{ "cells": [ { "cell_type": "markdown", "id": "17bf9cc9", "metadata": {}, "source": [ "# Expectation Maximization\n", "\n", "## Motivation\n", "\n", "Im supervised Learning haben wir gesehen, dass Lineare Regression (eventuell mit einem Kernel) uns helfen könnte, Daten zu klassifizieren. Beim unsupervised Learning haben wir zur Klassifikation k-Means und Kernel-k-Means eingesetzt, jeweils ergänzt durch Datenskalierung und Hauptachsentransformation. Dabei haben wir gute Ergebnisse gesehen, wenn die Cluster im Feature-Raum konvex und gut approximierbar mit einer Normalverteilung ohne Kovarianz (also gut approximierbar durch Vollkugeln) waren. Wenn die Cluster aber zwar normalverteilt aber mit unterschiedlicher Kovarianz waren, und nicht linear voneinander getrennt werden konnten, haben wir keine guten Ergebnisse mit k-Means gesehen." ] }, { "cell_type": "markdown", "id": "7c410d5c", "metadata": {}, "source": [ "```{admonition} Beispiel\n", "Formuliert als Expectation-Maximization-Verfahren ist das k-Means-Verfahren:\n", " \n", "1. Initialisierung (Clustermittelpunkte festlegen) \n", "2. Iterativ bis zur Konvergenz der Clustermittelpunkte: \n", " a. (E-Schritt): Punkte dem jeweils nächsten Clustermittelpunkt zuteilen und so zu einer Klasseneinteilung kommen \n", " b. (M-Schritt): Neue Clustermittelpunkte als Mittelwert aller Elemente einer Klasse festlegen \n", " \n", "Der E-Schritt (Expectation) heißt so, weil wir unsere Erwartung über den Wert der latenten Variable updaten.\n", "\n", "Der M-Schritt (Maximization) heißt so, weil wir eine Fitness-Funktion maximieren - konkret minimieren wir die Summe aller Entferungen der Punkte zu den ihnen zugeteilten Clustermittelpunkten.\n", "```\n", "\n", "Es liegt nahe, ein Verfahren zu verwenden, welches die Form der Cluster berücksichtigt." ] }, { "cell_type": "markdown", "id": "6bd6fd49", "metadata": {}, "source": [ "### Gemischte Gausssche Modelle, supervised\n", "\n", "Wenn wir von Daten in $\\mathbb{R}^d$ Einteilungen in $k$ Klassen (Label) gegeben haben, können wir für jeden Teildatensatz aller Punkte einer Klasse die Sample-Kovarianz und den Sample-Erwartungswert ausrechnen und damit eine $n$-variate Normalverteilung aufstellen, die diesen Teildatensatz modelliert.\n", "\n", "Daraus resultiert ein Modell für die gesamten Daten, wenn wir mit $p_i$ die Anzahl der Punkte in Klasse $i$ geteilt durch die Anzahl an Punkten im Sample insgesamt bezeichnen und mit $f_i(x)$ die geschätzte Dichte der Normalverteilung von Klasse $i$, nämlich die Dichte\n", "\n", "$$\n", "f(x) = \\sum_{i=1}^k p_i f_i(x).\n", "$$\n", "\n", "Dieses Modell können wir natürlich auch wieder benutzen, um einzuschätzen, zu welcher Klasse ein Punkt gehört. Dazu berechnen wir für einen Punkt $x$ die Dichten\n", "\n", "$$\n", "P_i(x) = p_i f_i(x)\n", "$$\n", "\n", "und wählen das $i$ aus, für das dieser Ausdruck maximal wird." ] }, { "cell_type": "markdown", "id": "910b0ddc-28b9-4939-af06-b6923be33f6f", "metadata": {}, "source": [ "Als Entstehungsprozess kann man sich das so vorstellen: ein (fiktives) gemischtes Gausssches Modell wurde verwendet um die Datenpunkte zu sampeln, indem zunächst nach der diskreten Verteilung der $p_i$ eine Klasse $j$ ausgewählt wurde und dann mit der Dichte $f_j(x)$ ein Sample daraus gezogen wurde, und das so oft, wie es Datenpunkte gibt.\n", "\n", "Nun kann es leicht passieren, wenn sich die Cluster überschneiden, dass manche Punkte $x$ durch das Modell anders klassifiziert werden, als dies ursprünglich der Fall war -- dagegen gibt es kein grundsätzliches Gegenmittel. Dennoch können wir so das am besten an die Daten angepasste gemischte Gausssche Modell bestimmen und damit Daten sampeln, die den vorliegenden sehr ähnlich sehen werden (vorausgesetzt die Normalverteilungsannahme war korrekt).\n", "\n", "Wir wollen noch eine weitere Beobachtung machen: das gemischte Gausssche Modell gibt uns mehr als nur eine neue Klasseneinteilung, sondern zu jedem Punkt zu jeder Klasse eine Wahrscheinlichkeit dafür, dass der Punkt zu dieser Klasse gehört. Das ist wesentlich mehr Information und kann deutlich nützlicher sein. Vor allem bei den nicht korrekt klassifizierten Punkten erhalten wir damit eine Möglichkeit, unsere Gewissheit bei der Klasseneinteilung zu quantifizieren." ] }, { "cell_type": "code", "execution_count": 1, "id": "2fc62322-b991-4b28-8fec-061419c28b58", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x720 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.datasets import load_iris\n", "from sklearn.decomposition import PCA\n", "from scipy.stats import multivariate_normal as mvn\n", "\n", "x, y = load_iris(return_X_y=True)\n", "# work in principal components, to plot later in the first two:\n", "xpc = PCA().fit_transform(x)\n", "\n", "k = 3\n", "assert k == np.max(y) + 1\n", "\n", "mvns = list(range(k))\n", "for i in range(k):\n", " # for simplicty, take only first 2 PCs here:\n", " mu = np.mean(xpc[y == i][:,:2], axis=0)\n", " sigma = np.cov(xpc[y == i][:,:2], rowvar=False)\n", " mvns[i] = mvn(mean=mu, cov=sigma, allow_singular=True)\n", "\n", "round_mvns = list(range(k))\n", "for i in range(k):\n", " mu = np.mean(xpc[y == i][:,:2], axis=0)\n", " sigma = np.eye(2)\n", " round_mvns[i] = mvn(mean=mu, cov=sigma, allow_singular=True)\n", " \n", "fig = plt.gcf()\n", "fig.set_size_inches(10, 10)\n", "ax1 = plt.subplot(221)\n", "ax2 = plt.subplot(222, sharex=ax1, sharey=ax1)\n", "plt.figtext(0.35, 0.95, \"First 2 principal components of Iris data\")\n", "ax1.set_title(\"kMeans fit\")\n", "ax2.set_title(\"Gaussian Mixture Model (GMM)\")\n", "xs, ys = np.mgrid[-4:4.1:.2, -4:4.1:.1]\n", "for i in range(k):\n", " zs = round_mvns[i].pdf(np.dstack((xs, ys)))\n", " ax1.contour(xs, ys, zs,\n", " cmap=plt.cm.Oranges, alpha=.7)\n", " ax1.scatter(xpc[y == i][:,0], xpc[y == i][:,1],\n", " c=np.ones_like(y[y == i])*i, vmin=0, vmax=k-1,\n", " label=str(i))\n", " zs = mvns[i].pdf(np.dstack((xs, ys)))\n", " ax2.contour(xs, ys, zs,\n", " cmap=plt.cm.Oranges, alpha=.7)\n", " ax2.scatter(xpc[y == i][:,0], xpc[y == i][:,1],\n", " c=np.ones_like(y[y == i])*i, vmin=0, vmax=k-1,\n", " label=str(i))\n", "ax1.legend()\n", "ax2.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4edbd04f-d789-4890-ae84-e1cf84ca0cb8", "metadata": {}, "source": [ "### Gemischte Gausssche Modelle, unsupervised\n", "\n", "Das eben beschriebene Vorgehen ist nicht möglich, wenn wir keine Klasseneinteilung vorgegeben haben.\n", "In diesem Fall ist die Klasse eine **latente Variable**, die wir nicht kennen, die aber in der Modellbeschreibung wesentlich ist.\n", "Was wir gut modellieren können, sind bedingte Wahrscheinlichkeiten, wenn wir auf den Wert der latenten Variable bedingen - also die Verteilung einer einzelnen Klasse. Die Verteilung der latenten Variable ist schwieriger zu beschreiben, wenn wir nur ungelabelte Daten zur Verfügung haben.\n", "\n", "Es bietet sich ein zweistufiges Verfahren an: zunächst ließe sich mit k-Means eine Klasseneinteilung finden (die oftmals nicht besonders gut ist, wenn die Homoskedastizitätsvoraussetzung nicht erfüllt ist) und dann auf Grundlage dieser Klasseneinteilung ein gemischtes Gausssches Modell aufstellen, d.h. eine Schätzung der latenten Variable gewinnen.\n", "\n", "Nun lässt sich wiederum feststellen, dass die Klasseneinteilung, die uns das gemischte Modell berechnen lässt, im Allgemeinen von der Klasseneinteilung abweicht, die wir zuvor mit k-Means berechnet haben. Diesmal aber ist naheliegend, dass das gemischte Modell eine bessere Klasseneinteilung leistet, denn nun werden ja zusätzlich die Formen der Cluster berücksichtigt (approximiert durch Ellipsoide aufgrund der Normalverteilungsannahme).\n", "\n", "Mit dieser verbesserten Klasseneinteilung, also der verbesserten Schätzung der latenten Variable, kann man nun erneut ein gemischtes Gaussches Modell aufsetzen, d.h. die Kovarianzmatrizen und Mittelpunkte neu schätzen, ganz ähnlich zum Iterationsschritt im k-Means-Verfahren." ] }, { "cell_type": "markdown", "id": "4e2c1ddd-47f5-4fda-8730-2fbf720cbdbf", "metadata": {}, "source": [ "Wir wollen nun noch eine Beobachtung machen: Wenn im Aufstellen der Kovarianzmatrizen jeweils nur die Güte des Modells für eine einzelne Klasse betrachtet wird (also der beste Fit), dann berücksichtigen wir nicht die Auswirkung dieser Modelländerung auf die anderen Klassen - die wird es aber meist geben.\n", "Es wäre also besser, im Iterationsschritt simultan alle Parameter zu optimieren auf die Zielgröße - das gemischte Modell mit dem besten Fit.\n", "\n", "Um für eine beliebige Verteilung einen guten Schätzer zu konstruieren, haben wir das Maximum-Likelihood-Verfahren genutzt, und das wollen wir auch im Fall einer Mischung von Normalverteilungen versuchen." ] }, { "cell_type": "markdown", "id": "62807228", "metadata": {}, "source": [ "## Maximum Likelihood in Modellen mit latenten Variablen\n", "\n", "Die Wahrscheinlichkeitsdichte im gemischten Gausschen Modell, wo $\\theta_j$ die Parameter $\\mu_j,\\Sigma_j$ bezeichnet einer einzelnen Mischkomponente, und $p_j$ die Verteilung der Komponenten, ist\n", "\n", "$$\n", "f(x) = \\sum_{j=1}^k p_j f_j(x, \\theta_j) = P(X=x|M=\\theta) = L(\\theta),\n", "$$\n", "\n", "das ist die Likelihood (also die Wahrscheinlichkeit der Daten, berechnet in unserem Modell), wenn wir mit $M$ unser Modell bezeichnen und mit $X$ die Daten. Die Modellannahme ist jetzt also: $X$ ist mit $f$ verteilt. Dabei ist $\\theta$ die Menge an Parametern $p_j$ zusammen mit den Parametern $\\mu_j,\\Sigma_j$, die in $f_j$ versteckt sind. Wenn wir diese Größe als Likelihood auffassen, dann als Funktion in diesen Parametern.\n", "\n", "Tipp: wenn Sie sich gern in der Notation $\\theta$ als Liste über $\\theta_j$ vorstellen wollen, setzten Sie einfach $\\theta_0 := (p_1,\\dots,p_k)$.\n", "\n", "Wenn wir die Modellierung, dass die Einteilung der Datenpunkte in Klassen, durch Wahrscheinlichkeiten ausgedrückt werden, ernst nehmen, können wir auch gleich die Einteilung als Zufallsvariable $Y$ modellieren. Es ist also $Y_i = j$ wenn der $i$-te Datenpunkt von Klasse $j$ ist, aber wir kennen die Variable $Y$ nicht." ] }, { "cell_type": "markdown", "id": "b74204e1-ef8f-4417-b364-77300cdf1ad4", "metadata": {}, "source": [ "Unser Modell, formuliert mit der latenten Variable $Y$, ist\n", "\n", "$$\n", "P(Y = j\\ |\\ \\theta) =& p_j \\\\\n", "P(X=x\\ |\\ Y=j, \\theta) =& f_j(x,\\ \\mu_j,\\Sigma_j) \\\\\n", "P(X=x\\ |\\ \\theta) =& \\sum_{j=1}^k P(X=x,\\ Y=j\\ |\\ \\theta) \\\\\n", " =& \\sum_{j=1}^k P(Y = j, \\theta) P(X=x\\ |\\ Y=j, \\theta)\n", "$$" ] }, { "cell_type": "markdown", "id": "af409d6d-1e49-4868-b81e-d2b6a24a71c2", "metadata": {}, "source": [ "### Nullstellen der Ableitung bestimmen?\n", "\n", "Direkt die Nullstellen der Ableitung von $L(\\theta)$ zu bestimmen ist nicht leicht, aber auch der beliebte Trick, $\\ell(\\theta) = \\log L(\\theta)$ zu maximieren, bringt hier nicht viel, denn\n", "\n", "$$\n", "\\ell(\\theta) =& \\log P(X=x\\ |\\ \\theta) \\\\\n", " =& \\log \\left( \\sum_{j=1}^k P(X=x, Y=j\\ |\\ \\theta) \\right) \\\\\n", " =& \\log \\left( \\sum_{j=1}^k p_j f_j(x\\ |\\ \\theta_i) \\right)\n", "$$\n", "\n", "und aus der Summen-Nummer kommen wir mit dem Logarithmus nicht so leicht raus.\n", "\n", "### Jensen to the rescue!\n", "\n", "Wir können unsere Ziele etwas abschwächen und mit der Jensenschen Ungleichung arbeiten (denn der Logarithmus ist konkav und $\\sum_{j=1}^k p_j = 1$):\n", "\n", "$$\n", "\\ell(\\theta) \\geq \\sum_{j=1}^k p_j \\log f_j(x\\ |\\ \\theta_i)\n", "$$\n", "\n", "Das charmante an dem Ausdruck auf der rechten Seite ist, dass ein $\\theta$, welches die rechte Seite maximiert, keine kleinere linke Seite haben kann. In Formeln: wenn wir ein $\\theta^{(i)}$ gegeben haben, dann ein $\\theta^{(i+1)}$ bestimmen, für dass die rechte Seite größer wird, dann ist auch $\\ell(\\theta^{(i+1)}) \\geq \\ell(\\theta^{(i)})$.\n", "\n", "Wir wollen feststellen, dass sich im Ausdruck für den Beitrag einer Klasse $p_j f_j$ auch eine fette $1 = \\frac{q(j)}{q(j)}$ hinein multiplizieren lässt, hier\n", "\n", "$$\n", "\\ell(\\theta) =& \\log \\left( \\sum_{j=1}^k P(X=x, Y=j\\ |\\ \\theta) \\right) \\\\\n", " =& \\log \\left( \\sum_{j=1}^k q(j) \\frac{P(X=x, Y=j\\ |\\ \\theta)}{q(j)} \\right)\n", "$$\n", "\n", "Die Nützlichkeit sieht man nach Anwenden der Jensenschen Ungleichung, diesmal auf die Konvexkombination $\\sum_{j=1}^k q(j) = 1$, wobei wir ab jetzt also annehmen, dass $q$ eine Wahrscheinlichkeitsdichte ist: \n", "\n", "$$\n", "\\ell(\\theta) \\geq & \\sum_{j=1}^k q(j) \\log \\left( \\frac{P(X=x, Y=j\\ |\\ \\theta)}{q(j)} \\right) =: L(\\theta,q) \\\\\n", " = & \\sum_{j=1}^k q(j) \\left( \\log \\left( P(X=x, Y=j\\ |\\ \\theta \\right) - \\log q(j) \\right) \\\\\n", " = & \\sum_{j=1}^k q(j) \\log P\\left(X=x, Y=j\\ |\\ \\theta\\right) \\qquad - \\sum_{j=1}^k q(j) \\log q(j) \\\\\n", " = & \\sum_{j=1}^k q(j) \\log P\\left(X=x, Y=j\\ |\\ \\theta\\right) \\qquad + H(q)\n", "$$\n", "\n", "Wir haben also eine untere Schranke an $\\ell(\\theta)$ gefunden, die wir schreiben können als Summe eines Ausdrucks, der leichter zu berechnen ist, und der Entropie der Verteilung mit Dichte $q$. Da die Entropie nicht von $\\theta$ abhängt, lässt sich $L(\\theta,q)$ durch maximieren des anderen Summanden maximieren.\n", "\n", "Diese Beobachtung wollen wir wieder aufgreifen (daher haben wir dem Kind auch einen Namen $L(\\theta,q)$ gegeben), aber jetzt erstmal einen allgemeinen Lösungsansatz diskutieren." ] }, { "cell_type": "markdown", "id": "d7362fe4-3f80-4786-9c4f-34e64000f04f", "metadata": {}, "source": [ "## Auxiliary Functions\n", "\n", "Wenn wir eine Funktion $\\ell(\\theta)$ nicht maximieren können,\n", "können wir versuchen, behelfsmäßig so zu tun als sei $\\theta$ in einigen Teilausdrücken von $\\ell(\\theta)$ konstant, dann maximieren, und dann die anderen Teilausdrücke konstant halten bzw. darüber maximieren. Um das zu formalisieren, führen wir eine Hilfsfunktion $Q(\\theta,\\vartheta)$ ein, die leichter in $\\theta$ zu maximieren ist als $\\ell$, aber dennoch $Q(\\theta, \\theta) = \\ell(\\theta)$ erfüllt und außerdem $Q(\\theta,\\vartheta) \\leq \\ell(\\theta)$ für alle $\\vartheta$ erfüllt.