h0/99bAERgawPx/zwZ7hf+j8msnE/aT2x9DjnuF4ecVo7Nqj/oKPDPZCbEChUN\nNh8IG2mXmaFHN4BaXIZAosVABZ4ZpMWnP2G8h7hGvY+IroPbypGtEjE15asAeubjrHDupDUDmZFZ\nsIufsAwz3OZ96osD0IWAdip1i75feLmPdSeupVULrKiFkkuCLIaUZmVsoSXNG52KaMtWRXQLH1U+\nJDzqU37eDqm+/gxVh1HG3szkBy8Dc4B3+UDggo4MfEwCfWXLOpaQ6pm9MgURijVO7Xnfoau8zsGh\nG4Qcw4nx0wF3R2ALxaexQixRZNhIkCvQInYbFLI8hsV6S6OHr1LIcQpLG1sq7ciS4UOXnKpfItM2\nMlxWe+vlTtHVV1+Nq6+++rC2oWkt4fKVr3wFJ5xwQvl+//vfH1/84hfXavC8887Dddddh+uvvx4P\nechDcPnll4/S9j/zmc/EJZdcgrZtcffdd+Oaa67B7/3e75n1+UtfD+ciVnccDbd5EMN3uxgMUTah\nCA0DoirldFvZ17KYKFrGhw5d63vmahK1ufS09Y6HmSzL0OqywzU0K8TYIJazJWMN1Qf1rhhgDMtV\nGvVy1iS6vm7G5UcdA0p6GueSQO7Uyfi5pJOj33qn9FazGvw+CLEWK1AxcQuCTP0AZk//a99DEabz\nEsFlaGkVXX/aXXfB90EsZX1O1Vfx+xRLorZuaR7Eqhm0lf1UoUlncOR8lPcdou8ohVhi9KvMuvpQ\n5GztRQB3I52+1xRRYEvXATHnIOt9IMtCgocHKPvxh8o5GRE0AAaCJ8KhIYjscNKBAwcGUbdvetOb\nDmt7wJrCJcaIW2+9Ffe///0BJMulbdeblKZpcNlll+FpT3sa2rbFi1/8Ypx99tl417veBQC4+OKL\ncdZZZ+GCCy7Az/3cz8F7j5e85CVVy8iJY69ZmQxDsOYxLJaiitL710njF3ipmOsx1Z2ZJ0e/pDpd\nxrI7dDmdeBddspBGfUGBK2LnevirMOYFbN1lBqbDnrMm7YDM5Fx/ycUSMtv5jTR+mYuQcPimaftU\nHNxWvl/OoDqfNUpiVklrT8IzRYXZjM+HDrFzfa4nZrwDsyAWwdXpA5G1ackCp/dbYNF0TleKiawJ\nlXt8lzpDh05dtn46ZqhTucAcBrlYBgdFqZBzFKkVADnJH5px2DQ7z8uaMMZQMg43EZO5XvieAsUl\np7q28EJoUwr+ENGt1DXDh+MzTNl1vjrPk2nq8zmXkEPJBokmZW25DnEF+C6aBxg9unKeRs6h6JT7\n7EthAcU+FbZcdP3DkOT7uM/lVa96FZ74xCfiuc99LmKMuOKKK/D6179+7UYvvPBCXHjhhYPfLr74\n4sH3Sy+9FJdeeul8ZWVhCjNN0EDshua+mNlt6Iovptzj+k0RpU7RfhkmUxBMwrojnIbg8gKOrR9E\n4hQcPCId+mozBFYE49jKKpq/7+C7JLSiBRXo/hYHqviicrmJ8wBilXWdy5BE1zPGrG2OIrJozKFp\n04vT8iB9iOjaPioo/aq01fIoYplfl+EvngeTGdLcinPbt93YSgKAHNbqm+STcQCapkVsfdIjShqW\nmII8kFKk+Ox3G+XJWgo/8vvl80n70KzQZahLFI7YOch5KJczSkQVmedDC996tJ1HOT/iu2HOtios\nlvZECH04/WiKxMdoWDlyeLFAPHktpECTJATK++fRHzAcVoLyvNOpdvSMVyVlcNnCASJiCCkxBZ3L\nSS8FI1jMAw4dGnQpz6UHJG3LIKIrK0cuDmE1CSGupWIRwaEhLhE8EqLMfpY+9X5bBB3DZf2p/rFP\najfQWsLld37nd/DYxz4Wf/d3fwfnHD70oQ8t9rX8JEjCgLvOp41JXNSJxi9MavQs08bumbOt2S0i\ncaC6fhMOYDGDgqQ5B4a+eq+EhiYOt1Z9mAwnzTBEVTPMWuh2KDHQpPl1qhLxVXSu6fsR2vQha7kD\nqyi0iBED524SVivEzpWzR6ZAEQrtYP6cJ8drPlPRAtVzN8IwyyznKKYQkpt2fkKMYAsgQzSrBDFG\nCzaM0BkEJGhh0VmZclMcC8c5KmHVMfkOs7M/NG2yaoJYdapWhsWM+ewFT4fIFz3Ku2l8I0pOXeNf\n5UZ6WIxy220iJcHM1wf3573o2q7AZ2x5WEw+qPxfOrLLK/+LWCGSDoYtF4bfIhw2sMrQ2O47ob92\nbrFHPvKReOQjH3k4+rJ9EgalBUJ2Eo82oZdUqF05HR2NCCPvW0REtLJSp0if+uY+AZCoNJ+hm+7g\nWEfy+a2Ki5293NYso5kQlocIHyUB4NC1YfJMjQ8tovPoXKgfoJzoo0QjdZ0fQ3jITEKs0AzhuaZN\nEKQWzhNjdsiH+UaJMGOfFVrm0yHlUcuHYl0JuggIeV6k79F1iFqISNWkgMySo7TyLiKEiK0mWcLI\nsJYEd4g10hkGp/QvRjeAOtPp+vluLKHyql+3gVEYcG14BDeF0CGGTrlQ8vtSsuXi8m+FjgH8ZofB\nO1VIDqZ33XdY/TgmAWO0bSWebNBCAowBDKyQXjj1Aq/JfxF+4PQX/4zLgmXPcgFw11134a/+6q9w\n/fXXY7VK4KlzDm94wxsOS+e2S86nQ1TpcfVnFTqgwAPI15B/cx5ot4zpEIayZNNbfXE9xFOgiOjI\nD+TswANlkThkX0cWinFglfQH02rvKvE5nJjyACZSPhI56LbaaooPI+H9QzNIHOrJ+ZqralYpAke1\n24QWK8vyWuLQniB9+K9o9Z1Hp99BA2TLaIUuTjiunaqTLE+TKwbj2THcp6uHRHph8ZjlLI8lUBPJ\nOhZ/4Bi+FGtvlLplKjCCosJqJOH6PePsYA1esgT0CJ46vZ7XZZkboBe2NR8aG05eUua3cJsxJcEs\nfpBkQaBNCmNaIxH4X8DfMUzJYjH5JcxfH4rkuvoXjYmVk/uDiCaHI9/nLZdnPvOZOOGEE/DYxz4W\nRx111OHq01pUDnWR89khJu1Y+VycpMHQkSpEpQwwjPwRk92IFguhQ5sDAdJ7KiJaNEDnC8brfUSn\nNOiChWvA2eyYCM3sXLfgGx/hIOlPjN3Im1T7o0I3hiHI6iuwiktZZLvoMqPsJpge9z0HMtTKqLMj\nwlBjjiSIXc905DBf5JebrUHJEV55/hk+lbMk3ndJKbEESLUBoJzoz7BSfxYpY/7Zki2HOaNHOWzp\nk2C02E06U5TLhi5ZwjNTIIJGnlPNdyZnT9rOm4JF7nNWktFSSVqHZip538GFVYGOOifKDAqc5kLO\nHhCnHfoAkvHYRfiohMIm4DaGPhAeYwjpLAx+BODHtWGoVDAlm/EqZwJzJexYklL24cwRHJKcXgXG\n51uSRdNl4bKxB4ul0/Wf+MQnDldftk8OBhwTATh7bRZHdU7El2ExX5iZ1UbPZLWAGUFqboz1Shrx\n9GrZDt3BtHGG0TW2BpkYgRtHTpVUFm0uGhPTLFFTDmgyI3ZTL95TyQWzAz4dRuzHJtEz6Zb+93LY\nNL84rcyPEmKhpv0r4lxtvb9j+r7ijLbe6KgVAtdDaDJei1IZ/iFH3LW+REHxnJX8a7WJrrTThOTz\nkSg6Hq8c8hyMVRgk1xeShixpYmTuZV6ET5a8XbUxy7h0BFdmop3L6e8F7sJGymTAdQ5iNpKg2Zpw\nlHOIOV0o89uGPrAk+B5q8l2HVpIn85qT10qU+jOJvPcRYV8Hd3IE+mN7hfH3Xehf5uUM66UXJOLY\n7yPTVvkaH6IE5HR+D6c1u9jnshbW86QnPQlf+cpXDldfDpn6nER5E+X3iKdMr/UNVZJfHgr5mPIV\nTaiRoTDNSBE7sTgyXdACSe6ZMclZ4y39wSgwoOTSKgcvM/PK7Vr+kqUpP7icQ4os8jTecrJamJcH\nhqfht485F+uKzyFlS69PR5+YfwlUEGYl1mgt7b/0nRjfQIAqkiSQw/4lAeJn5nCO+rWwMw4RZuyj\nE+9yqHXkOxxS8k1JVNQEfJTXGvQ+c/11NBnWdFTP1FA7DA9Ruuzc30jPcuCkj8iwWH4+DsAJAI6V\n5sfp8JWsK3UFsmo4woz9L+JvsesdQmgJSryP+1w++9nP4r3vfS8e9rCHYXNzEwDgnLvXCBwJHU0m\n9cYwQsglxtM1LdpyKA+wVq9YJyEkSES01fU6I5ZRO33w0qV+l3Z9isaJ6oxBj5kHIOyAnsPQTYV8\n1hjl8+Ll7xK8UTBnGmPfNgaM3OVNr89zeN+l80C+FyBidXSdK4x+9pAmAPFFxFLA6LpARgWCExhN\njZ75cO7DKDIpJNevX/XM2WXo1AXAxZy5YIHgFoe7c904SMUhCWruk+FzGSoJsYQDpyoiOoTJZyx+\nlZRnr1LIA85LRFUvIHrLJg5CcakDpc70fDtE77Li1Nk+l2TuJZ+Gp/nPLx1juEr6I34pjwh3bITb\nlJT4w5eCuWydAf0JfbFKZNb4zZQ6t5g48QNWiHB0iLKjdiI2cBAb2EKzCy2XtYTL3/zN3wBIAmW7\n73LZadoW5p7PEQAo2VWtsMeqs3OGvKQo6QjjJuekz9Fio/bAKTa6uiUkpv8ORfQMqvYRwUWstqbH\nzTCIMLKu86PsxLKZuwyZLTv/zx3KDD72B+5irB+hc9kqjNlvYZZxgEAWZnu+T/k+27fGEDwTh3r5\n3nG/6ICuwFgSOusjXIyl73Kt5ALLfS1JTh36nGHyfCoRdqXbkMAXDxdWgN+gM2F9+cknmP1Mg4gv\nw1Fuhf06lx3ycgbE8I1KfR0c3CoCB9O8BE+hyASLFYpIadsinZk6BilseQFJWLFmmeNXGcvn/oCk\nCBoAReA0+RxQCkXuT/DvJlpLHf/pn/5pfPazn8Wf/dmf4bTTToP3HjfffPPh6tsyylpRNS2FJM7T\ncI/E7BN8In8W5CHvMLF2lkBwTu6fOKHOvoSdoQRfpBc85cilps3O2MzkvBy4i3R+Id0dFIzjMjAt\nFot1itppLZyd14A5R9W+17B/P253jrzvyhmJwe+G38JudPjR+57Z9y/L6hMyss9FNOyUCXoM/fj8\nGgHrPT8DeK60tcoHKo01na3i8bUhtNVDkCRAst9CDvXNTEN/H59yR4p6alw7qH9O8Ei49bAQKVNN\nf6K+WAW0PkfvTWrRZxFw+dArVjmJrQgvZU36NH6PFZCjyvrx9elf+J0t4k/hA5F9Kn+xXFZFAOkD\npNIPeV2AQGbp857PBQDw8pe/HP/4j/+I97///QCA4447Di9/+csPS8eWkn4Rkpj/TWH0XYEVypv0\nRo5/RSWaxtCsQjv487UDctS/USp9pNPrA4E2wfxEo22atveblAYiJGVNzRcgDuDyHvERJDVk5Kl/\nQx9BH/XWmX4ggR0tYVBL8wEfyxkRZq76BVQ+H8oczJ8c1JQT21qByBYIh986jAWNhFOnSjDaEaXv\n2/QJySl2SyBvR4C6zERHwW6ijW+D0pJYctYiMVIryagwWedtyExQAGHQffRVPSNwib5Slnrxe2x1\ncHdnwcBKUpNgsR7OisVySdWl82aODlvOz5EKnS597AUGH6IcJq/sfx+mfVnl//dCkXHNNdfgS1/6\nEs4991wAKXHl1paVIe7IIRfGubJSRElXrBozTFfK5vBgpuQncHBbpNWSX0AOAqqaME7/khP55Ygf\ngQoWMbq5xJccIkv9huuj3zyd4ZDw3bngAh8oz1LoENtenxVG65tV8ivVzoIQHOlDzuXUDc2K2O/i\nlwAAIABJREFUQXSbWQmGlohYby5DS77NYePplH8KCQ6U0mRijH5sCVvNe69Ooc+RhPq6iNjZD8+E\nap3cmwMaSoRh3185UT8QtBmyiUiWSAs6ryKvZY6xnM5np/b02DMU5rMShaSEST/A9RSHflqPwSVh\nUNZM8Zf095V8XXcBuD3CRWXRKFisnHMp9aWRJiHUR4TxSXx2zvObIxMk50u9PBfi3Jc55ASVK/H5\nlLrS4cnkc9mdlstawmXfvn2DRJXf+9734CspsX9SJBsmNKtec+a17yhMkXBsSTXiyZkemhXaNoxS\nrcwyMmTm27AjOMEkGpIAYGZGdqx5yXtmqo1h4ODkaKTlSzRBUslHQnj1NkjG1bW+t3pCN543hs52\niCQ8uut8EeqjPG30TGyamW+phmC/gts7jhDLv/lILyPj+zHpq3RGH71P1rZYOGl95ms07zKOxNhX\n+Rubp3abzLgF9tKJFp3rGay+FnyLrvEUfr2mBTXYq73vInU5ooWv1/ljAD+UOmKB6lyTzo9ZByND\nhtzgXDpsOeCAiXe0q5CyFqA/5W/t/5ozn+EyttRSFFk6NNnkVPub2aG/G4XLWpLhla98JZ71rGfh\n5ptvxute9zo8+clPxmtf+9rD1bdtUYkuEe02hzUWrVnyi/E9hK3LwUZ5C+HgvMUCxqjL1WGxriT6\nE5x+AB9lTa4PFRXtWzcoDMmG95BTgTjxR4jfpWLViGWUhG6kPk2Ps1qO/Fl6/koItpPT/t3gUKxY\nG/2z68pfEd6j8G3Dz8C4fTMOFea5HFg7YehnkWwFRaEJvc8hjb9DE9oEP1LbIhzkbaPyvJyja+qe\nwbkNIu376Z/ZGCoTQcPvCmF4qioDJFDBWLcOMecaGzqh2VqpcRXnO4SwQnDUpyL4O5qbcX8QkK2a\nIeMGktUVQgcva8GNlTdzHDlHWqqjtzrkuyuWC0Nb/BbJVemPDjHuhc5qYP2IcGvI37KBg2jMdwQc\n2bSW5fKCF7ygJK6MMeLDH/4wzj777MPVt0MgCTl1g7BS0TKdCzllyXgFMqPjzSoMxCLBz0WIjawS\n10NvU+/LmCSX85IFoKNcS8JY+jEmhh19JVGhOPNrGQqE8YSY3uonjn+VULI4tZuhxqX9JYsoyhwy\nE+yFQgeP2LohrOPidHi4nBRvWmwxBJnbCs7In5XvkdBx9jmlvuxAeJ6swaXlZ6bSuey8FthvJneX\nc/kMkoKa+OCmRwdXsbA85vvOzF8OIgoT5jYCVvCxyYpTnuPRQcZhSnyp08EDxwHuRAzPxQDZoT+0\nyrj/Hl2yXLLAFzir5ndiC8Yea+9D6s/CtIPf5TyL5W/Zhy1sLH2/wRFEawkX/YKZK664AgDu0dxi\nAsEwJi/wgryDRGuq3icNW9KP2z6QXBedvRCn9qiMcqYKtrxSucrk3jjx8qbFJNBYFhYScaT10WIl\neRsy8yFr20p4pHEZUJJDSf+ix9VJOpYaBMMMmhJXrpXht0JTARFz9w0sS2vMh4MqL9QSaLeTNyQu\nOERbbs+CQ85MiBhI1no7EM7jpikrwMya6UkYa+jXXc5Ard+s6JDSBsXgBkzaF0gyjtZO6ZNDeVur\n3BPRwh3TAfcDCeyI0GVYLKjoLteVoIBy2r5ZJSusoAOxCCSOjnN0TUKLIxxZIO3ImukQipUiochD\nCC2lfdnNsNhawuXYY4+F5GS688478bGPfeweT7lvOzcBSf8i5PMhs9YFG7pxbU4OmA6STW1C/ba6\niI2kDTbKaikO5DF0I8Kgy+8KsccmDn1KcklW2CRZJ/SbrD1KKnU33tDjPiT4Z+WaoXA1/FIh5AzE\nGL5ISQIRgGQNNE2LlYuAhJBDBFmqq89kkIeSraGRP8I8nGpolzROcdZ3cVoQ8r0FUst9bzMEKGG1\nHh2CWyXIJ6de8U2L4FaIziE2rofqaOlIfSX8u2KmFAuu9UUYakXFjNLLWr8EyWrSDE0Ya4c+p5dD\nH75cDj5SIIhT9S1z9ifmzq2LEtefWJfggq74RUe0CbhjIoLrsuNcKAsr7XdrMqwohyMlmpT8Iugc\nulUYvMiN/Sg160UEjMBdHbpinXRwCAgJvsuwmqTaT5bLQWzg4OS8HYm0