{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "# Introduction to DFT and Fourier phase space for music analysis\n", " \n", "Eamonn Bell, Columbia University \n", " \n", "---\n", "Follows exposition in [Jason Yust, \"Schubert's Harmonic Language and Fourier Phase Space.\" _Journal of Music Theory_. 59/1 (2015)](http://jmt.dukejournals.org/cgi/doi/10.1215/00222909-2863409)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Import some modules and functions that will be useful later." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "import itertools\n", "import music21\n", "\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "from matplotlib import pyplot as plt\n", "\n", "from numpy.fft import fft" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Fourier transform decomposes a time-varying signal into a mixture of sinusoidal components.\n", "\n", "To take advantage of the Fourier transform, we represent a pitch class (multi)set as a pitch-class vector, where the _n_-th entry in the vector correpsonds to the cardinality of the pc _n_ in the multiset." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "C_major_triad = [1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can treat the sequence of integers as a a \"peaky\" time-varying signal, and get its Fourier decomposition immediately thanks to numpy and friends." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "decomp = fft(C_major_triad)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 3.00000000e+00 +0.00000000e+00j,\n", " -3.66025404e-01 -3.66025404e-01j,\n", " 1.00000000e+00 -7.77156117e-16j,\n", " 2.00000000e+00 +1.00000000e+00j,\n", " -6.66133815e-16 -1.73205081e+00j,\n", " 1.36602540e+00 +1.36602540e+00j,\n", " 1.00000000e+00 +0.00000000e+00j,\n", " 1.36602540e+00 -1.36602540e+00j,\n", " 1.44328993e-15 +1.73205081e+00j,\n", " 2.00000000e+00 -1.00000000e+00j,\n", " 1.00000000e+00 -4.44089210e-16j, -3.66025404e-01 +3.66025404e-01j])" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "decomp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nice. Each of these components are represented as a complex number (thanks numpy). What's the deal here? I thought that Fourier decomposition had something to do with sines and cosines. Well, it does. These components conveniently summarize the magnitude and the phase of the contribution of each component. Each component here is represented in Cartesian coordinate form; a little trig - or the use of numpy builtins - gets us the polar form, where the radius is the magnitude of the contribution and the angle ($\\varphi$) is its phase (in radians)." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "magnitudes = np.absolute(decomp)\n", "phases = np.angle(decomp)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[(3.0, 0.0),\n", " (0.51763809020504126, -2.3561944901923453),\n", " (0.99999999999999856, -7.7715611723761066e-16),\n", " (2.2360679774997898, 0.46364760900080609),\n", " (1.7320508075688776, -1.570796326794897),\n", " (1.9318516525781366, 0.7853981633974475),\n", " (1.0, 0.0),\n", " (1.9318516525781373, -0.78539816339744872),\n", " (1.732050807568879, 1.5707963267948959),\n", " (2.2360679774997898, -0.46364760900080609),\n", " (1.0000000000000007, -4.4408920985006232e-16),\n", " (0.5176380902050437, 2.3561944901923439)]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list(zip(magnitudes, phases))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The magnitude of the zeroth fourier component is the same as the cardinality of the pitch-class (multi)set." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "assert np.absolute(decomp)[0] == sum(C_major_triad)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The magnitude and phase of the remaining components are related to each other (because real-values?). Can you see how?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.bar(range(len(phases)), phases)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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XAb85ylUIWg39KJdtWDe6Sz5fBxysqrdPe55JVNWVVXV6Vc2y9HP5VFWt2yPGqvo34P4k\nZ3YPXQDcO8WRJvV14NwkT+h+313AOv7H5c7yS7RcDvzlFGeZWJLtwO8BF1fVd0d5TZOh7/6h4keX\nbTgIfLCqDkx3qomcB1zG0tHv/u7rJdMeSv/r9cDNSe4Gngv84ZTnWbXubya3AvuAL7HUiHXzqdIk\ntwB/B5yZZCHJq4CrgRcl+Srwou7+unCM/bkGOAW4o2vBtUO34ydjJaltTR7RS5L+j6GXpMYZeklq\nnKGXpMYZeklqnKGXpMYZeklqnKGXpMb9D5rc3P5e2qYmAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.bar(range(len(magnitudes)), magnitudes)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "So we are really only interested in the phase and magnitude of components 1 through 6. We can reconstruct the other components from these, if need be, but this symmetry is always going to hold so we don't have to worry." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'm not really in the mood for figuring out the pitch class vector for every collection I dream up, so I wrote some functions to help. strchord_to_char() takes a human-readable string and, with the help of music21, converts it to the vector form." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "def c_to_char(c):\n", " char = []\n", " pcs = c.pitchClasses\n", " for i in range(12):\n", " if i in pcs:\n", " char.append(1)\n", " else:\n", " char.append(0)\n", " return char\n", "\n", "def strchord_to_char(strchord):\n", " c = music21.chord.Chord(strchord)\n", " return c_to_char(c)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "strchord_to_char('B- D- F A-')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I also wrote a function that returns all the distinct transpositions of a vector representation of a pcset." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def transpose_char_to_all(char):\n", " def rotate(l, n):\n", " return l[-n:] + l[:-n]\n", " \n", " transposed = []\n", " for i in range(12):\n", " transposed.append(rotate(char, i))\n", " \n", " transposed.sort()\n", " filtered = list(k for k,_ in itertools.groupby(transposed))\n", " return filtered" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There should be tweleve distinct transpositions of the major triad, but only four of the augmented triad." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "assert len(transpose_char_to_all(strchord_to_char('C E G'))) == 12\n", "assert len(transpose_char_to_all(strchord_to_char('C E G#'))) == 4" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Phase space" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Phase is what Yust is most interested in. It tells something about the location of the set in tonal space. Magnitude of components is transposition invariant; phase is not. He is especially interested in the spatial interpretation of these values. We can pick any pair of components and look at the position of pcsets in the 2D space induced by this choice\n", "\n", "Let's look at the phases of components 3 and 5 for the C major triad " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(x=phases[3], y=phases[5], c='r')\n", "plt.xlim(-2, 2)\n", "plt.ylim(-2, 2)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Having done so, we want to know what are the interesting phase spaces and what are the disinteresting ones, given the harmonic materials we are interested in talking about.\n", "\n", "Let's write a function that takes a list of characteristic representations of pcsets and plots all the pcsets in all the Fourier phase spaces " ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "def plot_in_all_phase_spaces(pcsets, phase_scope=[1, 2, 3, 4, 5, 6], c='b'):\n", " spaces = list(itertools.combinations(phase_scope,2))\n", " \n", " fig, axarr = plt.subplots(5, 6, sharex=True, sharey=True)\n", " \n", " plt.xlim(-7, 7)\n", " plt.ylim(-7, 7)\n", " \n", " \n", " for space in spaces:\n", " xs = []\n", " ys = []\n", " \n", " x, y = space\n", " \n", " for pcset in pcsets:\n", " decomp = fft(pcset)\n", " phases = np.angle(decomp)\n", " xs.append(phases[x])\n", " ys.append(phases[y])\n", " \n", " axarr[x - 1, y - 1].scatter(xs, ys, c=c)\n", " axarr[x - 1, y - 1].set_title('phi_{} vs. phi_{}'.format(x, y))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "interesting = transpose_char_to_all(strchord_to_char('C E G')) + transpose_char_to_all(strchord_to_char('C E G B-')) + transpose_char_to_all(strchord_to_char('C D E F G A B'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Make the major triads red, the dominant sevenths blue, and the major scale green." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "colors = ['r'] * 12 + ['b'] * 12 + ['g'] * 12" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "data": { "image/png": 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h8GRi4jyMGWPM4p+rUSPWPD2JBW2tuPMey5oD1Xdh6vgJ8fHwwANR+F2IqPjP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\n/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FwOl/ZjrRst1rkz3Hsv3HAD1K8PCxeWrpzMTOjdG84805UzaJAbibZ2benK2bcPTjzR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.rcParams['figure.figsize'] = (15, 15)\n", "plot_in_all_phase_spaces(interesting, c=colors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recall the bar plots above that show the phase and magnitude of each of the components. What if the magnitude of a component is zero? Then the phase is undefined. It doesn't make that much sense to work with phase space plots where the phase is undefined. \n", "\n", "Let's write some code that will reveal if we have any components of magnitude zero knocking around. It'll come in handy later." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def find_zero_magnitudes(pcsets):\n", " components_with_zeroes = []\n", "\n", " for pcset in pcsets:\n", " decomp = fft(pcset)\n", "\n", " phases = np.angle(decomp)\n", " magnitudes = np.abs(decomp)\n", "\n", " # check components 0-6\n", " for x in range(7):\n", " if magnitudes[x] == 0:\n", " components_with_zeroes.append(x)\n", "\n", " return components_with_zeroes" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_zero_magnitudes(interesting)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The point of all of this, of course, is analysis. We want to ask ourselves what a piece looks like in this space. So here's a function that will plot a path through all the Fourier phase spaces, given a sequence of chords." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "def path_in_all_phase_spaces(pcsets, phase_scope=[1, 2, 3, 4, 5, 6], c='black'):\n", " spaces = list(itertools.combinations(phase_scope,2))\n", " \n", " for space in spaces:\n", " xs = []\n", " ys = []\n", " \n", " x, y = space\n", " \n", " for pcset in pcsets:\n", " decomp = fft(pcset)\n", " phases = np.angle(decomp)\n", " xs.append(phases[x])\n", " ys.append(phases[y])\n", " \n", " xs = np.array(xs)\n", " ys = np.array(ys)\n", " \n", " plt.quiver(xs[:-1], ys[:-1], \n", " xs[1:] - xs[:-1], ys[1:] - ys[:-1], np.array(range(len(xs))),\n", " scale_units='xy', angles='xy', scale=1)\n", " plt.xlim(-4, 4)\n", " plt.ylim(-4, 4)\n", " plt.title('phi_{} vs. phi_{} phase space'.format(x, y))\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a tonal progression that touches on all the notes of the chromatic." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "omnibus_strchord = ['C E G', 'G B D F', 'B- D F G#', 'F A D', 'A- D F B', 'C E G']\n", "omnibus = [strchord_to_char(strchord) for strchord in omnibus_strchord]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We should use the code from before to check and see if we have any magnitude zero components the any of the phase spaces in which we are interested, before we start plotting our paths." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "[3, 6]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "find_zero_magnitudes(omnibus)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bummer. Let's avoid components 3 and 6 for the meantime." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "data": { "image/png": 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IjPTmCEgRab5gjSpcEoz1SPuRGB3LjP4j2Hj6EDXOsfZkHl8c1fYT7+7bf5pl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\niEhTWnqO60dmNhqoAfKBr7S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AF19zPnd846M8+uUn2PSzVyYtuG5duoqNx/bzQuO+UbddXjmHe6+6hu81/ByA8oJqlpVd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\nnP7e10UIkG/5/P2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xHLHS0mOkpZ3ZUysUXCIiPaj1HLH1b0bmiG3IazlHbM0b21nzxnaGDh3EZZfO\nIjtrLhdeMPWUOWK/ePh1Jp2dys3/czHJyWfmRZgVXCIivWTIkEFckT2XK7LnUlFRzRtrd0TniH1I\n00WMqqrqeGXVVl5ZtZVRo5p+R+zkHLH09BE8/Os1bHxvL/d/7XrSx5x5v8em4BIRSYCRI4fwqWsX\n8qlrF1JScozVrxeQk1tAQWHLOWLPv/Aez7/wHmPTR7J8+Rw8Ogl606aP+PKKh/mHr17LpZfMStRu\nJISuVSgi0occKConNzefnNyCFnPEOnLj9Rdy911Zp5wb07UKRUSkx02ckMJtt17Cbbdewu49h8nJ\nKSB3dcs5Yq0998K7bN6yj3/6xg1Mn57ei9Umxpl5Zk9EJATOmT6WL925jMcfvZuf/Ph2Fl04rd11\n9+wt5q/u+Q3PPf8uiehJ600KLhGRPs7MqG9obHGNxLbU1dXz4/98hW/+8zMcrajupep6n7oKRUT6\nuILCA3zzW3+gurquS+uvW/8BhdsfpmZh//yhUgWXiEgflzFnIn985l4aGhqprqmjpvoENTUnb9U1\nJ6ipqWvxXE3NCdYc3McF8ycybNhZDB7Yf77u+8+eiIj0c8nJSQwfNpjhwwZ3af3be7ieRNE5LhER\nCRUFl4iIhEpcwWVmnzWzbWbWaGadThoTERGJV7xHXFuBzwBrAqhFRESkU3ENznD3AojMMRAREekN\nOsclIiKh0ukRl5m9CoxvY9ED7v5cVzdkZiuAFQBTpkzpcoEiIiKxOg0ud78yiA25+0pgJUSuDh9E\nmyIicuZRV6GIiIRKvMPhP21m+4ElwEtm9nIwZYmIiLQt3lGFzwLPBlSLiIhIp9RVKCIioaLgEhGR\nUFFwiYhIqCi4REQkVBRcIiISKgouEREJFQWXiIiEioJLRERCRcElIiKhouASEZFQUXCJiEioKLhE\nRCRUFFwiIhIqCi4REQkVBZeIiISKgktEREJFwSUiIqGi4BIRkVBRcImISKgouEREJFQUXCIiEioK\nLhERCRUFl4iIhIqCS0REQkXBJSIioRJXcJnZD8ys0Mw2m9mzZpYSVGEiIiJtifeIaxUwz90XADuA\n++MvSUREpH1xBZe7v+Lu9dGHbwGT4i9JRESkfUGe4/oi8KcA2xMRETnFgM5WMLNXgfFtLHrA3Z+L\nrvMAUA880UE7K4AVAFOmTDmtYkVERDoNLne/sqPlZvZ54DrgCnf3DtpZCawEyMzMbHc9ERGRjnQa\nXB0xs6vAvjwGAAAGjklEQVSBrwHL3L0qmJJERETaF+85rp8AI4BVZrbJzH4WQE0iIiLtiuuIy91n\nBFWIiIhIV+jKGSIiEioKLhERCRUFl4iIhIqCS0REQkXBJSIioaLgEhGRUFFwiYhIqCi4REQkVBRc\nIiISKgouEREJFQWXiIiEioJLRERCRcElIiKhouASEZFQUXCJiEioKLhERCRUFFwiIhIqCi4REQkV\nBZeIiISKgktEREJFwSUiIqGi4BIRkVBRcImISKgouEREJFQUXCIiEipxBZeZfcfMNpvZJjN7xcwm\nBlWYiIhIW+I94vqBuy9w9/OBF4FvBlCTiIhIu+IKLneviHk4DPD4yhEREenYgHgbMLPvAv8LOApk\nxV2RiIhIBzo94jKzV81saxu3GwHc/QF3nww8AdzTQTsrzCzPzPKKi4uD2wMRETmjmHswvXtmNhV4\nyd3ndbZuZmam5+XlBbJdERHpH8xso7tndrZevKMKZ8Y8vAEojKc9ERGRzsR7juv7ZjYbaAQ+BO6O\nvyQREZH2xRVc7v6XQRUiIiLSFbpyhoiIhIqCS0REQkXBJSIioaLgEhGRUFFwiYhIqCi4REQkVBRc\nIiISKgouEREJFQWXiIiEioJLRERCRcElIiKhouASEZFQUXCJiEioKLhERCRUFFwiIhIqCi4REQkV\nBZeIiISKgktEREJFwSUiIqGi4BIRkVBRcImISKgouEREJFQUXCIiEioKLhERCRUFl4iIhEogwWVm\nXzUzN7MxQbQnIiLSnriDy8wmA58APoq/HBERkY4FccT1I+AfAQ+gLRERkQ7FFVxmdgPwsbu/H1A9\nIiIiHRrQ2Qpm9iowvo1FDwDfAD7ZlQ2Z2QpgRfRhrZlt7WqRfdQY4Eiii4hT2Pch7PWD9qGv0D70\nDbO7spK5n14Pn5nNB14DqqJPTQIOABe5+8FOXpvn7pmnteE+QvuQeGGvH7QPfYX2oW/o6j50esTV\nHnffAoyN2eBeINPdw574IiLSh2kel4iIhMppH3G15u7TurH6yqC2m0Dah8QLe/2gfegrtA99Q5f2\n4bTPcYmIiCSCugpFRCRUEh5cYb5clJl9x8w2m9kmM3vFzCYmuqbuMLMfmFlhdB+eNbOURNfUXWb2\nWTPbZmaNZhaqEVVmdrWZbTeznWb29UTX011m9iszOxzWqS1mNtnMcs2sIPoZ+kqia+ouMxtsZu+Y\n2fvRffh2oms6XWaWbGbvmdmLna2b0ODqB5eL+oG7L3D384EXgW8muqBuWgXMc/cFwA7g/gTXczq2\nAp8B1iS6kO4ws2TgIeAaYC5wi5nNTWxV3fYIcHWii4hDPXCfu2cAi4G/DuG/QS2Q7e4LgfOBq81s\ncYJrOl1fAQq6smKij7hCfbkod6+IeTiMkO2Hu7/i7vXRh28RmYsXKu5e4O7bE13HabgI2Onuu929\nDvg9cGOCa+oWd18DlCa6jtPl7kXu/m70fiWRL82zE1tV93jEsejDgdFbqL6HAMxsEvAp4JddWT9h\nwdVfLhdlZt81s33AbYTviCvWF4E/JbqIM8jZwL6Yx/sJ2Zdmf2Jm04ALgLcTW0n3RbvYNgGHgVXu\nHrp9AB4kchDT2JWVAxsO35agLheVSB3tg7s/5+4PAA+Y2f3APcC3erXATnRWf3SdB4h0mzzRm7V1\nVVf2IYSsjedC95dyf2Bmw4E/APe26kUJBXdvAM6PnqN+1szmuXtozjua2XXAYXffaGbLu/KaHg0u\nd7+yreejl4uaDrxvZhDponrXzDq9XFRva28f2vBb4CX6WHB1Vr+ZfR64DrjC++jciG78G4TJfmBy\nzOOmS6ZJLzKzgURC6wl3fybR9cTD3cvNbDWR846hCS7gUuAGM7sWGAyMNLPH3f1z7b0gIV2F7r7F\n3ce6+7ToxOX9wIV9LbQ6Y2YzYx7eABQmqpbTYWZXA18DbnD3qs7Wl0BtAGaa2XQzGwTcDDyf4JrO\nKBb5q/lhoMDdf5joek6HmaU3jQY2syHAlYTse8jd73f3SdEsuBnI6Si0IPGDM8Lu+2a21cw2E+n2\nDNtw2p8AI4BV0SH9P0t0Qd1lZp82s/3AEuAlM3s50TV1RXRQzD3Ay0QGBTzp7tsSW1X3mNnvgDeB\n2Wa238zuTHRN3XQpcDuQHf38b4r+1R8mE4Dc6HfQBiLnuDodTh52unKGiIiEio64REQkVBRcIiIS\nKgouEREJFQWXiIiEioJLRERCRcElIiKhouASEZFQUXCJiEio/H+vthoPgc4bywAAAABJRU5ErkJg\ngg==\n", 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