\n", "\n", "Mit diesen Voraussetzungen kann man bereits zeigen, dass ein iterativer Prozess zu immer besseren Approximationen $\\theta^{(i)}$ an das $\\theta$, welches $\\ell(\\theta)$ maximiert, führt. Dabei bezeichnen wir mit $\\theta^{(i+1)}$ das $\\theta$ sodass $Q(\\theta, \\theta^{(i)})$ maximal wird (nach Annahme finden wir das leicht).\n", "\n", "$$\n", "\\ell(\\theta^{(i)}) =& Q(\\theta^{(i)}, \\theta^{(i)}) \\\\\n", " \\leq & Q(\\theta^{(i+1)}, \\theta^{(i)}) \\text{ (M-Schritt)} \\\\\n", " \\leq & Q(\\theta^{(i+1)}, \\theta^{(i+1)}) \\text{ (E-Schritt)} \\\\\n", " & = \\ell(\\theta^{(i+1)}) \n", "$$\n", "\n", "Insgesamt haben wir also $\\ell(\\theta^{(i)}) \\leq \\ell(\\theta^{(i+1)})$, d.h. zumindest verschlechtern wir uns dabei nicht mit unserer Schätzung!\n", "\n", "Es bleibt für uns, wenn wir diesen Ansatz wählen wollen, noch die Wahl einer geschickten Hilfsfunktion $Q(\\theta,\\vartheta)$.\n" ] }, { "cell_type": "markdown", "id": "ebc6d2ec-0e46-422e-987a-a74855a92d8d", "metadata": {}, "source": [ "## Vollständige-Daten log-Likelihood\n", "\n", "Die letzte Zutat zur Entwicklung des E-M-Algorithmus für das gemischte Gausssche Modell ist die vollständige-Daten-log-Likelihood. Das ist die log-Likelihood in der fiktiven Welt, in der wir tatsächlich die vollständigen Daten, d.h. nicht nur die Werte von $X$ sondern auch die der latenten Variable $Y$, also die tatsächlichen Klassen der Datenpunkte kennen.\n", "\n", "Die vollständigen Daten sind also $(x_i,y_i)$, was mir mit $(X,Y)$ modellieren.\n", "\n", "Es ist nun nützlich, die Variable $Y_i$ auch one-hot-encoded anzusehen: $Y_{ij} = 1$ wenn $Y_i = j$ und $Y_{ij} = 0$, wenn $Y_i \\neq j$. Manche schreiben dafür auch $[Y_i=j]$ (Iversen-Bracket).\n", "\n", "Die log-Likelihood der Daten unter dem gemischten Gaussschen Modell ist\n", "\n", "$$\n", "\\ell_c(\\theta) = \\log P((X,Y)|\\theta) =& \\sum_{i=1}^n \\log P(X=x_i, Y=y_i\\ |\\ \\theta) \\\\\n", " & \\sum_{i=1}^n \\log \\prod_{j=1}^k {P(X=x_i, Y=y_i\\ |\\ \\theta)}^{Y_{ij}} \\\\\n", " & \\sum_{i=1}^n \\sum_{j=1}^k Y_{ij} \\log P(X=x_i, Y=y_i\\ |\\ \\theta)\n", "$$\n", "\n", "dabei haben wir in der ersten Umformung eine fette $1$ hinzugefügt, da $Y_{ij}$ nur für einen Faktor in dem Produkt $\\prod_{j=1}^k (...)^{Y_{ij}}$ überhaupt $1$ ist, ansonsten $0$, und damit der entsprechende Faktor $1$.\n", "Die zweite Umformung ist nur $\\log \\prod (...)^t = \\sum t \\log (...)$.\n", "\n", "Man beachte auch, dass das $\\theta$ jetzt wirklich nur noch $\\theta_1,\\dots,\\theta_k$ ist, denn die $p_i$ sind in der Verteilung von $Y$ kodiert.\n", "\n", "Wir können noch weiter vereinfachen:\n", "\n", "$$\n", "\\log P(X=x_i, Y=y_i) = \\log \\left( p_{y_i} f_{y_i}(x_i) \\right) = \\log p_{y_i} + \\log f_{y_i}(x_i)\n", "$$\n", "\n", "### Erwartungswert über die latente Variable\n", "\n", "Wenn wir eine Verteilung $q(y)$ für die latente Variable $Y$ annehmen, dann können wir den Erwartungswert über diese bilden:\n", "\n", "$$\n", "\\mathbb{E}_{Y \\sim q} \\ell_c(\\theta) =& \\mathbb{E}_{Y \\sim q} \\left( \\sum_{i=1}^n \\sum_{j=1}^k Y_{ij} \\left( \\log p_{y_i} + \\log f_{y_i}(x_i\\ |\\ \\theta_i) \\right) \\right) \\\\\n", " =& \\sum_{i=1}^n \\sum_{j=1}^k \\mathbb{E}_{Y \\sim q} Y_{ij} \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_i) \\right) \\\\\n", " =& \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij} \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_i) \\right)\n", "$$\n", "\n", "Hierbei nennen wir die mit $\\tau_{ij}$ bezeichneten Terme **responsibilites** oder **Verantwortlichkeiten**, denn sie sind in unserem Modell verantwortlich für die Einteilung der Punkte $x_i$ in Klassen:\n", "\n", "$$\n", "\\tau_{ij} := \\mathbb{E}_{Y \\sim q} Y_{ij} = P(Y_i = j\\ |\\ X=x_i,\\theta) = \\frac{P(Y_i = j, X=x_i)\\ |\\ \\theta)}{P(X=x_i\\ |\\ \\theta}\n", "$$\n", "\n", "Wenn wir die $\\tau_{ij}$ festhalten, haben wir mit $\\mathbb{E}_{Y \\sim q} \\ell_c(\\theta)$ eine Größe, die wir maximieren können (auch wenn die $\\tau_{ij}$ natürlich eigentlich von $\\theta$ abhängen). Wir wollen die $\\tau_{ij}$ als Funktion von $\\theta$ betrachten, aber nennen dieses nun $\\vartheta$.\n", "\n", "Wir definieren also\n", "\n", "$$\n", "Q(\\theta,\\vartheta) := \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta) \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_j) \\right)\n", "$$\n", "\n", "Das ist für $\\theta=\\vartheta$ die erwartete vollständige-Daten log-Likelihood unter unserer Annahme $q$ an die Verteilung der latenten Variable $Y$.\n", "Wir bemerken noch, dass der andere Term $\\log P(X=x_i, Y=j) = \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_i) \\right)$ von $\\theta$ abhängt, nicht von $\\vartheta$.\n", "\n", "### Der Unterschied zwischen $L(\\theta, q)$ und $Q(\\theta, \\theta)$\n", "\n", "Wir erinnern uns nochmal an die Beobachtung zuvor, die wir mit Hilfe der Jensenschen Ungleichung gefunden haben:\n", "\n", "$$\n", "\\ell(\\theta) \\geq L(\\theta, q) = \\sum_{j=1}^k q(j) \\log P\\left(X=x, Y=j\\ |\\ \\theta\\right) \\qquad + H(q)\n", "$$\n", "\n", "und stellen fest, dass der Summand, der nicht $H(q)$ ist, genau die erwartete vollständige-Daten log-Likelihood ist, also\n", "\n", "$$\n", "\\ell(\\theta) \\geq L(\\theta, q) = \\mathbb{E}_{Y \\sim q} \\ell_c(\\theta) + H(q) = Q(\\theta,\\theta) + H(q)\n", "$$\n", "\n", "Da $H(q)$ nicht von $\\theta$ abhängt, können wir also $Q(\\theta,\\vartheta)$ in $\\theta$ maximieren und haben damit $L(\\theta, q)$ in $\\theta$ maximiert.\n", "\n", "### Der Unterschied zwischen $\\ell(\\theta)$ und $L(\\theta, q)$\n", "\n", "Wir stellen die Formel für $L(\\theta, q)$ noch einmal anders um. Dabei wollen wir die gemeinsame Verteilung $P(X=x, Y=j)$ durch bedingte Verteilungen ausdrücken, $P(Y=j, X=x) = P(Y=j|X=x)P(X=x)$ und erhalten damit:\n", "\n", "$$\n", "\\ell(\\theta) \\geq& L(\\theta, q) = \\sum_{j=1}^k q(j) \\log \\left( \\frac{P(X=x, Y=j\\ |\\ \\theta)}{q(j)} \\right) \\\\\n", " & = \\sum_{j=1}^k q(j) \\log \\left( \\frac{ P(Y=j\\ |\\ X=x, \\theta) P(X=x\\ |\\ \\theta) }{q(j)} \\right) \\\\\n", " & = \\sum_{j=1}^k q(j) \\log \\left( \\frac{P(Y=j\\ |\\ X=x, \\theta)}{q(j)} \\right) \\qquad + \\sum_{j=1}^k q(j) \\log\\left( P(X=x\\ |\\ \\theta) \\right) \\\\\n", " & = -H(q\\ |\\ Y_{|X=x}, \\theta) + \\ell(\\theta)\n", "$$\n", "\n", "Die Differenz zwischen $\\ell(\\theta)$ und $L(\\theta,q)$ ist also genau die relative Entropie der geschätzten Verteilung $q$ zur tatsächlichen Verteilung $Y_{|X=x}$:\n", "\n", "$$\n", "\\ell(\\theta) - L(\\theta, q) = H(q\\ |\\ Y_{|X=x}, \\theta)\n", "$$\n", "\n", "Damit ist auch $\\ell(\\theta) - Q(\\theta,\\theta) = H(q\\ |\\ Y_{|X=x}, \\theta) + H(q)$, wir verstehen also ganz genau, inwiefern sich $\\ell(\\theta)$ mit $Q(\\theta,\\theta)$ maximieren lässt." ] }, { "cell_type": "markdown", "id": "e1518734-5a5e-4223-b9e7-b8cdfda07385", "metadata": {}, "source": [ "## E-M-Algorithmus zum fitten eines gemischten Gaussschen Modells\n", "\n", "Der Algorithmus wird mit einer Wahl von $\\theta^{(0)}$ initialisiert (und das Ergebnis hängt im Allgemeinen sehr von dieser Initialisierung ab, wie wir bereits bei k-Means gesehen haben). Eine mögliche Wahl ist, bei den $\\mu_j$ (den Clusterzentren) das k-Means-Verfahren (mit k-Means++-Initialisierung) auf die Daten anzuwenden und dann die konvergierten Zentroide als $\\mu_j$ zu nehmen. Für die Kovarianzmatrizen kann man mit Einheitsmatrizen starten (das entspricht einer translierten Standardnormalverteilung). Das Mischverhältnis, also die $p_i$ kann man auf $p_i = \\frac{1}{k}$ initialisieren.\n", "\n", "Dann führt man iterativ abwechselnd den E-Schritt und den M-Schritt durch:\n", "\n", "* **E-Schritt**: Update den Parameter $\\vartheta$: setze $\\vartheta = \\theta$ und berechne die Responsibilities $\\tau_{ij} := \\tau_{ij}(\\theta)$ um wieder eine korrekte Formel für $Q(\\theta,\\theta)$ bzw. eine neue Schätzung für $q$ und damit $L(\\theta, q)$ aufzustellen. In diesem Schritt schätzen wir die latente Variable mit dem Ziel, die relative Entropie zur tatsächlichen Verteilung der latenten Variable zu minimieren (also möglichst gut zu approximieren). Je besser die Schätzung, desto näher liegt $L(\\theta, q)$ an $\\ell(\\theta)$.\n", "* **M-Schritt**: Update den Parameter $\\theta$: maximiere die erwartete vollständige log-Likelihood $Q(\\theta,\\vartheta)$ in $\\theta$ (während $\\vartheta$ fest gehalten wird, also die Verantwortlichkeiten $\\tau_{ij}$ konstant sind). Damit wird $L(\\theta, q)$ maximiert, eine untere Schranke an $\\ell(\\theta)$.\n", "\n", "Das Verfahren konvergiert, da die Approximationen an ein Maximum von $\\ell(\\theta)$ nie schlechter werden (man könnte sagen, wegen der Jensenschen Ungleichung).\n", "\n", "Bisher haben wir nicht benötigt, welche Form die Dichtefunktionen $f_j$ haben - tatsächlich funktioniert alles, was wir diskutiert haben, bis jetzt auch für beliebige Verteilungen! Wenn man sorgfältig arbeitet, darf auch die latente Variable eine stetige Variable sein, wenn man geeignet Summen von $j=1$ bis $k$ durch entsprechende Integrale ersetzt. So gesehen ist der E-M-Algorithmus eigentlich nicht ein Algorithmus sondern eine Schablone, um viele konkrete E-M-Algorithmen zu entwickeln.\n", "\n", "Noch allgemeiner, wenn es nicht zwangsläufig um die Maximierung einer Likelihood unter latenten Variablen geht, spricht man von M-M-Algorithmen. Das steht für Majorisieren-Maximieren und man spricht auch von Optimierungstransfer. Mit diesen Stichworten können Sie Literatur auftreiben, wenn Sie eine Verallgemeinerung des E-M-Algorithmus benötigen.\n", "\n", "Wir wollen uns jetzt aber doch erstmal auf den Fall einer diskreten endlichen latenten Variable $Y$ beschränken und uns in Richtung einer Implementierung in Python bewegen." ] }, { "cell_type": "markdown", "id": "dacc2085-13b9-437d-bed3-a10084dec3b9", "metadata": {}, "source": [ "### Konkrete Formeln für das gemischte Gaussche Modell\n", "\n", "Um den Algorithmus konkret implementieren zu können, müssen wir natürlich auch konkrete Dichtefunktionen verwenden, und das wollen wir nun tun, also uns daran erinnern, dass die multivariate Normalverteilung diese Dichte hat:\n", "\n", "$$\n", "f_j(x) = f_j(x, \\mu_j, \\Sigma_j) = \\dfrac{1}{\\sqrt{(2\\pi)^n \\det\\Sigma_j}} e^{-\\frac{(x-\\mu_j)^T \\Sigma_j^{-1} (x - \\mu_j)}{2}}.\n", "$$\n", "\n", "Weil wir uns das Leben leicht machen wollen, betrachten wir erstmal den univariaten Fall, also ist\n", "\n", "$$\n", "f_j(x) = f_j(x, \\mu_j, \\sigma_j) = \\dfrac{1}{\\sqrt{2\\pi \\sigma_j}} e^{-\\frac{(x-\\mu_j)^2}{2\\sigma_j^2}}.\n", "$$\n", "\n", "Im Iterationsverfahren haben wir nun $\\theta^{(i)}$ gegeben, d.h. $\\mu_j^{(i)}$ und $\\Sigma_j^{(i)}$ sowie Mischungsparameter $p_j^{(i)}$. Achtung: das ist ein anderes $i$ als der Stichprobenindex $i$ wie im Ausdruck $x_i$ und dieser Unterschied ergibt sich nur aus dem Kontext.\n", "\n", "Im E-Schritt berechnen wir die Verantwortlichkeiten\n", "\n", "$$\n", "\\tau_{ij}(\\theta^{(i)}) =& \\frac{P(Y_i = j, X=x_i\\ |\\ \\theta)}{P(X=x_i\\ |\\ \\theta)} \\\\\n", " =& \\frac{P(Y_i = j, X=x_i\\ |\\ \\theta)}{\\sum_{m=1}^k P(Y_i = m, X=x_i\\ |\\ \\theta)} \\\\\n", " =& \\frac{p_j^{(i)} f_j\\left(x_i,\\mu_j^{(i)},\\sigma_j^{(i)}\\right)}{\\sum_{m=1}^k p_m^{(i)} f_m\\left(x_i,\\mu_m^{(i)},\\sigma_m^{(i)}\\right)}\n", "$$\n", "\n", "Im M-Schritt maximieren wir $Q(\\theta,\\vartheta)$ in $\\theta$, indem wir Nullstellen der Ableitung nach $\\theta$ bestimmen, also lösen wir das Gleichungssystem\n", "\n", "$$\n", "0 =& \\frac{d}{d\\theta} Q(\\theta, \\vartheta) \\\\\n", " =& \\frac{d}{d\\theta} \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta) \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_j) \\right) \\\\\n", " =& \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta)\\frac{d}{d\\theta} \\left( \\log p_{j} + \\log f_{j}(x_i\\ |\\ \\theta_j) \\right)\n", "$$\n", "\n", "Als ersten Schritt betrachten wir die Ableitungen nach den $\\mu_j$:\n", "\n", "$$\n", "\\frac{d}{d\\mu_j} \\log f_j(x_i) =& - \\frac{\\frac{d}{d\\mu_j}(x_i-\\mu_j)^2}{2\\sigma_j} = \\frac{2(x_i-\\mu_j)}{2\\sigma_j} \\\\\n", "\\frac{d}{d\\mu_j} Q(\\theta, \\theta^{(i)}) =& \\sum_{i=1}^n \\sum_{j=1}^k \\tau_{ij}(\\vartheta) \\frac{d}{d\\mu_j} \\log f_{j}(x_i\\ |\\ \\theta_j) \\\\\n", " =& \\sum_{i=1}^n \\tau_{ij}(\\vartheta) \\frac{2(x-\\mu_j)}{2\\sigma_j}\n", "$$\n", "\n", "Wir können mit $2\\sigma_j$ durchmultiplizieren und nach $\\mu_j$ umstellen, dann erhalten wir die geschlossene Formel\n", "\n", "$$\n", "\\mu_j^{(i+1)} = \\frac{\\sum_{i=1}^n \\tau_{ij} x_i }{ \\sum_{i=1}^n \\tau_{ij}}.