lnDRL+969atfjV/5lV/Z\n0Q4dCpW8SfnchWTkZUesD11KzMevzR3JJ84fdggwVujgfZ/OQhLeDYq5BMPIwbeBj4fCoQXyiNH1\nuLbrmZ+56MUvUcWxtUVHAQeKLMumOnTx22QNjhl0/R5LQ+8PzEX0ebdE84w5jnT4nvJeGIkATOcr\nem7pXDp0V6IEXXbAN2EYor3Qz7aUkoLDfpA0Jh86hK5FGzzBsuu1W4TOVDaIBaT9Gfqa+Gp6wbVM\nmAAoBz77dthnl/ZrCh6IwEDQpfNawfUhvwBSmpfNYVs+l3VhNYTFRLi4nGDSpSzePF/9QUkUmMya\nGxFkw3DjrvTNFziwjxZrs3Bq0BbBsoEtHIW7907oW3THHXfgxhtv3Km+bJvEmVyjtGB6hikOV5+Z\nOsNiEkkm18spZ3Xy3OwHYhES+nS4y/oLIIKmkhHAR7hmlTIqW9qoOPvLD0PrQ+ZiZTLFzES9L5qZ\nhJmqzpazGVPadA9TJOdnh0CBEVmU+n6k8oKk8aCMn5z4PuLAShprjyJskrLgM2MWR3+fgHMZ+Xw4\nsu3CrHBJfcyHV3eIxKnddf8/e28ebFtV3f9+5lpr79Pei3SiNHJVbIiiIohNxNwk+hOokpdQeVVW\nxWiMsX1GLfOHqViVaMpKxVTyR/KzktiGVGlZvrISDL4X8vsp8hQicMEGDYhIo4hIo5fbnGY3a633\nx1xjjjHnmnufc9Ab5JJJHe45e69mrrnmHM13fMeYphYc6u1u1RxdPAkMzNX4zPcypsjac/qwWI2j\nhrqfCOLjav79Su5G2Lq6aHClVwKuKxMjQrVwDa1zRkmZeUurgh+t5GCTGbV15w/wysUpLdjRhsrn\nYPZccV01Z6eKbVBNqUpbSLKba9OYMWpjJrkMffsTQ2uqXOT7KngsPpA/pGKBTQaP9YD+WWedFX5v\nmob777//F24vl2CZmjiM/3838YwXI0LZScDODbq9KVDB2TGY5pWVFwZPURvvo8SUUBEGilbZy2dY\nP/xn1v1cuo+c3DW2DruORLBH9CzBYlRBUzINO/9FtxVmVvAtprQM8gokFRAluMJcQ7ydol8nrHAt\nztWkcGSa6LodFdILXmfYfOnxct/4CTIMvQzMJspKs7aNokyTKNMHcEQQWGB6Ob23bAccCnRK16LY\nRdr72V4J9KnIekwTDAkC9EyAlSVHJYK7knukiqBsO1jUjIWQBmp8vTPvuWRqsJXgqqRWGd5g0ioE\nXSuAhc6g7PpfVnUEuVkygWWByZgJfCbjY6GyNFAPBIjMx2emxpuZMmTMAmMayuC9HG1tR8rl8ssv\n1xOripNOOonBYJsprkeoyYRskr0qguIQ2icthYOiLPKsrW4hS7xAsHkrKK3bvN1mmSY5nk1UQmVG\ns0IlEBd2wAcQKm/7MDc8s31ocT63YVYGZO5cI6CFsiseWNHh97nERIFUPKxQ9j6fGJtWFUBfCfot\nAbqYBT5Dv5fc6OKfXOUFV4gnVEQWangugTfpatZlvJ6is+K3ik2k49Dfv13nZyPwWuLdSB9nkY7z\nQeQucN3R9tUcihlm9h5WWQdPOukDECeyJp5LfD37dwzRCfxUA8WgCbCYhazKUiqMmwrGHSlAlVfs\n8StU6TpCgnolNru+Ns+rSmUaeS/i5diYS0XZ9X0SwWINjiXWWWQz+44ezW1HymXPnj1HqBs/WxPI\nILevSg7KCgHaQifCLGutdy+DIUubzIC4tDyJLPKik13+fltmgyeWK3R/V00SczF1mES4FOCqRgV5\n79ptyMAXWmiTCGYvCGSsWm9BSjOXlPyABhco4LnmFUXGS0i693BjB5HA72C7edUVeq2jIgv9uXAC\nhcStTCBSNSDSy8Vj4bfNzuzSSI2zynMGK3E7TQReSz6Iv/X5EEWzO+ivNwddEwSnFf4SK7TB/RDH\nacWDN4mJ3anq4cVKrMF1ZJm6ex/RxPO7VzqFpKDz5Iok671oYGEcYjGOhqqcUjk9rsDT72nKzgm1\nXsk0UjhglY+UgJmgeTD9mEtJ3dGOfRB/kU0c7X97LgB//dd/ja2InP7+7ne/++ffw222wPfPCFLN\nPLYnEI4tOktwHl8jZTDl7i/kARGwqXUq/ZBgoA3q9q6XFEacd1/Z3nfL4LMErovK64lOwYRtmMUa\nds5vN9CopV1vMVWKTpRNOlXjEMs4J3a33xyinO19FGaMPUv/TNYTDFayk/pkVuDVtFSdcVLTJgw6\nESYlDXXOgMCzvTT4noGbhInoJM+ja2Wn/BMqbMjEdxrsj/J/ZnjPqRGS0morPMxk9x+Jj62DcSHG\nWjrf3Yzz9bt89eMQixB4b6s5bcZjxnZ//l5lm+zb0pVySZShxJyKwbSD7vw8KJ0G/WXvFd80cdI2\nMcJqPPVaPBa5twbr4wrI/lgPkQ0ZMWTEAiMW2aSkZmWyxmK7CcO5w/KoaztSLjfeeCP79u3j4osv\npm1bPv/5z/OCF7yApz/96UeqfztuMpHKsows1oKGykFbFoEumzYJxltYzOEZWtvdzyXUhkIDkgKL\n5e4psFjpfBJVUxVeAWRKnXthOB+GlKzvOs3tCUJJmWbZ84GZ1XIdtMHSbGJ4I7qG0D1FsMQVdeVG\nEs8KHpfTUiYiRNM4hY5Fg4TxixnC395L+i6B2xBT6hP4Zl/GNQEWk73Q9bu2q4o8ZzdTrBDefhN2\nVnwNZVMFpRCNmW85WCxNVNTPFQRL32n0vN14CuwU3a801OF5lSCSeeO6Mj45j6cs6igeU3Z+ACVB\ngtkil85BafJ9ig4C8+WYFL6KFUp3PyfbhGvfpDCl9FnGVNakfD8x32vwvg5PK1saLzAOymXAmOXN\nCYtN89hWLnfffTdf+9rX2LVrF+CTKi+66CI+9alPHZHObafZqse9vR/E+p+RH+FcGyyZhwMhhPt0\nAnT29210Dy/cHt79QimTbZzuC2/WoZTLdpowr9KtwWR82yjWotnJojxnMsLohJqrA+GhF/ZI3qNA\niIRxm125V6zp3L2LoqEpfJZ/73ldq/GVDhZzRYtr+sJ1u9uliYIvXAqLtTQz5sk8+rEokzztN6YO\nqxFSzHwPcp4YAOm9tvIsio4tVuRBzjlejKhCb0gVlEY5tWENxbBYEeaFzcQv8KV/XNVSuGmk6EPM\n1d7bdfUHnWTO98vnl9QeBq48OaE0/RHlVXZ+rPdGFBKLs+4FGvOxFRljW2J/2CkXgGptipsSbbl8\nNLQdKZf7778/CuAPBoNHfD8XmbCNK2dajLlAJBAmay6Okr9O/jgb7/DWfEMpkJOLrUg5Q+CFpHhK\n5p6ZjYQ6Qeitfw/HVa4OU1iP89Tc3P7f0iTfI/u8hS6cqZkqfUWu1lweNIn7nqM+h1+LtqcEXAfN\n9fpurHKXCFk6GrMkdm6rWVgM9TrVUp0BYc4QyBI0lpiAp+Ka2ErHlKuoqV1DXWh5/rroYDFbFy28\nD2ttd2sgIRDYiIv0f653l/Q7VxnAjrF4U/a5S3ysw8Kgug99nZ8Z5tVoMFyFsSjLUCNQ1juFL/Ba\nmbHu5ol4QLJufIZ+HdaJVRqpUVh0ycYSx7T3FKUpayEtVhkXpfQQ2YBJ8L4rJiywySKbLDJiiQ3v\nzRyawhg4dVuv51HTdqRcXvva13LeeedxySWX0LYtl112Ga973euOVN8eVpMYwSSBoSzFNkuXNULF\nTyIf4I4okkXMY5emEIucT3d3nZhx64RXIRBeh8ebtefM9bRPTZY8YJ9RA9pEnkFhFl5btb7ifrep\nmMZVYjZS6l2JMIR8oqVYoDICOg55ZlJUMFQC6U1hoBV5S/G7tEHrWfCmT6K0n0o/RFAUM4WtxBzC\nlsrilUkF5qqIrGgPpzQB3myTZWWFcGzVP/xYlFwrnePqCcgd9b4CAxVhxto+xfEQCba7uisKaSm7\npRplBR2ku41HsfeOYkdlF9DHrq82wH2FI9qiOcRYCqBsEWg09KlI15yPuVWDaURRFnp4gN+YUhUT\nhosjn/wc+qvjWqNMvbiQ5ZSKMjDBBBaTmEuL65TNlIVOsazUayxujhk8CEdhPH9nyuW9730vF1xw\nAVdffTUAl156adjb5ZFsYbIWJogpCyCTCKiBRcVfA3trhzTRtGkSmN0fJobFHLNhMd9foGi6Gmh9\naGFe/0J5lWK7QJg2JRyIpPDqQZ5rFgPJCmB7jQKJinR9s8rPwGK5oqDiJZaJkssr6/mtKBvKVrfO\nlT5X1ExBadZFGyzk7QSdRdn0KNQdyeLn1VKLOTVwarSUjSiKBqFLC0yZzkeNKWaD8B30JVoj9lrm\nzL+y26GSaUjQTeHMeXW0FCJThVG4OqrUjXxXTHGhZExszNm4kldEaiRaL0fGy5/r7zEcTqiKdD8X\n73mJAvfXVbaYN85UIWmi5DT0ZcCEBQnmj0csrU8YPATu7rmv/1HbdgT8N03DzTffzIEDB3jnO9/J\n8ccfz/XXX3+k+ratVjil+uaMp5SmqE1QaaUbpm2rWEp0rFi78xaeEYz9BddQdfGIYk7eiyjMCP1C\nEsn6Qq6QigEzWqipZK6lfbTbuSbPUvjd/0qzmPW8fqB3VhPYaG4mfMZblM/Tuk9BoBRNrxz/zGt3\n5d4pfMC3B5Vs81n0mTClTNRCj8rgSAVmE7PyH6f7j8x+P1EfC4Xfet/NUAgSM5gPZMbec0HTvXu7\nu6Jfg8KeisZChDb1jGepw7inxR3lPUiFbFtSxRNTWg9/OusV9fsh8ZWqmFC5OCclVUpl0VANp5SF\nblUsxSntetCKx2oEWXhs0FGOB13VY/FWlllnmTWWRmOG+1vcj4D/BG6d8woepe1hbXP86U9/GvjF\n2OY4bbOCiTJpt5PAZiGE7QAXJQ1lEmysXLeFcVFnF5y2fH+3fC6Hp2FWs3NCnOsghbA4DGS2BYtn\nW4ohHBv/Pa/vcUa+ssRyFFsL0UTXyAqQREg6xfsj+IqmJ+RmNRsDiIWegY7kuA7erFxs8Wr1gq4E\niev6FJI07Xgr1LTTZF3bHx2POvo77ru/t5yXxg9yiiK5We+eQPdO53smeg9BF/R6qb8tsFu8H1A3\nnuW0K5kf77OiymwanqOgDTs+lsl30i+/bqcMy1EoRaPX9Neokt9jQoDEXKQY5STEYHxG/iaLnYIZ\nbE7hJ8D3YfofMH5kbfQj0h712xwrrKUQztbneHpgCov5OEsSTDbCUDnyO2siMDyG7AXIdtliZU8o\nbE/wM2c/+LpooBGIaEagn5hBJ/CUr5DWJONk4hIoRbbfpZpiznPLWMcU8j6sM7t5QZVCocI0+lkY\ngWk/Z3vEO7iOUczzW9t7/1Yotjhqp5CZJjcWpFWRc0Hsma0BV0tSoirNvAER/1TUHrYqrELOndv6\nsvfFNCgcIW/4GIdW3tB7acwyZ1j1DA0zLlbh+x8xNhTSktiIQIvpj4x9ygwb4jpvRasdLzAOb3mJ\nDVbadVZH6wz3T+CHwLfhmnth7SS4aHtv5VHTHv3bHAdLVgOAYN1o/+K7T6PzdAtTwVGH2ZId6f1S\nBSNYflE0IVku5/PYkh0CLxRtniYcdmXsWXLtzIXTAoUrQ+b9zCb7qJRCuczTsWWMpLaYi0bYxlJs\nOZJBOHcWhAOEmEugmSbKQBa83EX6Z4Wb/K6MsU6kFnVUgXdekwq2vk81rqiTpFGtmSZ/O1OFOhcv\nCjkVoa8zPEtiJqNDKNWxByLQo+wVkoW+3GyPzIVnVCp8FI/Izb+M4gxeVVlHfbf/Fi4O/ksriSHU\nVK3KtVMv09EZdU53cAwl84vab3PQfS7wuMJTcdHIFM7ydb+K0D8bG9Ggv37u8AU6NaNfvJt43xaJ\ntYjHIm2JTVaadZYO1lQPtHA78CWY3gvTk3pD9qhvO1Iu6TbHn/3sZ/nABz5wpPq2zWYXYh1Z+n22\n2BQh5vYDEeLnt2Hx7TSz3FJYbZ/6cI/vd4CJkDyRTLDTwA/CkKJjyeCc1pNyYjV2JIaO8ltUkhjq\nRXO4aMYmkH5beu8sy3w7kKGeGwuOcA0TgxBBkqov9Zgsky3etCln/4v34pmDhW637CSrugwepI+5\n1Dhn6NaZ+Jko26l+YOpTtUH45wRniWcqiTch8zOFO38WT0jvVVPgzEwSJd/POM95QkIo3w5U2xuj\nDIHG3i8NvgM+bhKYmLWZC0U0Rqm1UBYtVTcP/bWk73XyPIYNZqDxiprGjH9B3dGFR0EBWqiwoKFG\nCSaSJCnlXNLA/dBsXzxgyiqHWanXKPc3cDccuBVu+gbsmcCJP1N9+l/Mtu1HatuWl73sZZxzzjl8\n8YtfBPiF2uZ4HsSQTnabHyETsaEIAsseB1OgnHP1uZ0K95cSIsJsU2FJ1w9vddd00JAkK26HseoU\nHsl1QXDoGpBcjlnbHFsFY6/nobA4aU4Fo4KSFhZTAapj4DHrae+dzH+8+cF+tSR9/3rkgw6OS2un\nRdfJQISWGZQ2EVY2HoO5t1rikBbdtEq334ft3defrSo+59FI34xv1hO8s1rfY5bYQkNV1Gb92Fyx\nLpbWdr+X/ieOKcbwVtV5QpLvY5Wa9F8qS+g86ryKYurjMc7G1ei9E+mjpWKnHpR4OnZve/+5xGbq\nsJak/Esaq5LjK+O1LLGJh9om7JoeZtfaIYr7W7gFDv0n3DiFY58Lu18481U8atuO9OVFF13Et7/9\n7V8YhQIKLVh81n/uoTLrRucFo7BZmpm1xRya45JrsgCi5LEuRmPPsTTdrSjF9jqyEOReuS1ke7BW\nxjlzrqXsqg9LYqG9dvpMAilsVVvMwizz8nCSk7ZWmqHNYEgh2/naeML2xzZtQndNab/WSxJPZx7m\nFsriB49RGVtBYUuRTHmvHUSawlECS/rxjeuDeJjSUQfB2idFyDPE4zEbrrTrocAbImXVbJtaPQsW\nkzUic0WEs4xXSDQ1SkE+8TGcGPaTNSkeS4DQ0OKXqXdYGuUisRb5PvVw5LtB4u00OCpkm+Np9ONB\nYQnej1hgkwVGlNQssMnyxiZLP27hLjhwA4xugPOm8PinAr84IvXn1rYdMHHOcc455zzi1OO0pUwr\nibPkaiwJuyNeaCLhWnN+7rj5ORbOfG+PE6w5bgrozGKLaSxCy2No/aTG1z+i7VXQDZtKdWVMhLmj\ngscLvaLsii7OEfBZ2APBoXfmefRYeo7AnLKMHHtOKgxSIZBXIJ1wLD0enxPWQiuFOPire6XMfo6C\nJjrOlhoJ/XWSgKljFmJs4Z3a/s6DxbYa53gsFFpKBHH3/u0Y6vPHZU7smNs+uOgY3aNGvQttBU3Y\niVWhMKI+SR/Kator0mq9D42/tfG86MYzpcPbeaPP0s78Lj13kJRvsedoBWTdpnhg2GF+A7BRxwzz\nJV6WWOdx0wMsH1z3Qfxvwrd+CDcswPOfD49/FnDyFq/5Udh25Llce+21fPKTn+T0009nZWUF8Ern\npptuOiKd22nbLiyWusNi9Qu+H7vu/WulC8kWk5QFYCGl1LPYTm2xVNCJu68ftFHndJE3IeYyN6hv\nep/1fJJmLUp/VvydnC8enOcqKWRmj5v3nrTulIVu0kTM2dTt3PvKf26hxJ17OWFfFicsqPgdWfgm\n3jzL0o6lZnQ/iB8r2v59gegoUZo2Q9/CYr35g8b3cnM6ByVbJWGTay3dOvUG4jETZTGN5ppAxTHE\n5ONv4j3HsUglmtgse6t85EcgSW/gaEl82c9e4Ns0T0Xega0XJpUi5JpV8Go0K18YYoudgllig4V2\nxOqhMcN7G7gVmi/Cyu1w3LFQnA88EziBo65ty3P5nd/5HQDe+ta3cvvtt3PllVdy+eWXc/nll/Ov\n//qvO77pFVdcwTOf+Uye9rSn8cEPfnDmcfv27aOqKv75n/957vXiyWEt1ThjN7WMyg5HtYIgf+2t\n6ZvpYhJBmXpPqVsvWy6LIPACa/a9ct6T4vuzoQ4RClKYETfLcu1bf3kvTpPHIsx9C0E967icMLLP\nnMtPKtPxDH9nBGNRJ9axWvxS1cAliYix5Tz7uYrM/BFYzM69hzM2qeWdY5Jt1VJPejvPMg9anPcs\nkVck24hn1p8d27Ksuy2tRanJfJpG45Eqn9i7UbTC/8QKz9KcBcEQxSAbhYky8V6IMr402z6uIVZG\n33uvRRIntcTLOivr61QP1HA7HP4WfP6H4ArYexoMnw08iaOuaCVsU7nceOON/OhHP+ITn/gEu3fv\n7v3spNV1zdvf/nauuOIKbr75Zj796U9zyy23ZI97z3vewwUXXBD2jMm1nJDSaqUpXBAn1fnWv7ad\n2HZhzxLeKpT1Xi4RUH3oIobF7PdFl7EcX7u/QJkyi+Xa3UdzPASukZjLLPfB9n07AjE/HhrMluv0\nFEpXT0qs7Vnjm4fmbEJlHwYtaKmKOpTwiPvWL/4YvjPbCIiA1bYVHGeu7aZRjMIqvr5XMv+a+rwN\nORp6Ok4OTe6zzCs1kmKmloW0rLIO57l4DslctYJ6lnEi87tI7pvu8FOEbYn9e7TvJ04nUC/UBuD9\nvdvQf/EoUmVs4y7WQ7HjIHBfESkSTZJUhaLKSbLw/Y+HwhYYsTzeZPnQJks/aSl+AHwdmi/D4cNQ\nPwMGe4EzgMdDuzrz9T9q27Zgsbe85S38+q//OnfccQfnnHNO9J1zjjvuuGPbN7z++us544wzwq6W\nr371q7Oss//5P/8nv/Vbv8W+ffvmXk8ntLrAYCGP/Dn+Xy2/HYrkZTyD7TaLB/eSMdHgomNrWEwo\nxrYWUmB8FS1UPpclxbtDccmy9UX9TDHNyLNK92/fouXGOP5OoEXPKcsxs2aNrfbLQomiNGJm37wW\ney/6mQ3Qp1Niu+9bYlYtljmVlCmhzziLIScL3/i/Zf7NggpnPQ/Eiar5Zweb32KNG+unB0s4AAAg\nAElEQVRNiOLJ3NznI7ntGRo979ZWdMYz9nQum7hXqQrf9lGKqerW0DE8az1meRYl6aiCE6Ug6y/1\nzK2SLGlY6DwXcBEsJizPtjNQh8ZTkXyWhW6HyRXWWF6fMPwpPhP/NvjBt+GO78BLCzjhFOBZwBNg\ndKyjWS5Ymju6j762Lc/lHe94B7fccguvf/3rufPOO6OfnSgWgHvuuYfTTjst/H3qqadyzz339I75\n3Oc+x1vf+lbAK7CdtHgRxZPPwiIBKsq44PZaqXVjvSO1lrcWUikstsVDZI+ZRTkVGue2WtlAYQPa\nsz2GFBabB2vFx4HCklttLBALr5ToZvtgoaB+37f2cF07R0i6ttunpJ+QN3ts84rBGQGmz2daZj8b\n/3FclsQ+V094m/5FhoPxiv1x8RyO31Hc1KqvdZ+b6Lni9WQ9dlGWIRbS7flSmXen0JV55m7bB1lX\n1huy0Kvuc59CZCn0Z5EAq6w0NqLPoefb+EnJNATnNQbTJt6MZYZp8H6FNVbaNaqNrsTLD4CvwgO3\nwneWYflXYfkF0J4K48fDxuoCm8PFzNt4dLcdBfT/4R/+4We+4XYUxbve9S7+4i/+AtlGeR4sZlsO\ngkoxecnXyIFh+lu8ta8V3qmV5ysD5AStrT1ks/bVe7FueIsGFnMhZvluXuriLEURBLxTb8WWzM/t\nFCkpeBYaShWtWMB5wab5RAJjBAHjPJtNoBYfVLXwo4UVRTHFXmmcNS9UX/PMZRP2bAf16CxsI1Wo\nxItrGrfl3vW55EIbjJadBy0kE3sVsZDMwp1Jy7GsUpXWh938HC9oke0fcnFF8YhTeM7RxeYqwtJI\njaMcvCfvExRO699Pqy3EMZFYGSvBpr+O4/Wja8x6lPK8Ygg2SKLktPvX/5fCeQJ7Oeiy9X1MpTBy\nw3suk1A/bMCEgsazxOoRK+sjqv0N3Avtd+F710HxPfjVY2H1ecAzoD6h4PCuBTaqRaqjbRtKdqhc\nfh7tlFNO4e67tcb03Xffzamnxrvk3Hjjjbz61a8G4MEHH+Tf/u3fGAwGXHzxxb3r7X/fh8KEG+59\nESt7zwXoTWDbimjSieDP1cISN3i+QlQYLIYfbJOcBGGcSN9UCQqzqPRJlK4IizqtzizVjhs3QPbu\nFpZOfE8VZLOEl1hkmoznf0v3OvGLNR1JtUaldto8+CR6js49sR6PH8Gdx3jkWW2im3qtPgnW9aa6\neK6ziRD2uloXS5TC7FyR/vnWk+5/N2/MrMDVczRRNb1XquitsJeWQks5peHoGIdF36u3/SnSuZnp\ng1W61uuMf+8TSNIcFcuGk/NtbEYVYxzbUuVBoKHbIpQyT+KdJDWL38JmgnV4T8d7LkI5rpiyzDpL\n000GD7UU9wHfhfZq+Np+OO40eMW5QBfEnx5bcqhYZcwCi0dYuVx11VVcddVVR/QeafsvVy7nnnsu\nt912G3fddRcnn3wyn/nMZ0KVZWkWanv961/Pq171qqxiATjuff8XBT4DdsQCzlgxFgKTiTZFqInq\nq7gwUX3hyhSSEWUwu4kAET5+vJ8Lph9y73xuQ2JphyCnLhwbdM21oFDKdmblYw+LYWIurRkNvY6n\ngfrrTWdeLL5vy8AodLnu1goj9ZwsnGIt9/iYJggtwv/zPqlVNkIFl57lqL4i+C0M2iK1pdTbsHBk\nX6g2Yf6otzKnSgCtEZ7zqcHy/CpAY0qwHVGJF3mquOQMyTn964W1U7RdmSHbv2lkuOn4avVtH6vw\nOz/mPBfrkchn6s3H3pNSkZVyHHs7AiOWRhlMezJAFVJt5pUlWmj5F4G9GhwLbIbYCqiJUdCEfBaB\nxQZMWBmvs3JwHfcAcDcc/ib86P/1hLATXgS8FHgycDw0ywUjt8SIAYXxwo9E27t3L3v37g1/v//9\n7z+i94NHQLlUVcWHPvQhXvnKV1LXNW94wxs488wz+fCHPwzAm9/85h1db1YhP0iDqSD8eM1K0Emd\n5qVEQWDs5NwO9dMrGrm/BCvjCgL2Xn0CQP9ZyHon221hUZZ9WCx/bN9KlTa/v7HlKp5NWirFuQbn\n8gUz03tJn3RzJy8g5u7K2RUuze3zLpZtqlrKUgPQOSVuvaz0c31O3V+9f1ysvLa73YKNEciPqAB5\nHpvgKOdUWONoNiyWCuEg5IspDKbJmIkxZvKqZqwJDdTbmEsTnZ8+lyoYuVcZhP+s8jyWKaYekFKW\nY9gt3tBLjrEMsGGnKBqKiI6cQnZ2Z8kV1hi0E5Y2Jgx/AtwLfBvuvQ3+Hwe/+XTY83x8Jv7JMD6+\nYG11wJpbZkrF4LEKi/31X/91+F3iIPI7wLvf/e4d3fTCCy/kwgsvjD6bpVT+8R//ce61UmvGuu7e\nC5EYiRV4lgKs7q5XAHlqsrXoUqEzS9CmWLoNfOZYV7Ms9N5xHZOsNUU2fQwhvqZY9sJoasVrKxoc\nimXH1NBc/EgzkzWAqmMhi7LBmWe2ilyfP4xB4eMudmyVFZan66bNjq+FetLxVEpu7hq+TE9Z1bSN\n691LKxI00fjaUiuONntt6ZcqAXPtkuDEWAGfGhD5eExrvC8Nqlsvr88kUyVbhDHvw2LKYPM1v4qq\n9jtBojRnC6PGfVLmZqo0rbcT/55mzGs2vsTi7DHqreixFkoL7zR4OyXi0VWhHL73IiVXRb2juoO6\nfAylpgxZ9wMm3RyFgoqSOiRJLrHBYrPJytrYx1nuA26Hn14Do6/DMxysnA28ANonwehEx+bqgPVq\niRELTKhYeKwql0OHDuGc49Zbb2Xfvn1cfPHFtG3L5z//ec4777wj3ccdNetCkyxq76v0K+na7Gpr\nTYnQkIk+q0mBS6l4axe39XZk8rcoT7+OhFKre5o4LQVucfeCRndurInyXHIVmO3z2Q/S/TFSPD0H\nW/SvG+ddzIpOxZnoue/7yiP2EmKrVaGVPuSW8y7kPdoNngAq4oKkRee5uBnPkfZ6nidjFZ0KZS3Z\nbj2XtBU0FG1LMy17HqbMJynFaRVcafqTKjV9vzFtt3ffxIORKuEpfCbnx8hBvLJk6wTJUUlZaxbS\ns7CeC8cqFTkeT10/sgGYxPtiyEyqRjTYMvgCjdZoWX57XppxP+hyWYrwDv0xix0ctjT1dcOqh6C4\nH/g+cCNcdy+MFuE39gDPBZ4GzRMcG6tLbFS+QMwmi0EdH21tW8rlfe97HwDnn38+X/va19i1axfg\ncbuLLnpkt7iRyZwTgGLBzDrP/yvYbr9JXoMEFrfui15bXeh+YNWWf9FF6vlZdbhGmvDZZ0jNei5f\nabaNqK4FPi8mlER39Oo52WtYiufWz63QogqKMvpOruWv1/UFjQVIywm8+fee8e6LJvP5zsgCqfKQ\nvpThGfW6VnGJeC2Tv+WaufuksFQQ0GgVZHtMlYxb7vmsknFoaR3brNeg9+t4dGVNVU3BaT/E0MkZ\nWzYPRZSKJc+4EDBP37l6v3GRyKLnMWsRz3jMpNx+mvwcszy1WoA12vx9vEKpKUzSZB1iKQqLeUU0\nZMwya6ywxtJoxMJ+Au14ehMcugJ2/xSKPcD/AJ4Fo1NL1o4dcrhYZsywqz62QEPB5AjHXB6JtqOY\ny/33389goIMwGAy4//77f+6d2kkrk8UhTZLHZllo/lylP4prnGsxXjzL+gbM9zmrVq4/2y7ejr3c\ndoURVUDLQk4ZXtk+FA1F1fSqIs/yzHKQo+6IEwdL/QgUSGzBCuV4XLr+F2ql2hpkaRPobUxs8XrL\nVOHA9P0obOd38smNr4xn4VoaZ58lfm8ShFboTt/nVsyxPvSUfh/De/P8JqvIc4pblEDcV39NmR+z\nYMb0elVRU1b97RFiGE8hudz6iGNM2h8xlrz3HpNwnLmerEuF0tR7Ey/DwmICtcUKSSnLlvklSkNI\nGl5p6F4sLS7QjGWPF7nmgAmLjFhu11kYjeEA8GPgFnjwm3D5AXjx8fBLZ+K9lj0wftyQg8VuNllk\nwoANltlkEWi3JMw8GtuOlMtrX/tazjvvPC655BLatuWyyy7jda973ZHq245bgdYP8hMzdsNBxP/A\nLOAYOtBFM8V1zCfJ4LcLyC4iXei5Ps0KDKuy0niJwhxpE2jJo92ND4gnsNjscWmixb1dAz7tuy4u\nxbb7AkWsyBiamSV4PMQTU5Ct8LCGQUwxzscm9N3lBkYJBSlk5IqGonXBs8v1N/68HwexnoodJ3uf\n/nPkvYm0fBDJswLBsq8SwQzqRVhFlIuXxcpYgu1dHKOoqQZ12K20CspLySqx8aTPL7/b9ddKcmXX\nI/s86Y9c11L2NVifUpenCExoa4cpeqAMPAt56XvSLYuBcAzAYqdoBBYT72eBEcuss2ttk8X9Ux9n\nuQsOXwOHroKTprD6LCheAuyBjSeWHNy1xAF2M2VAQ9Gp1rJT/EffbmE7eqL3vve9XHDBBVx99dUA\nXHrppZx99tlHpGM7a6oMZtUKs00tJ4WebIwk5u33r5G/nl8IMtlTKEQtL100/X4aYeeIFslWrCJR\nPmIJ5vqo126hBUtztjBY7j5aGHMWU0rLv8zKVYmUlSNcK2+n7wzCSvtuhZBYv7b4ZU5B2V0U1QIW\ngTiM7hMznNJselEi8VyItok2GfrW0NAYil5vO2Ru+379HCCab/E15e84CG+PcbSh5peeaI0qIQ/E\n5W88LKpEGuv1yvyWvzXPJU6klLmo723aeWMlVvkoPCmKPYbkBEaWdRHHXDzhp69QWhbZ7KjHbWCO\nyY+QDJbZ4BgOMDg89bTjHwJfg2/+AL5fwW+cDsvPBp4J7RPh4PIuHiqOYZ2VzoN0bHaF+aFlchQq\nl23v5wLQNA0333wzBw4c4J3vfCfHH3/8I76/S9+61ECzda9FaeQojTH0o1BHuui3xv9j4ZQmMKbw\nUIp1h9/LJrvhkj/OF2SsygbXtBSN4szRWJTgyhw0V1MUdbLPy1Z5M3E+xPzjcnTRvlCXfe4tlDGr\nHxaOSGGTrd6JnJ+Oe//vWEDOesb89TVg74/LQYF1mHv6eb7aMwCtg2mJrzEaMyJzcyb9W54rd5z9\nzjabVBzWTFI9WxMUYyhT30s8Huk49ytBaPDeVjVOPRm9nmWk2SKSsdKxRSxtkF7OGQS/wV5H2WS2\ndP5iF3qXEPwK66w2h9k9Psjgp1P4IdQ3wwNfgPI2eMIxUP4q8GxoT4bpCY714RKH2cUaK4y6WMuY\nhdCbo9Fz2ZFyedvb3sZXv/rVkPS4urrK2972tiPSse22/oTVidkvya6sMTk211L4azsCLF7M/d/T\n6/VhnPm26SzhvZ1mF+nOz8uzmWYlc1r4IlZq/ZhVHwbpP2OO+dWv9htj9mXo3+zguRV6Icjb1bjS\n/klSo/WEZr8r8RqskSLzLh2/Wcq6JDdv+8ohF8/rG1qxgWOVU3wNTd601ypcQ+UmHXXXQmmqYFRp\nYv6O+64Qlnrhti+iDOw4a3ViC4PFxSZjiny6qZfEVmIIMq5mPO7iLnXnmYhS2Qw1wxZNkuRiV0Z/\nlcPsHq+x+mBNeW8L34H1G+GKn0JzLOz9JVg4C9gDkxNKDuxe5mC1i8OssM4SmywyZmgyaPzTHG1t\nR+ryuuuu4+tf/3qAwo477jgmk8kR6dhOmixqaz3a7/oBfS0TYgP6VgHl76OT3DYbw5HJnUZgrECb\nFbCV53DkKjpnzuliLvIsMcTVFzTQZVEXNU0rVOf8mMUUVw2G1ubZ7XcWyrDXSOFBRzuTt+Ci35Ul\nZQVSTjnR3TmC/oJg87kO21Ws9h3YZ0y9v5gRlVOyGgO0cyO9V84jm9csBJleKx4nrQbga2LlSRsi\nyHOetIi9tHkixWz6ic4LHRvfpyL7fPZd2c28AGpayi6vZEoVlEQKo9m4krDU/DWVZmxhsaqjeEj+\niv/eB/EXOyispGaZ9eC1DBlT0rA8XWfp0Ah+BNzhtyy+50o4CTjhl6H4VeApwONhulpx2K10vLIV\n1lnu+jHp/l/h4L+Vy3A4pK51sj3wwAMUxY6cn597y1trfQEtk1yd+b7wT3MA7IKfV3U4ZzXaoLZ8\nHwveGDLoKQMXW5pRNeYu6Y8airqfU9F1qsszyFvaKkTt8yv0IZ9tzV/rt9jTiKGxIADKOqILx0I4\ntn5z198OLbt/Tl8Y5X7mXSMHY4nR0XSCTALFdmzTIL7LVByOnrcBphVF699LnMBp4xZWmeTWQoNs\nheX7WIT3kbuvC+8qJq7E3oAooGm4TkMZjS0ozGYVqAh/1/XDH6d5KTLn5L5xVWR7TOyxWm9HMudl\n7qtxFPsK/j15JSOxlZaig8VGDJgyZhCSJRfbEYN6wtKBmsG9LdwJfNWX0f+PAfzWU+Ck5+B3ljwZ\nmhNgvFKxxiprrLDBMiMWaRhHvXW0pEzPo6HtSLn8wR/8Ab/5m7/J/fffzx//8R/z2c9+lg984ANH\nqm/barMEg1USaQ0lm9Q4yxKUa4gQmkXVndUnhVQ0pmBFtV3kugdKt5AzlXl7mdctWHmSg53iZ5ET\n8NVuzWEyDvnnUEt2NhzkFVJL0TvOFqtMkzzt9fPeGj0vcTZuH8cEtgMhyvFpAUS9j+L8/diUvefs\nZuel60yb7g9cQW/u2fG214iNnbR2nUJSGn/zQeP4vvb9SExR4xMW7kzhprSKs/C9ct6iJaLYHwnQ\nl13/dX3G97fvTphnFVPjuVjoyzK/NDYjnoovWxorl4FRioPOS9K6aHWAwCRLf4V1VibrLI7GDDZb\nX5DyTuAmuO1q2LwNzt4FKy8Eng+cBhwHo90la0tDNjoobNQBbPJWJdoDMH2s57