\n", "$$\n", "\n", "Als nächsten Schritt betrachten wir die Ableitungen nach den $\\sigma_j$:\n", "\n", "$$\n", "\\frac{d}{d\\sigma_j} \\log f_j(x_i) =& -\\frac{1}{\\sigma_j} + \\frac{(x_i-\\mu_j)^2}{\\sigma_j^3} \\\\\n", "\\frac{d}{d\\sigma_j} Q(\\theta, \\theta^{(i)}) =& \\sum_{i=1}^N \\tau_{ij} \\left( \\frac{(x_i-\\mu_j)^2}{\\sigma_j^3} -\\frac{1}{\\sigma_j} \\right)\n", "$$\n", "\n", "Stellt man die Gleichung $0 = \\frac{d}{d\\sigma_j} Q(\\theta, \\theta^{(i)})$ nach $\\sigma_j$ um (durchmultiplizieren mit $\\sigma_j^3$), so ergibt sich\n", "\n", "$${\\left(\\sigma_j^{(i+1)}\\right)}^2 = \\frac{\\sum_{i=1}^N \\tau_{ij}(x_i-\\mu_j)^2}{\\sum_{i=1}^N \\tau_{ij}}$$\n", "\n", "Schließlich können wir analog über die Nullstellen der Ableitung nach $p_j$ die Formel aufstellen, die $p_j$ als über die $x_i$ gemittelte Verantwortlichkeit von $x_i$ für Klasse $j$ darstellt:\n", "\n", "$$\n", "p_j^{(i+1)} = \\frac{\\sum_{i=1}^n \\tau_{ij}}{n}\n", "$$\n", "\n", "Damit sind nun neue Parameter $\\theta^{(i+1)}$ gefunden." ] }, { "cell_type": "markdown", "id": "e715cdac-c429-453a-a083-3d9173dab0de", "metadata": {}, "source": [ "#### Spezialfall k-Means\n", "\n", "Wenn wir $p_j = \\frac{1}{k}$ und $\\Sigma_j = E_d$ festhalten, erhalten wir die Formeln\n", "\n", "$$\n", "\\tau_{ij}(\\theta^{(i)}) = \\frac{f_j\\left(x_i,\\mu_j^{(i)},E_d\\right)}{\\sum_{m=1}^k f_m\\left(x_i,\\mu_m^{(i)},E_d\\right)}\n", "$$\n", "\n", "Ein echter Unterschied zum klassischen k-Means-Verfahren ist, dass wir heute hier mit **soft assignments** (weichen Zuweisungen) gearbeitet haben, d.h. wir haben für jede Mögliche Klasseneinteilung eines Punktes $x_i$ eine Wahrscheinlichkeit $\\tau_{ij}$ bestimmt. Im klassischen k-Means legt man sich aber fest, man macht ein **hard assignment** (feste Zuweisung). Wir können auch einfach $\\widetilde{\\tau_{ij}} := 1$ zuweisen, wenn $\\tau_{ij}$ unter allen $\\tau_{im}$ das größte ist, ansonsten $\\widetilde{\\tau_{ij}} := 0$ setzen. Damit bekommen wir\n", "\n", "$$\n", "\\mu_j^{(i+1)} =& \\frac{\\sum_{i=1}^n \\widetilde{\\tau_{ij}} x_i }{ \\sum_{i=1}^n \\widetilde{\\tau_{ij}}} \\\\\n", " =& \\frac{\\sum_{i=1}^n \\widetilde{\\tau_{ij}} x_i }{n} \\\\\n", " =& \\sum_{i=1, y_i=j}^n \\frac{x_i}{n}\n", "$$\n", "\n", "Das ist genau das arithmetische Mittel der $x_i$, die in Klasse $j$ liegen. Verwendet man stattdessen das soft assignment, ist es ein gewichtetes Mittel der $x_i$, das denjenigen Punkten mit ungewisserer Zuteilung weniger Gewicht gibt- auch eine offensichtliche Optimierung gegenüber klassischem k-Means." ] }, { "cell_type": "markdown", "id": "e3e6e97c-d9b6-4b35-984a-2227bcface8c", "metadata": {}, "source": [ "#### Allgemeinere Modelle implementieren\n", "\n", "Wenn Sie allgemeinere Modelle implementieren wollen als das, was wir hier besprechen, müssen Sie den Teil, in dem explizite geschlossene Formeln für $p_j$, $\\mu_j$, $\\sigma_j$ berechnet werden, entsprechend anpassen. Wir konnten geschlossene Formeln finden, weil $\\log$ von einer Dichte, die mit $e^{(...)}$ geschrieben werden kann, eben besonders einfach ist. Als Faustregel sind also alle Verteilungen ähnlich zu behandeln und können anstelle der Normalverteilung verwendet werden, die auch von dieser Bauart sind. Eine präzise Formulierung wäre, dass alle Verteilungen aus einer sogenannten exponentiellen Familie geeignet sind." ] }, { "cell_type": "markdown", "id": "1f38f6a1-2c08-4ebf-a196-3e8710b20378", "metadata": {}, "source": [ "### Implementierung in Python\n", "\n", "#### Univariate Daten" ] }, { "cell_type": "code", "execution_count": 2, "id": "8bba2c3d-46f3-44bf-9960-d15f3adf65fa", "metadata": {}, "outputs": [], "source": [ "# Variante für univariate Gausssche Mischungen,\n", "# nicht-vektorisiert (für das bessere Verständnis)\n", "\n", "from scipy.stats import norm\n", "\n", "def EM(xs, pis, mus, sigmas):\n", " K = len(pis)\n", " N = xs.shape[0]\n", " \n", " #(E)-Schritt\n", " taus = np.zeros((N,K))\n", " for i in range(N):\n", " reg = 0\n", " for j in range(K):\n", " taus[i,j] = pis[j] * norm.pdf(xs[i],\n", " loc=mus[j],\n", " scale=sigmas[j])\n", " reg += taus[i,j]\n", " for j in range(K):\n", " taus[i,j] /= reg\n", " \n", " #(M)-Schritt\n", " Npis = np.zeros(K)\n", " for j in range(K):\n", " Npis[j] = taus[:,j].sum()\n", " pis = Npis / N\n", "\n", " mus = np.zeros(K)\n", " for j in range(K):\n", " for i in range(N):\n", " mus[j] += taus[i, j] * xs[i]\n", " mus[j] /= Npis[j]\n", "\n", " sigmas = np.zeros(K)\n", " for j in range(K):\n", " for i in range(N):\n", " sigmas[j] += taus[i, j] * ((xs[i]- mus[j])**2)\n", " sigmas[j] /= Npis[j]\n", " sigmas[j] = np.sqrt(sigmas[j])\n", " \n", " ll_new = 0.0\n", " for i in range(N):\n", " s = 0\n", " for j in range(K):\n", " s += pis[j] * norm.pdf(xs[i],\n", " loc=mus[j],\n", " scale=sigmas[j])\n", " # compute new log-likelihood:\n", " ll_new += np.log(s)\n", " \n", " return pis, mus, sigmas, taus, ll_new" ] }, { "cell_type": "markdown", "id": "7c16f899-221f-4e5c-9d16-d930109684bf", "metadata": {}, "source": [ "Wie auch beim k-Means-Verfahren wollen wir nun zugucken, wie sich im Laufe der Iteration der Fit verbessert. Dazu basteln wir erstmal Versuchsdaten:" ] }, { "cell_type": "code", "execution_count": 3, "id": "27a5fd4d-337a-4c69-91ac-a2083b5f56cb", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "np.random.seed(12345)\n", "pi = 1.0/3\n", "real_mu_1, real_sigma_1 = 0, 1.5\n", "real_mu_2, real_sigma_2 = 6, 3.5\n", "component1_sample = norm.rvs(real_mu_1,\n", " real_sigma_1,\n", " int(pi*1500))\n", "component2_sample = norm.rvs(real_mu_2,\n", " real_sigma_2,\n", " int((1-pi)*1500))\n", "mixture_samples = np.concatenate((component1_sample,\n", " component2_sample))\n", "\n", "fig, ax = plt.subplots()\n", "hist = ax.hist(mixture_samples, bins=51,\n", " color='grey', alpha=.5,\n", " label=\"gewichtete Summe\")\n", "bins = hist[1]\n", "ax.hist(component1_sample, alpha=.75, bins=bins,\n", " color='navy', label=\"Komponente 1\")\n", "ax.hist(component2_sample, alpha=.75, bins=bins,\n", " color='gold', label=\"Komponente 2\")\n", "ax.set_xlabel(\"$x$\")\n", "ax.set_ylabel(\"Dichte\")\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "id": "9144677a-6b29-49b9-84a5-8f3f499922c4", "metadata": {}, "outputs": [], "source": [ "# Initiale theta aufstellen:\n", "pis = np.ones(2) + np.random.random(2)\n", "pis /= pis.sum()\n", "mus = np.random.random(2) * 2*np.std(mixture_samples)\\\n", " + np.mean(mixture_samples)\n", "sigmas = np.sqrt(np.random.random(2) + 1)" ] }, { "cell_type": "code", "execution_count": 5, "id": "5da2c828-1efc-434e-9cf6-ce564ccb8bc6", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x720 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Darstellung der echten Parameter vs. die initialen:\n", "fig, ax = plt.subplots(figsize=(10,10))\n", "hist = ax.hist(mixture_samples, bins=51,\n", " density=True,\n", " label=\"Daten\")\n", "xmin, xmax = ax.get_xlim()\n", "norm_pdf_domain = np.linspace(xmin, xmax, 100)\n", "ax.plot(norm_pdf_domain,\n", " pis[0]*norm.pdf(norm_pdf_domain,\n", " mus[0], sigmas[0]) +\n", " pis[1]*norm.pdf(norm_pdf_domain,\n", " mus[1], sigmas[1]),\n", " color='blue',\n", " label=\"Schätzung Mischung\")\n", "ax.vlines(real_mu_1, 0, .2,\n", " color='purple', label=\"wahres $\\mu_1$\")\n", "ax.vlines(real_mu_2, 0, .2,\n", " color='tomato', label=\"wahres $\\mu_2$\")\n", "ax.vlines(mus[0], 0, .2,\n", " color='fuchsia', label=\"$\\mu_1^{(0)}$\")\n", "ax.vlines(mus[1], 0, .2,\n", " color='orange', label=\"$\\mu_2^{(0)}$\")\n", "ax.set_xlabel(\"$x$\")\n", "ax.set_ylabel(\"Dichte\")\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "6538d8da-3ff3-4bbb-898e-49eb3d4b6511", "metadata": {}, "outputs": [ { "data": { "text/html": [ "<video width=\"720\" height=\"720\" controls autoplay loop>\n", " <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAIGZ0eXBNNFYgAAACAE00ViBpc29taXNvMmF2YzEAAAAIZnJlZQADTtttZGF0AAACrgYF//+q\n", "3EXpvebZSLeWLNgg2SPu73gyNjQgLSBjb3JlIDE2MCByMzAxMSBjZGU5YTkzIC0gSC4yNjQvTVBF\n", "Ry00IEFWQyBjb2RlYyAtIENvcHlsZWZ0IDIwMDMtMjAyMCAtIGh0dHA6Ly93d3cudmlkZW9sYW4u\n", "b3JnL3gyNjQuaHRtbCAtIG9wdGlvbnM6IGNhYmFjPTEgcmVmPTMgZGVibG9jaz0xOjA6MCBhbmFs\n", "eXNlPTB4MzoweDExMyBtZT1oZXggc3VibWU9NyBwc3k9MSBwc3lfcmQ9MS4wMDowLjAwIG1peGVk\n", "X3JlZj0xIG1lX3JhbmdlPTE2IGNocm9tYV9tZT0xIHRyZWxsaXM9MSA4eDhkY3Q9MSBjcW09MCBk\n", "ZWFkem9uZT0yMSwxMSBmYXN0X3Bza2lwPTEgY2hyb21hX3FwX29mZnNldD0tMiB0aHJlYWRzPTE4\n", "IGxvb2thaGVhZF90aHJlYWRzPTMgc2xpY2VkX3RocmVhZHM9MCBucj0wIGRlY2ltYXRlPTEgaW50\n", 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matplotlib.animation as animation\n", "from IPython import display as ipydisplay\n", "from sklearn.cluster import KMeans\n", "\n", "def init_theta(samples):\n", " pis = np.ones(2) / 2\n", " mus = np.random.random(2) * 2*np.std(samples)\\\n", " + np.mean(samples)\n", " # a better way would be:\n", " #mus = KMeans(2).fit(samples.reshape(-1,1)).cluster_centers_\n", " sigmas = np.ones(2)\n", " return pis, mus, sigmas\n", "\n", "def em_iteration_draw(run_nr, ax, samples, history):\n", " pis, mus, sigmas, taus = history[run_nr][0:4]\n", " ys = np.zeros_like(samples, dtype=bool)\n", " if(len(taus) == len(samples)):\n", " for i in range(len(samples)):\n", " if(taus[i,1] > 0.5):\n", " ys[i] = 1\n", " ax.clear()\n", " ax.set_ylim(0, 0.2)\n", " ax.hist(samples, bins=51,\n", " density=True, alpha=0.5,\n", " label=\"Daten\")\n", " if(len(taus) == len(samples)):\n", " ax.scatter(samples[ys], np.zeros_like(samples[ys]),\n", " alpha=0.4, c=taus[ys][:,0],\n", " label=\"Als 0 klassifiziert\")\n", " xmin, xmax = ax.get_xlim()\n", " norm_pdf_domain = np.linspace(xmin, xmax, 100)\n", " ax.plot(norm_pdf_domain,\n", " pis[0]*norm.pdf(norm_pdf_domain,\n", " mus[0], sigmas[0]) +\n", " pis[1]*norm.pdf(norm_pdf_domain,\n", " mus[1], sigmas[1]),\n", " color='blue',\n", " label=\"Schätzung Nr. %d\" % (run_nr))\n", " ax.plot(norm_pdf_domain,\n", " pi *norm.pdf(norm_pdf_domain,\n", " real_mu_1, real_sigma_1) +\n", " (1-pi)*norm.pdf(norm_pdf_domain,\n", " real_mu_2, real_sigma_2),\n", " color='red',\n", " label=\"Echte Verteilung\")\n", " ax.set_xlabel(\"$x$\")\n", " ax.set_ylabel(\"Dichte\")\n", " ax.legend()\n", " \n", "def plot_ani(samples, history):\n", " fig, ax = plt.subplots(figsize=(10, 10))\n", " ani = animation.FuncAnimation(fig, em_iteration_draw,\n", " fargs=(ax, samples, history),\n", " interval=1000,\n", " frames=len(history))\n", " video = ani.to_html5_video()\n", " html = ipydisplay.HTML(video)\n", " ipydisplay.display(html)\n", " plt.close()\n", "\n", "\n", "max_iter = 210\n", "tol = 0.01\n", "pis, mus, sigmas = init_theta(mixture_samples)\n", "taus = np.zeros((len(xs), len(pis)))\n", "# record all values in each iteration step for plotting:\n", "history = [(pis, mus, sigmas, taus, 0)]\n", "\n", "for i in range(max_iter):\n", " pis, mus, sigmas = history[-1][0:3]\n", " history += [EM(mixture_samples,\n", " pis,\n", " mus,\n", " sigmas)]\n", " if np.abs(history[-1][-1] - history[-2][-1]) < tol:\n", " break\n", " \n", "plot_ani(mixture_samples, history)" ] }, { "cell_type": "markdown", "id": "32f0608d-777f-400f-84bf-e63603e3b9e3", "metadata": {}, "source": [ "#### Multivariate Daten\n", "\n", "Für den allgemeineren multivariaten Fall mühen wir uns nicht mehr mit der Herleitung ab, sondern lesen direkt den entsprechenden Code:" ] }, { "cell_type": "code", "execution_count": 7, "id": "537343eb-8f22-43f4-ad84-1ee0e32d7289", "metadata": {}, "outputs": [], "source": [ "from scipy.stats import multivariate_normal as mvn\n", "\n", "def EMmulti(xs, pis, mus, sigmas, tol=0.01, max_iter=100):\n", " \"\"\"vectorized E-M for multivariate Gaussian mixtures\"\"\"\n", "\n", " n, d = xs.shape\n", " k = len(pis)\n", "\n", " ll_old = 0.0\n", " for i in range(max_iter):\n", "\n", " # (E)-Schritt\n", " taus = np.zeros((k, n))\n", " for j in range(k):\n", " taus[j, :] = pis[j] * mvn(mus[j], sigmas[j]).pdf(xs)\n", " taus /= taus.sum(axis=0)\n", "\n", " # (M)-Schritt\n", " pis = taus.sum(axis=1)\n", " pis /= n\n", "\n", " mus = np.dot(taus, xs)\n", " mus /= taus.sum(axis=1)[:, None]\n", "\n", " sigmas = np.zeros((k, d, d))\n", " for j in range(k):\n", " xcs = xs - mus[j, :]\n", " sigmas[j] = (taus[j,:,None,None]\\\n", " * np.matmul(xcs[:,:,None],\n", " xcs[:,None,:])).sum(axis=0)\n", " sigmas /= taus.sum(axis=1)[:,None,None]\n", "\n", " ll_new = 0.0\n", " for pi, mu, sigma in zip(pis, mus, sigmas):\n", " ll_new += pi * mvn(mu, sigma).pdf(xs)\n", " ll_new = np.log(ll_new).sum()\n", "\n", " if np.abs(ll_new - ll_old) < tol:\n", " break\n", " ll_old = ll_new\n", "\n", " return ll_new, pis, mus, sigmas" ] }, { "cell_type": "markdown", "id": "df33041f-34b3-4756-a01e-ca6a580df1ee", "metadata": {}, "source": [ "# Anwendungsbeispiele\n", "\n", "## Aufenthaltsorte\n", "\n", "In `data.csv` sind Aufenthaltsorte aufgezeichnet. Die Daten kommen mit der MIT-Lizenz aus [einem Blogpost](https://towardsdatascience.com/simple-gps-data-visualization-using-python-and-open-street-maps-50f992e9b676),\n", "in dem OpenStreetMaps-Einbindung erklärt wird - das ist hier aber nicht erforderlich." ] }, { "cell_type": "code", "execution_count": 8, "id": "928a9666-38bc-4ec6-a296-317e0e04204d", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data = np.genfromtxt(\"data.csv\", delimiter=',')\n", "fig, ax = plt.subplots()\n", "ax.scatter(data[:,0], data[:,1], alpha=0.01)\n", "ax.set_title(\"Zu clusternde Daten\")\n", "ax.set_xlabel(\"latitude\")\n", "ax.set_ylabel(\"longitude\")\n", "ax.plot(np.mean(data[:,0]), np.mean(data[:,1]), marker=\"+\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "b0c983dc-3bb1-438d-a668-7ed541ded978", "metadata": {}, "source": [ "Die Transformation auf Hauptkomponenten ist wenig nützlich bei diesen Daten:" ] }, { "cell_type": "code", "execution_count": 9, "id": "13f1453d-af47-47e2-be96-825a96efeb6f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.decomposition import PCA\n", "\n", "pc = PCA().fit_transform(data)\n", "fig, ax = plt.subplots()\n", "ax.scatter(pc[:,0], pc[:,1], alpha=0.01)\n", "ax.set_title(\"Zu clusternde Daten in Hauptkomponenten\")\n", "ax.plot(np.mean(pc[:,0]), np.mean(pc[:,1]), marker=\"+\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "id": "b1918b28-be78-445b-8028-585358fbe204", "metadata": {}, "outputs": [], "source": [ "np.random.seed(1234321)\n", "pis = np.array([0.2,0.2,0.2,0.2,0.2])\n", "mus = np.random.random((5,2)) + np.mean(data)\n", "sigmas = np.array([np.eye(2)] * 5)\n", "ll_new, pis, mus, sigmas = EMmulti(data, pis, mus, sigmas)" ] }, { "cell_type": "code", "execution_count": 11, "id": "7713d7fb-b66c-4641-b206-71f5814d90d3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ys = np.concatenate([mvn(m, s).rvs(int(p*2000))\n", " for p, m, s in zip(pis, mus, sigmas)])\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(data[:,0],data[:,1],alpha=0.01)\n", "ax.scatter(ys[:,0],ys[:,1],alpha=0.01)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "ef7a3638-b851-4c59-ad9e-d0a4d6f93c2a", "metadata": {}, "source": [ "Eine Interpretation wäre nun, dass wir die längeren Aufenthaltsorte damit identifiziert haben." ] }, { "cell_type": "markdown", "id": "2bd0f4fc-48fb-40c1-9370-e40025a8f23b", "metadata": {}, "source": [ "## Iris-Klassifikation\n", "\n", "Wir werden jetzt die GMM (Gaussian Mixture Model)-Implementierung von Scikit-learn benutzen, um den Iris-Datensatz zu modellieren.