m85jWv4ZxzzuGL\nX/wiQHaTr//qJhVOU5xXm6XFgn3kwixWKZFfkw/mbtUslJSDxeQY+W0WRj67xYFVAKbgmr6X1S/y\nN+0EkreoC6cCbRYsZhWwFK60VqyMm8XBoUEKV84Tug6foOeKWIDaMbF7xecpz1YBSKJcbG278E7l\n3QyCoNkqr8deQ+5vSwPliCOWEpwG3/X3Ao1vxBTbXJOxFc9F57f3k2ZDuDpmDQ4343nz5+m8ETaV\nQoxt9Ex95RmXpRfF7JWTw8Z/VJGm8Rcdf2+ExZCfVRY+R0X7lRoFalw22KKUAp0NGTNhEGIsLUTF\nKNvWsTxdZ3l9zPBQC4fw+7N8A/h3+PoDsPsJcMFZ+HyWp0JzEkyOg83FIRvFcoDENlhizDA8d03x\n37CYtF/7tV/jD//wD3n7298ePnvTm97ERz7ykZ97xx5Os9Z7ToDI58prUSqszdHPCRiZpFLXyLY6\nY3Vbj0XOERGYZheX+DyX9L4Wt47gnMKXiHFNqyn9aesy9G2md9Q3ly89khvPdFxyz5meo2MtVrUm\nzBV4FpIKrCKy4O1I5jB/EeS5wpUueY/972II0tZms0pVmx4vz5TG9qz3mxuz9L767vt9VyMo/jyG\nPuVK8bhrjse0E1aSI5LGd9Tjst+lRIl4leTjTyU1tNC0RVfFOy6norFQv8Jy20PEFOKUEFFG70fX\nggb7hXotCmfImCHj8LnSkGNorKFgwDhSPAUNK6yzyIZPnGxbVtYnDA+0IFn4t8B9N8K+fXB6Aac8\nFV/t+Gmedjw9oWB9dciaW2adpVA7eZOFTrn4mKhk3swyEB7tbUdA35133skHP/jBqFzzVtsQ/1e1\nWZ6Andz22Dgga2tYkVwjz5ia1+x+EvFCVJbL/PO3DuymbTswULh+0Zrqv3EymijC1PrPkSWkWVih\n711sn21nN92KBbT2zSbuKX1Vva0yuUYKu6T3y80ZC02lO472+zSvSnLsiUWQTxHH1WIF3VK6Goqm\nNxbxM6mwnTXu6kWl3mnsMeT6rsK4juatXT/gK2y3jaNtbXl89WrTcwo04tBfh5oyIEaJ3Wsl7Zte\ns+7Nocqclyoer3ymLHSZ9otGBSx2INYyGyy3a1RrjVcsPwZuh+mX4aHr4LvAic+DU18IPBV4Amwe\nV3FwdYk1t8yGITKPup8xC0wYRmToo5UttiPl8rjHPY4rr7yS++67j1e96lU89NBDR6pf2252YoHC\nOLny3EoTTYWBUkBzginNW8g1rS0VU2Dz9c1yrBZrrc2LnfiAvgTD5dzwHUrrtILFekM5YZjbcXL+\n8/ZjH7Na1hMsG8qiCX2VsUq9hLQf9pn18/n9tdWYVVH2rz2vpR7OrGe0fbZ9jRVNlz+SwQ2DsHdA\nkQ/66zP1M/ltH62ilHUhEGK/71JpOP7JQZF23EsaXNvSNnbPGquYrfC3fdH5Y72u9P5ynbRP8rzi\nbVg6cU6xyLbFWuVYtifeDHRjTzXeZJl1Vpo1VtvD7G4OUR7QDHyuh+tuhtsehN9ehFOeC5wNnAKc\nCONl77FsGpU1iu60aLJpjm7lsuPMnaqq+Lu/+zsuvfRSzj//fPbv338k+rXtpth3H+NuE2tVmj3G\nFsmLr2stTg+x2QUxuz8xJm0Xg9wjLlypcI0KTaCzAG2AMmJIuda/vQK0QsEw9MHJxZM+AWa/8vne\njrX27e8Kr2heh8JCeQ/HssZs7oFVIrk4yLz+pZ6ghX7EOt6qWUvXKog+JOpjHHJt66lZWGzre6V/\nT5NPu/flaqhqCjcNxtK8wpGxAo7jfvK7z53XGJL1BOQa9keO0UC8ln3BvHsaqOsCBv5eA6Mo5Hj7\nrv3z2NinjaP0PeA6ML+sxyOFJksqJghbzSoVoRsLg2whKBeJJU2DYB8wCWVeakqWN0fsmq7T1lA+\nCPwA6m/A2mWwsR+qJ8JJvwKcCzwZ2hNgvBvWF4assdKpsKHxgxYipeIz8l0gKTzmlYvdc+V3f/d3\nOeuss/jQhz70c+/UzloeChOs2AoHH+voP7IVEPazXEsFtT12KwFpz5tXJiXf4qCpE+VSzoDQyjZk\nwNtryPlpXo59NqukZfyUqTM7e90rYUcKGaVKzOEhIS23IuQAoj6lCigVfun91TuLEwft+1VFPV8R\n2CS+9BljCCumxqYQo82p8mXeZ1RNCP2d+hFyLUVVeyMiam1yz7znAhIM91EHP/N9xCv37qzXYJWA\n3e9E+iexDGlNXVBPS8q2oXL6nTWWSnNdybuRe1TR88fK3bLANG6i9cNSo0AVjMZQBky7rBJhi3lF\n0lAwZAzAYuex+L9bFtamDA8D6/gA/k3wkxvhskNw3m54ztOAFwNPB54A7eMca6tLHB6sss4KDQXj\nbq9Kq2R8EH8Qdrb0M3F+sdJHa9uRcnnLW94S/X3OOedsuZnXkW7zLNtUCAnOrPkmDQpBaVny1NpS\nHHlrZSCLJM1pSRVP3zLWV+GtxfRZoKLpfJ5O+FctroyVXSqIrUAlPFfM5BIhJVatfZacF6LfxQmA\nIghySjNSWs4rvsJZimobCaxU4YuAskpCvb9Yefj7xc8i0J+OO0Go1eG8vOEw67NUKTfEm1ulijAa\n38LHvnIC33suDWVVUzndOthez86vNBblP++/H8C8ZxmvPD1cYa2mU3fxGGvQfkpbO+pxhVtuE8Uh\nJBiNaabesP9XFYL19OU5bbFJO480KK+MNn+tSZd5P6GmCspE4S+fEKkEG1hmnaVmg8V2k6qcMjg8\nhfvxsZbvwj3Xw/f3wenA8S+G4teBZ+DzWY6H8Ypjs1wM2feAqUgmaZMDasrwtyAmDT5j6Ghr21Iu\nv/zLv8w111zD6upq2H1SmnOOgwcPHpHObaeJi18RFxBM3XnbdKIrRNBmrGG7OOXM7fXJC6rU8pXf\nc16D9lO+iyEnuaZ5CFgAKhWUImRykEnK+ulb17M9tVyQXbqQQitbWWBWkdnPFHLL4/yz4M2cB0PX\nEwvlaGVc/5ml9qqRIYw9S23180rmky32GQt2ey+JH8VjqM84jWIucYXsbj64xpe7L2bHd+y4iUGk\n+534bJJcEqW9TswWs0ysQTJ+6nX0lNW4pNlYhGPEYHNovCVNpNSxTN9vHzrz4LBVqtIny/iydGkp\n4TLsRDhI2XwPm0mZfR/cV0NogU2WN8esjEcsFyOqn+CLUd4JXAl33gbfXYH/8+mw64V42vHpMDke\nxqslG8MFNtxi8FCALrLjlcuIISOGZtWV2N1EH7OeyzXXXAPA4cOHj2hnHk5LhbedyLnjWhzTsKxi\namgRJls/E1uszlkWqZzvF29sQYoF57NpXG+hah4JpFRZe39fdkOhAVdBUc6AqsoaV2iWst3QKr/R\nlL3PrAx5GySOx0ZAyBRaiSGLKUVnsdn91XVh9Sna4nH1++jjTzkIbV41hbjP8rsK5zRO06/lMOt6\nvum2CC2VEc5yzxRSywl88HGxwWAayt3LvBGFlyZRxueLEI7PEap0dB/iOGL8uUJNKWzln7V7thG4\nNUfZpEmmGl+Tc5SKTIDEtNaXeCiauya+etWVY7FwnWzuJVBimVxHd5P0MRmbvzJkFBRfQcNqu8Zw\nc0J5EMoazwy7FTZvgCtvgcUD8PKTYelXgedD82SYPgE2lhcYVYOuItliuLpDPBdRdZ4h5r0UH5Vq\n0FhLGnc7GtpRUYrTCmtpammqFSTkOMH3093orDuu126ixZ2DSWzTxZqDhrT+1rzgr6i+LR7aey4D\nfd54x71UiM3qk1pvqYcgQskv5jIoSXtNa036ZxtEFvjs50vhNx+NyPejn8ktx8XwX9w/8ShiJl9K\nEVYLWwLe/QoOFmZU8oha+wo7xnMkhlWlb6nhkvYHoHQ11WAayBf2tZdINYfY47PFHOXuAr3IvFBS\nibAI46RGea5pMtYxzNbgwnUairUWHmxxp3vzyW4EFpeLacx9nHppKHuvQOMpFm4UFpgN+vtAfWGI\nFUpPFlZYTRU2/hLRL7XCSrptjJspK5vrDA5M4UFgA7gN1r4K930BDo/hpKfBk14CPAd4KkyeWLF/\n90q3CbJXZZuGdlxQd9GdQQjujztfSY4XD1re0dHWtqVccnCYtEceFmuShZq35P0EnyIgCFigqA2L\nJ3bNG3YChdnFK1CVwlViz0rZjNosbEsdbiIlYRe8XzyGhZaJuWiHWlyhCsD2UzaWjPsAACAASURB\nVMZMLPycUp0HlfXHNcX6+zEgzWnohJZrophLCiXZc1PLX/qeS6KUPik81QSr0EJgFvIhHGe3nm6w\nkKtVbOl8y3kj9t/sOJY1rks6zJJAipaqiHM7pG/+mv43fY9x/6wCF2He0M/oT4+z/dbfFe6T71qj\nYF3ZwtBDeWIWxSVlYnhX4jIWWhOFYqFggYvEI0kLVgospte21Y69OJ/SMGSE7NMiP0tshLEY1hOW\nDjaeFXYPnnZ8DXzvW/ClCfzmiXDqs/DMsKfA6OSCQ8cscoDdCBpRU4ZEyRHDUJdMADr5EeVSd2rY\nwmNHW9uWcvlFhMOkxcoghXPUggLdtFEsJhF61nKwwsBa5dZzSVvOEk6P831UBoyHKDT+4C1nrWVm\nz9PfzfVc28Vc4ucvgzBtfeA8PEsseNK4TwpHybOLgqzNgi+ICQEiHPyzzafIhr+dvjvpQwwPiaXc\nohWS+zEx9VT6Fq9azHZexONo35cKt7iMjDxH36PV2IyNTfSfuzXj2M81Kmh8drvzPzpvdWOr9D2q\nUM3tcxNfX6HYaZgbaV2x0hg70ieFliQvReAoYYB1kOsxDa5qKEvvT6VrUg0ly0CrIsWT/lgoL1Yg\nNuZS06IKWJlgkxBzKfG7RjpaFrqS+SusschG8IYG0ynlT2oPhd0B3Aw33AA//T68ZBmOeymU5wFP\nBk6B9d1LHKh2s8ZqGGOFu3zZTF/SpYqeSnhxEvUp8TtQ+s26H6PKxbb9+/dz2223sbm5GT572cte\n9nPt1M/SZNGnuLSffBJ5iIEnqUtlFVNOQch3qfUnWHZqhVqBbwW67lui0MmsOIv93ffRad9KcEX/\nuFQQW+hLrzWfzpuD5mxCaM6KT69tBW6c9xALS4eLxjWm5uZgymk31o7cu7LPoGys1AiJkzBnvevU\nYBEFlEJzdqxTQTnbWIjzXFTxC6FD42X2fUg/UkaivV9K3vDWdYGtaODM9zLWcVxD3kOsbL1y0wrW\ng6UNFqpDVMWks8hdcg1hKqqSFbKNXE/YYhrurjuL3vdd9l2x2fqSxzJkhHhVGuXwSZI1JQuMKWhN\nEZZNlthkYTJiOKoZ7G8oOsUyuQEO/RvcfRh2nwznPR+fJPk0aE6G0YkFBxdXOMBuDrPSjaEfjVFX\nmH/EQlDdPpivOS7iX9n4VyqPjpa2I+Xy0Y9+lL/927/l7rvv5uyzz+baa6/lxS9+MVdeeeWR6t+W\nLSewpFkLNhUA8q8sKG8d5VlMRbcstzsBUgVkF7g0q4T6sYM4lqF9MNCNa3CDFlfln1GovirgY8hD\n7ptCLtqP2BucBe9YoSYCIy37Ya1rfTbNI7HCVbwi6UP8HlIIKqUbx5CUZevlytDodVXQWW8g9/7s\n9WyhSvsO++fG+ScltX9/hYy9o3AC13nhH28j5WMgynDUOma52JategAqvETRxgmtcaJjPC5NuIf8\na2uDiaJYXBixNNwIeVXWqBKPMoa74rmoXo16JRrP87NhEmIp0xDFWGCELz45CdfxFOMysMIKGhbZ\nYMjYVzdmndXpGiujDYZrLcUhPAx2B3AD/PAG+OwBeOVuePozgb34KsdPgPq4kkNLKxwqd4VdJdWT\nazsFMuigriZ6g5OOsyYQmlRDlpjLLILGo7nt6In+5m/+huuvv549e/bwpS99ia9//escc8wxR6pv\n22qxQGzMBBWhGFMYbb5KDsaIj4vx65xwjc/pW8WzhHdpPs89z6xmr4fJ0LcLtqL2wqqXgGevEcMp\n1svoKark+Wcpmnke2LzrF5HgEUs9FoCaVa7v2F5nVn5N2ncbFI6VeD+Pafa76ytoHRuFfubSvJ2H\nLcVrLplSuWmksComWEJC6rnE817jEXZOp7BaOu9iZaB0djEu4qrIdXRf+XzoxiwWm724iCQ+pnES\nhdtSOFIVUbo9cZp5nzLM7I/sJikRkCU2WGaNZdbZNT3E6voGiw+1FA/i6cbfA26Em/bBzbfBeS2c\nfC4s7gV+Ca9cToR6d8FascLhsD+LlNIfhoRJ2b5YFIgE86Wn4n+JZLJS42hrO/JcFhcXWVpaAmBz\nc5NnPvOZ3HrrrUekY9ttqaJI4QP7r7QCyUNRy14swVio0ru2FczSrOUtgjEnAIS1488pegu7wJZW\n77OUNPbTULqph8VKG7TPB8QFStA4gWf7pILCN8XtY0GkglXG0OZViGWvQt6WTcGcoxCMCJIJRdQP\npWTPf+d9wZ5CUnnjIPViW/O7wjnxtgX6+zQai5zn4nr3iGnVcl4R/R57r1bQxspAPe10PK2y9ONX\nRs8lJoj9TI4VZS5CXmNs8XEQMzFFsfldGiW2aedQrJDsmMr7kViJLYefwom2XL4tQGkrGotX42hD\nZa8WF7yEVQ6zsjFh4aHWVzd+ALgT6q/DoX+FHz4Io+PhwudC8QL8pl+nAoswflzB4ZUBh11cQn+R\nTTwNehoiUhMqCoaJmeF7Lv2p0cx8MS+OtrYj5XLaaaexf/9+fuM3foNXvOIVHHvssezZs+cIdW17\nzbr16f4YdgHIccKgt6LLLm5126311yDYb665aGELxKDXtsLP9juFUqyysUI+tqCNAhzgFUwQLkY4\nld57ybW4WKR/Xu3TLAWV97TscVZJC/XZCid9zlQhSPKnM5/F7KectS2BahGUqRFhz1OIp+6NvXgG\nKfvMQndiHPjP43cqzL+WsntupQTbcZN7gTcK7H42BW23cZUaIXbc1HBRFZEyjLT2Vo1sFuZomeIC\n/BIrwT6tOhb+WudLN1UTCEvL6g+ZsMCIqitpIgrDjp0qTK8AhIpbhPtMifdbsc/toqpcA/MjisQr\nximLbOJou6yTDcCrxKJpOGZykMGB2tONfwx8H7gWfvof8H8/CM9bgL1PhuLXgCdBe5ovoe+A8fKA\ntWqVDZZZZ5mNrpS+GIA+E2cYoDEPQaqJIP6b91ZUuYjH8piPufzLv/wLAO973/vYu3cvBw8e5IIL\nLjgiHdtuSxeDXcjxboEiDDwNEuLscuu5WEhm+32wQgSs5R5BWfTzXLYq/S5neYEq7CzP0CkKjXGk\nlrkKXmUDxVb4rATFOhIkkFNCscKzQjx9lrgvs2m9+XGNz0shqdQLsZ6HssnisUz7IQtblImFoLQf\nGj+wwjL1amIPt0/FBUi9IsCInzjxtD/WWlGiJA2KW2WQxresWorjKmlZnbLzW2wiog32CzNQ+ufF\n6qibn0Uy72ypRs2QFw9c+6eeRwrv+fiO1AVTBTVkHJSKeE8LbFJQd7vVb3T9bCinLSv7a9wDracb\n3wXsg2/tg5u/5zeQfOq5sPwrwLOB42Dy+JL140qqac16MWCDxeCxCAQmnrnslBlHylR1yyrV1NIS\nSayG1ph7R0972EmUe/fu/Tl242dvLvxY9lA/8bFF81xiCy626FIhrGrHNxv8r82CSuG1VLFA7CnZ\nRDtvyQgspkFjWajaA4/XU9VQ2gB4Quk1dF87RtofTT4VIZdTUCW+cGV6nPavDzk5tHxNKizk3jq+\nTccgikkOoijyffIZ+nac+wo6Zr3F465N7uXZZ/ZzeYZ+PMZ6E5q4WARlZd+HvbfNrbLXEg8uHj+7\nX4l6xv5esrdoypbrs+fEmxLBr/3LeyviwfaNFIWsGrRAqfdcxqjXrvEaNWqa8HfVGUl2r5iUCZaO\nXUPRKR5VLFOq4K14D2rMYqfkluoNVqZruBYWq03cCHiwhR8Bt/kKx3f8L7jnPhjsgrPOgdVzgGfh\nC4gtwnh1wIFiF4vDERsssc4Kmyx0vy+H+/u5SFAqcZTJqmQPiwlbLI0WH21tR8pl3759/Pmf/zl3\n3XUX06kP9DnnuOmmm45I57bT/ILsW/9+kavVSbLYUkhFaJpbJQ+KMIz7oMLfCgJLClBqtMZcVIDm\nF7jth+1r8ETKmqLIBXFrynJK6TRomlrQLY4UILSJndbmmiWUVbDX4fnmeSTWM8hVR5ilKKxSs0In\nVUAiADVWIVUbbKC6H4D3mHm8g6L1NHT8+x5FWk1YxjY1TnRsS//8ZRNKu6gwVkjUeg05ReRnbz/7\nXbPutZKxqFdrPImJZbc0tvXXbHxDFaU+j8TXKpoAUUnwvzHjlAvqe2XjwtzSPVamwYMp0R1fZcaI\nh7TQ7W8vhS6H3d9eyW0yoGR5PGJ5rcFNgabR7Ym/A5NrYf+X4OqD8OTj4YKnAb+M3/DrVHyV4wrG\niwPWWKGmMoVjFgNVwMNfk+6ZfEKkBfY0qC9An5+NygusgjH5mIfFfvu3f5u/+qu/4tnPfjZF8YvE\nblCKpp3EPmwdL35ZImCFWJp7EQsxWUweM53dB6/EirB49R4KH9H9Fgvy+VBSzgIuaKJ96Le6Rk5R\n5byqXMzI9lXuJeNqhahD6cjpPfQ9pP3wkE2/j7HiTZ8pjZHM8ly8sE8hSIF/ppHwlWunFrsow9Y8\nT25zNXl2+Tf2CsQAsdRzPy7W0JDYk+sEvKXo5u6V3yysQVR/0QlyVScQJ1FamC+GK8X7sO8zl3kv\nMJWsk8B+65SOKmQVtzFsrNcQaEwVq+bVeF6W/26hK+nSUER8rUVGACyMxriHgAm+bP79wHeAr8B3\nvwFf/Cm8fBH2PBuQCscnQn2SY+M4P1/Wy4UuUdIxYmj4Z54uMKHq9oCZdqpeOWw2gdL+DW0YeXmn\nMQ3p6Gk7Ui4nnngiF1988ZHqy8NqVgGkwsUykoCw5HTSqiXVUITjrYWX3sueL81b3lK+REtlCGQk\ni1JaP+aiuLNAF/K5/bECxrnWF38s+g44QFX4cu2a9Bgz0+wmWT6OMzX9ITpWMvTt9edl6DuzXGz/\nYwMg3bI4jmHoSClDz8ZS5P2pkG+NLdiH4+w7k+tJ31tjjVuFIGNt31MMZMSwVQyLxQq2p7Q6wkXs\nrYoXE28xHHtQCn1akaRIvlRFzrPFavoVeON348e4QeMcfYrxtBu7OCBfInu/uOCxxIH62qzHmBAw\n7JRQSlWWZx5QIqVdhGbsvYBC93hsRixNNijqlsGhFn6KVyw/xdONr4Gr98ED98LZC3DKXlh+MXAW\n8ARgFSa7Kw4OduFcwxp+R8mS2qiuxVDixUaUym6FTJMZOE0+A6F7iDlW9uTB0dJ2pFz+9E//lDe8\n4Q28/OUvZzjsdj10jksuueSIdG47LWXuqACK2V3eAo0z9CV+IbkGqSC3QkQmQr4PKhgtRVS/68MT\nFh6KlZhg4f04kIW3HC1VNaUoZzO49F41DktO8IChHuNbWh5dzp/3zP3v+5RoCx/Fn7ch1hLDYGoU\nWM8ofSaBNl14h7ObzQ4veuPt34cweGLRECvVOIbQhyNjbyd3jZSK7D0rsd4raqbG+rc/KWyYwm/K\nFlQDB8CyxeyxVvzFkQH/TkR52O0L7DyXeTzoRK8ojaY7tzTPFBNyvXKK81YmXVH6cS/W5AWvMz6D\nB6j823OssM5ivcniaMLieoMb46nG9+H3Y/keHLgBbv1f8KMaHv9EOP95wEvwiuUpwCqwCPVyyZpb\npmQagvYV08BPGwVVODS+WYUvVJkG9BXstLNTPm86ufLfngvwT//0T9x6661Mp9MIFntklUvec7G4\nsxWW6TmVmcAyme0iTinLJH8L1CZ/q0Xez7yX5hVVzNrZDixWICU/OgUk9aiC8DHxktJ/p0ouxsFr\n8lCSNLu40ziDQEsyRlb4Nti4hQZ0dXzqaNzlXaVKLX1ftrhnYcbF0n1Tj8XmS8QQlQ0ixxn8uXec\nft6nIscQqvCbcs8hAFUV3l0dvATJNJfn0tiUZcup19XgknGoEWS/MXPOssXS57JK3CoZvx6m0X1j\nFl4ZxlHz0nNzwCot8WI8ZbkyCkdrgo0DlCbjJetriQ2W2AiFJ0um0DqW6nWW16cM1hrcIXxV43vx\nMZYfwMGvwO3fhK/UcNHJ8MznAucDT4d2jy/rUg+gqRzrVcUaK1RMWfdFYhgyZtyVcRFV6hMjy24D\nMF9CcxIplzhqKSvI1xzT0RaY/jHvudxwww185zvfmVkh+ZFoOavWlqiwQgBAQoh5aMAKINliyQVL\nbtY9rfC15TVST0M9prhmlkzBKvS5zzKT5/JwQicUqnpmFr49zwqJ9Bli5bydsY4VRUqA6JMEYqGf\n80AabIXq2efECq7NPlNOQcQKOvWe+nkwKmTj4L8dS6vA+nXK1IuukucQ6M0+vwTHbR/tnHLhmqoY\nPSRURvPbnqM90T1mWtMH+/5SBaXXkr+Vnq6ejXo8wt7SbH7Zt36C3YdFlJBu4uXHR3Y8STPtB11s\npsF7lFLR2HswG1RMcLVj16EJxeEWdxA4ADyE3+Trm8DVcN0P4d4JvOk4WH4RuHOBpwGnwuZJA9aO\nG8oECjTjmtLAYL5m2qQL7EtwX2AwgcX6pG4lWVsMQj4XdS3e3tHWdqRcXvKSl3DzzTfzrGc960j1\nZ8dNhWPMMLG0ZLGonFn40EaL0bLHVJj5KE3Oms01VWzTsCCtIJHzZILNwvYt1KGJaDFUJTEXKRli\n6ZwlPomyL3w1TmDHxiq0FCaxP3GgX55EFah80s+dscwy7YMqiaaDg/IQnypo+149FRmsoovzJkSw\n27HOKS25voiEOO6mYwLxXizyvmXcZc7UxPR0Cz8pW0xiLtp/gYOkv9XM9xCTBmTOWIXnUAhXjpXP\nFU607DDdYtj2JwZ4bMFIF3k8UnRS7mdjRvY5RHG0iLc2DsppIWKCaQJm2ykon764zkqzxurmBtOq\npK0LigP44P1+fILkPdB+HX5yHVx2JzxhCuefCiv/A4pfAvYATwROgtHKAgfdarjXBkusscKQcYDF\nltgI1cxUPXrvZEIVYLHUVxMFI6NgqeCShAA5IPnoaDtSLl/96ld53vOex5Of/GQWFhaAh09FvuKK\nK3jXu95FXdf8/u//Pu95z3ui7z/1qU/xl3/5l7Rty65du/j7v/97nvOc58y8nmDuVtCkMRdQ5hfE\nAVo5RhZYmowmZT/Eg7HCx19Xs6ttsxai2PR+G9g6EjypJ5FTKCUSfO+S1wrdYtfNmKJWAOas91mK\nUp/RMptUiajDL8d0BRgRCMsyxJSdZUvayPOmitY+ryhqeb4iGaNYqcSsNCtQY+8jhvys1a/vs6+c\npaXfOdRbk88q+oVQpZqUozX72UyRStcCE9kExlTBqMB1Sf90TAX2pPeNB5nEC7IlfmIFN6XurPGS\nVNFa2KymIi5xL8JT+z8J/1rKsqPtvJ2J2R1yHH4sUw6gZsKIBVbaNRbrEQtrDQuupp2AewCvVO7D\n1wq7EW6+Cb5xB5wMPOtsOP3F+K2Jnwg8HtoTYHRcwaGlRQ5yTEjIlN0kHW3o+diUy5QnEs9lwhBL\nebEB/NSLEaWu2T6TaKYebW3byqVtWz7ykY/wpCc96We+aV3XvP3tb+cLX/gCp5xyCi94wQu4+OKL\nOfPMM8MxT3nKU/jyl7/MMcccwxVXXMGb3vQmrr322t61RNil1qddgBoM9aFTzW2IYxkqRFWApd6M\nWMZps1ZqhQR9NRbijxEAyDNqUmFqlZwIdZtE6b/THBRFd6WPRpm5hsLVpArKpm5p2ZXS9F+D0da5\nl+WRPrNdQqBWsrWCYyAgjpGk703HKR8LESVnqciqWOLr23NihRDH5grzeZooKu+zRBlOysyqM32P\nvTm1Y1UoFzS+anXX19a8T+2/TUKM84nkXj6SEnuCsfEgQf/UjMKMlUJWtvwKEJSCrCHNP7HKpaZK\nlEaLC5CYFcvioXigaRCSHu1+jbZkvtzbP6sfjV2Tw6wc3qR4CFwDbOKVyj3A7TD9Fly3D+79Cexe\nhvOfA7teAjwPr2mOBR4H7TGO9aUlDlWrHGa1y4+ZBrJz0WXNCNUgLj7jVal4JVMqBh10ZgP6/nuN\nrWh8RQL8uiKPxrYjz+Vtb3sb3/72t3/mm15//fWcccYZoS7Zq1/9aj73uc9FyuXFL35x+P2FL3wh\nP/zhD2deT4RAahHLS1OarMY7oL9ZmGLnCg3o9WU/7/5EsEmUuWaVg/RDizWC9SpiL6FfT8v/Hlvg\nsQDrhFxXcVeVU3ys7XtKPrD9Fq8npSJbSnBKRZY+2iBzX+jG1XpTAR0rHY2DxMF0VZ6xjdhEY+LJ\nExq3qcJ51qbvj5GIA7lvQ5rX0/TGVJSUh6ViynJk8CTJrxYykpLtmsCoMF+FfQdpEqWyymLlqk8q\nwt96htZzjr0frdIsGfaqJF0QpTY3Ra5fMu3qA486JlkcU2nB0IpHgQlmvRivXOJ1tTraYHAAD4GN\ngIP4Ui7fhge+Bjfvg9uBpz8eXvoM4KV4Rtge4HHAMkxXHRu7StbKxQ5oW8b7lJNAOS7wYFwaCRoH\nH60KysUSqG1ipJgIkpkva19NrSIc95iOuTjnOOecc7j++us577zzfqab3nPPPZx22mnh71NPPZXr\nrrtu5vEf//jHueiii7LflWh9rBje8EpCcGC/WJV4HJ4LK2Djcii2xlhNGQmkdG8R8QQsXGEZSbLo\n7LFWMOUUk4X4xJsRCGUWbBPDSbakixXwQonNs6Nywj/XJB9Gruu9lnyfqsxzitVtg9xyXauM4rFW\nxe/PiynABX1F5syz6nca61ElZHNN0vGNBa99r3Ffa7xPHJf11+eN32kV5syUsvMxbDkcK7JU4Ep8\nRzecKomZX9ZnLMw4W+Vi75UG00VwqgJS78pXI1YYTbwNKSQJsND9rcpHa38Nu0KTS2x6GnEI0m+y\nxHrYGHjYjqjqmqL1m59V1YSFjdonRP4YH7y/D/g23P1luOUuuKWAS06B084CzsFXNj4DOBnaBZgs\nwOZCxfpwuSuZ78vmS79lBETdjVlgwiZx9n0VFIwFLvt+uppG8ndB0/tOZvjR1nbkuVx77bV88pOf\n5PTTT2dlZQV4eDGXnbDNvvSlL/GJT3yCa665Jvv9f77vnwFPU9y192yeuPfpQagAkVCTF6gLMmbk\npJaxpTN7oVGEBRk9DwpxNEbApYJOmrUi02tgBHFqyXvL1waK0zwIm60fK6cUAZbjxJpWmEzhuDQe\nYc8NJWhM3wAkuzx3bgodzoLFtL8xkwlij80qJQsZWWWcjl/8fZ+QIMq37wVJTEkTUK1oKcLcyRkP\n+sxtNz7xs8XeoXyWVpiwdbfkHcRjpgF28Xfk/RbEOx+mHpUoARGdDaWJkaiHI88tRpRQi22pGCCq\nXGwVkMZm/DFLXZ3hJdY7mvGIhXbEsB4zHE0ZjFvKKbQNLBdTH1/5MZ5mfDds3gL3fhm+ugYLi/B7\nJ8DyrwFn4ku5nA6bp5SMT/SklWlZMSoWursJRWApjI3sHOlozWha/ppGj9QzEQgsTjm1CsQqDwXf\nLS3myCqXq666iquuuuqI3iNtO1Iu//7v/w6ocmjbh8dxOOWUU7j77rvD33fffTennnpq77ibbrqJ\nN77xjVxxxRUce+yx2Ws9530X44Dj+Ck/4bhIKMQeShzgBaKFKwtRFY2UnyiQpLkWDZSmVn0KK6TC\ntMCWbFeBHu97ogQBuWZs5XrcXwVc+lOH72ww1F7LP9cAYcGlyi/93UJTlnKbwlki7LWCEr3x6Y+Z\n9xZrYlhMjk9JCKk3kb9eDIlJfKAPy9mxis+xDCfr/Wif7DtW2xS0oKnG++If9ST0nhIArymjuaBE\njFgBDJAaXmUY6/QZ2q5vSlf21r+U4td3Eis0qV7sZ3sRxkHHxcdG5J7eI5kElpe8G/FwLMylrLBN\nSgYsscEqhzvF4nNXlpoNFkYThps11SYe+hqDm0A5wReevAO4BR66Fr53C/zvKVywCs9+OgxeivdW\nTsLHV06CjV2LHB4s4v3JgjHD7m7qM8lcszSESVAUMUHa/j0xSsRDawpgWq9FZrKsfYnHWK/mSLa9\ne/dGxYbf//73H9H7wQ6Vy549e/jGN77BV77yFZxznH/++Tz3uc/d8U3PPfdcbrvtNu666y5OPvlk\nPvOZz/DpT386OuYHP/gBl1xyCZ/85Cc544wzZl5Lg8zWKY0plXbBtjgk3XCWYBVBLn97q7KKjon7\nYFk0DktFToWhtBSrl2tXyXQUm8ZCWlYA2meV8bACMIbVFAqxglgUnYVx4vu35vgpkneQPp89T8cm\nhlXyAlcUZj/+Yvtu37PCXXGBjbjPkq8kQrsPn6UWv4UpRakqlNj3di0NXPrr6xUr+aBMni1OWkwr\nA6h30ETCfWret84XvZ71YvWdNjRMGVBQMMBnmksSrsZRbOkVvXdNGbyRvnLzRpeWZPFKZNKtE4m1\niFIR2Gux42NN8NsP+6231llhjeVmnaW1MYP1lmIDnwy53v1s4uMst/uKxgf/P7j6J3BfA69ZgBNf\nBINzCPkrHAPtCkyPhcMLyxxgF0sB3hp2vVgMqm+BUccK082+JmYHyXTTL511dsXGEJcN6LedzNE3\npMrkv6nI+G2OP/rRj3LJJZfQti2vec1reOMb38g73vGOnd20qvjQhz7EK1/5Suq65g1veANnnnkm\nH/7whwF485vfzJ/92Z+xf/9+3vrWtwIwGAy4/vrre9fqW3myoLVOl13cKjRmwWJxkFmWcuoNWQFm\n/05/t/eUlrrBNvNZzxHqbgzliFKcJRDtuFgLPYVoLDPKWk2x4E1ZURpI72/4lZIm4qB4fGzMbrLE\nTTuG9hh9RwoHSp4LaJ0r62UpVBVXe07fsU2aVJZenGsdK6xc4N8qNZ+HbfsudrCwrKw3ICTWAc4o\nirj+W0HdsanGlCHD3YVxz8Vc/Dg6WqadABugiY5N1Icc5TmlRKcxmYImQF3jpNikpxhrQN/ue++Z\nWX7DsF2d57I83mR1fUS5Du4wcBhfyfgQPmjfJUau3Qj33Aj/ew3OGMD/cTIc/yIongnswTPCngAs\nQTMsOLx7yKHBCmushpXvqcTDCLCTvVnkTZTGi1HwM838sStQIbA6mtH+byG6xP6zXvcxTUUG+NjH\nPsZ1110X4i1/9Ed/xIte9KIdKxeACy+8kAsvvDD67M1vfnN0r4997GNbC/pR3wAAIABJREFUXscK\nCfm7j7X74LxgzTb2MhsW0/pMIoBtUC4V5KmgTIVQYRa8jbl4Qdb3tPS54ikMyhKy15a/U0vZ9jHu\nS8zKsvEW/VxqgqWehlCXY4vZj28cnI9LtWhcSN9VDB3K57FijGMiAgPKvqLxfjZxaRd531axKsxk\nj1NFmHpbqgTspl5xsqn1tqRHVpFptWkdC/veBPLU+01NvzVwbp9LIa98zMV7LkXokfhSaUC/RDfx\nEjhLnmgQAKJJUG5VV+HCw2IimgcssBn65L2TTcMC86Fz2cdRPITdHGB3c4il0SaVKBLJtD+ArxF2\nL7Q/gJ98Bb52D9wygVcM4Ulnw+oL8LXBuvwVjof6eHBDaArHRrEUtiWWuSDwlt/vfhgpEYmdCEyZ\n1gpLWWHydjS7qx/Q179dkCVHYwA/bTveLMzWFPtFKLsfC51YGPiEQ3XrhfefCnf5zgZaVWj4CTGl\nny1gPRL1lqSYYBpwb4Io9PBcDI2k0y0tjChNFaAGmvueQWpX2UC8pcQ24dnt82if+tUFRNlaOCj2\nNuJ72X7Yc+yztwwi4WyfuUzGMVaAaWykoW9XSpwjZXqpl1gk51X4vI/U0LBjEcNRsXKUd6xKU68r\n8R/L0hIPIR0zAEkmtB6GeAjC5koNGYm5yOwVI0lKxshfMrYaTdAyLEWnDqWk/DB4IuMOZvPP55WH\nh48GTJE9ZhbYZNzBTQtsdhsDr7PY+rhKXZS0zjFhwO61DRZ/WntFcggPf8ke99+H9W/BfdfAF4Dj\nHLx6Fxz/Mqiej2eCHYenGT8O2uNg85iKpoK6LVkvllljlXWWGTAOpoPNwPHFKSdh/U6oqKKRUaWT\n81ziWSBUZFUyU5SKDITPrZfjzzm62o6Uy+tf/3pe+MIXBljssssu4/d+7/eOVN+21SQzPBUAujjF\nKpTc+DYRfiJ8BZIQRdN2SkDYT8LgsSXl43yLVMjaWIm/nwqfFs298NeIWVPq1dSR8NOAcD/oHHsM\nKtCtV6QKwMZkNJ4kVnYqbG2eSxp8tHkuU2ypkbb3HKmnZMvkWO8mhc80zhAHwnU0+zEX68Xlfrdj\nGIuJ2COxMQfLBbKWv95XFGRpzovhJhFkaoTURrno88s9pb8CL1kPNlbeGob289b7NwK5eIBQqcg2\nPyUNVcuszUFiwy6gL/Dh0MBd4tEsMmLcRTaWuljLMhss1xssH57QlBPKYUOx0DA8MPEssAfw5fEf\nwCdF3gH33gA33w37gFcsw9OeAbvPBZ6Ebu61AuyCejeMdhccWlimLfwI+m2JfeB+saMci6IYB9Wp\n0SQ/Rpo4KTNYV1N/poi/awP1li2mEsbLIGsSHs1tR8rl3e9+N7/yK78SaMGXXnopZ5999hHp2HZb\nSVxnSSxF3WnPYvkpZBMrjVSY5H63ysmF6aSMrcYIEYVi+uy1lFBgf5/14/MbqiDwY2EXwyzptVP4\nJrWuU2ZWrAhi4ejHvW+/6XNZenD/mpbpVvSOVYFdmc/0OO2zf+9t9HmqpO07lHeeekmq7FIFKGM8\nQSgg6i32x0kMDMHXLSPMBtq9Z6QZ7A26cZRCcOKxqHKxysCPddE7b2CUg2z+MMUzxdRr1riYZm2M\njQKZhLFZCAmQkxCY91a2f08LbAahu8goGGPeW6lYbDdZbtdZLtZYGa+zsj6iOtjiChgMRywvjqke\nbH0VY/m5Aw5/B267Cb4xgsUhvPFxsPulMDgTOAU4hrBrJENolmC0XHF4aalLivRv3m7uNWIT1/lW\nlhht81dEkVgIzOa0WMXQB2AVxJXMMpUOwhSTzxWilHOPtrYt5TKLtnb55Zdz+eWX8yd/8ic/107t\npKVwhbXM7eciTERE2AUmwtYKZo0PFN1ij4WSCEn/uwq8JlF0VijLBJIFXoWpmDKlFEpJYRjx0vpW\ndgyX2dhP3BefrCfW7KzYTF8hxcSHVFmJ4Iy9IvVSYsXZ9ywEYqqIt9u1ysIhJXwUgowVvcZdrGgQ\n4Z16I/Z5hWEXQ2taC833s69UNSTrSakgew0WveurQmwiRVCjrCy5Zo1sXjcJ89FmW4Av/9L3wjQD\nXoSarhQtnGivKWUYbRkXOadiGkSz1PySOlziochcUs+lDZ8vTTZZHo3YtXyY5dGY4YHWw14tFCUU\nZesz7O/E/3sL3HYLfOseuKOFlx8DZz0VyhcBv4SPrXR7r3ASNMdDU8JooWRjOOyK8i+FGWEZYRMG\nkefSry9QhXFN81RkdfV5j3GSZByH0ZlomwXga+IcmKOpbUu5rKys9BIf19bW+PjHP86DDz74iCoX\nv2CFcRULXSuIRaD4gJ7rFkG8S2EK4wjfvw+RCO00FoAlPjYTB3L71rP023ok1vtIFYK9RmxRqwIR\nXD2FhGT62yC2/0/6MaXspoH1oKxis8K+xANkdqwU+rOMO8I143DohFgpxnvIK0NLx1qPs8mbaW5H\nnyBqr6HvLIXCpmEMUrLp/9/emwdbVpb3v5817fmc093QjA3SdNPN0EwiYOIth3iR0hI0aJSYEqfE\nqTQxZYzJH14rt1S0NIOUqVxTpaJo1GiZ0ihS6E/4Jfcn4FWU+AOHFrqhm7m7z7THNb33j+d91vuu\n3c0v+As09HE/Vav2OWuvvdZ61/B83+f7THou4n8xGA8s/TFMj1efJXd9/fDiQ+W/uBIsaqmEmNq1\n0Ax3pcWE1sps9JhSYj6tBUqJ+c9hZiPsQjsuv1ikZtUreAl4jKuIL78DZERMaC0U9SV2GWKA0JR0\n8wFhXNJICxorhrlGn2RQii9F2w+nSIjxL8H8FPp3wP/YDQ+MYb4J79gIrfOBHQgFthWxWCTUk/H6\niPG6iDKUKzBGyrlMaFVPpBaUSa3zXlmKg30narlgp18uV8WBgb9OxC+K4wpHHVzqRZ+JsGapuJDl\n31jL5c/+7M+qv1dWVrjmmmv4zGc+w5VXXsm73/3uJ+3kHo9I5FNYzXyj6sXUmbSbOcv2Bzuc/axr\nX8HCdJ0rP7y1vo3bzlFt/rxGraPpB1DPScvJO2XsgMf/dNv7FoRPBdUTHzVYoA5yrmSOG/O0YV/P\nQPe3i6C2f98ZqtTjwZaNrzSL2jXC2990XoWfRDitlPX11d/7FoL/v1qJvjvW5a1ouf86waGRWf7k\nQcsJ1QMTcjRfpO53i/BB052/y153YBjRIKPE0WUlYUVV6X6SKcvCtzzqdXsdbVZ4VppaLPrM+ln0\nul+/jEtEwZhWpZ4bZLZHfWDtwYIOI3nmTEm7HElBztzQWc1JWgOCIYRLhm6YEexDsuv3AwMkGuwh\nmHwf7toJP1iEDnDxMXDWqcA5iG9lkyzFMyBoQyjzRibtJv1QgKQgtn3uJZNGxzum5dFfSTUdK4gr\nf4tv5wI4YlLubla729N5LT45HlBMPaW6D6XvNaDCJ8PXqjxun8v+/fv527/9W77whS9w1VVXcfvt\ntz9m1vzhFH9GqbdZelO4bHZ10vtUGNQd+sJf1wv/6SynPoOu52JMc/uHppIcoIF7yZ1Dvk4ZuX37\nIOPCcUUJO578UBSVA5q641lzFLTHplO2Pvur/oe6taPbFZXydwrZlWehUtw6Dj8g4lChvHotfILi\nYGoxr11zdy0OttTc/uvhzX673kPH/Ez7sepBE/71ctvrp0+L+f6sOlDLPuqWUYELPVaAKC3g+FFk\n0z6Rwk6qDna6Z2i0kpZ90edTZ+J1WsyVvVeg0QlBixFdBrQYVZaL9LQXiqlVjgkCQ1SW9PopRAVk\nEC1C1CwlX2UfhClSE+w+xK/yCEx2wtJt8J0RTAo4swnnb4fe6YilcjywETgWzHGwenSboFHSSqXF\n8biRMKJTTXlSa19p+ZaAkmmfiV4DeUL8gjcOXOr0lgtUV6Bxdir40zalIdXnps9CQUxo75muc55E\npyXWmjxuy+Vf/uVfePOb38x//Md/MDc392Sf1+MWBRF/hqjzAXGtmuoF1QbBjrKoO7L90FpVegf7\nE+pAoedQz/Wo70+PoaJEk+YfTAPDwfMi52eQ8/YTR+u1xXwH9fQY/P/9a+DAsk4NHspakONE1f7r\nloRrvTutgH2LpH6vxAum3zVtUUNHF9ZfPV/hHzxRmParOBBy2Qn+Pp2F1GTCiDZiIUhFX2c1OKvR\nP77/mXjbqPLwgd5X+j4Q1MHTWdoxIRoeHGDIib0yKvIcFMRIsuK4AgW5fi6vS5RizHQosl5rV7XY\nRX0puMdETJjQZmiz6GWJyWWfBjrDCXFcEoUl8aAkKo3QXYsIfWWtkyoC7BfATth7J/zPByUK7LdD\nOPMUOP4cYDOSCLkRCTHWZV3ASjJP2YBuY0BIwcAWjsGOK60sl6a9t4YxrYPApe6010WmNXqtQzQf\nxX9i3RRI/Ux+oLmch07N7J01MUUZEYSlbYFR1p5U7Ju3Fi2YxwUuf/M3f0Oj0eADH/gAH/jAB2rf\nBUHAysrKk3Jyj0eUbqorw7pS8Sks59Cvz4ILnHPUKRRXXl6VhT8TnvbPiI/GlRqZVnb+A6Rg5St9\nf7/T1JI+3qqApJRHHYT8BlluRq2KwiXiqfKT49WBph51dCgj311vv66WXm8dl1JIfm7K9PVQOqnE\nVJZYg7QGSn4GgbtGLnJu2rqp+03EotAIJr2+09urNTftC3JzWnePHJXlmmBN57lMP5/OCnJUrSry\nBmk1ZQEseDQpiao5t94bn74KEWu7aXui+PW7HNCr5VJ/zl1QgVotaVWaRSsvqxJs06Bn1XizHNPO\nx4RxSRFGhGVJY7Ukbo5JGinBkhFfyggJKS6RJl73ybriZ3DgDvj/9sLeHNYl8NY5WHgWNLYhoKJg\nsgDMy1KsCxitD1lNugiTIM+zRoHpWNVyyWhU72oxdbf0ujmHvbvTJa7Q56GmVXrt9DnPp54YoHpy\nKm9lGZJnMVEjVxdLbbqkltFvLLiU5cEvzdNFVNn5vbp9ZacvUYCpHg71OPhKa5recol2ARot5vtt\nfGd33eo4dEjrdIZ+hEY61Svo+ufhz3z1ez/3IPHyJRJvRn6oxTXZkkikwCoz3wrwqZz6eOq+GAeM\nOreT7QyHrl6gr7dPAtRJB1MBmvL9/kTBB3Uda+zdX11f94W48F0XmVe39NzvtGik0lh+gKp7nlwt\nLUfhNaaiuab9aQqg/v3z1Z0PbmrVJNbnop4CoAJe/QysklSQqgfUunbDogTFDspwkzG1XNw+JxWp\npFaY3vWu5rgXYzqrOc04p4gDjAmIlkuSCJpRKeXvJ4g/5RH7uRfKn0P/Z/DDR+HOkeQ7PvcY2LId\nkguRzPoNCJjMeUsX6EHWixi0OvTp2Wshz/3IZtCoaEJkRoL6vzQcQRt86XvoCFh/quHAx1/8p1AT\nKlUORYPVfm8EXJI4woQHb+fu02+oQ//pLE6p+aHI9Wgx5/Nwfhefd9YZjsbzO6rKRUAdCrSmy8zI\nb1RJ1RWZZui7fvI+BVIcdO7OUV5Xxjrm2OYR+4lvDvzM1DkV+NFEhYVk2dehwGia0srsyBz15753\n7k7zGIreUY0H9w7xaa2QwkYfOYtExiXnNH2tD0VfHkzJTdfzclF2On6nwB2g+Ey8e4YOTWn5oKMK\nQ5WUT4nJ5AYv210c5UpVBbjWvwocsXdujcqxLkmMBc5f0qoIoXEFqArl/jXxfS4NUhu4K4tPk0Wl\nnL8JA+ZZYX48oLM6IVyGMIEkMpAbsUzkcRZfygpitewF7oNHdsLPdsLtRlwol/QsqOxAQou3AgnQ\nRMKLu4hXvyP/j+YiBq0mfbr06RJAZaGpf0VF70xqLRehuBKcDRyjcY46PfPDOHTyqdU43GQ0OujN\n0Pvsr9P/dXJREpKXMVkW02w5ICmslbQWrRVfjnhwUaXmaA6n0NwsUSKmStQL42g03+ntAMpx+OAc\n/74F4Nez8kEkJqpoC1+h+jN6Uc4ubNa3HDTfwgcbR63k1ZjdcijLo+6Y9n02vsLVsfn+h2lQ1LE6\nYBB3vrO0XLCDjM1ZE75SS7xj+xaW0lZ+5BPUQ3gdpSNVDZwV4FsIRW3c9fGH3v3wfSWOGpsGIEcx\nOYrNTIGLbDepPS/TtKkPaNMO/cj7TCqqKrPgEFbpfyUhGXkt10TjwJqMaTGqrKimzUHRCZQ/41Za\nTM9vGpTajGhlE5qTjLCQ2lxBAzY0DtAdj4lXEF9KjIBJilgrKUKH3Q08BMW9MLkL/vs+2D2CKIDL\nOnDiNmifhaDMKXY5GZCeCwIyLWnqVbYDxp2ASdJgHAr9NaRDiKHDkILInnWzenYzEsY0kcKTBeo/\n8cM3wAGCH0ivNBmIL0uDfPIKYFycaF0cOexbe1UNBxNQZDHGeAnUZUgZhJjAUWu+NbRW5IgHFzXz\nfW7cBwY/vFQiRfwQYOeTCAg95eZ8Lkoh1Gkrp8gdfeWiqpyS9me+Ls9FwC2qndehLAalJ/yF2jbu\ne38mret1Pw60FGCEiZfr43pw1MuO+Hknmp+RVwoqxFfm0z6XOsU3bfn5UU2+0tZZuNyNg0vQOLCu\nWzwyDmdNuDIozqKqEyD+xEGTU7Paubm+73ml0MvqOXO5OgkuVFitZeyVUBBWP4hGI+k41TJpEFeT\nG40QKwkrS8oQ0GSCOvWbjO1kKaJJSscWOElsNr0+N6oUSzvh0QZXer4JGS1rtXQY0h6NaY4K6aNS\nAIEhbGZs2LBIezASK2XRDq9AfCu7EKf9IvA/YfdOuPNh+EkpRsnz1omznmchmfXrEMrrBDCboDgJ\nqYRcAhGUCWStgLQZM4kbjIOm7fYiABNgmNCsqK3c5u0okGgEmIb0+DamKnx90n1eIUS5APccO9LX\nD7pPakBwkKVSTbks6JQRZRpT5DFlHEJgwSUUgFnLcsSDi76Ih1JicHBZfVHsasmb6pEr7Auos0uX\n5W+qY6iSg3oZkWlHsFokibdOjw31Ss46W52ubOwref1MyMlxPhqnoOvlzn0rJap+7zKxSzse6Qbo\nFLXmyBzMROv4p6mnOj3kA3HIwVbE9O8Sb9++zyWzM0/fGhXqMsZ3quu80wHatDPfjU1n+44izLzz\nyKptIu+aqgPdXceg6qSoLL6j8DSkXZ4vUe7O5xJS0MD5ubRpltJier9dxFdZWRZqeTRxKYEg04yW\nrTTcslWH24zsmF1HGb2Sfoi47D+VKsXFkM5kRKNviIZUDbowECcFx4RLBFqiZR/Oab8M/AyyX8BD\n98JNq3CghGMieGMbNjwTmhpSfCZCeYUI/XUcpBtjlta16TVHxEUOQUDWiMiimDT0u8S0cCHGZQUu\nShLqc+9PWfQ+ZLjQFKGilH/wM9LkrZD/hQ4LcO2IXfJk5O3L0WL1XJaw2q8hgDKELIHSC+YpA8og\nrPahU8u1Jkc8uOiDVbda6j6Xg8HFffphwvUIMHXQijJQ8HGK2I+yms5CPzjSSmgMqclUV4guA1xn\nlNPWiq/wdax6TsmUIvXBzflipi0bmfeCi6ZTgJ6mj3yfi7MMfLJBfUO5d080sstPhvQd3456c+Ai\n42mQVpnUPnUVejN/PX6Jq5ag55VMjV2jsfSc6n4g9ztnPeVVKLJLLBSLQKsESwFJV4tLQcGnG53P\nRcfqCkg630bmXRu5Ti3GlR9Bt/MdyeqAV59Rq+qpOPIoMud/U0WoV7skqu5DmzGdfERrNKG1aqQi\n8QBpzpUBJQQRRAMjYcS7kU6QK2AegskuuONuuGsgeZHbA3jBSXDSZoTy2gochfhPtiO010Q+i6Nh\nON9gkQ2U7SWapEh2vF91LbGJkc0qOTKkZGwz8DU5Uq+39mlREAmZ7skSV5MgnyrzQ170zdV3AlwG\nvalpiMB76+SJMhTVW1Zld5URZCFlHlGUEUUUURQRZRBQRn5uzNrzvxzx4OLPzONqZuosDJ2BioPO\nL3lfrwGmyZeqbKetH6WP/JBhXxGrUk8Ia3SWb5C71mOyh2nazHfoq9JxFkh9Ft4grRSibx2Joqu/\nUuBHbdUjmqb9BHVayQGlJlGqY9pX/mp1GEs5+Era7aewL7tPXzk/hERIiQ9B80381rkhhtQqEkfV\nSSCHno9GV0lHxKQ6X7WMfNBxkwRpwhVS1lrxumvgeqgYNGRaVV9azZD9YymISfSRnJceT5/JRhVI\nO8ZFdBUVoAS40ita06okqCgsfQ5bjG00l3aDHxObnMDYCM8gIA9UiboCionJaOYTWoOCZMWII37V\nW0ZUAEMA7AF+Kcv998Jdi3BHLmW+dnTgFRuhtx3CU5GQ4nmEBusCMeQnCdUZDoAIJgsJg3abPj20\ncZijq/SpSSx5KFdFo7kUJPTp1Ofb5aA457n6MxwguK6QvqNe96U+Pz/QXn9fp9ZE9A134BDU3i+U\nPrS335jALg5QXKLE2pIjHlzUL6Iz4XotKlMp2sDaCn4SpVJSGs7sb1sHlxzt+udTT4fyk/gpUsmU\nYg1rsxNTKUMHDPXSKKqgFTD98FndvwtHrud4+KDrW2KalFdWV6SoZml1i6UeFeWaReXWxnB5M/Vi\nh+6aK53nU3RJtR9XXQAcvamKOPKOoSCe0QCo9qEO2gxHTU3TWQp6+r+rbJBVQNwgQ+lGBZcWE+8e\nuPE5Wiy1s+2wur4RRe06+vcgtE9GgKk12FVfivOBjKuuiOpfUWoGoGX9K5HV+m1GdOkLvVWOaGdj\n4qwgLAQTykAKO5ZRSBHZII6iJJ4YkqGRro/anGvRfq7aT+0GuQird8Hue+CWgaw+PoSXtWHTKdDW\nqK8OLqy4Zf9uQBkELC90aQYZ3caEMoRRs0k/6NGna5uTOYe4fxdTa7mosz7EVNdHLRydVOXe2wYC\nVVo6X4Ii4srim+YHJHJM7o9Gix0qjnLaynC+mXo9sWopAwEXL5ujLANK40KY/bDktSRHPLi4xDSn\nCNUBK987RReinLgoJUdJaVCAzvSdX8MdI6Q+43XzGt/n4vj8ulIN/acLIeySKXDxldKhfBUKUpqT\nAOocTvHpnrr1c3CEmWZvKx1lcBV2p6kll0fjckXq9FtWfQIVjegvzvfkIuSmqTxN7lQKKrZKXi0X\nvx+7qhAFyRFtAgvWjmpyFJ7/HLgShlk13oYFkmkqzFnE7jomFS3manG5QAPfcpHqW36whdx3U/lJ\nfHBRyqvJmIZ1XGu/ebWBAwwdRnTNkLAsIDRMgiY9BvTKPr3RmFZfyq/UpsIh1mNun8EC8akoqCwh\n4cP77WJrgJX3wv774KY+7ClFWewAzn4GbNwKwVbEMjkJsVYKYD1itUTA0UAsDuzVeI40GhHEOUUY\nMoikNL54ioYVQBRW0fueL21jJryAAxEtm6/vYY6WZ4lQv5c+qc5yUWd7PbxYmQ3N//KBxBVCctM8\nvcC+RaTApJMeQwCFgEuZhZRlCCHi3I+c038tUmKwBsBFE878UFefNlKFH9hbCeL4qztbBXRUIUuY\nZh2g/PBhcL1g/Nmv5h+4hL2i4sh9w9fPsVGGWTs8+IrRn7n7VJDSUDL+9CAw0vPRirliwbnqtxpN\nozP6EC15UTINbg1LMwF2Ri/9O5Kqiq4DIx2bumL9c1IndUFcgarmbujM3xBYi6HEVQXOq1n8OhZp\n2/IjOo4JLR7lGDtG58NQYqVlq/b6EV6+JSHA5YpG6rkntKvft2x5FaBWfr5l+4OAJoGKb0oDI5xF\nkqKZRRIR5qwWyesRqkULQ6rV1GFAxwxsVJFcj042pJ1NiDND2B6RJauMgxbd4YRGvxCzIkUUvaEO\nMuCAZYiAi3Z8fATYC9l9sLobfrwId6eCPSeHcPl6OPU4iE4BTgGegfRSKajqfzFGgMU67icbAoIY\nyAL6UZc0jiuQHdKpyLwOQ8E/z3LJ7bRNn1q9q0KPNiyV5nwmxl7vwgK1i5ZziQYaEHIoyqusvsd+\nOvp4uhqdvr9QD2uW57+eC2PyQK61R4uVhY0iqwHZb3gnyqej+A5hP7JHHHdKabmaPn4mrD+rLC0t\nlthpn86068dQ6suVbqn7VURFi8J2tJhvHYFywaZS3DqLdjSdUk6OvlE6pyCulK7O1utKte7TaFil\n6EJnswpMHbi4ki66zXT+8rQ1Ek+tV8sDsECrs3sHJDrr1HH510azzqezzZ3lkjHPKm1GllbLqu07\nDCs/iVpyWQ10qY7jg4+CmgKVUl2q9N3kQLZX61bPsWFDqnyfiyow2WdUs47Vbdyy5yznPkJ9DQkp\nHTMQuypIpJbXeCzg0gpokNKdTGj1pcxKq8iY7wzImwnNfkZ4AKGxNO9E3Tylt6QIAC1R1fvKd8Hg\nF/DTA/DLsaSubAKe2YPTj4fO2RAegwBHBwGV4xBn/RChwY5G6J8umLZQccNuCxNBUBj6UY8mEvFm\n0CZe6qhvVtdGp2x+6K/SY85yiar/1efiO+kPBhethBzVwKXElWeVyxR6gOLX2aiT4KIfRPxa6REh\npbGRX4G1atIADkAxDimLkDWIIY8pawRcXP6BKoQ6R65VXsVxr+1M/d4eClD6OwUlLMWhxxJ6yy9K\nWFSvQIOsRp/5Pom61MtvCBCGuNYBLvJJFZNaB0oRtRiTkXgA5rK+p3t76HVQf4G+eP6Y6zE6mXfu\nqUdZyf4nNCvl6h/HgUtKq3KOu+0iJCygXiJegThFE/t0Wz2Grp9nhQ6jivoKKVnPAZ7BvXQYVL4S\nne0KRTrBWMDXKLAWE2J7LgoWES5xMiGjw6iyhrQkCogDfUyrdm46t5UMfQdaCS5azKdROwzoMKBp\nUtpmBKG1+Iqczihl0hyThBlzkz6NgaGMAoKwoIxCmqNSfCMZJGNDN58QbNhPYykXsFhBLAgFmJy6\ntbIMPAzlfTC+C35yAH46lp9uBM5owavXQ+sZED0Dqqivhn10IwRMNiLgsgzFAhQbIBnDpBOS2Wz0\nYdTGBAFhVDKgQ0FIhxEGGNGpikqmNKvn3o/YKgire6lgo743CQOXKZO8Ua7asdBbQlDm1Tb13il+\nhJhGelUAgQsRls864PgUt1o1AmCFOOsJXLpThlCOngooC4kiK6dcOvDoAAAgAElEQVT2tdbkiAcX\nnxZLqkdQZv0auRRVL7fym0GNFpsGF6XFFBSadl/qf/BzLVx+hvxWKZjpWW+Ia9yk5JGLg5lUZraz\nPOoOdaW0XPixm/GrotPFbywl4yk9GmpcmfEaWtthyByrFXipz0EbwbqIK99ycbSTOuc1O79pA0in\nrR0FDFfe3Slzd93HlbXkA02LEXOsilK2896cmC5DNnCgAp2odn5F5bNwXRRteRNy27EQe5zIC3gd\no05dBWwFkg4DxhZcOwzQJD4FfbFdxXIRB3JRWaYZCUEpJePnkj7NIqMzSgm6cjeSSU5z1dANRpRx\nSNuGB0ehIckKoBBgWUTAogHJqGRhmEqI8IOIRTJErIix/RyAOQDl/bByD9y5CLdnEnW8MYCzWvDs\ndRA/A/GdHIWzRo5DwMXY/ZXAeig2QrYhoBEZxt0G415MOxkzTpqksSDRgG71TAzoVBYLUIUX+71W\n1PdU7wIkd1KpMd/nojQYYOks9bnIm24sDasg4VsuauloPorLZXFRfRrCLf4Y5ScStLq1ih8dVpYh\nhYkkQi+IKNMQlqAcR+JzMUAeQul8NX7ezFqSIx5clLJSJe7P+sE5vPUB0RBkcNFiGqXSsHN35beT\nyofilKv4MKKKdvKtE90uqRSpUjVqLdSTKR2/72ixegFC9Zu4JlL+bLokrGpBxZ7SngYcFy2miX+O\nolPfwTwrU79zhcrlWgaen2DiqQRnMYFEbvldDXX/6nPRbHNXrmRSgWRkwcBZYpPKr9Egq6gktXpC\nCroMWM+irY01pkFGyoQWDSKcz8W/FxrltZdNpDRoM6r8PS0b6iuz5LJap2VeWpbKksiuCQUugi+x\n9FpISdNMyIOEqCxoFClhUZLFCWEBndWSufkhcZbTWDGEZUpgIBoDy9AOJ5gIcayvIg75IaKY1OE+\nwdXjaiGlVx6031snfbEPxg/Cfftg5wB+YWRXJ0Tw3DnYfiy0n4GEDB9Fva5XD1gH5hgoN0M4QSLL\nMmA9pOsSVjstFoohadKgH7Yp2y6xMYCqqGRIyYgOAVQ5PBrFpcDhLFvnzcxxtrTLpFdrxL0legy1\nQuTTp8UOBhelwnQbF0zg/ColwUH7MMYGAwSu8nQtZrSMKIsQE1vwSYB5MFFgS8AEYJwVpNFra1GO\neHDxKZvERk35VJT+rdEoWJABV7TQmeMJmQWUxCpY+Tu31Epu6RRXBdf3Uej22lMjoV0pwulIdlWk\nmXVOam6Gvy+NanIUkTieC6IqczvxXj9NqKv7NLKKVmoxYURK5M2SElLaDJk7CFz8ZQJ2Nu77G/yq\nukod+iG0kQUNlzdSVH4etYz0HBtMKKz1oECqf4dIzkePVTpegcWSkC4D5lmxiYSTyn+ieS66nQv/\nlTlzhwEbOECXPtK6N6yis1rWusNeN913aEq6ZkAayD3rmgFZKKGwcZnTSDPyOCIsDY1JThGlRDkk\nE0NQQt5IMQUEi9BpD4nSApYh1nwSS1slpRH66VH5H4A2Qm89apcxVLcxB+4BdkO2B+7fB78cwK5c\nsKYHbI7h97tw9GahvNiEUFvqR2kgirBhlxYwB8XREYsbOnTSCd1mChNIFwKGrQb9oEejnTIKpWkX\n1BMb1UoJKRnSJqSsAEd9LkrWalkV39GuvWj8+MLS0mKFvUfOmtFiPHEFCOCKJemE0hVwOlQRSvHP\nTEtpwagwYn1EYd26mQafovSskAawAcoKXJCsfbP2LJVpOeLBpWmVkkZIKYeujkO/P0VkOU513NXz\nE1xCoihI1yyqaZWrWkaaJOfnQTgHrysjohRMw0ZA+VWRsylarMvAO99p57mjqQoiNGS1JKrRTI5u\nyi0wTdA8HrWIlCZy1y+VTG1GqP/Ip/N8yyX1XLDOaplUihvEcnGOaiqg0QgoAD+BsGXpMwcWw+qV\nV4tIwaXLsLJQNP+jZfM8XKdEjSLTXJExgPQjsSHAbcYssMJ2fsGxPGJ7vwcCzmZEtxyIIxpoFhO6\nkxHtxkiaY41S0s6QpMjpTiYU4QQCCAtojKFISiggGgGJEUCYABnEEfL/EixsXCYYGwGKjl0/RPj5\nMQIuD8i2lIiSGiHe9ofsets3pbwX/n0Z7kol6CtCKq7sSOCidZCcijThUkDRcOGu3a9qgdAuMWIV\n9aBYCFkJ5ylbq4RRRpwahp0m/UQ8R83G2LYQ6xBgauAy8SwX9VOppaEB4S4URqyFDK8XSkU8uzAd\ncD1T9O1Ql7paO6C9bDSIJ0ATKrU8rS8+PeVHhOlxtCGhQSK9SpxjfrqgZVmEFHkMBorA5hZ1xH9j\nikCsz0L6vEjvJ1fif63JEQ8uzvcwRvMV6r4Tp/gK69jTGxni6n+5cg6uxIhSPeqsVoUtVVfz2ixf\nFTsoh59bekYoJAEkEaXm2oxQp3KXQfVbzaXwla8m3eksSWd6OuvXBDwtna6WTot6naqUxhS4yCx+\njlUkkiuv6Dq1SpqWsspIaDFhbPevSl4XuaZJlUWuFJlaDBpQ0aVZUWX6qZn/DrhcAyvxV8RIyt3A\nFmp0YDTPSrU+MRl5EDOmSURBlyGlAgdj2uWYjpHfbIweYb5YpmsGsq9oQCcd05mkmK4tS5/mtFYN\nnYUJlJCsGjqNEVFakqxCIlHCQheNIUpwWdmxW49W/s2AJZhfNxanx/2Iks8QCkxzTUokK34/Ak4F\nsA8Ge2H/A3DvCtxdCjblSCTwtgRe3IETNkLjeARhjkEA5Wi7LOB6pST4dTZFJPRNSrR0YNKLWA17\nUiE5MjSbE4ZB23Z46dFkUnmqJM/DvUNKgUk9sBYNMo8Wk7ssmfdqcaiPpF7N2e+sU3fcxx4QaGMw\n+V8iPZ2vBG+Yfvix79h/LAVfZbKZiCKPiMPc25+GObu4VGOCahxEiNXpYgrkhpV+BYFZnsvTUpTC\n0GgopULEcnHZ3PJQRhWvq0lW0z6XJrY3uFV6egz1dfgUmWaa+3kbWCewnofml/hFAxXI9NyblvIB\nKktB/TnTkUzqY8pIKopJgafNkJRGVULdp6eco9qfGYaVD6FHnwHdan+q5JUWi+zROwwZ06oATymj\nlrUU5VgjW0CxUQGPWi6SYT2urq+ztjKrTPpokY0mY9pmSIihCKRpVZsRrXJMtxhQhCG9sM9cIBnq\n7WxEo8ygAVkQExUl3XSICQJ68YBeOKA3nNDNM+aiMcf0HmXdaEh3klMGAZ25Ea00JVkxzBcClkEK\nwSq0O0MoIFiCTpgRTBDKSsElR0AksX/37d9a5FF9wClinYQIuNyDWA9jxBrZZ7/rA3fDo4/CQyuw\ndwL3FrBiZDdHAae14ZINcOIJiDWioDGHgMg6b1lvP+fBdKFsIX4dA2EpOZaBPqIBlDGk7Yhhu8kw\nEKskCVKKIKrqKI9oe3arZs27THctMCmWS9NSv2q5uCgwJXYNBb7l4CLH4sofogCmUWF1K8NRXn4R\nSmfFOOBy74CbbLpQ4yknvd3foRp6OXrNlrktxSqpRFsJlCEUoaKb9d0Eh9jj2pEjHlwaTCgrqkgU\nsVI36jwW5S5lDjWDF5zl4uLrZTYEVLNq/VuOJZRVUVkMfikQZ7k4Cspx+H7IoZj/2hgrosWEHn2A\n2ozezerzCjCMfYh1puV/12ZESgMNBVarzflBNBvcOhahAoIuAzILeGr9KMDEVtnnuJLvsb3Obe88\nBcwjS5IMKuusY4Z0zJDAGMKgIA0TS08NbfRXSsOkUhIjDCr10DVDOsOUICgok5D5eIW5YJVuMaLT\nLyjCgm5zxFxrlbmyT3eSEqclAUPSJCHMQ9p9ic7rtSfMtVdJBgXRBJpJxsbuPtqjMeEqBAa67SHJ\nOCdYhCi1N8uCSG/doLIewgyX4a7goqG+aq2sILPVFAcuSn3tQ/irZaReF8B+GD0A9z4Ku3PYW8Ij\npey6CxwbwAubcOwCtDdAshGhuU5CLJQJ2l5VZso9u2h3x3lgASbzAZNWQprYKDdTEpUFcZ4TFoag\nFPTKk4hJ3GIQiE2oOUUlYdUBsm63NmuKv4qOs5aGa43WxI/48nNa5L1Iaoq/7nORzHvn7axn3xvr\nNwVnnSi41BMW1cHvLCD/O3W0+/6UEslhyYuI2AsjLku7j9CeRxliCk0JjSiDSMDFRAIwogBcyDJU\nx1xrcsSDi0TshBWgqKN87IGLi1QK0VwLSYSq133ShxmoLAH9W5276nj2I5rc7HyMRpmpk9E/voqv\nhCUKS3wBGv1VTy9zilytA4l4cf1YlHrqMaj8T/7vE/IKMDQQWqVJysSGIg/poN0JuwwEQMuURpaS\nJTEmhNRSGULlDcWayEa08glBaciTiE48pBcOkJyOEe1yQmuUEpWGJC4pOwMLLiPaZkw7HZGkpSQL\ndgPCQBReNx/SHBRExkAzY35+hTmzSmcyJFyFMISumbC+cYDeYEyyUhCOoZsWFAsjyiKo+o+0zJh1\nzSXilQKGELczNhxzgObqWKinwNA9ekA0st0VB2DDm2AR1p+4JBbJA/Y7BRdwfpVV5I2aIFaIRnkt\n29+MoFyG7CFIU3hgBX65KE0bVxD8aQMbI9gWw+9GMHcUNDYhPpMNOL9IDwGVYxG6a8keN8RFkXWo\nWgbn8wGj+YhB0mUSNNH8kDAoiaKCJMorKx6ECtKKxBNalQ/MEHj2Zgu/6XNOXgOXlEb1vI5pWq+L\nRGOKdyxBQ4cVDHIPLKThdD3s2EV7uTKk+k77pVfU0e+Ap1600lFgzorPidHAFPeuBpUn1piAIo8x\nSVp9XxahPLehOusDTBFhlGZUy8VnviwtttbliAcXdexqVdiQgqYZ0w6E222XI7rpkCCEIgzJo5gi\nUMulJMkzosK2f20EMtNAfRGS8KWWR8u+EhnNKsRWHc3SU2NERqOyNgwB3XRApxBnsLH+PAIpJNiJ\nhhAa6zdYJcR4bWfHlngQ66FtRnTzAWUUEgU5QeBaCjdMRqsY0w37FKEkYroeH1KCvV2MaJUTorjA\nBJptE9IsBCznoxUOsAHNeG+bEY0spZEWxKkhTjJojigbEan1Z3QY0jN9OqOM5thACWVckHVGjDsr\nBBi6xYDeZEizbwhyCBs5hiG91oCWGdGbDGmtlgQ5mLAgLgesby/RLiZ0l3OCVaCEuF0w11ulNxnR\nWrb5HiE0wgnr5lZorBSSoW57kbTDMSZHnBJAOx5x9Pw+4qUclqExl3Jc+SCdVUlJDwz0upkAwf1g\nU2CErlqE3rqJaP9diMJWGkuz3kcIQhT281EoRrC4DI8swf4B3F+KwaIY1AOODuCcNmzqwrFdaM5B\ncBriKykQyuwoJN+kjUuMbNttjrHf6znJzEV+15b1k7mAUbtBPxE/yYRmNcFyFbQ1ZF6c15rAqMmO\nIYW1TkrGnl2tRSWlNItkzfuWizzuBk2n1cmbthhW5a1gUPkqcPRx7gGQWkcKFppY6bfcm7ZU/MlU\n4X0HWiEnsN+JFRNZdmI6iuxQPhlThRXLb00ZQ+H1c1EfVhnIIoX8hD7DJl7OfC5PT+kypCgjWvmY\ndjwkLkq64wlZZ4SJoGkmtCYlYWkow4IsySkjuZlhYUgyQ1hCERlMNMJEAZSG7mREtznERNBhSERe\nKew+vYqOatsqtb4ib2YT4rKgbIS0spzWxDg+GwsyUUGvMyRq5LSyMb24TxCammO+bamjBhmtYkJ7\nUGDCnLhRErVECURlQZLlNMcFvdaYsimNjhSkegyIyehOUprjjLiVoxGRARBnBhMnzHVWK0usWwzp\njsYk41LooQyixBAUKSZcZRy1CIOSbjGQ7VbLSrGFMbSiCfOdZUoCeuMJrZVCQKKAKIZWUdKNpUZW\ne6kUbZtDEEKSwjHxPpIsI1hEvishmhSsW1gm6UO4HwGXAFrxhHAuJd5XigViy5skpY3UeljG2mv3\nSY4aET8q8bmN1YJjjl8hsL3eKRAlsAzsRpSzOuY1gmsM3IFYBn0EuAaQLsPiCuwawv4c9pXwaCmn\nEtjN1wGnJfDsJsy1YW4bNHr2GCchtJW2Dz7F/q+W0QJioTSoIs9IgGMkmTFdH9AIjUSoKbgk4leZ\nzAWMmm0GUYdV5qyfRCwXtdxd3lRWWQZKUanTPaKwFoyp1qfUQ4m1Rp3SSj7Fpem4DlwUNKIKFLSA\nqk8X+Sm4Ci4uWz6qLBffOV8vUDRdxTisFL/6Yf0QaJc3Uw83roCmCGsti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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's