\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "4339ab3d-bf7b-47bd-8a94-4872c34c6781", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initialization 0\n", " Iteration 10\n", "Initialization converged: True\n", "converged after 17 steps\n" ] } ], "source": [ "from sklearn.mixture import GaussianMixture\n", "from sklearn.metrics import accuracy_score\n", "from sklearn.datasets import load_iris\n", "x, y = load_iris(return_X_y=True)\n", "k=3\n", "\n", "# Zum Darstellen in Hauptkomponenten transformieren:\n", "xpc = PCA().fit_transform(x)\n", "\n", "# Fit mit E-M-Algorithmus:\n", "gm = GaussianMixture(n_components=k,\n", " random_state=42,\n", " max_iter=100,\n", " init_params='k-means++',\n", " verbose=1).fit(xpc)\n", "if(gm.converged_):\n", " print(\"converged after %d steps\" % gm.n_iter_)\n", "else:\n", " print(\"could not reach convergence\")" ] }, { "cell_type": "markdown", "id": "31e13c11-adb7-458c-9291-84308d388f96", "metadata": {}, "source": [ "Aus dem Gausschen Mischungsmodell können wir auch die individuellen Wahrscheinlichkeiten gewinnen:" ] }, { "cell_type": "code", "execution_count": 13, "id": "d24214e4-8f17-4f86-8198-c2633a3ea968", "metadata": {}, "outputs": [], "source": [ "y_pred = gm.predict(xpc)\n", "y_pred_proba = gm.predict_proba(xpc)\n", "y_pred_maxproba = np.max(y_pred_proba,\n", " axis = 1)" ] }, { "cell_type": "markdown", "id": "d49a3a82-c10a-47a2-8dc5-100a2ca57acf", "metadata": {}, "source": [ "Hier wollen wir einmal die Permutation finden, die die höchste Übereinstimmung mit den tatsächlichen Klassen liefert:" ] }, { "cell_type": "code", "execution_count": 14, "id": "35596a33-7f64-4044-853b-b80e66d4521b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Genauigkeit: 97%\n" ] } ], "source": [ "from itertools import permutations\n", "best_accuracy = 0.0\n", "for permutation in permutations(range(k)):\n", " y_pred_permuted = np.array([permutation[value]\n", " for value in y_pred])\n", " this_accuracy = accuracy_score(y_pred_permuted, y)\n", " if(this_accuracy > best_accuracy):\n", " best_accuracy = this_accuracy\n", " y_pred_bestperm = y_pred_permuted\n", "\n", "print(\"Genauigkeit: %2.f%%\" % (100*best_accuracy))" ] }, { "cell_type": "markdown", "id": "7938a27c-cf7e-4ace-b882-49476c29e74e", "metadata": {}, "source": [ "Und schließlich plotten, wie das Ergebnis aussieht:" ] }, { "cell_type": "code", "execution_count": 15, "id": "ac35d6e6-5523-42c8-b20c-bd361a126861", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ " \n", "# Wir betrachten direkt die Marginalverteilungen\n", "# in den ersten 2 Hauptkomponenten:\n", "mvns = [mvn(mean=mu[:2],\n", " cov=sigma[:2,:2],\n", " allow_singular=True)\n", " for mu, sigma in zip(gm.means_,\n", " gm.covariances_)]\n", "\n", "x_wrongs = xpc[y_pred_bestperm != y]\n", "\n", "fig, ax = plt.subplots(figsize=(8,8))\n", "ax.set_title(\"mixed Gaussian model, sklearn EM-fit\")\n", "xs, ys = np.mgrid[-4:4.1:.2, -2:2.1:.1]\n", "for i in range(k):\n", " zs = mvns[i].pdf(np.dstack((xs, ys)))\n", " ax.contour(xs, ys, zs,\n", " cmap=plt.cm.Oranges, alpha=.7)\n", "ax.scatter(xpc[:,0], xpc[:,1],\n", " c=y_pred_bestperm, vmin=0, vmax=k-1,\n", " label='Daten')\n", "ax.scatter(x_wrongs[:,0], x_wrongs[:,1],\n", " c='red', marker='x',\n", " label='Fehlklassifiziert')\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "313a0545-927b-460a-9194-d9575daf6a28", "metadata": {}, "source": [ "## MNIST\n", "\n", "Auf dem MNIST-Datensatz schauen wir uns an, wie gut GMM funktioniert und wie man damit auch generativ neue Samples einer Klasse generiert." ] }, { "cell_type": "code", "execution_count": 16, "id": "b1461ff7-2482-40d3-b82a-314943d1be0e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "kept 29 of 64 dimensions for 95% of variance \n" ] } ], "source": [ "from sklearn.datasets import load_digits\n", "x,y = load_digits(return_X_y=True)\n", "vargoal = .95 # keep so much of variance\n", "pca = PCA(vargoal)\n", "pca.fit(x)\n", "print(\"kept %d of %d dimensions for %2.f%% of variance \"\n", " % (len(pca.components_), x.shape[1], 100*vargoal))\n", "data = pca.transform(x)" ] }, { "cell_type": "code", "execution_count": 17, "id": "dfde9366-bd91-4e71-82cc-c2123051913c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 100 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_digits(x):\n", " so_many_rows = min(100, len(x)) // 10\n", " fig, ax = plt.subplots(so_many_rows, 10, figsize=(8, 8),\n", " subplot_kw=dict(xticks=[], yticks=[]))\n", " fig.subplots_adjust(hspace=0.05, wspace=0.05)\n", " for i, axi in enumerate(ax.flat):\n", " im = axi.imshow(x[i].reshape(8, 8), cmap='binary')\n", " im.set_clim(0, 16)\n", " plt.show()\n", "\n", "plot_digits(x)" ] }, { "cell_type": "code", "execution_count": 18, "id": "715c78f9-0cb6-4d80-8102-fed54dfd4b8d", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[ 1 11 12 15 24 49 50 62 65 98]\n" ] } ], "source": [ "gm = GaussianMixture(100, random_state=23)\n", "gm.fit(data)\n", "\n", "new_data, new_labels = gm.sample(10)\n", "new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", "plot_digits(new_data_in_old_coordinates)\n", "print(new_labels)" ] }, { "cell_type": "markdown", "id": "a4c47178-d237-4934-a0e8-878c1cfcf0f0", "metadata": {}, "source": [ "Diese neuen Ziffern hat das GMM für uns generiert. Warum aber sind die zugehörigen Label nicht die Ziffern 0--9?\n", "\n", "Weil wir im Training gar nicht versucht haben, pro Ziffer genau eine Normalverteilung in der Mischung zu haben. Mit den hier verwendeten 100 einzelnen Normalverteilungen klappt es aber, neue Ziffern zu generieren. Wenn wir die Klassifikation noch separat laufen lassen (etwa mit SVMs oder auch direkt als latente Variable im E-M-Algorithmus), haben wir ein Modell, mit dem wir auch gezielt neue Ziffern einer bestimmten Klasse generieren können (z.B. gezielt eine $7$).\n", "\n", "Um etwas Einsicht in unser Modell zu gewinnen, schauen wir uns einzelne Mischungskomponenten an:" ] }, { "cell_type": "code", "execution_count": 19, "id": "74e47f30-54f8-43fd-94f5-b280a76f9d07", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(10):\n", " mu = gm.means_[i]\n", " sigma = gm.covariances_[i]\n", " new_data = mvn(mu, sigma).rvs(10)\n", " new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", " plot_digits(new_data_in_old_coordinates)" ] }, { "cell_type": "markdown", "id": "5c54b0b3-c7b7-44da-b20f-d2651e001960", "metadata": {}, "source": [ "Wir sehen also durchaus, dass die Mischungskomponenten innerhalb einer Klasse bleiben, es aber eben verschiedene \"Nullen\" gibt. Wenn wir nur 10 Mischungskomponenten verwenden, sieht das Modell schlechter aus:" ] }, { "cell_type": "code", "execution_count": 20, "id": "c0193b85-cba9-469a-9f5d-9b439fb41ff0", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[0 1 1 1 2 5 6 7 8 9]\n" ] } ], "source": [ "gm = GaussianMixture(10, random_state=23)\n", "gm.fit(data)\n", "\n", "new_data, new_labels = gm.sample(10)\n", "new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", "plot_digits(new_data_in_old_coordinates)\n", "print(new_labels)" ] }, { "cell_type": "markdown", "id": "87c93ec8-9633-4287-9ec3-f7ab23523531", "metadata": {}, "source": [ "Um in unserem Paradigma ohne zusätzliche Algorithmen z.B. eine $7$ zu generieren, können wir direkt auf dem Teildatensatz der $7$er trainieren:" ] }, { "cell_type": "code", "execution_count": 21, "id": "e6e441f7-6d6b-40da-9fbd-f68e3297f459", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gm7 = GaussianMixture(10, random_state=23)\n", "gm7.fit(data[y == 7])\n", "\n", "new_data, new_labels = gm7.sample(10)\n", "new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", "plot_digits(new_data_in_old_coordinates)" ] }, { "cell_type": "markdown", "id": "29437463-22e5-4251-ba8c-2c16fbb623d6", "metadata": {}, "source": [ "## Fashion-MNIST\n", "\n", "Einfach nur weil es geht, gucken wir uns genau das gleiche auf dem Fashion-MNIST-Datensatz an:" ] }, { "cell_type": "code", "execution_count": 22, "id": "3d6e3226-797d-4faa-8db8-0823b48eb61f", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "from itertools import product\n", "from urllib.request import urlretrieve\n", "import gzip\n", "import numpy as np\n", "\n", "filepattern = \"%s-%s-ubyte.gz\"\n", "baseurl = \"http://fashion-mnist.s3-website.eu-central-1.amazonaws.com/\"\n", "\n", "def load_mnist_labels(filename):\n", " with gzip.open(filename, 'rb') as file:\n", " return np.frombuffer(file.read(),\n", " dtype=np.uint8,\n", " offset=8)\n", " \n", "def load_mnist_images(filename):\n", " with gzip.open(filename, 'rb') as file:\n", " return np.frombuffer(file.read(),\n", " dtype=np.uint8,\n", " offset=16).reshape(-1, 784)\n", "\n", "def load_mnist(kind='train'):\n", " labelfilename = filepattern % (kind, \"labels-idx1\")\n", " imagefilename = filepattern % (kind, \"images-idx3\")\n", " urlretrieve(baseurl + labelfilename, \"./\" + labelfilename)\n", " urlretrieve(baseurl + imagefilename, \"./\" + imagefilename)\n", " labels = load_mnist_labels(labelfilename)\n", " images = load_mnist_images(imagefilename)\n", " return images, labels" ] }, { "cell_type": "code", "execution_count": 23, "id": "ab39812c-f04a-4493-8354-7b2858706915", "metadata": {}, "outputs": [], "source": [ "x_train, y_train = load_mnist(kind='train')\n", "#x_test, y_test = load_mnist(kind='t10k')" ] }, { "cell_type": "code", "execution_count": 24, "id": "ee64b034-8898-4581-82bd-450641d9a315", "metadata": {}, "outputs": [], "source": [ "def show_fashion_image(raw_data, ax):\n", " im = ax.imshow(raw_data.reshape(28, 28), cmap='binary')\n", " im.set_clim(0, 16)" ] }, { "cell_type": "markdown", "id": "4df6bba1-62f4-4064-9e66-8d9d154eebb2", "metadata": {}, "source": [ "Wir schauen uns an, wie lange PCA.fit und EM (der gm.fit) auf diesem etwas größeren Datensatz brauchen:" ] }, { "cell_type": "code", "execution_count": 25, "id": "cb13e55c-8cb3-49b5-9aea-dc3415fd424e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6.53 s ± 392 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n" ] }, { "data": { "text/html": [ "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: 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input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>PCA(n_components=0.9)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PCA</label><div class=\"sk-toggleable__content\"><pre>PCA(n_components=0.9)</pre></div></div></div></div></div>" ], "text/plain": [ "PCA(n_components=0.9)" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vargoal = .90\n", "pca = PCA(vargoal)\n", "%timeit pca.fit(x_train)\n", "pca.fit(x_train)" ] }, { "cell_type": "code", "execution_count": 26, "id": "8028a575-a1f0-4751-a7f8-990e2ad3a6ad", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "kept 84 of 784 dimensions for 90% of variance \n" ] } ], "source": [ "print(\"kept %d of %d dimensions for %2.f%% of variance \"\n", " % (len(pca.components_), x_train.shape[1], 100*vargoal))\n", "fashion_data = pca.transform(x_train)" ] }, { "cell_type": "code", "execution_count": 27, "id": "f89f9871-7fdc-4853-bad0-7e438062af76", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 35.4 s, sys: 45.6 s, total: 1min 21s\n", "Wall time: 7.47 s\n" ] }, { "data": { "text/html": [ "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GaussianMixture(n_components=50, random_state=23)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">GaussianMixture</label><div class=\"sk-toggleable__content\"><pre>GaussianMixture(n_components=50, random_state=23)</pre></div></div></div></div></div>" ], "text/plain": [ "GaussianMixture(n_components=50, random_state=23)" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%%time\n", "gm = GaussianMixture(50, random_state=23)\n", "gm.fit(fashion_data[y_train == 1])" ] }, { "cell_type": "code", "execution_count": 28, "id": "7a5855eb-e2ea-481a-8f3f-4c618d155b38", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def draw_gm_sample(gm, pca, n=10):\n", " new_data, new_labels = gm.sample(n)\n", " new_data_in_old_coordinates = pca.inverse_transform(new_data)\n", "\n", " fig, axs = plt.subplots(1, len(new_data),\n", " figsize=(8, 8),\n", " subplot_kw=dict(xticks=[],\n", " yticks=[]))\n", " fig.subplots_adjust(hspace=0.05, wspace=0.05)\n", " for datapoint, ax in zip(new_data, axs):\n", " show_fashion_image(pca.inverse_transform(datapoint), ax)\n", " plt.show()\n", "\n", "draw_gm_sample(gm, pca, n=10)" ] }, { "cell_type": "code", "execution_count": 29, "id": "3ab8baba", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 56.7 s, sys: 13.6 s, total: 1min 10s\n", "Wall time: 6.65 s\n", "CPU times: user 4min 53s, sys: 1min 52s, total: 6min 46s\n", "Wall time: 34 