compare this spectrogram with the spectrogram of the linear sweep, and let's actually do the computation since its simpler in this case. In the linear sweep we vary the instantaneous frequency linearly from $\\omega_1$ to $\\omega_2$ over time $T$. We can write\n", "\n", "\\begin{equation}\n", " f'(t) = \\omega_1 + \\frac{\\omega_2 - \\omega_1}{T}t.\n", "\\end{equation}\n", "\n", "Integrating this equation, we obtain that\n", "\n", "\\begin{equation}\n", " f(t) = \\int_0^t f'(t)~dt = \\omega_1 t + \\frac{\\omega_2 - \\omega_1}{2T} t^2,\n", "\\end{equation}\n", "\n", "and the linear sine sweep signal is given as $x_{\\text{lin}}(t) = \\sin(f(t))$. Note that the first idea we have for generating a linear sweep could be to say $x(t) = \\sin(f(t) t)$, and vary $f(t)$ from $\\omega_1$ to $\\omega_2$. But this would give a wrong result, as we would miss the division by 2 in the denominator up there (due to the integration)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "f1 = 50. # Start frequency in [Hz]\n", "f2 = 10000. # End frequency in [Hz]\n", "T = 5. # Pulse duration in [s]\n", "fs = 44100. # Sampling frequency in [Hz]\n", "Ts = 1./fs # Sampling period in [s]\n", "n = arange(0, N) # Sample index\n", "\n", "om1 = 2*pi*f1\n", "om2 = 2*pi*f2\n", "\n", "x_lin = sin(om1*(n*Ts) + (om2-om1)/2/T * (n*Ts)**2)\n", "\n", "subplot(2, 1, 1)\n", "plot(n[0:int(fs)], x_lin[0:int(fs)])\n", "xlabel('$n$ [samples]')\n", "ylabel('$x_{lin}[n]$')\n", "\n", "subplot(2, 1, 2)\n", "plot(abs(fft.fftshift(fft.fft(x_lin))))\n", "xlabel('Frequency bin $k$')\n", "ylabel('$X_{lin}[k]$');\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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P6SZ4DAYDysvLUVlZaZlbhxPBae+pp7SuQD8OH9a6An3w91YweU43wQOg069l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\nQ0TUS/TKFg8REfVevXI4dVd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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "specgram(x_lin, NFFT=1024, noverlap=4);\n", "ylabel('Normalized frequency (1 is $f_s/2$)')\n", "xlabel('n [samples]')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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pOTJXCen2j70nFwEfy7W5Y+UwpVmey9///d+bENjm5iae9KQn4UlPehLuvPPO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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that in both spectrograms, sweeps end at the same frequency (as they should, of course). Try to generate the linear sweep the naive way described above (without dividing by two), and see what happens in the spectrogram.\n", "\n", "Now for the next things: It is not a bad idea to hear how these sweeps sound like, so let's play them." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Audio(x_exp,rate=fs) # Playback of the exponential sweep" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "Audio(x_lin,rate=fs) # Playback of the linear sweep" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fascinating, huh? This gives us a lot of insight into how human hearing works. The exponential sweep is actually perceived more linearly than the linear sweep. The linear sweep seems to linger for too long in the higher frequences. As an exercise, please read up a bit, and explain this!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Auralization\n", "============\n", "Measured or synthetic RIRs can be used to recreate the acoustics impression of the corresponding space. If we convolve an RIR of a cathedral with a *dry* sound sample (anechoic sample, recorded in an anechoic chamber), the resulting signal will sound as if it was recorded in the cathedral. This is used for example in virtual reality, to create realistically sounding virtual spaces. Check out fantastic research by our colleague [Dirk Schr\u00f6der](http://lcav.epfl.ch/people/Dirk_Schroeder). Another application example is music production.\n", "\n", "To provide a truly immersive experience, we should do more than just single channel (monaural) auralization. We should either reproduce the complete original sound field using appropriate algorithms and sound system, or provide *binaural* auralization. In binaural auralization we aim to recreate the impression of an acoustic space by presenting the sound through the headphones.\n", "\n", "For simplicity, in this Signal of the Day example we will consider only monaural auralization. As you will hear, even this simple convolution can evoke correct mental imagery about the space we're auralizing. Consider the following dry sound sample (a question \"Can one hear the shape of a room?\" recorded in an anechoic chamber).\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "mat = io.loadmat('Dry.mat')\n", "fs = mat.get('fs') # Sampling frequency\n", "y = array(mat.get('y')) # Anechoic sound\n", "\n", "Audio(y,rate=fs)\n" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sounds dry, huh? Now let's auralize! First, let's hear what happens when we convolve this dry sound with the impulse response of the classroom BC329." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy import signal # To get fftconvolve which seems much faster than numpy's convolve\n", "\n", "y_room = signal.fftconvolve(y[:,0], h1[:,0])\n", "\n", "Audio(y_room,rate=fs)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 19, "text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now let's do the auralization with the cathedral's RIR. What do you expect to hear?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y_cathedral = signal.fftconvolve(y[:,0], h2[:,0])\n", "\n", "Audio(y_cathedral,rate=fs)" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", " \n", " " ], "metadata": {}, "output_type": "pyout", "prompt_number": 20, "text": [ "" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Exercise: Auralization + Structure of RIRs\n", "------------------------------------------\n", "\n", "1) Recall what you read about the structure of RIRs. It might seem that early echoes are the most important part of the room impulse response. Indeed, for some tasks, mostly localization related, they are essential. But we now want to show that for the impression of the space, the reverberation tail is very important. To this end, try convolving the dry sound with only the early part of the cathedral impulse response, and then playing it (say with the first 100 ms).\n", "\n", "2) Next, try convolving the dry sound with only the tail of the RIR (from 100 ms until the end), and listen to it. What do you hear? It sounds very hollow. The reason for that is that the early part of the RIR also contains the direct sound path! Without it we are really listening only to reverberation, without the direct sound.\n", "\n", "3) Find a way to add the direct sound back in (but without the echoes!) and listen to the result.\n" ] } ], "metadata": {} } ] }