s\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AaDSCYRi88cYbMBgMqK2tRTQa5R2+uBw6dAgOhwM7duwY6ccgKHq9HnPmzBnRtaM6gRKLhGxEFotl9NIJzFB+64GBASQSCZhMJjQ1NY2jVHz+9re/jahoWa1Wo6CgAAaDAbFYLMUCrqqq4inUMyWd6/vDDz/k/VxcXJw2e5g0hwAGDYSzdUpavnx5xjXAzQYkbjpSdN/f34+NGzeOl5jDIpfLwbJsygZPGgEQspEhnm24rtFM4ZSzdZpLZuLEiRkNWYlEgsLCwnGWaGhmz5495CGB4Pf74XQ6odVqYTQaodfrR5TcRRCJRKPKC3jqqafwyCOPYMGCBZgwYQJMJhMSiQQ1Tr1eL3w+X1oFKhKJ0NraOuZwWrZxOBwj3r9GrUDlcjlNgxY6IWQk3HbbbTxlmClAThICjEYjjEbjWctcBAZT0v/pn/5p2O4a3C4pUqmUl5HJZbRJSelobW2lf+uBBx6gj69fvx7Hjx/HDz/8gCNHjkCv16ec5Ej2H3djH03iQLZQKpVU4X/22Wf47LPP8NFHH+H3v/89Nm3ahL6+PnqtSCSCWq2GXq+HVqvFJ598gttvv33cZR4KnU7Hi2+zLEs9QMCgQbB58+azJN2PJLvAuZmu2VibQvHMM8+gtLQUSqUyo3Ih3XLOhfgcMHjyS+cxYVkWgUCAeixI9is5EcrlckFyJQi1tbW4//77EQwGMXnyZCxZsgRXXHEFFi5cSK/hdp3ict5559H951zgySefHPG1o1agpJUUAPznf/7n6CQTgE2bNvEWv9frTftPUqlUmDFjBt38k1uejTf9/f2or68fsVXY0dExIstzrEyaNIl+n3yCmzFjBhYsWIDa2loAg+6h5BO0Wq3m3djFxcVIJBIIh8OC3rhc1q1bh2+++QaNjY1YsWIFVqxYgRtuuAG33nor5s6dC71ez7ueZOACg+voXOGJJ54AAOTl5fEsdlLSQ1qpjTWbMtsMldAUi8VoiZnNZsPnn3/OCwmcTbgbZaa47V//+ldqbJ1NuHWR6fYBsjeTGne5XA6z2Yxly5bhyiuv5JV2CcVbb70Fq9UKlUqF4uJiVFZWoq2tDcFgECaTCcXFxSnGt9VqxcqVK8/6fszlr3/9K7Zs2TKia0d9TCCba1NT07DJOuMF9wQ6GjfF2YZkgg5FJBKB0+mEWCzGxIkT6eNTp04VTK4LLrgg7ePE1eV0OnmuxUyxmKamJhw7dkyQPpbpWL58OViWTenFPHnyZOpWSoff78euXbvGQ8QRQZIyWJZNKXqPx+NntU4uHb29vRl/R5K1wuEwEokEmpqaeFnZZxur1Zq2yQaBmwB3Nqmvr8eVV14JgN+YhEBO+uT0r1AoYDQaUVJSgpKSEmg0Gpx33nmCyed0OmGz2aBQKCCTyagS9fv9NGmM9JnlInQDjbGydevWETUHGpUCJZmBAMbFohkpP//5z+n3YrF4WPfhuZI5vGzZMiiVSp77k5sk0tDQAKfTCaPRiMrKSrz44otUcY7UQhoLN954I+/nhoYGGj+02WxwuVwZ3ckWiwW9vb3o7++nJ8/S0lLBZOVy0UUX4eqrr6YnnPr6evzv//4vgMETMknGSmbBggXjIt9oWLNmDSwWCy666CLe4x6P55xyd6Ujud6WfBUXF59zLt133nkHFoslpfE8YbgM0vHkm2++AfBjeCTZ+CadtYDBoQpz584Fy7Lw+/2Ix+NYu3YtTbbMNkajEb/61a9w4YUXQqVSgWEYzJkzB3K5HHa7PaUUDwDsdvuomyyMF0ePHs24x3EZVRYuVzEJlfk5FgYGBiASieBwOKi/Px2JRAIvv/wyHn300XGWMD0VFRXUAiM3A2k5CAzG9Liuo5qamrOi/EUiEQKBAGQyGQoLC1FQUJCiFGOxGGw2G7xeLyZMmECzGMezrnLDhg24+eabqat2xowZmDJlyrDPmzZt2oiSusaThQsXppQXcDfDc5lky12hUNDEs4cffhhbt24V1AAcDbfccgsvo5QLy7JYu3YtlEolfvvb346zZKlwmym0tLSk3eC5ORNGoxF5eXmIxWJobW2FTCbL6kQhwssvvwy9Xg+fz4ddu3Zh5cqVUKvVOHDgAORyOe3yxfVYkmTUwsJClJSUZF2mM6WzsxMnTpxAVVXVkNeNWYGeiwy3sTidTpw4cWKcpBkZXq83YyyL1KGdDV5//XU0NDRAKpVCp9PRkVlkpFlydmIkEoHH40E8HqeF0+PdlODYsWNYvnw59Ho9HVlFiqIznT6BwaYY3L6j5wLc5AsCiX2di3Wg3HKWZDcddw3LZDI8+eSTZ1WBnjx5Em63GwzDZFSewGCs32Aw4PHHH8fjjz9+VptscE/u/f39tJ1nMkTGcDhMx3MxDAOv1wu1Wi3Iezh8+DAKCgoQiUTgcDggl8uhVqvR3NyMiooKGAwGSKVSxGIxqkRjsRikUinMZvOImxaMJ83NzTh16tSw5Syj3p0ZhkF/fz9uvfVWRCIR5Ofn47XXXhuzoGOlrKxsxFnAwWAQLpcL5eXlePXVV/HUU0+lWPdnC5lMhoKCAuoa594oJSUl8Hg8aG5uRnNzM2KxGORyOYqKilBXV0djktm6KdasWYP169dDoVDgzjvvBDCYfchV8MSlnIxIJEJRURFYlkUwGIRarUZ7ezuMRiO0Wi327t0reO3fE088QU/G7e3tqKmpATC84ffrX/8av/71rwEMGi0jbX4tBL/4xS+wbt06XrybkEgkMGnSJMyaNQv9/f1nQbqRwb230n32P/nJT8ZTHLAsy7tHpk2bhjfffHPYrOtkBUXuzddeew333HNP9gX9O3v37sWiRYtwzz33oK2tDeFwGGvWrEFpaSkmTJiAO++8E0VFRdDpdCnyRaNRtLa2wmq1wmKx4Morr4RGo0FhYSGUSiXmzJmDbdu2ZVXeVatWYcKECQiHw9i2bRumT58Og8GAaDQKlUoFvV5Pw39kPcRiMeTn55+TxiDh9ddfHzbhbdQK1Ov1wul04qabbsK1114LAPjv//5vAIMtnJYtWyZI0sg333yDK664AgCwe/futDehy+VKG7MgTY3Ly8shFot5xcOHDh3CsmXLUobEjhckJkFu8EQiQa0zMpCbYRjMnz8fWq1W0GzAWCyG3t5eunknEgneBpjphM+yLM3CJUOLvV4vrwh9PHrNcjdJnU6HcDhMXclAaoJZNBqF3W6H2Wymbv/nn38eX375JY03jRcajQaff/45Fi1aBJVKhT179sBkMvGMFYVCQQ2EmTNnjqt8Y0UkEiESiSAUCsFms2Hq1KmQSCR49tlnsX37duzatYvGxx5//HE8++yzgsjx2GOP4cMPP4TVasXy5cupkicJROmMUK1Wi87OTp4bLxaLYfr06bjzzjvxxhtvCCLrokWLAAArV65EXl4eNBoNysvLoVKpeMZscpcq0o3t9OnTNA4dCAQQDAZht9uRn5+ftf3j9ttvx1tvvQVgMNSk0WgQDofR0tKCjo4OiMVi1NXVIZFIoLe3FwUFBbzQGndfUSqVZ9VoTce6devw05/+dNhGGqNWoGR6RXJyAzBYQH3s2DH6czbdBZdffvmQCQjRaBT9/f1pr4lGo7w+qCROd9VVV2Hu3LlwOp0oKSkZ94ywdP10SdYicXuJxWKo1epxsdT0ej2vvZ1KpaKxK4ZhEAwGh+1rqVQq4ff7EQqFeNmCmZI0sgl3vRGXElGisVgMbW1tvOtdLhf6+/thtVqhVquh0+mwaNEiXHPNNaiurkZrayu+/vpr/PKXvxRMZrJeo9Eob4P54IMPsHDhwrTNzgGc9X6yI0UsFtMpMi0tLXSCzGOPPYbHHnsMu3btglwup2UPQinQBx54AHfccQc8Hg/q6+tp/1a32w2JRJI2VCISidDZ2UlDACQpTq/X4/XXXxdMgRJmzpw5Kk9ZIpFAMBik+5hOp0MgEADLsvD5fMjPz89a/PzNN9+EUqmEz+dDf38/Jk2aBLFYTLNxDQYDysrK0NfXB6/XS71nBO69GgqFzvoEpGSS+/5mYlQKlGVZ6HQ6qFSqtKnUXMb7A5HL5TRDNXnmn16vR1lZGeLxODZs2EAbBbzyyivYtGkT7r//fqxatUrQsWxVVVVYvXo1qqur0djYiHfeeQf79++Hx+PhuWLITaBUKmksKRAI8BQocd8NFb8ZC+eddx6Kioqg0WhS4iUymSzFZURI/l9zZQeAH374YVwyXQsLC1FfX49YLIa5c+dCKpXC5/NBJpOhpaWFp3Si0ShisRiKiorgcDjgcDjQ2tqK2tpaeuqbNGkSFi1aBL1eL1gtayKRwMmTJ+H1emE2m1FTUwORSEQ7TCXX/DU1NeFXv/qVILIIgVgsRmFhIfX8cO9Nr9eL+vp63HPPPZDJZDRjOtuQsNO8efMADBqupDws3T1EysskEgmN23k8npQZlSaTSRCjm9wvRHm63W40NDSgtLQU+fn5cDqdvLpt4McpPWSuZX5+PoqLi9Hd3Q2FQoHzzjsPPT09WS0h+v7779HY2IjNmzfT+t5bb70VwWAQXV1dEIvFMJlM0Ov1KQeAZNf+UIcjoXSJ2WxOKXkDfhzOEYvFhi2LHPUJVKPRQKPRoKOjg3bpGA8GBgZSCuG5eL1eaLVaxGIx3j+D206qra0tpd7P5/Ph1KlTmDx5MtavXy/YaaOzsxNfffUVVCoVrxG9zWZLMUbILEJSFM09vVmtVkgkEkFOdNu2bcOSJUtS+mySBv1isZi6kIZqwE56JpNrx2v2I6mV5c6Glclk8Hq90Gg0vPVKJrUAg/F0j8eDrq4u5Ofn825u0upPKAV6/PhxKBQKFBUVQSKRIBgM8lrLJSvQ//iP/8AXX3whiCxnysaNG3HdddelnPQB0JgYmeIkl8uhUChQXFwMj8cDvV4vWIw8HA7z1jNZn2SfSCQSvDIL0pQAGFy78Xic11yEnOaESPAzGAz0xEb+vl6vx8yZM+n+p9Fo0rbTJHuz0+mE3+/HqVOn0NHRAYPBAL1eT2d0ZoN0RrPL5aKn+8LCQphMJgQCAfT19UGlUtH2lED6vtQWi2XcSt6A1GxxAsMw8Pl8vKZBmRjVCuB+aPX19eju7sasWbOoAiDusqeffno0f3ZEdHZ2plWgAwMDOHz4MJ0OwP0nAfwEgsbGxrRTVOrr61FeXo4HH3xQUHdduthwf39/StyWjIQiCpR7mrPZbII1uP7222/x85//HDU1NbyF43K5wLIsxGIxwuEwGIZJa5mR5CHSco4wnl1c8vLyeJudQqGgsXFu7Dt5A9DpdKipqaEnJO57yTT2Kht0dXVh9uzZMBgM1PXN7XyT7HI7WwMQRgJJykmeXQkMGjelpaUIBoPwer0wmUxQKBSoqqqC0+mEXC4f0kA+E8hp0mKxQKlU0nGGZJ2EQiFeJyLuKTndCXXLli2YOHGiICejJUuWIBQKwWq18vIjuJ8N2RcyQYZad3V1obe3F+FwGFOmTMHx48dHJINcLueFvIbj4osvhlqthtvtxokTJ2AymZCXlwe9Xg+73Q673Q6GYVBSUsLbm3t7e7F161bU1dXh6NGj+PjjjzF79mwYjUaYzWbcfvvtOHz48IjlOBO+++47vPrqq7j66qsxd+5clJeX0zyUoRizCbVixYqUGW7RaBQDAwOCpKhPmTIFsVgM4XAY3d3d1F2rVCpxySWX8K7lWjckBiMWi7F58+a01nFnZydeeeUV/Nd//VfW5R6OH374AaFQiAbRFQoFKioq4HK5aF0r90adOXMm7HY7otEojEYjbrjhhqzJ0t/fT2ufuIkT3Hl/fr8/5VREXB1k0yfWcWtrK/R6PYxGI44ePYrZs2dnTdZkHn/8cbS0tMBsNvNOcCKRKK1VK5FIaHyrvLwcZWVlacuJHA4Hdu/eLZjc11xzDYDBz5XMqB0YGEBRURHy8/OHPI2eqzz00EMZfycWi3Ho0CGaEDhv3jx8++23aG1tpZ9FtiEZ4m63G4FAAJMnT+b9npzcuCSHSUKhEBQKBYLBIObNm4eJEydmrDc/E3bu3Imnn34a5eXlsNls0Ol0EIlEsFgskMvlUCqVMBgMGQeXd3V1wWq1QqvVYvny5TCZTHSu6e9///sRyTAa5QkAixcvhtlshl6vx913343i4mLIZDLs3r0bbrcbIpEIF110EXQ6HTXME4kEGhsb0dPTg9tuuw0LFizAvffeC2Awg/7EiRNoamrCm2++OSpZxsqSJUuwfPnyUT9v1L1wuZAaI4JCoUBBQQHPhZYtvv/+e4hEIuTl5fHcF+lcGckyisVisCyLmpqalOGvXEa7cLKBxWJJ6w41GAy0JCQZpVJJT60ff/xxVuXx+XywWq0ZXZakf2xyKUskEuFt8GVlZbwYwnCW3Jnyxz/+Eb29vdDr9ZDJZLDZbLTpeqYJEAUFBbT1WDLRaJSetoXG4/HA7XbDZDJRZZ5uRuy5XodNGEqxyOVyMAzDe38mkynr8fxkyHDy5FNjuh64pMifq1QZhqGuXKPRiHg8Lkgi18DAAJqamqgbUSQSQS6Xo7S0lHpEANDxYMnvxeFw8AaCk0OOkHvbli1bMDAwgHg8DpvNRutUFQoFTCYTysrKUk7NYrEYCxcuxLXXXsuTbWBggHYxmjBhAi1FExKSA8FlpMbqqO5I0oeTu6mThQX82HFEiHjRW2+9RRc/tyRCJBLB5XLh9OnTOHDgQMam0B6PBxdeeCFuuummjI0LOjo6si43gIxzMfV6PS2ITqdgZDIZwuEwPB4Pr4NIXl6eIJspSSfv6+vDqVOn0l4jk8mgUCh42bikVMHpdPLWBtcTkK52NNtwS5F6enrQ3t6Ozs7OjO3CtFotqqqqUmSLRqNwOp1wu92Ix+OCz4Ts7e2l8RipVAqVSpVW6f+jKFBu9yeiCAhisRhyuRwdHR3UcKyqqqKDCoRAJBJBo9FAqVTy1mQkEkF3d3fKwYC40LmbPsMwtDGHTqfDoUOHBJN33759cDqd8Pl8VF7i4iZ7F8MwvDXCMAx6enrg8XgglUohFosRiUTQ09OD/v7+tAZZtjhy5AjsdjsikQhOnjyJ5uZmasxOmDABkydPTru/5efnY8aMGfjmm29w5MgRAMCuXbvg9XpRVlYGhUIxLjXDFouF1tsGAgG4XC6cOHFiRG0GR+XClUqlYFkWbrcbarUaEokEpaWlcDgc9B9KXA/Z5u2338aFF16I66+/HtFolNcezGAwDBunCoVCuOyyy7B8+XKsW7cOn332GXp7e9HX14e3334bGo2G1jVlG26njZkzZ2L9+vXQ6/XQ6/U0045Me2cYBn19fbR3KIF7k3u93owZsWdCOBzGZZddlpLM0dvbS61ak8mUspFLJBKqhDo7O2EymaDRaHhJR+ORHLBixQr6fTgchk6ng16vh06nA8uyaQ07cpL3eDw4ffo0SkpKkJ+fj5KSEkSjUeh0OkFLiMjIKa5BEgwG8f3332PatGk8ZXQutc8cik2bNtGMVZZlYbVa0d7ejtraWiiVSlx++eXw+Xyw2+3o6uqC0WgUdLKMVquFz+ejJzi/3089WenqaYkRAwxmwJPG7LFYjJ5M0jW6yBY+nw96vR7Nzc1wOBy8rl9EoWq1Wp73TSKRYOLEiaiursbRo0dhtVpx4sQJmM1mzJ07F6WlpbQbULYhsUNgUNHX1taipKSExnLb2tqwdetWVFVVpa33zMvLo/s3143f1NSEr7/+OuvycrFYLIjFYrx7UKPRUHmGa3046hioUqnkuUEYhoFSqeTNrhQKq9UKjUZD44LJhf6ZYBiGKiCxWIySkhJMnz4d1dXVUCgUUKvVsNvtgs03nT59Orq7u3HppZdi3rx5WLx4McRicVqrLB6P09IbLuQz93g8gpYIJcdVgsEgNViIZTsUZOg6MNhJ6WzVd1VVVaGwsJC6Z202Gy/+nfw+JRIJtFotvZ7b3F/IJhssy0KhUPAUiFqtxvTp06HT6Xg5BkIYpkLw8MMP0+/lcjlqamoQjUZhs9loIpdSqYRcLkckEoFcLodIJBLUzci93yQSCUKhEB2oPhQkG1MqldK1TBqcCEVNTQ2USiW0Wi1CoRCvAiGTe1wsFkMkEtE1olKpYDAYIJfLqdIUKobONUwlEglUKhX1kpFBGcQQ5TbCj0QiUCgUmDNnTooB1draikAgAKPRCIVCIdgJmmTAcw1YIpfP5xv23h+TAiWuvnA4jEgkkhK/4PbFzCYej4fnVonFYrSnZSKRgFwuh0wm47k2IpEI+vr6UmKlZrMZSqUSVVVVMJvNOHbsGDZu3Jh1mQHgpptuwg033IAlS5bwMlKj0Sh6e3uh1Wrp58WybNq6KYLdbudlk2Yb4kokXU0ikQhEIhF0Oh0vJsR1lZMWYvF4HFKplFrJZFHu2bNn3Nq3BYNBNDY2Yu7cubzH29vbeW63eDyO06dPI5FIoLKyEnl5eTS5JBQKwel00u4qZBxTttHr9bR2L3kjJ0lymUIS5zLJreJEIhHNhpbJZDTJpKCggNYck/hZXV1d1hv7c/tNsywLlUoFq9WKUCiE6upqhMPhjPWc3BpsrgIWEpIUWVlZSV2jXIVNymiSCYfDOHjwIIqKimA2m1FQUACbzQa/3y+oEfjOO+/gZz/7GZ33yQ3zKBQKRKNR6iUkBkBfXx92796NSy65hL635uZm1NbWwuv1Yvfu3Zg/fz7OP/98PPfcc3jkkUcEkT05fON0OtHa2oqCggJh6kAB0DiZXq/nKU+GYdDW1ibYyKLNmzfj0UcfpYlAJBPNaDTyNiDuqUehUFA3Kan9ksvlmDx5MrWGSLD7sssuy7rLQC6XY9myZbzHAoEAIpEIEokEKioqUhoWcG8On88Hm81GC6crKiqGTZw6E/r6+gAMKiJSnkRqThmGwf79+1NioKFQCA6HA6WlpSgvLwfLsti5cycuvPBCAOPb+1StVqe4XWw2G2prazF9+nRapiSVSmmCQvJNolKp0N7eDrfbjZ07dwo293ZgYICOipNIJJgyZQqvXSPLsjQ29I8K8UiIRCJMnjyZnui7urpgNptRVFSEaDRKE6luu+02/O53v8uqDF1dXZgxYwbPuOaeKBOJBE+BklOTRCLhNSwYGBig921JSQmuu+46fPrpp1mVlXh6gB9DU0T5sSwLhmFgsVjSGtHkgEH2uXg8jv7+fuj1epSUlODaa6/F559/nlV5gcEY6EcffYSLLroISqUSnZ2d8Hq91G0skUholziiG5RKZUoYqq+vD0ajEVKpFFdccQWKiorg9/uzvh64dHZ20vuvpqYGBoNhVPkaY/K5EpdTclu3dJlh2YQ0SCaQyR/J1nsmBU5OxgzDpPRirKioEGTGaboaSOK2Iyc6rouZa92SmEtyXaOQ7Nq1C36/P+3JRyaTQa/Xo6CggFe7yrIszz1ETqTpGA+XbvIJwWQywWAw8AwT7v8/EAjA4/Hw1o3RaIREIhE07mg2mzFp0iSYzWbk5eWl1NcmNwD4RyQej8PpdMJut9PEHKlUCrlcTk8jnZ2d6OnpoeGZbEPc4IlEgn6+3FO/WCxOSYpLt4ck96IVIm67ePFi2O123olRq9XSwwLLsigoKEi7r8jlchiNRtqXOi8vj54CFQoF1qxZI1hTE7VajdraWtTV1UGn01FPFOlaV1xczGvQQhKICMFgkDaw0Gq19GCmUqkEbbHqdrtpO8+xtBQc0wk0OcHF7XbThuLE9SQUbW1tWLBgAXUvcjdycnrixrei0SgCgQDNwgMGFZPP50M4HIbf70dhYeGQ5S1nQrrEFa4b2uFwIBQK8W5st9tNs9hI79BMrFy5MqulLJs3b8aNN94IvV6fdhYed9ETSGyUNGaPxWKorq7mdVMRGu6mlxyfGi5u293dTa1Q4volLQ3b29sFkRcYdO0XFRXRzSKRSNCTA+mOw+2eNG/ePKxZswb33XefYDJlg+eeew6PPfYYgB+bnHNjWGSzJZDOSo888oggsS7SmITUMJN9gFu3zL3HSMwzGAzC7/dDIpHQhulEGfl8Pp4xny0WL16MgwcPwmKx4Nprr+V5f+RyOZ2hmY6ioiJotVo4HA5oNBqYzWbIZDKoVCqo1Wpcc801mDhxoiBK9NJLL4VCocA111wDh8MBj8eD/Px8aLXatP2zuUmgR48epUle6e5dIRvN2+12uFyulHmlhOG8qaPe3WKxGDweD89S9Hq9kMlkgnZsIXR0dMDlcsHv90MqlfIUqEKhQH5+Pu/ERmqhgsEgZDIZZDIZlEolHaVjNpvR1dWFHTt24H/+538Ekfn48eOYPn16WuuGlORwT5YFBQUZO+A4HA5IJBL6vj/66KOsnlJMJhNuvPFGHDhwAN3d3dDpdMP2PVYoFLRrCgnAC5mlOBxkg7HZbAgEAmnLUKLRKHp6eiASiXDeeeel/N7r9aK5uVmw0iYAtPer2+1Gd3c3IpEIb95qUVFRyhSbSy+9FAUFBed0bDR5tirX2A6FQujp6eE1MygpKaHv84knnsi6PH/+85+xYcMGBAIBMAxD9wmSYMPNFudCTnIMw8Bms1GPEWmoIERS17PPPov77rsPRUVF6OjogNFohFgshsPhoDHjdCQSCUilUrqvJRIJhMNh6PV63j4ybdq0rMsM8I1UbsLWcMMnbDYbJBIJZs+eTT1EsVgMjY2NKC8vx44dO0bcQWm0FBcX47LLLqOeH+6pftu2baisrKT7WiZG7cJNl5Uol8sFTUPn0tbWBo/Hg0gkkmIdaDSatFl1pH6LNDlPjnmR5COhkgOIsvP5fPB4PCNyc2e6UZRKpaCt8cj/MS8vD36/H3a7nRZij0Ruh8ORkuEqZA1aOgoLC3H69Gl0dHSgr68vbSo6ObGme0+xWAx+vx/BYFDQRgokOYmc4IlrU6lUZrR8DQYD7rjjDsFkygZDJV1FIhHe/hGNRlFUVEQ9QMOVDYyF7777DgqFgp6Eue7jYDCIeDzOM0LTNYwhWaNchDoZRSIRGAwG3gBqsjclEgnE4/GUjmDJCS9isRgMw6Tsy01NTYLIzN13SRYu97XJhKfkQR+nT58GwB8SH4lEMDAwAIvFwpvulW0uuOACKnvynupyueipfyhGrUCJG4EsqIGBAZSUlFAlQT4Qofjkk09ob9bkeGC6+GA8HqeuUJJB7HK5cODAATQ0NMDr9VJL5G9/+1vW5Z0+fTrKysogEonQ0dGB+vp6WiQ9lGIhDSkGBgbg9/tp0XlyJ6ZsQ2J+pB5SLpfT0hpygyYSiYyyHzp0CC0tLfRnp9PJ+3m8+Oqrr2CxWGjJQjIymQwVFRW8ZAyPx4PNmzdjy5YtNIYk5BxTsgGTeNCcOXMwY8YMTJ48Oe1cW4Zh4Pf7sXbt2rTv6VwhWQF5vV7aYEOpVNITaSQSQVNTE2bNmoW6ujrB5LHb7VAoFPRUxg2hkLaYyZC5xwSVSoVAIACfz4d4PC5oyZ5KpcLSpUthMploCKSkpAQKhQKBQACdnZ1oa2vj3YOkxSmXcDgMlUqFWCyGzs5OfPHFF4J9ztyEIJVKBZPJRJUiwzBobm6GzWZLUaDcRjwEjUaDGTNmQKlU4quvvhJEXoDf8AMYzNR3Op3wer2oqqpCZWXlsN69MQWoysvLIRKJIJFIUix4oZv/2mw22povGAwiHA7TobjpUrslEgmNY5B6xtLSUhQUFEAikUAul6O5uRn9/f2CtOY6ceIEgEGlYzQaYTAYRjxJRa/X0xhuun+kzWbDzTffnFV5CZFIhLovSEeeTFY6wzBwuVxQKpVYunRpSsr92ahfrKqqwoQJE6h7kMTMh0Kn0+Giiy6CRCKBWq2GUqkclzmmAFK6UTmdzpTmE1KplOdS4g5KGG8+/vhjXH/99Wlf/4UXXsBtt90G4Mf6WgA0E5MYgMQrNNKi9TOFuDm5qNXqFG+PSCSisUQCdx34fD44HA7B3PuvvPIKfvKTn2Dq1Kno6uqCTqejiTnERev1enmnI5LUSZKxSOkQMLhuqqqqoFarYTabM04hGStTp07N6KoNhULwer1IJBIpE2yUSmXKXOm+vj7aFrCyslJQ7xXDMGhtbaWZ1hKJhCY6ZZrDm8yYzKhMNy3DMILGjAharRYajQZSqRQul4tn4SZDNiW3242+vj56HRmvAwy6cVpbW1NiN9nC7XZDLBYjPz9/2A5CiUSCZxFncsX4/X54PJ6s18wBgxtEcks+YnGTgm3uGiBJWQzD8JQnwzDQaDQjXoxnyqOPPkq/r6ysRGlpKZ1FSdrzDQXLsrSGjrRRFDrrGRh0F3E3tXg8nvZUlM6tK+T0oKG4/vrrM/5u0aJFaR+PxWK0nzWB+/kKPSQ83b41VJKbXC5P26eauPeF5OTJkwAGjeR0yUparZZncJEevQqFgjbNTz4ly2SyrCtPADh16lTGe4tkDms0Gl4uRabB3j09PXA4HIjFYtBqtYImEPX19eHjjz+mhhJZn6NhTCdQEngno4mIrz4UCtETl5Bwa7PcbjdN1c5EXl4e8vLyMs7Rmz17Nqqrq8EwTNabswM/xkDz8/Op0vN4PAgEAggGg6iqqqLxDFICQhpa+/1++Hw+XuYd6UwyefJk2vYvW9TV1cFms6Gjo4MmAg3Xyk6lUqGioiJlsff19Q2ZQZxtXnzxRfzpT38CAMyZMyfl91yllEgkaCcrhmFou7mqqiraAnD//v2CDEbgcvr0afT29kIikVDXZqZON+FwGN988w36+vogFovP2VhopqQPbqY7y7KIRCJ0qHFvb29KA4ZsI5VK6RoIBAIIhUJDumLJKZRhGOTn59NJOSS5TkhOnDiBdevW4ejRo3A4HGmrG5JlVygUMJvN9LTsdDrp7FVgsOWeUEyYMAEbNmxATU0NCgsLodVqYTAY6N7LTSQDBtfyvn37IJVKMX/+fDAMg23btiEajaKwsJAmOwnplSCNc7Zu3YpVq1Zh0qRJKUlXwzGmEyix2tRqNYqLi+nJqri4eFwsdi6k3ZLX60U0GoXf789o3bAsm5JkZLVa4fP5cOTIETz//POCyEhiqySGWFRUhOrqakyfPh3Lli3DjBkzeJZwNBpFMBhEIpGATqfjGQxerxcffPABtm/fTh8bbj7gaHjggQdQWVmZklCVSCQQi8UQCATg9XpTynPEYjEvEN/S0pLSGvFsuRs9Hg9cLlfKqc7v99Nm/vn5+aiurkZVVRVVXk6nU/BGBjU1NSgtLU2JtWbKfFar1XSWppDj4cbKlVdeiXnz5vEeI/claSASj8fR19dHY3Q2mw0ymYzXAlAISLKIxWKB1+sFy7LD1p0qlUqIxWJac15UVIS5c+dix44dgsq6a9cuFBQUYN68edQY5CZgkVKnodDpdGhubsaxY8fQ2NhIjUsh8Pv9WL9+PQKBAGKx2PDlH1Ipr7sZ+d9ccMEFWLhwIVX6vb29gsl81113ARj0Vl1wwQVYunQpDAYDnQ+b7IlLx5gj4SSQns4KEhruP4e4CEh2cCAQyLiwuJPmgR9LFUicTqgEKFIeE4vF6OmClCmQeEWynOTzTTd+qa+vjxefaWhoyIqcUqkUl1xyCWQyGfLy8ujnGAqF6A1LEqCGc63s3Llz2BR2IUjn0nY4HAgEAjzDSiQS8SaFqFSqlHgnGQQsNKQXLJd0JyOxWAyTyYSJEydiwoQJKXNwzyYqlQqrVq3CQw89xEvMYlkWXq8XVquVelzC4TCvRtjpdNIh10LhdDppuYrL5Rrx65FxiGTtqFQqaDQawT1txPPBbSpA6taDwSDtNkQgpTbkxAwM3s+hUIgqAjLjVCj27dtHSwWH6zEskUhSMnWVSqWgPYaTIbOUVSoVr9QtEAigv7+feleHYtQu3GAwSAuMy8rKIJPJ4Ha7aVp1piLfbEKy6mQyGe+Nk2B1phuDtPIibjsSqC4tLcWSJUsEk/fbb78FMLLOJWKxGHq9PuUEePz4ccjlckyaNAn/9m//xvsdt9j+THj//fcRCoXQ29uL+fPnU7c8V+50Ltl4PE4D/xKJBNu3b8cXX3yBu+++m14jRH1fOqZOnZpi/ZKTJzfpgiSdcctGSMJCMBjEli1baJ2mkLS2tuKrr76Cx+PBXXfdRbPc8/LyaPYzQalU8lx5559/Pvx+vyDZ46Pl+eefx+rVq9Oe6MgoLu4pm5u4c+zYMfj9/rT1uNmira2NGqyxWAz5+fkj6npE/gekP3JZWRm0Wq1ggye4NDU1QaVSQSKRIBaLwWQy8RLLuHuEWCymJ6fe3l7U1dVBoVBgwYIF9Jqbb74Z7733nqAyk9IQYLBmX6PRQKVS8VoUEnnVajW9Nx0OB88ob2trE7yig0x++fLLL3H33XfT9UfqaJNlTseoFSg5anNPn2TDSiQS42JBkP6KyW9Oq9XS+Gw6uAsuGo3yBlOXlZXhl7/8JdavXy+IzGSqA3ltUjCffEoj2c3JpOsA9PTTT9Mp89nIyJw3bx51XQCDsVbSuYX8bTIXMblwmoy6SyQSKCoqwtKlS3l/+w9/+MMZyXYmEHdo8ufD7YcqEol4HWqSN3yhMBqNqKmpgd/vh1arpQlaLMtCLBYPa8n/+7//OzQaDV566SXe4w899BBcLhdqa2vx5JNPnrGc27Zty3jiXblyJY0fpUMul9P5lMRDRax7hUKBW265RfB5sbNmzaLDvL1e77DNQQikmQIA3uFAqIEOq1evRl1dHcrLyxEMBlFeXp6xJpyLWCyGVqulI8vSbfxXXXWVoAr0/vvvp9/7/X5qkEaj0ZTTJhlQwZ3xzD0IuN3utJ3QsgXRWVKpFDfccAMvuYrMfM00MYvLmBQoKfhOtoAylZJki4svvhhXXHFFRgUK8DdFAneUGYFYoVzWrFkjmALt7u5GXl4eLashrazMZvOY2t11dnbiqaeeogoUAL7++mtcddVVI/4b6eIUJKOZuD2BwRMZt/F28ug60leUKNDi4mIsXLhw1O9JKPLz89MaJsQITGd8FBQUjMsQcL1ej+rqagSDQWr5krBEuhBJMkVFRXjxxRfx4osv8hRUtlm2bFna9XLllVfi4osvRnFxcdrNhqwN0pKNxMjq6+upW5240oRCr9dT7wMxSIYzTIajtLQUDz74IGbOnIl7770XwKABOtYyvq+++irl3j1w4MCIlCcAmt2sUqloW8pkFi9ejFtvvRWbNm0ak4xDceedd+Jf/uVfAID28o3H4wiHw2AYJsWtS+YLcykpKUF3dzdNsJwxYwbuvfferCU/pVu/gUAAe/bsgdPpxOHDh1FTU5Mya3UoRKOZnCISiewAhM01zw5VLMuagX88mf+B5AVyMo8XOZnHh380mXP73PhAP+dkRqVAc+TIkSNHjhyDCJf2liNHjhw5cvx/TE6B5siRI0eOHGMgp0Bz5MiRI0eOMZBToDly5MiRI8cYyCnQHDly5MiRYwzkFGiOHDly5MgxBnIKNEeOHDly5BgDOQWaI0eOHDlyjIGcAs2RI0eOHDnGwP8DtqAXlVOoaOoAAAAASUVORK5CYII=\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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7UHIPc+DjooDc3AzJJZBiAbIutFotPvOZz6C2thZmsxknT54sqvq1EIaHh/HQQw+hpaUFCxcuhEgkogqTFFixN5/f76eWJUE2m0UsFuMcRhaLhd77Sy+9FF1dXdi2bVvZ8uZCIBAgHo9zQs6BQAB6vZ4eorlGAPBx3qgQTCYTurq6CnpW5WLhwoVQq9XUSwiHw7TNqRTIZDK0tbXB5/PhO9/5TkVlFQgEuOKKK/CrX/2KftaCBQvQ0tICvV4/ZYuIUCjknG9sbNiwAQqFAmvWrIHVasXu3bsrJnNDQwPn/xMTEzhx4gReeeUV2O12znPsM0MgEJAqcygUCloMSNYKSZUMDw/PynomGB8fRyqVQiqVQnd395RGCrnHBLkRokp7yrk1Em63G36/n+N8kXYchmEgk8kqr0DJRavVahoGIfjKV76CtWvXYvfu3XjggQfw2GOPFfv2+OIXv1jwue3bt2NoaIjT75hOpzExMTGl1+v3+zE2NsbxUPm8kSNHjhQt70xx3XXXwel04vDhw3juuefg9/shFovR1tbG6ZcFJr0KlUpFlcPatWvR1dWFVatW4eKLL+aEJXt6enDy5MlpQw1TwWQy4dixY3l5EiKLw+Ggi40o7Fxvn+Tj+A4liUQCv9+PM2fOTBnSKQW///3vEYlEkM1m8dprr9FDZc2aNbRSsr+/H3a7Pc8iFgqFea05BoMBFouFHjinTp2qeEpiZGQEQqEQ69evp7n4ZDKJ8fFx+pqJiQlEIpG8+xkKheBwOAoeTH6/H6Ojo7MWjWlpaeEYT2q1GolEAn6/H8Ck0i+Uwy0EhmHQ29tbSTE5+PKXv4zjx4/TNpb6+nrU1taipqYGNpuNN6dIioZmgk9/+tMVkzW3N5IUaG3fvp2jXNm9uABo8VY2m4VarYZUKqWRrVQqhUAggMHBQbS0tOCJJ56Ax+PBT37yk4rJTdDQ0ECdltWrV0MqlSKbzSIYDOaFT0lbIcMw8Hg86Onpoc+RyuZKQiAQcDx8k8mE2tpa2moDgLZWzZs3L+9s4ENFmYja29vp7z/4wQ+wbdu2vBLsQviv//ov9PX1FcytXX755bj++uuxYsUKBAIB6k2QHGyhytZsNotIJAKv14tIJELDN2fPni3y6srD4cOHceTIEdjtdrS3t1MlKJfLS6rKBSYPy4mJCfj9/rKsNbKASH9lLpRKJe2VI0UguSB9iIXg8XgQDAZLvtZCsNvt8Pl8yGQyaGtr410/pHx+JpERlUpF+1+BwnnTcnDzzTfnkV4IhUJOtSEJ3bLvNbt9ha3EEokEvF4vbDYbYrEYLXyZLcjlcuod63Q6aDQaCIVCGp3I9fSJ7IUiQQKBoGilWwxI5X00Gs1LG5AK61wFSvL4BLnGVyWLyqaDXq/nVD5PTEzkFcuR8C47FUH2qlgspv3LZF0bDAb88Ic/5DWay0U2m+UYH9lsFm63O88gIRXD4XAYsViMpoASiQTvvqtE0ROfoyWVSiGRSEoyOsur8cekpaDT6aBQKDgVlePj43juuedmvNC+//3vY8WKFThx4kTecwMDAxgdHeU0RQOTOVESDi2EbDYLj8eDiYkJyOVyRKNRqnRCoRC6urrw05/+FBs3bsTWrVvxla98ZVaKoNatW4e77rqLFrqwkVudVghsxplIJIIXXniB5lNLgUKhQCwWw9mzZ6HT6RAIBOg9ZSM3DyiXy/NCi2zFmEgkMDY2hoGBAcjlcsyZMweZTIYWFVUSWq0WWq0WEomE9p+NjY2hsbERTqcTTqcTS5YsoQqGDx6PB3q9nrZYEPh8PiiVSuzYsQO//vWvKybz66+/DmCyhWfjxo0wGo1UUfr9fhpezG0ZIcQlAKghKJPJkE6nEQwGYbVasXHjRqTT6YpXK7KhVqvR19eHTCaDBQsWUAIHn89HexcJGIZBMBjktAIJhUKkUilIpVLodDoolcqye2ynwr59+/DTn/6U9zmdTodEIsExSAQCAfWOjEYj9erZdQYOh4PjHJRbxJeLwcFBHDt2DBs3buR4TcePH8fAwADmzZvHMZoFAkFeexFJv5Dn+OocKtklQZBKpeDz+aiTIBaL4fF48vLFxBAk3mlNTQ1NETY1NXGYmB555JGKtd2w3zcSiVC9ZbVaUVNTA7VaPeNOibIUaDweRzweR01NTZ5X0tDQgNtuuw233XbbjLyjmpoazsYDgK997Wt0Uba3t9OeIYlEgrGxMfh8PjQ2NtIQKB+jhVAopDR1JDzX3t7OUfa//e1v8dvf/hbAJJPJY489hk996lO8fYXlYOPGjQAmGVECgQCEQiFWrVrFqZxjg3gb0WgULpcLcrkcDQ0NNIwaj8dhsViQSCQ4pd4zxZ49e/D000+jvr4ep06dwsDAAOx2O6dJnoRjiJIPhUKQSCRTtgUQmrpVq1bxUhc+88wz6O3tRSqVKniwFcKPf/xjvPbaa7j++utx0UUXYfXq1ZSZqb29Hb29vdSStFgsdG2QQpVcRCIRyqSVi56eHggEAvzsZz+rqAIFJpXoZz/7Wc7eINGV8fHxvFwYAMr0olQq4XK5qAKVSCRQKpXQ6/UQCAQIBAIVDSvyYf78+eju7kY8HqdeDjl8RkdHOa8lhS2EKtLv91MvPxKJQKlU4v333581Wffv309/J/eMRC2IEsw9e7RaLRQKBSQSCSKRCIaGhiAWi9HY2Aij0Yi2tjbYbDY4nU6sWLECL730UkVlbmtroxE90vEgk8nQ1dWFFStWAMCUhnM0GoXT6aQhYalUCq/Xi5qamormFvnoQxmGgVwuRzAYpMY3IU5hQ6FQQCwW84ZKFQoFJ4pyyy23VEzm+fPn44EHHsAFF1xA+9+BSccglUpRhZ5rUPOhLAWaTCYpvdVUeP755/GFL3xhytfkWq18sNvt8Pv9WLJkyZRhWzYEAgE0Gg0tSZ7OY1u/fj3EYjGOHDlS9kLz+Xyc/CaxCE+fPk2LiNhyspFMJpFOp2k4w+/3Q61W03tDng8Gg7Db7XjqqaeKli+RSODaa6/Fu+++i5GREfj9fgwODkKpVEKlUnF6fUmOk12swAdSxaZSqQpGBq677jr6e7EK9Atf+AI2b96MlStX0uIfkUiEaDSKUChEe84I2Mqb73sn95GA5JZkMhkYhoHFYpkyNF0ONBpNXvRBJpPxhkAJyPWxw2QSiQQ6nY7uh9kMh37wwQe0mrGxsREOhwNqtRparZaGwnIPRHIQiUQiyGQyaDQa2g9NzpDZlJkNiURCCUnY32vuemavcRJdI60twGSoPxqN4oUXXkA0Gi2L4jEXRMkTZDIZjI+PY+7cuTOKNmUyGdoHSqJWxNN2u90YHx/HwoULZxz5mgq5OVuPxwOj0QidToeRkREolcqCSjK3UhjgRtlma99ZrVb09vZiw4YNnM/T6/X0/CK9v9OFdYtWoPF4HC6XC83NzbT/0ul0wm63I5lMwu12QyQS0XL6X/7yl3jggQeK+gyBQIBt27Zhy5YtuOGGG+jjTU1NtAiFVN8Ck0UZdrsda9euzcu1CIVCqsTi8Tivl8owDB5++GF897vfpYdyJXIcer0eb731Fnbs2IGhoSGat7jiiitomNTtducZAtlsFvF4HFqtFkqlksMCJJPJKG1iJpPBrl278Pzzz8+40piNzZs3Qy6Xo6mpiZbr/+lPf8LSpUuxY8cOJJNJiEQiqFQqpFIphMNhXs+TrfzHxsag0+k4vJJvvPEGli5dinQ6jVOnTuGqq64CwJ+PmA7t7e1YtGgRstkszpw5g9HRUVx++eU0PEUiC4cPH6ZtOCRywZcDFYlEiMfjlCaSPbBg3bp1s9ozd/3110MqleLIkSOIx+PYuHEj/T5Izq2QBZxOpxGNRpFMJmm1KFlHle5NZGPNmjXUqGLnPn0+H2pra5HNZjlFbqSPUiAQwOv1wmAwcKI/Uqm0oqHPQmCTTySTSZhMJuqVFWLDIaitreX16M1mM5YsWVISLedUkMlkSCaTGBgYwMKFC6FSqdDV1UXXIlFSuSDXGI/HaWV0T08P5bEmfLRutxsvvvgihoeHy66IX7JkCSVNePXVV1FbW0tlUygUGB8fh0QiyWMjK4QTJ05Ao9FwqERnAwqFAk1NTfB4POjv74dQKMzrwkin03mRiVwUrUBTqRTdqFKplIb7yKFPGqsJSr0RTz75JJ588kmOAiWf43a7odfrqfXS0NBANyXh5CRgH4Ds3N6LL74IuVyOVatWwWKx4NZbb8Wtt95Kn2d7h+Vgy5YteWEOtmVFKkjZGzidTlMFCkyGH0kjdSQSgcvloh7p2bNnS1KeBPF4HM3Nzdi8eTMuuOACJJNJ6HQ6iMVi9PX1IZ1OY8WKFRCLxTRPlEgkCnpJpAiHja6uLhqSZBsvU3lahSCXy+Hz+aBWq9HR0UHvCzA5mYFwqWq1WsqLSwi6+ZShQqHAvHnzEA6H4fF4aC8jm7dztpQoWb8XXHABbQchClOtViMUChW8R0qlknp9uVzO3/ve92ZFXj6kUin62WNjY9BqtRwFybbwM5kMvF4vp28VAH7+85/Pupy/+93v8I1vfAMKhYJD+elyuWA0Gme8351OJ7xeL+2r/NKXvgQAuPbaa/Hcc8+VLafb7YbJZIJYLOYUPJEQrkAggMfjoUQrBAzDUC5wtVoNlUqFuro6eL1ehEIhZDIZui8XLlwIu92OUCiEZcuWUXKaUmC1Wim95CWXXILh4WGax2ffU1JnUAjZbDav0Imgu7u7ZPkK4a677sKdd94Jo9HIMUaSySTC4TAMBgPEYvG07YFFVeEST4jPKi40lil3hEy5EAqF6O3thc1mowUpJP+STqdnXDV55swZHDx4EO+9915F5ZsJRCIRvF4vhoaGKHNL7mbIDYubTCZahONwOODz+aBQKGgYr5xGaZPJhPb2djqVgBA0kBw3AGq9x2IxeL1eeL1e3vfi81DZxQtNTU0IBoNwOByQy+V48cUXi5b3wIEDtA+ZfVgPDQ3R39nGklarLXhIEmNGrVbTYgsSvgVQ1uGSa/xNBbVanddqNRV9olwup/stEonkMRZ9ErBarRz54vH4tMMcUqkUPB4PpXUEZueAzMWbb75J1wc74kNys7lnGultzgXJkeXmeWfabTAd2JEHtmdLImvEgUkkEhzDmTA65eb5SV7cbrfD4/HQ84LdmVAurrzySgwODkKtVqO2thaDg4M4deoU5zVutxs2m43X2CdTmxiGgV6v54R7Q6EQHnnkkbJl5ANfUWEgEIDf76dyTltMxObXnO5n1apVTCgUYkZGRhiCVCpFfz958iQzMjLCjI2NMUNDQwzDMIzL5WJaW1sZAEX/FEI6nWai0SgTiUSYdDrNMAzDZDIZZu/evUxfXx+zYsUKhi1zsUgmkyXJm/uj1+vz3tvn89HfvV4v/X3lypUMkTedTjPDw8MceRiGYfx+P/PGG28wd999N3PPPfcwu3btYn76058yf/vb3xiGYUqS8dJLL2W+/e1vM9dddx3T1NTEXHrppcxtt93GHD9+nH5+X18fE4lE6P8dDgdz+vRpBsAHDMPgI9k5GBwcZA4cOMAcO3aMcbvdTCaToc+dOHGCeffdd+n/y1kTDoeD8Xg89B4RjI6OMlarlRkfH+c8TmSebl309/eTayz557e//e201/KjH/2IfuahQ4eY8fFxzp4qRmaGYZivfe1rFVm7AJh7772X9/HTp08zTqeTiUajDMMwTDAYZFwuV1EyP/PMM8yf/vQn5qWXXqqYvFP9CAQC5v7772c++OCDgveOLXM6nWbcbjfDMJP7r7+/n/PaY8eOMWfPnmUYhmH27t1bMTlzMTAwwBw6dIhX3sWLFzPMR+dcV1cX4/f789YOG16vlxkcHGROnDjBrFixoqL3t729nXnkkUfoZ/n9fqa3t5c5d+4cMzAwQD+/s7OTYVjrIhQK8cqayWSYiYkJ5te//nXF761UKqX3dGBggOnr62NGR0cL3jeyLvh+ig7hqtVq2gNGkuekWkyv16OxsZGjtU0mU8US7MFgEIlEAmazmVpnLpcLZrMZQqEQl1xyCQB+q4FhGBqumS4RX6nkNV/8XKvVUuYLqVRKPT122JmEEEmTMeHMZRgGbW1tNAowd+5cZLPZslhn3nzzTfzlL3+B0+nENddcg2g0Sr1iUu5NrHQCk8nE8fxIfpHcV1L8tGDBAhoCCQaDSKVSMBqN6OjooJ7K//zP/xQl70MPPYTvfve7CAQCyGQyqK2tpcPViSzApKebzWanzbMWGlrc0NBA201KxUyo6W6++Wb6u1KpnBH7CRuBQABKpRKpVIr2BVcKP/7xj3kfX7p0Kf785z/TwsCp6NgK5RbZhWSfBLZu3YrNmzfTEL/dbsfo6Ci6urp4SUiIN0dIL3IjK/Pnz6fe3vr16ysq69DQEORyOerr69Hc3Ew9ZjK4W6/XU2YyApFIRHPShUAYzywWC9ra2nD8+PGKyGuxWLBlyxbOmaDT6aDVajkRiVzZ0uk03G43VCpVXuTC7XZzCPEJGIbBz372M/zgBz8oWV62l066O5LJJIaHh2EymaBWqxGPxyGVSqf1QEsiUhCLxbT5mHyp2Wy24BdYqd4/h8PBCdMB4G1N4APZMOfOncPIyEhF5CkFQqEQJ0+epAOFu7u74XQ68yqP2dWCRMmSkXHNzc2ora0FwzCoq6sri8YPmGyf6OjowOc//3ksXboUjY2NEIvFtEglt8hJJBJxFCqTE+4i4Q+2XPF4nJIesEma77rrrqJkJWPnBgcHKXMPWz6Xy0XzhoTcYaqwPimAyb3/CoVi2nFQ0+HZZ5/FL3/5S97ntmzZAgCc4gqj0UgPaj4WHELxyEYwGEQmk4Hb7caBAwd4D8Xca6sE/vnPf9Lf+Sg0CQoVb33S2LBhA6c+w+Vy4dy5c+jt7YXT6cyTkZxpY2NjCAaDeekptVpN00bljsxjw+PxUNIRYPLe1tXVIRaLwWazobe3Fz6fD4lEgvO5JMUCTJ63Lpcrz5gSCoWQyWTU0akU/vrXv+Liiy/OM+T5wvnsx0hhIp+RFQ6HaXsW+Tuyjos9M6YDqWy32+2U1S4UCuVRrPKhpG9eJpNRKj/2FyGRSHDu3DmYTCZaWFDKeCmC22+/HTfddBOdTkCG4Z47dw7ZbBZKpRLt7e10Ugkpk88Fae7OZrOYmJjA6dOnMW/ePBgMBtTW1s7q0Nm1a9fi8OHDnMeampqoclmwYAGHQYTAZDJhYmKCVuICk5t6fHwcP/7xj/Hee+/RySZf/vKXy5Jx+fLlmJiYwOLFizE6OooFCxZg586dGBsbg0gkwpw5c+iBQioD2chkMnTTkwrMXMo+uVyOuro6+v2kUik8+eSTRRtXIyMjYBiG9sIRkPdNp9Ow2+3Q6XS0IpQQ9+du1GQyCb/fD4fDAYVCAYPBAJ/Ph+bmZtTU1GDbtm346le/WpR8uSi0tvbs2QNgstXp9OnTkEqlWLduHX2+p6cnb1pIKpWi3gmpLRAKhZDL5TAajXjzzTd520Fmowjqb3/7G52FKZFI6KDpRCLByd8zDAOfz0fbV8i4qv7+flit1orwIs8EhECFtF10dXWhq6uL97Wk19xsNiMajUIikdCcI2EoamhoQCqVwtGjRyvKhcsuavnggw/Q3t4Og8EAhUJB6xx8Ph+HLQv4+DtOpVIYHR2l7UEkOgd8XIswNjY2LdF7MbjsssuQSCTQ19eH8+fP0zymVquFy+WCx+PB4OAgrSgmUCgUqKurg0gkgtPpRG9vLxYsWACZTAaTyQStVovvfe97ePLJJ3H8+HE8+uijuOmmm0oaB8kHMleV6KrcCUapVCqPfzgXJSlQUvSSuzHVajWampo4j5fTgP6b3/yG9/FFixZR2jJg0ovInWzPhkaj4cz/tNlsEAqFdBjxbCpQPn5dvV5P7x/z0bDZXJBqOuDjQ4hhGHoIEe8okUjAbreXzSV6/vx5DhtMKpVCJBKhvbMEfEVhpDeUXdhC5CaMOUQROBwOpNNpyGQy3Hjjjfj6179etKwul4su+lAoBJVKRTeVUqmkkzbYPWakvJ8NqVSK1tZWmEwmJBIJJBIJGAyGkpmd+HD33XdP+XxNTQ0WLlzI8SwzmQyampogk8nyroH0XALg7MGhoSE8+uijFZObDbFYzFv88fDDD+Nb3/oWgMloA6nEZ3vP6XQaXq+XrqNMJgOVSoVLLrkEmUwGc+fOxcMPPzwrcrNx8uRJfPrTn0ZLSwuCweCUaQ9ilACT81VTqRSEQiEcDgdEIhG9/zKZDEuXLsUzzzxTMTl7enrofN/6+nreFpmpom4SiYSGJRmGofuC3YImlUorzklNokFms5kyCgGT64JNYpMLk8lEp55YLBaYTCYwDMNpI/zDH/6At99+GzfddBMA4NZbb8VDDz1Utsw6nQ5Wq7Xg8wzDTDuNqWhVTnJ3ZLgzAM7mImXsoVAILpcL999/f7EfwQv23ERg0poii5zQhBEm/enQ1NSEhoYGaunNJm8oMGn9/vWvf6X/V6vV6O3txaFDh6YMEZAF7/F4MDo6Cp/PR4doE0WVzWbR19eHb3/722XJR2aVAh8zcpB+Mj6Z2CC9frmbnQykZltxhCGlHLJzdm45dxguKeHPPfBzFWju3xiNRkp3RvoDy2kPYstXCCQUZTabaSjXbrdjZGQENTU1tAmdfQ3k+yfXQCIXua1SExMTHCKMckCYpXLf7/7778fu3btpi4VCoUBNTQ0ndE9GQ8ViMYRCIaRSKbqGRCJRxfOHheBwOBCNRmnPL1lDZLIQX8UtkVEul0MqlSKZTFIjlkCn03EqisvF7t27qQHS2NhI91Q6nUY4HIbX65127yiVSmg0Gnr4x2Ix9PT0IBwOU9atSoZwn332WQwNDYFhGJhMJo4BSvrICw1iJ5DJZLTVjfBWk72zdu1a/Md//Ad97X/+539WTHayPkl0b2RkBFarldbtTDeIvSgPlN3CYrFY4Pf70d3djf7+ftrgTqDRaMoOzxDr+sILL8T777+PgYEB9Pf3QyQSYcuWLdQbIuPM+Npo0uk0HA4HUqkUbfQmJNhSqZTT8J/7uZWCUqmkQ5RJzqS9vZ0aI7nysgtylEolPXyI7OvXr8fatWtx8cUX4/Dhw7j55psLtpXMBCSf9cQTT9CePEJgTQ5oko9taGigoU8CiUQCo9GIdDqNsbExevjrdDrodDqOsmpvb4fNZkN/f3/JMyvZm5E9wIB4nbW1tRgYGKByJBIJ3r65aDTKWTOEcEMikSAej89KewU5iG+55RZs3rwZANDX1wev14u2trYpG87FYjGSySTGxsZomMtsNuPFF1/khPHj8XjFSfvZ2LBhA9577z04HA40NzfnfY/sdIRKpaIcxU6nEx6Ph4bNyJBq8r3MJmnF3r176e8ajYZ6oKR9ie+zJyYmoNfr6b1k97QfP34cYrEYS5curSiN37lz5zA6OsqhmMtkMti3bx9WrlzJMU5yjaNoNIpoNMrxAJPJJCQSCS2eAia98UrmbZ966ilce+210Gq1CIfDlClrbGyMErTkKiLC9kPy57lMRXV1dXjrrbeQzWZx2WWXcZ6rVKSFFGUS8NFnToeiPFAyLJl8uEajQUdHBxYuXEh77MhIHSCfHqtUsHujZDIZFi9enPcachDmWslk0DMZBEwGUbNBGu1nCyQHSkiWAeRRERKZyZBttvdjNBrR0tICs9lM77vZbEZTUxPq6urK9pQOHDiA999/H+3t7di6dSuuvfZaNDU1oaamhip40iwN5I9SIhAKhbwej1Ao5BT3NDU1Yf78+SUrfb1ej3A4zCnyicfjGBwc5LyGGACEmjA3VJ9KpZBMJnkLSEQiUcUZfRiGoUxHZAwbMMl72tnZCY1Gw8kh5k61EAqF0Ov1MBgMHCWVO6Agt0ex0mCHP0lOeiYQi8Wora3FkiVLOGcJwTXXXFNJMTE0NIRNmzbl9eOy+5Kz2Syv8iSeKZ8h4vV6qbddafzxj3/Evn37OGFakUhEmZMIyPQSAhLOz6UqTSaTdA15PB6cO3cOdrsdH374YcVkdjqd2L9/P95++22cPXuWKkbS8UC8e3bvKklD5a6dkZER+vqLLroIy5cvzyMTKcdZYIM4AYlEIk8HzDQqWZSGy2Qy1AM0m81UERFrKZlMore3F2KxGAsWLJjW/Z0pyPvodDrMmzePWulutxvd3d1YtGgRp10iNwdDCOWj0SivUh8bG6NezWxYwffddx927dpFPclcho5gMEgXDcMwCIVCiEajnDxFS0sL9ZrIpHahUIg5c+ZApVLljWkqBm+99RbOnDkDtVqNb37zm/SAMRgMdLGyZ32ycytskFmxuV51NptFT08PZDIZpcuSy+VlFQOcO3cOQqGQ8rKSIgZSaMH2igrlNEmOlrTtEFkTiQSkUin+/ve/lyzfTEDy1mKxmCqloaEhDA0NYXh4GC0tLXmhNtJgz1aguXn2hx9+uGD9QCkYHh7mcJ6yQ/Lnzp2DVqtFY2MjAoEAFi9enBfK93q9GBwcpEYCAA4bEMHOnTsBVG4Ptra24qmnnsqb8ESMbVLZnnsmEM5YvnWTSqUwODhY0fMtFzt37sRVV13FibSw51OeOHGCd2SdRCLh3HsyCIL5aAweGafocrk4Hnm5CAQCePnll2mR4KJFiyCXy6HRaBCNRhEIBBCLxTA8PEyNXmIcsvP4iUQCAwMDSCQSmD9/PvVe+/v7Z6VOJRAIoKamhrInse+31WqFyWSavkWwUIMo3w+7KdrhcDDhcJj+P5FIcAgWGIZhuru7K9YEe80113De2+v1Mt3d3cz58+c5j2ezWUpKwDAMli9fzvkb0vw9PDzMIQcgqJS8uT+F4PV6mUAgQMkf2Pc4EokwkUiEyWQyTH9/P9PT08NYrVb6fCqVYo4fP162XBdffDEDgNmzZw/T19fH9Pf3M3v27GGOHj3K9Pb2FpQdUxApnD59munu7uaQRTDMJMHC2bNnGYfDUfL9ZiORSHA+k42JiQmmv7+fQ6YAngZ/j8fDuN1uJhgMMjabjT6+bt26in3/L7/8cu69m3Jd8N1nInMymaQyOxwOzudcccUVTF9fH/3b9evXV3z9fulLX6KPf/DBB8zAwAAzNjbGOQ+IzJ2dncz58+cZv9/PeY9QKMTE4/FC1ztrey4UCjEDAwOMzWbLW5tE5mXLluX93cmTJxm73c5ZbwzDMG+++easnBfHjh3jkKmwQchjPloPvIQx8XicQ9qSTqeZZ555hrnzzjuZrq4upq6ublbk/upXv8oMDg7myRwOh5nz588zHR0dDJE3HA4zLpeLcTqdea8fHh5mBgcHec/oj76riqwHhpnUZbmEKwzDMLFYjPF4PHRd8P2U7AKQasVYLAaGmRz9wg5pjIyMVDRMkDuzTygUQqfTcXICbCJwArYVyQ4vazQa3pzpJw3ScMznjZGyedKOkcsheubMGTQ3N5fdB3rddddhy5Yt6OjooJSBZCKEUqmcNkTMMAwlhyAwGAy8dGgGg4Fy7VYC7HJ8doUwaUVQqVRT5lrJnFKhUJhXndnT01MRGYHCw4AfeeQR9PX1UWt8JohGozAYDHR82OWXX07Xz80338zJ1bFHeVUCyWQS11xzDf3+li5dCrPZTAdLpFIpjmdEwra5aZNQKJTX6zrT6y8XjY2NtDWED+y1mclkqKdCCswIDh48WJBsohwsX74cK1asgF6vp3OLAVBSlemqxCORCDKZDOd8E4lEEAgENI1UaYpVAolEArfbnVfoJJVK0dDQwLnnKpUKJpOJMyuWQKPRQKPR8BZMFTvBaSoEAgFotVreWam583j5UJQCzWaziMViiMfjdODv8PAwEokEnfpOsHfvXjz22GPFvP2UWL9+Pd5++20cPnwYIyMjlCyZ7XZ7vd6Csevh4WHE43HORPZPEnyHAymPZ4M0xTscDjAMQ6fKm0wm1NXVQa1Ww+v14uTJk3j55ZdhNBrxta99rSzZbrnlFjz22GNobm6GXq9HQ0MDamtraY6VvbjfeecdWrLOvjaHw8Fp4m9oaODMWgwGg9QQIDMVK3G4s40qnU6HgYEBHD16FMlkEjU1Nairq6OHHh8Jgc1mg0KhgF6vpy0WBJUcUVUIt9xyC/7whz9g7969vK1I7NwMyfOSMBgpvnjhhRcwNDSEt99+G1deeSWAyfRGKWT9UyEYDCIajeLaa6/FoUOH8Prrr1M+YmJoTUxMcNqh5HI5x7COxWLYv38/nE5nHlFFLBarSOUzG6+//joefvhhWK1WRKNRqNVqWjHMx0DERjqdxrvvvouJiQk0NzdzDPO9e/fiN7/5zYzYporFbbfdBmByPXu9XvT09FDWnumYpmKxGCKRCJ3BygYZN5dMJjk9x5WARCLB0qVL0dDQAJvNhhMnTnAITCQSSZ4DQMAwDMbGxjgENwaDgbICkX5jADh16hR+9KMflSQje3h4IpFAT08PRkZGqAFNxtWxDbvpFGhRbgApEtm3bx8uvfRSiMViTlP9+Pg4nE4nwuEwjEZjRYswli1bhssvvxwAOLPaSMtBLBabsjSbncNxu92QSqW0PP2TwD/+8Q96uHk8Hsjlct4ZeaRgIBKJcJ4PBAJwu90YGhpCZ2cnOjs7ce+998Jms+FXv/pV2fI1NjbC6XRCpVIhm83S/qxcsumLL76YV+a2tja0tbVRpaPX66kCzWazCAaDCIfD0Gq1CAQCEAgEJbcw7Nq1CxdddBEMBgOam5tps7tEIkFLSwv9nRQIJZNJeL3ePNIGrVZLS/0FAgE1qhKJBG//bqkgvZJsHDp0COvWrcszrI4dO4aBgQFalcv2FMRiMdra2uhBnk6nYbPZ0NDQgLq6Ok7Pms/nw/z58yt2DQDw/vvvQy6X45JLLsGqVas43gFp9yg0K3ZoaAherxcWi4XzvQeDQfT390Mul3Oq+CsFcmYAk/ueDJn2eDxwuVxobW3NU6TsIshNmzZxZA2FQkin09i0aRPcbves5Mnvv/9+ahQTA1ssFnNqJ6LRaJ6zQAqf2JXcXq8XYrEYWq0WJpMJSqUSExMTsxJ9MxqNtLUq957mMjYlEgkMDg7m9aQS6kSdTkfzntu2baMsQdMRG0wFtgEkk8nQ2dnJUZZDQ0PUIJxph0DRIVylUgmLxcK7SWKxGC2vJ+xBlQI7VEcWFZm+wtevmAt2xV8qlaKjoNjgY+evFNjeBZmCMFVDdG6YJplMUuuSRAAAfr7dUhGJRGh1n1wupxMgiunZDIVCCAaDnKIm0ihNejH5rONiUF9fTw8LYNK4YFOfkTJ+UtBEQvfsDZTJZPLuPzFYCMVYpfDOO+/kPbZ27Vo8/vjjeY9bLBbMmTMHS5cuxdy5czml9ezpLIlEgkZcyHUSL9rr9VZkni0f2PuI7EN22xUZB5cLUg2de3BHIhFKGTnbIL2URE61Wg2JRJLHUpVKpeByufLWPelnJUbPbEUo+vv7MTAwAAAcRQKAFgSRdBUBqZLPZTQjxiQw6UQsWbIEy5cvR319fcUmyACTDs7q1avR2toKi8VCZSZV5bn6QiAQ0B5MNlQqFaURZSMQCGB4eLisnlu+giD2d0w89GKK2EpKRLF7irq7u5FOp+kGYfcvVRIHDx7E8uXL0dbWRhVINpvF4OAg6uvreWPYwMeVww6HAxqNBjqdjnes1euvv47PfvazsyI7MFkpSfoOx8fH6cLS6/UQi8WcFpFAIJA3kZ4MTBYIBDSUVonKNIFAgMcffxxr1qyByWRCKpWi5fDpdJpW8eWSrucqmFgshlgshmAwCKFQyBmsHAqFoNVqkc1m4fF4aO9tqWTWq1evRnd3N7q7u9HZ2Qm73c7JdbLvi0gkorNj2R4asYAJOw674m4muY9iwJdLfeyxx+ggYjLf0WKxcIbGF0IqlcLp06chl8vzGtSDwSDGxsbQ09OTR01WLlpbWxGPx5FOpxEKhegaJrlYAj6Dq9A1pVIprFy5knos5ZCE5+Lqq6/GDTfcgFWrVqG1tZXjsZEcGzC5ltkUiKlUCj09PZQdp6GhAXK5nPaak797+umnKyZrLj744APMnTsXNTU1HMIYMkQhd+gA8doYhkFPTw+0Wi3q6+s5e4Gsrc7OToTDYaxcuRJvvvlmReS94447qLdO2t/i8TiCwSAlsGdDKpVi3rx58Hg8HBY5softdjvOnz+P2tpaGAwGxONxOJ1OnDhxAjfeeGNJQ9hzIzLJZBI2m43WDLS2ttLK5VgsBqFQOG2nQFEKlPmojYJ8AJlNZ7FYaHybYRhYrVa89tprRV7e1IjH47BarXSSODDphnd1dVHWI3LAs/MoIpEI8+bN4xRWDA8PQ6VS0QktFosF//jHPyoqby7YYZOuri5aEECIBwjYfapkziPJaZD+STIPdeHChRXx9G+44QZs374dP/jBD+jBQmTIZDKwWq3weDzIZrMwGAyQSqWczct8RL3lcDjyprqTa5fJZJDL5RzjJZfPthiYTCZKvr5y5Ur6OPHQmY9YUQDQEBYbSqUyj9OXQCwW08k+lcLBgwc5Cu3CCy/EvHnz0N/fT4su+Ab48hHhC4VCrFy5krO50+k0rFYrWlpasGTJEs6g8UrBYDAgHA5jaGiIGnT19fV53kVuwRDpba6pqaETTlKpFHQ6HVpaWujrXC5XRZXSrl27cOGFF9L10dzcnNcsHw6HOfMfgckWG3aYmazvWCwGg8EAgUCAF154Afv27auYrLk4fPgwrrzySkilUmpMS6VSzv7hO9wFAgHmzp1LJyKRv2UXIC1ZsgR2ux3XX399RRRoe3s7HSzONrTJ4AhijPLxUROFGQqF4PV60dTUBJFIhPr6ekp5CoA6Tq+88sq09HqF8NJLL3EYjTKZDEcvAB+34jmdTsjl8mkJSYouIiJ5R0KNRaoBySZKp9NwuVwVG5VDEIlECoYSRSIRkslkQfo5vutwuVwYGxujlmclpslPhX379tFGf41Gw2FOKhQyIGFKYrCQ0JhWq0U6naZhnkrgrbfeQigUomFcAlIcRvLFCoUiL0wnEAggEol4N7Tf76fjroRCYcV4ZvkGZIfDYXrPSpkAUoggohIYHx/Hrl276L7o7OzEqlWrIJPJaKFYMpmkdHfAx4OGc5FMJjn3Oh6Pw+/30+kzhFmn0kO2SThfLBZDrVbTfmQCsu9y818krA+AVnYTjmQ2iHKtJBwOR96oQHZ6gYSfpzooCS+0TCaj6/eNN96oqJy5aGhowMGDBxEKhSAUCosqCBOLxfRMJBAIBJy1JZPJ0NHRUZEqYvY6YxtTCoUCKpUKMpkMmUyGTg7iQzQahcfj4YRuSX+21+ul02/GxsZK7mE9ceIEvY+EH6AQSKh8uqK2ojxQdqXtwoULefNYpJCDL0xaDkZHR9HQ0ICmpqa8hDQpXDAajZxKW2By87766qtIJBK47LLL6Nw8n8/HYaGZbTYiAPjCF76AnTt3oq6ujiqi5uZmKBSKPCVKWDpUKhXkcjl6e3vhcrnQ2NhIQ6C7d++uWB7DbrfD4XDA6XRCqVQiHA6jra0NIpEIFotlWi5LNrcwwdGjRyGVSrF48eKKUoft2rULV111FYBJK5d48IFAgNLYFQrp5yKZTGJgYIAqhWQyOSve29atW/Gd73wHEokE8+fPh1qthkKhQHNzM5qbm+lmJda73W6HRqPJu45gMAiv18spigsEAtBoNJyq57///e+UlLwSSKfTGBwchEgk4njSNpuNphasVis6Ozvzwrns6wImC9ZMJhNisRg1fPkq0iuBvr4+xGIxDm2j3+9HMpmEQqGgdJPsgzIajeLQoUOUclClUkGn09EQ/8mTJ/G///u/FZeVje9///u45ZZbMGfOHBgMBvT19VE2omPHjqG5uZkjcygUwv79+yGTyWioMh6Pc0K4hF9Wr9cjHo9jzpw5uOuuu3DvvfeWJevExAS8Xi8MBgPNyQPcnCMZIkGMLEJIQbxkktPlG504MDCANWvWQCqV5pFiFINkMolnn30WV199NWpqaqY0mjQaDWKx2LTTooo61dLpNF2IgUCAKkmv1wuPx0O5UsfGxipGt0QwOjpKDzaxWAy3200HKpMeIyCf4kqpVKKzsxMOhwN+vx9NTU1QKBRU9vfee6+ick6F48ePY8+ePfjmN79JH8vNtWUyGYyPjyMUCqGuro6Gw1QqFaxWK3p7e9HZ2Qmj0ZhHUVYuSPtKOp1Gb28vgsEgzcvlgq+cXiaT0Ryu1+uFVCpFW1tbnvI8dOgQwuEwnYlZLNiVkYcPH8a//Mu/QCKRQK1WcyqxCd1foSHqhHWIHcoNh8Oc0FclYTabaa6YjxuU3D92SiL3dbntYgA4rDSkz89kMpXFTpULkg/MzX2Pj49TzmGVSpUnm0AgoKT4sViMrncSAgY+NhZL4SKdDgqFAkajET6fjypQIgfbAWCvUYlEAr1eD5/PR4fJs5XBsmXL0NraSnPYs4Xbb7+dKkN2mmLZsmUwm80cmWUyGRYsWMApjsyt8Far1TQE3dPTg5MnT5Y9NJ6AfK9ut5vzPZL1LBaLoVKpqCElkUhgMBjgdrs5fNYEkUiE8kYbDAb4/X5oNBq89dZbeOmll/C73/2uaBk7OzvzGJ4AUM+c9K4DmDY6SFCUycd8NFZrZGSE42qTak1y+LAJCyqFcDjMWTDBYJB31igpYCEQiURoaWnBnDlzeGXq6enBU089VVFZp8J0oe1UKgWv14tkMslpYyHexdmzZxEIBCrefrN8+XJIpVI0Njaivr6eJu35FKXf7y9oIHm9Xni9XoTDYdTU1PDmK6LRKHw+H+/sypmArdzYs1TZSpKsVafTCa/XmxcuJHm53ByjQqGgm77SMJvN0Gq1nNAaabMha5uE3wr1KZIcTe61kEgKoYXUarUVN2L5KmzFYjFnEksuBAIB9fTIbMhcRCKRWavClUgk0Ol0nPOKjDIsdDiSlhFiUPJFefj4uCuNQhEENkc1AR9fLvv6vF4vjRQAk/fcbrfj0KFDFZGVKNDcEC1JCRHjih1l0Gq1vK18DMOgv78f4XAYQqEQtbW1dJjGli1bSh5/t3jxYt7IVDQapWkfNhFIbqEWH4ryQCUSCRobG+H3+zEyMgKHw4G6ujrOEFjywYV6Mru6unDq1Km8x5mPCLb/9V//lffv5HI5Dh06hBUrViAcDtNKVjL/jmxsUgbNhkwmQ0tLCyfk8eqrr+LVV1/FH//4x2JuQdl4/vnn8fvf/z7vcWL5iMViNDQ00LwYgdlshtlsphuBHSopF08//TQuu+wyHDhwAF1dXZDL5ViwYAEGBwc5h7DP56NKia+EP5lMwmg08oZ733jjDSSTSSxevJhOISkVDz30EL761a/CbDZzJjWQRnkANPRCJkHkepSk6Z+QgBCFxXzE88s+cNva2jA0NFSWzMAkOTYZ4nvkyBFks1lotVrMnTuXc9ix+1NzQarPSQ6HKAKytj0eD1KpFJqamvDss8+WLTOBw+FAIBBANpvFyMgILf5he0bTgV0wBHxcnHP+/HmYTKYZh92LgUAgyOOKbmpqoq0ghWbx5p5pwKTn2tfXhyNHjuBzn/vcrBceBgIB+P1+uN1uvPPOO7SaOJvNcqaIEJlzwTAMzpw5Q+soSGEUKbJrbm7G9u3bcd9991VMZnbfciKR4BQk5kIoFOZNH/J6vRgfH8fAwABaWlqoYj537hySySQ9W0gBXjEYHx+Hx+PJ+17ZE7ByR7FVVIES6PV6Gkd3u915FprD4chjqyHgU57A9K7ypz/9aXqIrVq1ChdccAGvApmKRZ/IS/oGK9nrN1O4XC44HA6o1WqIRCLav8VWoLmVmORLT6fTuOCCC5DNZjEwMIATJ07g+uuvx4oVK0ou2tq1axcleJgzZw5CoRA0Gg06OzuhUCioIvH5fHRKDMnfsZFMJuF2u+H1eqHRaKgRQNDe3o54PM5rcRaLvr4+PPvss9iwYQOWLVsGhmGoQUU2mF6vh06nK0h9JhaLMXfuXI6MJLcuFos51zc4OFg2wfmHH36IaDQKk8mE9vZ2DA4OIh6Po7W1tajcH5EvGo3SEW0kxJ7JZNDR0YFIJILjx49XdMD2xMQELWghxBQajSav73AqWK1WWgxHmvrNZnPJofyZ4JlnnsG9996Ljo4OOo6R/d3mUn8Wgs/nw9GjR+HxeBCPx6cnGS8TfX19mD9/Ps0Lfutb35qSvD43XJvNZuH3+2lond1/29PTgz/84Q8YGRnB2rVrKy47iUZqNJoZrW1C+RmNRqFQKDBv3jx0dHRwzneLxcKJcMyfP79oBbp+/XoEg0Hs27cP69evpwZbIWeP+Wh60lQoK2svl8vh9XrR19dHQzOzFcK96qqrIJFIEIlEeEkQSCXYVBfMMAz8fj96enrQ3NxccaaWmSIQCGBgYACnT5/G2NgY7ZXig8vlwvvvv4+hoSFEo1FYLBZIJBIEg0GaUOdjupkpiPIEJsPEVquVTmlvbGyExWKhFZOkqIlvujwZguv3+xGNRvMOpebmZrS0tFRkggWZ7kEqNkdHRzE2NsbbrF2o6pdUrLKR27xdSezcuRNut5vKqFKpKIWgSCSis1TdbveMDLvccBPwsfGoUqlmhUghlUrRHkSn05lXMTvdYePz+SgdHd8A69nKKZ49exYajYaSkbBBqrbZspPcOEEqlcLExARd20KhsOxZx9Oho6MDfr8fmUwGOp1uRvuGhMJJTQohjDGbzZy5x9FolHrSe/bsqbjshNt2phX38Xgc4XAYHo+Htrvlnu8mk4njyfK1d02HtrY2pFIpHD16FMPDw3k1ArkVt4lEYlo9VnZpZFNTE7VuSEh31apVuPHGGytqAbMPeuDjJlibzUZzXPX19bx9aQQajQbLly+nA343bNiAe++9d1YH+fKhs7OT5hG1Wu2U7BdmsxkSiYSGJEUiEaLRKFavXk2txwceeKBkWQQCAVXeQqEQPT09tFXJYrHAYDAgm83yDh5nQyKR0IpSgkgkQmkWOzo6KkZO0NjYiLvvvhtGoxFOp5MqZwA4ffo0RkdHOaQYqVQqr80m12CZmJjA/v37sXHjRkil0oqzzLzxxhuw2WyIRCJYsGBBHslBMpnEyMgIrWINBoMFafGAydB0brTF5XKhubkZDocD3d3duO666yoWxl22bBnOnTuHTCaD5uZmSmtH4HA4KDVeIYKP+fPn50Ug2B5gJcLkfCDtXolEAg6Hg+YWk8kkDh48iJaWFk6hHOl9jkQimDt3LrRaLRYsWEBH5b388ssFU02VRE1NDX7xi1/gyiuvRGdnJ06dOoWhoSG0tbXBbDbnHe6EYEUul8NoNObl0O12OyQSCS688ELs3r0bO3bswF//+teKyuz3+6FQKPLOi2AwyDECSJsIMR5lMhkaGhrylC4paGTTPL7zzjsl9eD29fVh27ZtePDBBxGPxzE8PAyXy0XJf5xOJ+1xJ5SEFeXC5QNRnolEAlarFVqtFkqlEp/61KfKfespIZVK0d7eTiu4SIUwmXBeCC6XC4ODg5zQBfswnW1les899wD4OAxOMJXMq1evpmHyVCqFsbExpFIptLe349FHHy27d+6VV17B1VdfjdraWmzevBlOpxPd3d202Z0QZqhUqqLCjSqVCpFIhEM3GA6HaV6qVGzatInmMd5//31s2bKFMzM214NjU+AVQm1tLa666ipq+bInCXV0dJQsK8GxY8dw55130uELuTlZuVyOFStW0EOPFF4UUqDE44/FYvRvDAYDZQiaP38+PvOZz0Amk5V9SJJK9fb2dmqlazQaetgRCrncQd+54OupczqdSKfT0Gg0nOrqcnD11VfjxRdfhEgkwt13340dO3bQ59j3k/Cw5rY0kMlScrkc8XicGmBkv1566aUVkXM6/Pu//zu+8pWvUGWk1+thNBqh0+nyWt/IYAGSI+eLaI2NjdHwucFgwNVXX10RBXrjjTfS3wn5AeErJ2kGojBzkc1moVQqC3qrYrEYixYtgs/no9HDz3zmMzMOvTscDhw4cABbt26lYXxgcr+1t7dzeulzi7AI+cRUqFjjFamq7O/vr/hEBWByLBOp1OPjQyRsM3w9lQSpVAo2mw0HDx7E9773PfzkJz/BK6+8wnkN38y3s2fPzljOQnPjyE8po3jYOWaJRAKXy0V5eysx8eZzn/scvv71rwOYtHo7OzthtVoxMTEBj8cDv98Pj8czo17Z3AVHKAEJRkZGyq5wveCCC+jvp06d4oRetVptXjUo33rge4y9edg5fPZ0kZmA/X0DoN5KbW0tHA4Hjh49isHBQbhcLk6okO0xkPDRVAZLJpNBNBql+VCVSkVJxtva2rB8+XI8/vjjeYfp5z//efz617+e8bWQ4hNCZweAYwSR0XFsQpXc9yC0kLnVth6PB2fPnqUefyqVKommjY2XX36ZDr647777qFJnV2wTNDU1Qa/Xcx4XCoXQ6/W0r9Fms+HQoUPUEFQqlfi3f/u3GctD1kKx5As7duzgeHIGgwG1tbXQ6/VQKpWcNUzahUhemu/gJ2T6BBs2bChKnkL485//zPm/QCBAIpHA6OgonQqUq4yI7Lk1ColEAtFoNG8qSm9vL/75z39yPM/pxt8xDIPa2lpcc801ePrpp9Ha2so5i6RSKUep54aNp0oB0dcUM4NPIBC4AFhn/Af/7zCHYRgz8H9P5v9D8gJVmT8pVGX+ZPB/TebqOffJgN7nXBSlQKuooooqqqiiiklUnjuriiqqqKKKKv5/gKoCraKKKqqooooSUFWgVVRRRRVVVFECqgq0iiqqqKKKKkpAVYFWUUUVVVRRRQmoKtAqqqiiiiqqKAFVBVpFFVVUUUUVJaCqQKuooooqqqiiBFQVaBVVVFFFFVWUgP8PQ8ognhRQAUcAAAAASUVORK5CYII=\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AbGpqgkajiet4brcbQK8fQ1lZmWBIxf/8z/9g9uzZGDZsWNSFI9D7Py5cuBA33ngjXnzxRcHvPPfcc2xj4vP50NXVhebmZjQ1NQmaf+RyOVsoqlQqqNVqXH/99Rg5ciS++OKLuK7zQhCJRJg+fTqee+457Ny5E0DvfTt//jwzKXCx2+0wGAy8TQy9zwBw8ODBAR8rqJyUvLw8LFy4EAUFBdDpdBg2bBiGDBkS97H6PIFKpVLIZDKeM0hdXV1fDzMgdHV1YeLEibz3QuMsqaOIVCpljgBU1w4gobtnr9cLg8EAn8+HSZMm4bLLLmM2ZTowBgIBNhHJ5XIolUpkZGTAaDTiwIEDOHXqFEwm06DJuGTJEohEIsyfPx+1tbUYPXq04PdCdxlisZi1CWqHGTlyJIvfpQx0ZwB6B3HucYcNG8aTT6VSQavVxmW33b59+4DLFy9yuRzBYBBOp5O9Fzphejwe3ucAoFarmUYm0RQUFADolZMOhNz7TP5p44rkeLR//36cOXNm0OT74osveG2DOtJYrVZceeWVvLFACI/HwxbpbrcbJ06cwPHjx2Oed86cOVEH/3j7wVtvvQWr1QqZTAa9Xo/MzEzeJBOJtLQ0jBgxAgqFAo2NjVi+fHlc5xsIKisrcfPNNwPotZ9zF0z0ugkh6O7uRnNzM86ePYvDhw8D6F34fPnll5g/fz6uuOKKQZOR/jfFxcXo7u7mnYsQAoPBIOg8GUq/MhGFdmquWiSRxPKQAsALjhWLxbwtus1mY39cojAYDNDpdEx26g3GlVcsFkOpVDIVeXZ2Ns6cOYMTJ06gtrY2YbJqNBqe4w2344YOiNyOIZfLkZubi5ycHAwZMoTnvJAoTCZTv9Sxe/fuHQRp4kOv10Ov1/O8RIU6cUzHhgSxZcsWAL27o/r6erbr4S6uhbQTdIFrsVh4u+1EMHnyZJSXl4MQgngSD9B7TceNZNz7c+fOsedSqRQ6nS7unTOAhOw+udDducfjgVgs5rVnLtSkRQiBy+WC2WyGWq3GXXfdlbCFbHV1NZ555hnee3TRF48pol9hLNxOHQgEmFok0ej1ehiNRlRUVKC8vDymy7NIJGKTUn19Pd58802sWbMmQdL2cuLECV7j7+npgc/n4y1K0tPTkZ6eDr1ej/z8fEycOBEbNmzAZ599Nqi7Ty4vvvgirr76agC9O/2TJ0/ydgotLS3sOZ08Q2269H6PGDGC971EcPbsWRgMBpjN5pgLvJ6eHrhcLthsNuzatStBEoZTVFSEsWPHYurUqfD5fGhvbw9TKdNsL5RkqpxvuukmAEBHRweMRiOys7N5kycA5uEstJg5d+4cPv/884TISpFKpdi1axfLnOP3+2GxWMLCLihpaWm8XWpf1HtCxJoY/u3f/i3sPRpO5fF4EAgEeGEXoZB/hgnR3d22bdvw6aefXpDMfYWOA3V1dcjOzmby0jBDoHcsyMzMZF76Wq0WIpFowFX58fDBBx8AAL755hvU19dDJBJh1KhRyMjIiPnbPoWxAL0TKJ2onE4n2tvbIza+weatt97CY489xhq1zWYLS0lHU3dRO6lSqWTu9/E6wwwkdOfZ1dWFrq4uDBs2DBqNhpcKLdTGCADTp09He3s7ampqEiJnYWEh9u7di+zsbFx11VW8+LempqawnbDNZoPFYsGoUaPYe263G4FAAGq1Gs8991xC5KZMmDCBydzZ2clLXxZKZ2cnCwFIJvfeey+efPJJTJkyhaVBC1XXut1udHR0wOFwoKenBzabDVarNUkS9+4+hw8fjuHDhwt+TgiBTCbj9TWDwYBAIID169cnbAcqEolQUVGBiRMn4pFHHmGD4/r16wFAsM8BvWp1n88Hn88HlUqFn376Ka7zbd++He+99x6+/fZb3vtSqRQKhSKiGlZoslu5ciWee+45ZGdnR/U38fl88Hg8SE9Ph0qlgkqlEgy9SQTnzp1DaWkpe93c3MxzjgR6NVylpaWYMmUKiwse6LjPeNm7dy8WLVrU599dkAqXBu5GanyDTWVlJW9Xw1XXcgldFQO98T5c9WSioLt3GmsZaoOJNMjn5+cLxlENFj6fD52dnYI5dm02W1jwOc3Py8Vut7MJYKA8LOOFa4eTyWRRvSFpIPdg5EHuC59//jmOHz/OBhEhG5rP5+MlhZBKpWwFnQziycFMPZwpgUAANpsNJ06cGEzRwnj00Udht9vZ5BkMBqFWqyO2D7prlkgkrG03NTXFPI9Op8OcOXNwww03YMqUKbzP9u3bJ5jQ4Le//W1UlXLoGMuNLKD4/X7WL0UiEZRKJfOQTjShjoN0VxranunYTHegXM1WIqmvr+/X7/o883ET8GZkZEAmk+Gyyy7r18kvFIVCgdbWVuj1eiiVSiiVyrBGJZTpJxgMIi0tDYWFhRgyZAiMRmPCZKb2gZEjRwq62nNlNZlMzNZYVFQU0TV/MNi6dStuvfVWFBUVobOzk3ksnzhxAlqtlpeAgtoxlEolnE4ny/Sh0WgS6qFNbSpisRg+nw9NTU3weDy8lbAQKpWKuf8nm/Xr1+P666+HRqMBISQs8w2d7LnXNGPGjESLyWhqamJq2qamJgwfPpw3aMtksjDnrREjRqC+vj7h6vJ//OMfeOSRR7Bu3ToQQlBfX4+FCxeyz2nWIuBf3voTJ06EWCxmHtyRPOeB3gX88uXL8fbbbwsu2gHwPG7feecd3HDDDRgzZgwA4P7774+Y2IVrR6ytrYXT6Qyzj0skkrA2nAz/AwD41a9+hcWLF7OkGdShKVofKykpCduxJwqakc5iseD06dOor6/H3LlzI2pWKH2eQOnKhqJQKGK6bA8Wb7/9Nl577TV4PB643W7eKjcSbrcbRqMRmZmZMJlMCZ08AeDbb79FXV0dCgoKIJFIoqoWLRYLpFIp9Ho9XnnlFbzyyisJk/Obb77B9OnTsWDBAp7Ndt68eWHfFYvFSE9Ph1wuh9lsZmFDkZwHBpOuri7k5uZCqVRi9OjRPJUQV9XJVSV5vV4oFIo+OWYMFtu2bWOLEZVKFbYgzMrKuigmegrXe3Ho0KGQyWRh8bYU7u6Pq+pPJHTh0dbWFrMCiZCT4tixY1FVVYUpU6YITqb19fWw2WzQaDQxM40tXboUxcXF+Pbbb1FSUhIzK5rb7UZ7ezvGjh0Lh8PBk4/uSOkmgt73aBP+YEMdnjIyMiIuKEKJV0U+0LzwwguYMWMGcnJyMGvWLIwZMyZq2BulXyrc0JuRrIsGwNJWhXqyCuH1euFwOJj6i5s4IJHY7Xam0jCbzTCZTIL5OGlcl0qlwg8//JBw+8DevXsjJnvgQhdVWq2WlboKBoNJUe2Hrsq5gzkNlgb4bSRZdpdIyGQyVqItdHEll8sTmr+5L0TLH2oymZLmrc8lLy+PTTbR7IPUYz8UugCYO3eu4O/ohBXJGWbSpEm81+fOncP333+PdevWRZXbYDCgtrYWXV1dAHodDbn9i16TSCRCd3c3bDYb/H4/85ROFhKJJK5oCcp33303iNJE5sSJE7z5YOjQoUhLS4s5NgzICJdo+1YoarUaarUadrtdcNAOBoPo6OhAXl4eCxUAkPAQFgq1i1BVssvl4k2gdrsdbW1tPFvJwYMHEy7ntm3b8Jvf/AZvvPEGG9QVCkWY3Za7i9br9SCEX0tzIBJrxwuVo7GxERqNBkqlEvv370d2djZvRcmdQKntKJqdNJHk5AiXHuRy9uzZqPGVicTr9aK6ujosJptis9mwf/9+jB49Gk1NTdBqtdBqtRCLxX0qSjAQSCQSnDhxgtUK3b17N8aMGRNmHsnIyGB1Wt1uN6xWK/x+P1sECDkBcXfbkRwU77rrLl7UgkajwZNPPhlT7quuugo7d+5kHu30WijcthsIBJiPRaKd90KxWq2or69HIBBgqupQ6urqWP+LJ8Z2sCgpKQHQq/nT6XRMsxmNfu1AAbBdRrJX7z/99BPbdSiVSsEJlCbd5jZwr9eb8PgoClUbU9Vnbm4uT26z2RyWYpAmRk80NEuMXq9HVlaWYOA5t/NmZGRAo9EwLcWhQ4d4dqbB5pNPPgHQu0LPzMyEQqHA5MmTUVRUxIL+qcx0d61UKiGRSNjq/mIgVsdVKBQYM2YMZs+enSCJIkNT8jU3NwuOB4QQaDQaTJw4Efn5+QgEAmhpaUn45AkANTU1PJPT7NmzBX0L6G5OJBIhIyMDI0aM4AX8//nPfw77jcfjYYNwqPc0Ra/XY8KECex1vAUlampq8PXXXwPojV3kalOA3rGELh7VajWysrKihrskApvNBq1Wi6lTp6KkpCSi06ZOp4NSqQy7pmTQ3t6O06dPA+jVbsYyQ/V7AqXp5s6fP9/fQwwIp0+fZrYMWmU8FL/fH6aKTGQO3FDq6urCVI208VOHjNAOmMiqMVzogBCNaDu3gwcPJnT3/Le//Q0AX3Wbm5sb1nmDwSBMJhOsVitLf5aoGNt4iOURrFarLwqbLUWr1cJsNgv6Q1A7Pvd1shYrdXV1MJvNLHtaJPUinUC5nxsMhqgLG7lcjkceeQRA5B2oWq0WDJe45ZZbYsp+/PhxWCwWVFdXh2l16ARKCGGexYmMuxaCOzdQmeiiiRACu92O7u5uZGVlQavVJmVBFYrNZuvTRN7nCdTn88FkMrFyV8kM5AaAm2++mYV3UFViaMORSqU8m4TRaGT5ZZOBUqlkmTfOnz/PG3QCgQA0Gg1KSkrQ2dkJm80Gt9uNhQsXJnQnR+F6WFO1kMVi4S1AIk2gNTU12Ldv36DLyOXQoUMAepNa05zHQtAaic3NzdDr9cjIyEhaSkoh0tPTYTKZeDIFg0GWGCInJwd2u31AEvIPFJMnT0ZOTk7YQkStVvPUu7RmazQGK/xi9+7dqKiowO7du/Hjjz9G/B43LpuSm5sb06uVJkpYu3YtZs6cCQC8HafJZMLo0aNx77334uOPP2bJKIQWbzSRCYXmd7755pvDUmzSMmgmkynpEydl27ZtYRsFqqGgDlF0oZiRkYHx48cnXMZQxo0bhxtuuCHu7/crmXxmZiZycnJYkddkwh28XS6X4GCuVCqh1+vZ5O90OpO6A83KymJeqzKZjKe+FYlEyM3NRWFhIdxuN9ra2nD69Gm8++67STGwU3UGAFa3MbS2pkQiYVlSKH6/H3q9PmlJNnw+HywWC8/Tkruro6o5rl00npjGREB3OVKplNc2qA1arVYjEAjA4XAkLW4uEj6fL2IKRYfDgcbGxrgyl9GJZaChmW+KioqYdoWOC1xcLhc6Ozt5C5i1a9fG9Nz9xz/+AQDYs2cP+++4x/7b3/6G7777DuvWrcOePXuQn5+P++67D9dee23YsULDfLh9UQiafIOSrOgIytVXXw2n08nas9FoZLtMmuKPa+9PdFxwKP3RlPVLhUuz5Wg0mqRluqDQgdvlcsHj8URVA9Ai1jRNWrLIyMhAWloa1Go1e04Ri8W8TmAymVBVVZU0hyduo6K7eyo79/2enh4WjBwMBuFyuZCZmZm0nb5YLGYLpaqqKjQ2NvK87MRiMXQ6HVMt0gn3YoDunEPTyAFg3s60XFWsAT3R9PT0ROyDx48fj1ulP1jtRiKRIDMzE8XFxRg+fDgCgQCsVmvYf0/LbDU1NeH06dOw2Wz45ptv0NXVhddee03w2A888ACzadKKSUVFRbxF5LZt2/Ddd98hGAxix44d0Ov1+PTTT7FgwYKYsldUVKC2thYGgyEsSTtFLpezDHHJdMgBgJkzZ8Lr9eLQoUMoLy/njbkSiQTZ2dlsp2+325OWEpayefNmnD17FkDvYqWxsTGmWeeCvXAvBr019ZYScu/n7kjVajW0Wi2kUineeuutRIrIY+/evczmERq7ylW/jBw5EsOGDUuqbe7ll1+GTCbD3XffHbEyC9C7sqeLKWqP6e7uTnicLWXq1KlMpW+xWKBSqXg2w7S0NOTk5MDn88FgMEClUuHSSy9NiqyhUDVhWlpaxEQUEokEBQUFmDVrViJFC+Puu+/Gfffdh+LiYowePRoajYZ3n7nZyq688sq4j0vLYQ00VVVVWL58OTQaDW688UZs3boVw4cPDws70el0vAQQXI0V1xmNy969ezFx4kTk5uZi6dKleOONN8Iy8gwZMgQKhQINDQ247777MGTIEKxduxYPPvggdDpdxEXcxIkTMXLkSFRVVeGyyy7jpf/kQhdckfIPJ5phw4bBarVi6NChzFkICK+alZGRETE0KFGMGjWKjWGRPMpD6fME6vF4YLVamYfXhSZXvlDEYrFgDVCKz+eDw+FAeno6LzYxmWnbTCZTWApEobJVaWlpF4Vakaq9gV4PYaVSKVh0lns9Uqk0qdqJr776CjNmzEBJSQnGjBkTsbSUTCZDT08PdDod8vPzkyBpODRnaDzxc8mqxUv54osvBG1ylGAwiM7OThBCEpqKMhpjxoxh//W0adOQkZERM3E49z5HKoFG1b3p6en4+uuvBev2BgIBtiAOBAIoLy/Hxo0b4XQ6o2pA5s2bh6uvvhqXXHJJXAlKQispJZO8vDzBUoJutxsejwc+nw96vV4wxWEiue6663hhQkDsGPE+qXADgQDOnDmDXbt2sYE92a7SVOVJG0tojki/34+amhpUVFSEFfpNFlarlbczC1V77d27F7///e+xf/9+1NbWwuv1Riy6myhoJYWOjg60t7dHnNhp7FxfgqcHmt///vf43e9+h9OnT0OpVAo6lnHx+/1QKpVhnSdZdHV14eDBg2Exnh6PB42NjWhpacG2bdtQUVFxUTiMUBuXUOgGrftYV1eH9vb2uGosDjZXX30122EMGzYsbPIMBoNobW3l2Ry5i0GhxSMXh8OB//3f/xW8VrfbzdS8ZrMZ+/fvh8ViwX/8x39EPF5+fj6uvPJKzJkzJ+rkyR375HJ5XJnZEoFQRh+fz4dTp05h27Zt2L9/v2AimURTUFDA609UFR6NPu1AJRIJpk2bhmnTpsHlcvECi5OF3W5nfxDN2cpFpVLhkksu4b3n8/nwzTffJEzGUILBIOrr6+F0OlFcXMziEClXXnklU3cZDAbs2rUraWrcBQsWQK1WM7d+oVWiz+eDzWaDWq2G2+1m1SviSQgwGNDiwTQVIiWS1oFOnMl2YqDI5XKeOon7/ogRIyCRSJjMF0MihWeeeQa/+MUvsGHDBgwZMiQsF2686rBE4XQ6sXfvXowfPx5ZWVlhqlCPxxPW1rn9UyhDESEEn3zyCRYvXsyOsXz5cnz44Ye8vssNp9Pr9bxan4Bwyb+mpibceuut2LFjB+bNm4dTp04xvw/ucY1GI1QqFdvtJaM0GJdPP/0U8+bNQ15eHhoaGpjdHui9hzNmzMCMGTNw+vTppC64uZjNZrS2tkIqlSIzMzMsF3UoF5RIobm5OakFiAG+h1sgEIgZ/+RwOHD+/PmkOl/0JUarsrISu3fvRklJiWAe2oHk9ttv51W00Wg0eOCBB5izWLSYOVoInNqZMzMzYyYDGGxCdwDcydTtdrNYOqqSS2ZoExetVssyOnGhcYnc1frJkycTLF04nZ2dEIlEKCkpiTvNIHXWSAatra1oaWlBW1uboB1RKpUiLy8vYs7hSP2ATp5Ar8p36NChYQtf7qTW1x0ibc/Dhg3DyJEjeZsFiUSC3Nxc6HQ6eL1eEEKSvqtTKBTIy8uDRCJhmZ2EFrGFhYVhC4JkcODAAZjNZmg0GuTm5iInJyemtqFPEyh39WSz2XDy5EmsXbu2f9IOEM3NzUx1JBaLI9onPB4Puru70dTUFLbqSzQ0CF7I7sJtYBUVFfj666+xe/du3HTTTdixYwfMZjObsAY69Rwt3AsA69atg9VqxS233AK9Xh9VVS8WiyGXy9migHpp08wpyYJ2SKPRGNZxPR4P2traeGrHWGECiSQtLQ1Wq1XQM5Hayjo6OvDZZ58lWDJhNBoNrrjiCsyYMYOXKN7hcLBUbvv378e+fftw7Ngx7NixI+rxYg1cF0JlZWWYVzYXbjjIyZMncerUKV4Zs0jFH0IR0g5wYx37GutK7bA5OTnIyckJ8zmgr202G7q6upKe2ae0tJTdx9zcXN7iiru4Tk9PR0tLC37zm98kXEYua9asgdlsRn5+vqBmQog+qXAJIaitrYVMJkNBQQHS09NRXV2d8LJEXPbs2YMZM2ZArVZHHeT9fj+ys7N5FdKThcPhwIgRIwRtAxaLBTt27EBxcTEmTZqE559/HoQQFBQUoLy8HJdeemlCcrZy6xh2d3ejvr4eUqkU1dXVLK0fRSqVMu+61tZWVv8xmUUGgH8lgQgEAmG7Bq1Wy7vGEydOCKZnSyZCNVZ9Ph9PtXvmzJlEixUTbtugOZSNRiNmzJjBdnXPP/981GMMpvbihhtuwOWXX85T0QoVTaAexDk5OczpSK/XR/Wf6OjogMlkgsfjwQsvvBD2+datW9nzsWPH9knuM2fO4Lrrrov4eTAYRENDA8v8lOyqPdxx1uv18lKB+v1+fP/993C73bjttttQUFCANWvWJLW27VdffYV77rkHwL9iwmNNon2aQEUiEWQyGVsdhrp6JwO/3x9Tf05T41FHo1h67cGGW43F4XDwijnLZDLo9XrmLOD1epndIJFJCbgeky6XC3a7HXa7HUqlEhqNRtCZgToP0Y6b7LhKutDweDzwer1RPVYbGxsvCo9nLjKZTDBdH72u6upqlJeXJ1qsPiGXy5Gfnx9msjhy5EiSJAIWLlyI8ePHs3bq8/l4Jp1gMAir1Qqfz8dUpdTxp6urK2L2tYceegiBQABerzeuhQ3NilRVVYVVq1bFjAyoqakB0GunE0rEb7PZ4HK5mM05kjYuUXC1O0J1mocPH37RFHAAeucJ2k4lEgn8fj8beyPRZycibgxUMqophJKTk8MGmY6ODl7mC6B3AmpsbITX6036zpPS2tqK+vp6BINBHDhwgNktgN6dEXV66urqwl//+lesW7cOzz77rOAAX1paOij2JO7CyGKxwGazIRgMRnQIIYSgpqaGp6JKtk2jsbERDoeD5bsN/f87Ojpw5MgRaDSapO+WubjdbigUCuh0OsGFitvtxtmzZ7Fu3bqk25kpp0+fxsSJE0EI4TkWCoUPGY3GpC6uuJoHu92O9vZ2Xq1Yt9sNg8GAjIwMVlCZ63QoFJ4yd+7cPmviuLvwVatWoba2Nur3d+7cibq6OtTU1GD06NG8++p2u+F2u+PKXZ0oampqYLPZIJfLw9L0KZXKMOfOZKNWq5l2h26yBnQC5erc29vb0dramrSamhRaSolmFVGr1Tw55XI5a1QOh0NQLZZoiouLUVRUBL1ejxkzZgjGVTocDlRVVcHlcmHo0KHYtGkTnE5nWPWNgZw8aT5NoHdhsmLFCkyYMAEWiwWFhYUR4yRpqAJV4xJC0NHRkfQQi+bmZthsNkyZMkVQFZObm4vS0lLk5+dj27ZtSZBQGO5OOfQeymQy6HQ6ZGdnX1Qq5w8++AATJkzApEmTIuaLdTqdsNvt7D9JZrFnm82G8+fP48iRIygtLeXJnJaWxpuIbDYbjh49yl5Pnz497N4PhBkrUgJ6yrhx4zB69GgWc8ttGwqFgsXkt7a2wuVyoaqq6oJluhDmz58f1/c2bNiAX/ziF4MsTXycP38eEydOZHVtYxUC77cXbn19PRoaGpKWaYYiEong9/vh8/mQmZkJrVYbUaXb2dmJlpaWpHtbcmuS5ufnIycnJ2yAb2hogE6nw7Bhw5Cfnw+n0wmFQoFrrrmGrYoGw5P4wIEDAMCqZVB7Vug9DV04abVatlr3er3o7OxMuhcgdWaKZsfIycmBTCZLelEELjQlYjRidexE4/V60dXVBb/fL5hAw2azoaOjAw6HA4QQzJgxIwlS9uJ2u9Hd3Q273Y68vDzk5+fzvGND27rD4eDd75/97GcDLlM8MYe0f8XC6/XCarUmNd83F27lnVCVrdfr5TloJZNrrrkGQ4YMiTuJCXABqfxqampw7tw5QXVGIlGpVMjLy+Op5yLtfKxWK0wmU9JtXbHis+rr69HU1IQbb7wRpaWlsFgsKC0thV6vx9ChQ1lnFnJSuFCoSv6OO+7Ar371KwC99tDu7m6YzWZWpZ3bEahtnJKWlgaHw5H0nf6oUaN47YI7oLhcLnR0dLDPN2zYkHD5IvHHP/4RzzzzDLKzs3mTkdVqxYYNGxAIBPqUFi8R3H333dDpdCgqKuJNNjabDe+88w6qq6vx4IMPshqtM2fOxOrVq5Miq0KhwKhRo3jewqE4nU5W2srr9WL+/Pl46aWXIJfLw2rznjp1CqWlpey6lUolenp6MHLkSIwbNw7V1dUs6T8hBBUVFWHlCf/yl7/EjA6IpvLk2k/ptSU7S9z27dtx6NAhnD17FhMmTMDYsWPDkm243W5cf/31SZKQT3+KdfTZC9fj8UAsFuO+++7D9u3b8e677/b5pAPJX/7yF2RnZ2P69Ok82wbF5/OhsbERwWAQhYWFKCoqSnoR8Hnz5uHtt9/GokWLoNVqw5xbuJ3baDTi4MGDKCsrg8fjwY4dO3D//fdDLpfjnXfewZdffjmgtRVpblWuDfTIkSMoKyuDTCaDTCZj9pZoaDSapAdHb9y4EcXFxZg7dy4MBgOvcklaWhpzqzcajRELICeDnp4e5OTkhDmBBAIBVpw62YNjKJWVlbjxxhvDdsYikQilpaUYP348mwD8fn9YPcuLiWAwCJlMhqFDhyItLQ21tbWsTJ7X6w3zAxg6dCgv5pg+b25uDiup98ILL+DLL78MO+ejjz4aUy5uSJPZbOZ5DkulUtYvW1paYLFYkp5M/rrrrgvzGqaJ+AkhcDgcCAQCKC0tTYZ4ETEYDMjOzo5Ly9MnFa7b7ebFT40bNy7pqiQa7xTJYcXv97PCyTqdDiqVKq5ckoPNgQMHcOTIEVRWVvLK/ITS2NiI6upquN1u2O12VFVV8RweHnrooQGT6Y477mDPuYN3TU0NrFYr8zD0+/089SwhBDabDe3t7SyAe8SIESgsLBww2foDDV9xuVxwOp28AUcikbAJPtnZtEIxGAyCamexWIzc3NyoSf2TRXd3t6B3u0Qiwbhx43g7Zp/Pxyu2fLFBCGHjGi2SwNWwhHrYch0ZY/G73/2OedMKEa3P0PJ8DQ0NaGpqCtsIuN1uNDU1oa2tDV1dXTGd+Gh4nBC0lmk0nnrqqZjfCYW2a5q9LJk5ySNx7tw51NXVxeUE2WcVbn19Pbq7u3H33Xdj1KhRuPfee7Fq1ap+CdoXhgwZImhvffzxx/Hwww9HTJwsk8lQXFycdJduLvPmzcNDDz2En/3sZ2z3yR0wrVYrmpub0draio0bN+Ls2bM4cuQIpFIpGhoaeNeyYsWKuM6p1+tj7lQnT56MjRs3QiQSIScnB2fPnoXL5UJDQwPOnz/PdmoZGRk81aJIJEIgEEB7ezuOHj2Kq6++GhqNBn/84x/x+uuv9+XWDCgbNmxg2V7Gjh0rGHcL4KJbAW/fvh21tbUYN24cTzuh0+kuOtUthdYqDUWlUoUN0lu2bEma+hbodfh5/vnncfDgQWzcuBGzZ8/mTf5czYlYLMb48eMxfvx4LF26NOxY/d3l5eXlYcmSJZg9e3ZYFZJIJqjhw4dDLBbD7/cLLrhpWCFXPfzss89GlOH9999HQ0MD9u7dixMnTuDs2bN4//332edHjhzByZMn8fDDDwMAli1bBq1WizFjxmDmzJlhquxQrFYrRCIRG8/S0tLY7pz6JiTbU1+I06dPw2g0ssVfNPocxpKVlcWzf0UalAaaSM5KP//5z8Mmz1D7nNvtRk9PDy8TRjJDcG666SZoNBqYzWZmtObKrFKpMHbsWOh0Opw+fZqpQ2fMmIHly5fzOtirr76Kp59+OuY541HzLliwQDBM5YEHHsD999+PMWPGRPxtZmYme9D/45prrol5zsHk0UcfxUcffYTW1tawgt/c+53M4O1InDt3DhkZGRF3CBcbtJB0LBYtWoRvv/12cIWJAXfC+utf/wqtVst7LxAIsGpIsfjyyy+ZarqgoIAV4o5Fe3s7VqxYgdraWuTn56O1tRV5eXlRw1Co74FIJArLnx0IBNDc3Ayr1Rp37mGDwcASO4waNSpMm3jZZZfx5Fm8eDHsdjtkMllcJg+q6dNoNBg5ciSAf3mYi0QidHR0oLq6+qJr44899ljc3+2TCpdOoNwk4dECYfPz83mf63Q6jBo1CpMnT+b9MdHsOYSQMDsCl9DYvtDJSCQSsQLPQK/zyLFjx5Jae+6KK65ARkYGW41xd5+EEJasYsSIEcjNzYVCoYDRaOSly6M89dRTA7KIueeeeyLu0mmoRzxw05MNVk3HeNm5cycOHz6MLVu24Ny5c7zVLvc+xgp6T0awt9VqjWpn5tpzhViyZMlAixSVSPeQe+8++uijpE+eoZw/fz4sXy0hBC6Xi5eKL1I8IDcd59y5czFz5kxMmDAhrnN7PB60t7ez2rmxdmM5OTnQ6XTIzMyETqfjTaB+vx/Nzc04f/58XE6S6enp6OzsxJ49e+B0OpGTkyO4o+SqpqdOnYrx48cjNzdXMHNTPNCxjm5skh3FccFw86rGepSVlREuJpOJXHrppQRAxMfu3bt5vzEYDORPf/oTeeCBB8if/vQnEkpzczN7/sYbb5A1a9ZEPf61115LPvzwQ7J7925y9OhR0tzcTKZNm0YiyVxZWUlWrlxJzGYz6ejoIJs3b2bHOnbsWNRz9fexadMm9ry4uJgQQojf7ycmk4nJ9U85w+RduXIl71hffvll2D1bvXr1Bcl3+PBhYjQaSW9z4LN48WICgJSUlJA33niD1NbWEo/HQ0jvyHiMEIJp06YRp9NJTCYTKS8vJ11dXfTzqI+KigqydetW8tFHH5G3336bLFq0iAwfPjzse1qtlmzZsoU0NDTwZIt1/Pb29rDroTJz77PFYol6HEpo+8jKyiKTJk0i06ZNC/tNbm4uuemmm9jr22+/nfzyl78kS5YsIatXr44pP/dauffZ4XAQo9FIXnrppZgyD0ZbjvYwGAwkEAiEyUz59NNPEy5TrMfq1atZOxFqGxSPx0MeeeQRMnv2bJKfnx/WNggh5MSJE2G/6w9PP/000el0vPdom+FCxwzCaRsWi4UQ0js2r1+/Puq1X3755eTee+8lGzduJC0tLX2SsaqqKua9HTVqFPn8889Je3s7sdlsxOfz8cY5u91OampqeMdNZlugdHd3k2AwyJXpGIkwJ/Y7jAXoVdsdPnw4qrdlqMNDXl4eJk+ejKysLNx5553s/ebmZhw4cAB2u52FT0yePBnFxcWYOnVqxKoTs2fPRkFBAbKyspCZmQmNRhM1gD8nJweTJk1iq73Ro0fjtttuw6xZs1BWVhbvpcfNzJkz8fOf/xwAcOuttzKXbW4N02g8/PDD0Gq1EIlEuOSSSzB16tSw71yoDY/mjKV5ILl8/PHHKCoqwqxZs1BaWoqsrKyw/1skErG6rCqVCh0dHXE55mg0GmRnZ7P0f6NGjcJtt92GgwcP4vvvv0dDQwOWLVuGu+66C9OnT4fFYkFHRwcUCgU0Gg2eeuop5tUXil6vh91ujyv7VLxOZWVlZfiv//ovzJs3D0VFRVCpVCzmbs2aNUyWY8eOsUTaa9asQUZGBsrKytDU1IRLLrmEhTGRf6rjQlm8eHFEtRbtuLEciRKdn3rWrFks/RlXFci9vgkTJqC4uDjpxRy4XHrppXH9/3K5HP/5n/+JtrY2GAwG3HXXXYLfGQheffVVAL02SNo3YyVZEIlEUCgUbIeXmZmJX/7yl1F/M3nyZPz617/GpEmT4pbNbrejoaGBl1giEk8++SQmTZoEuVzOciJzUalUF00NXi590ehd0AQKRE+2O3PmTKb7pohEIowdOzbsxv35z3/G2bNnIRKJ2ASak5ODkSNH4osvvog4SVxxxRUoKCiAWq2GXq+PGTqRnZ2N4uJiWCwWZhO78847WSaMP/zhD3juueeiX3Qf2LJlC4DeGpWzZ8/mJbCOp8Op1Wo8+OCDgp9t2rQJU6ZMQUFBAT755BP8+OOP2LVrl6DK+6WXXgoryq1Wq/Hmm2+y188884zgeeK5HxKJBFKpFCqVCk1NTXFXNqH/gUajwZQpU5CZmYmJEyfi2muvRVdXF+/aaXam1tZWLF68GK+++mrECTQrKwsmkymq3ZbLpk2bsGDBgpjfGz58OK666iree+np6Zg+fTo++eQTyOVy3kJs+vTpzHZlMpni6pwff/yx4Ps0LZ5IJIrp4bx58+aY5xlIZs6cCalUimAwGDFMbNy4cViyZAkef/zxqMdasmRJzCxLixYtiljTt6SkJGYWnqFDh2Lq1KkoKSmJy9YJ9MpPnUpWr14dVl4w3iotQtTW1qKyspKnCl+5ciWeeeYZplrt7OyMWmNXaOybO3euoCllyJAhKCkp6dPkGQwG0djYiKqqqricp6gZwev1CpZwjOR49n8JEemDfUckEnUCaBw8cQaMAkJIDvB/T+b/Q/ICKZkTRUrmxPB/TebUOJcY2H0OpU8TaIoUKVKkSJGil/7rHFKkSJEiRYr/j0lNoClSpEiRIkU/SE2gKVKkSJEiRT9ITaApUqRIkSJFP0hNoClSpEiRIkU/SE2gKVKkSJEiRT9ITaApUqRIkSJFP0hNoClSpEiRIkU/SE2gKVKkSJEiRT/4f9IWDq513jocAAAAAElFTkSuQmCC\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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ca/369YjH4/jLX/6C3/3udzAYDPjCF76QU2ihUqng9XoxNDSEpUuXghCCUCgkaENzCCqVinllNLwtk8nwpz/9CWq1Grfddhu7v9VqRUVFBcRiMXp6etDa2iqIKqTTaZhMJib4vV4v1Go1vvCFL7A2NDRJn0WxdOnSWYsxCCHMUqcTJhqNwmKxIJFIwOFwoLGxESqVCp/5zGfY77JzRdQ4CwQC0Gg00Ol0+OxnP8u+P3v2LGQyGZqbmyESiRCPx+FwONgY8SMsy5Ytw5o1a9j9KU/PBuq9K5VKQYRHpVKxSBA/b0iNQIlEwqIvfOGSTCYF4UXqSWWH4fjPmkvJUw8uuxYCAAufBQIBuN1u1NfXA8jwBg01/uAHP2Dte3t7sXDhQkgkEni9XoTDYSQSCZSUlDCP22w2M2Xn8XgwPj7Oxo3/blqtFkuXLkUsFmOGAQU1OKiA5RuGQCYPGQwGUVNTg4ULF7I8Z742fDlWVFQEn8/HagLMZjPj72g0CofDwdJWhw4dwqpVq1BUVCR4fltbG1NefNCiJsrXHMchFAoxmUj7vra2Fk6nkxmv2WkJCq/Xi4mJCSxZsgRARvEsWrQIqVQKvb29aGtrYwqVyvJly5ax31MD5EIUKF+BNzU1wefzYWJigtUOcBwHu93O9FBnZycqKyvR2NgoSHF5PJ6cXPiCBQsEuiAcDrP0oNPpBCEEl1122XnROW8Fmk6nc5hNKpWyYg0+9Ho9IpEIbDYbOI6D0WhkhKdSKRBC2OT1er1MWOfzWCorKxkj8EOjNIeo1+tZaDA7tDtXVRvN31ALTKVSQavVsgKW7JBbOp1mViS1qvnf0ec7nU6o1eqcUK7T6WRhh7KysnlVv/EFqsViYfkbu90Op9OJurq6nBC7UqnMm8+j+NSnPoVPfepTrC9o34dCIbhcLlgsFhgMBma00CIECvq3y+VCZWWl4NlUQNfV1SGZTMLpdDLhS61TsVjMFCkf2QVFQG7BDw3R0IlEre1878sX9HRiU56i95VIJFCpVDPmpfm8RENhEokEqVQqb66nuLgYarUaIpEIfr8fHMehvLycFVhoNBpEIhEEg0FcfvnlOcqZb6hkgwompVIJpVIp4EOz2czmqslkYjlI2ofZfEvB53WO4/J68Pwqbnq/2eYYpUOpVObldRoF4EeCYrEY9Hq94DkAUF9fz8aGFo8YjUZWFCiVSgXFemq1moXFw+EwYrGY4J1qamoQiURgt9tnpF+lUuWMrcFgyDHIaeSJ9mtpaakgSkbD6lqtFjabDbW1texdqIfF5+/a2lpmoIVCIaYEaFQpnwLlh6iVSqVAoVJQ42kmxUbnA4348fuBfq/RaAT1HDQqQNun02koFAqk0+k55W8ymUQsFmNh8nztDQYDxGIx409awKZQKCCVSrFgwQLodLqc31Kjmp/S8Pv9LNUBgEWqhoaGoNVqc8Z1NlyQB5ptcSoUCoTDYfh8PpZIp9fr6urw+uuv4+jRo9DpdMx7oAlrikAgAI/HA51OxwQsZXh+IQHfA3A6nUin06w99QLnW44dCoUEjKJWq3H55ZfDarXC7/ezjqfhPX5uTSKRMKsZANrb25n1Eo/HBZP59OnTOHv2LIqLi5nFWlFRMa+YO7/PaO6svLwcS5Yswfj4OPbu3QuLxQKtVgudTgetVguNRoObbrrpvO7f2dmJM2fO4M4770QikUBnZycMBgNaWlqYpUqLTijS6TSmp6cxPDzMPPRsfOYzn2H3c7lc0Gq1Ak+ZCodAIACtVotUKsXyW1qtFlKpFAaDgYXCqYKUyWSCHMjExARCoZDAEp6amhLk8ijNdHLTnCs/qpKvqISPRCKBqakpRofZbGZ89/bbbyMajUKhUGDDhg3sN6OjozCZTCgqKkJ7eztCoRA2btyIw4cPw+v14vOf/7zgGcFgEA6HY0YasoUTXyFqNBqBYSCTyZjHSemklaQTExOsMASAwOClfD4wMMCK5BKJhECxyWSyWcO4VGbwBRPf0BwdHUUqlUJVVRUbK5lMxoRcOBwGx3FQKpXsuWfOnEFDQwMLB8fjcQQCAUEU4je/+Q3uuOMOxlupVAp2u53JKEqPWq2edbyVSiVKSkowPDyMqqoqKBQKtLa25gjrnTt3QiaTobS0lHlBarUaBw8eZMpl7dq1LNzP/30wGEQymRQI9rq6OjidTpw5c4Y5BgaDga1KyO5rfp2HSqUSFAeGw2EEg0FW9EVD33yMj48jFAohnU4zL5dfYEM9Y5lMhvr6ekxPT0OpVEKv1yMcDucsU5pNEfHbejweeDweuN1uLFq0CBKJBOFwmBlqlZWVgsIn4K/Gt1wuF/QZAPziF79ARUUF1q5dy7z/cDgMj8eDUCgEh8OBq6++GkCm6ru5uRlisRhVVVU5fTIX5qVACSHw+XxwuVyCXByQKZiYnp5GR0cHsyhoOfYNN9zA2gUCAXAcxzqQWp51dXWsjc1mg1KphMlkgsfjQSAQgE6nQ0lJCWM6n8+HWCyWU5E6G2Za87hkyRIEAgF0dXWhoqKCCeSqqip4vV5MTU3BZrMhGo0Knse/H7XGLrvsMrjdbkSj0RzrWaFQYOnSpSwkQoVK9vokPuLxOI4fP84m7jXXXJNTIEKhUqlQUVGBpqYmpNNpdHV1QaFQoKWl5byrOVevXo3Vq1cDAE6ePImf/exn2Lx5M+688078+7//O0ZHRzEyMoLJyUn2m3Q6zXIt2VWzfMjlcqRSKbZ8AcgovEgkgpaWFrZkgBZ6yeVyttSAeln0A4AVbtG+GB4ehlgsFoQXOY5DT08PW15AQQhhORB+W4poNIq+vj5WsUrpoR4/LUygoFWMTqcTixcvZoqVFoYkk0mUlZWxFAe/etNisQgs5c7OTixZsoTlcfLB4XCw3CoffCU2MTEBr9eLhoYGVqkqFotZjQH1kKgxR3OBfMMmGAxCoVCw6mwgM/do3j4UCqG2tnZGYUlziNneLOV3v98vKPaZnJwUpDtotT5fPgCZED2QMVj5Feb0mQBw6aWXCq5rNBqBscvHTLlyiqqqKkxOTjIjxWAwIBKJ4LnnnmOGDz+10NHRwYxtvhH1yCOP4Nprr0VDQwMCgQDa29tx6NAh3HvvvazNm2++iXQ6jWuuuQZms5kpiEgkgr6+vrwhV1oVLJfLBTxN+zESibDrfENrfHwcXq8XEolEMA789q+//jrWr18Pg8GAs2fPwmQyoaqqis2zkZER1q9Op5N5cXxnh1ak8+lNJpOQSqWw2WyQSqWwWCyIRqMsQlJWVgaJRMJoSaVSOHXqFLRaLcxms0C5p9NpVpvwve99j10/cOAAamtrUV9fz+YGfc9kMimQi5OTk2hubma/o2u2Z8O8FGg6nYbH48HU1BRTAhS0OCcUCrG8Zj709/ejtraWdb7D4YDD4WDhwfb2duahVFVV5a0aBMAqCoFMXqS3txeVlZVYsWJF3ucmk0nYbDaUlZXltTL0er2gipFCp9MhEomgqKho1tBwOBwWVNdKJBKBNxaJRFgOF8gYDmfPnsX69esRi8Vm7C+r1YqJiQmYTCZmfQ4NDSEUCqGyshKBQIDlgIxGIxMEtHw8u1CLj9deew2bN2/O6duuri4sXrwYgUCAhRBpqPzYsWM4d+4cRkZGBL+hXsZcirqoqAhlZWVM6cnlclZ5yN94goKu/eNXWVKIxWIW6qM0UEE/PT3NxoemBPhCUiQS5fAB/9lVVVUYHBxEOp1m96dLQqinqtfr4ff7EQqFUFVVxTzxt99+GzabDWNjY3j00UdZkcLp06dRXl6eYzA1NTXB6XRibGwM9957L9555x089dRTsNvt8Hg8efuRhtr5iosqa6VSydIadAE5rcIFwKpgs71CqVSKeDwOm80Gg8HAhFa2p2U0GpmRmK3A0+l0ThEGDUPS8eULpmx+MRgMgkjAbOttAWDTpk0zfseXBWfOnIFKpYJerxfUaZw4cQJarXbOiAOQUeb8FAfNUWcrByCTaikqKhIYc0CmAp625acZ+Ar06quvZvm+7PQFP3UyH1AZmt3fNIeebew7nU7U1NSwsCmVTyaTKSf0zy/yo9EDiUQiWJs+PDws6CN+xIcWgZnNZpZO44f76bPj8Thb+sg31O12O0QiEaLRqIB37rvvPgwPD+OJJ55gz8yme8GCBdi/fz9GR0fhdrvxne98B0Bmbnu93llTKMA8FWgymUR/fz+6urpQXV3NSt9pwr66uhqlpaWIRqNIJBJ49tln4Xa7UV5ejssuuwx6vR6nT59m1iOQsZDkcjk8Hg8ee+wx/PCHP8Ttt98OmUwGj8eDBx54IG9YkC8Q169fz0KKP/nJT3La0nV4586dg9VqRV1dHbNu+LnbyspKNrl6enqwcOFCSKVSgacBZBTM3r17cddddwHIrI3iCxK6fgrIVL5OTk7iM5/5DAuRAZlwT3t7O9auXQuXy8WELA01isVinDlzBjabDYlEAosWLWIMdfbsWfT09DDhZjabsXnzZpSUlAgYaKbiAEDITDPtGiUWi/GJT3wCAwMD+Pu//3tUV1dj9+7d2Ldvn6AtpYuu2xoZGYHNZkNdXR28Xi86OzuhUqlQVVWVk5wvKytDWVkZ7HY7E2RUcSeTSdTV1bFKPCDjdQaDQZhMJojFYphMJuzZswcAsHHjRnbfXbt2MWG5Zs2anPc7nzB/9vqwfHjqqafw9NNP4+DBg2zSf/GLX8zb9plnnoHJZILFYsHu3bsF9JrNZsE47Nq1CxKJZMaKwEgkAo1Gk7OLj8/nAyEEer2eVZpng1YgTk9Ps0KXtWvXQqPRoKmpCd/5zndQXFyMG264AYsXLwaQsc6pQKyurmbrW/lLR+RyOXw+H9xuN3sWv4rVbrezpQNFRUU5YTkAedfszoTHH388x8DgF3zx8dBDD2FychJisRjXXnstK0y67LLLsHr1avzbv/1b3t/R6EoqlUJ/fz9bjL969WqIxWKsWbMGXq+XVcXS5SBFRUXMAx4bG8Pzzz+PU6dO4amnngIAJtQpjh07xiI/QCY3u23bNixcuBALFixgUbFEIiHYkIGChtBp1XT20pxAIMDC43q9nhUX1dbWCsbA6/XC5/Oht7cXZrMZarUaGzZsQDKZxN69e3HNNdcAyBR10nnFNxL4xsn4+DjUajWUSiUriOLTS0G9PiB/JIC+h0ajYQWUQEYW7N27F/39/bj99tsFUdErrrgCBw8ezNvXQMagMpvNMBqNuOmmm+D1egEADQ0NuPHGG7F8+XL4/X4cO3Ys57cC8Mu15/pccskl5IUXXiD33XcfGR8fJ11dXeS5554jLpeLzISRkRFy6NChnOuBQIDceeedpKOjgxBCiEKhIAAIANLV1UU2bNjA/pbJZIQQQnp6eshbb71F/vCHPxCXy0VcLhf55Cc/ydrRz4oVKwilecWKFSQSiRCHw0GGh4fJ2NgYsdvtZGxsjIyOjpLx8fEc2tLpNHnwwQfJ0NAQIYQQr9fLvnv11Vdz2n/pS18ivb29gmuxWIz9P5FIEL/fTzweD5mcnCR/+ctfcu7R0NBACCFoa2sjTqeTJBIJwT3mg2eeeYY4HA7BNY/HQ7Zs2cLeN7vPZvt8+ctfFrw/77t28m4fj46OCsa5q6uL+Hw+0tvbSx5//HGyd+9eEgqF2Pdut5uMjIzk0J5MJkk8HifPPfccufbaawkAYrFYzvvdBwYGyLZt2wT080FpXrx4seA6x3HkxIkTpKuriwwNDRG3202sViuZnp4m6XSaWK1WMjg4SEZGRsiOHTvIn//8Z8HvX3nllfPqy/3797PfjIyMkNbWVnLkyBGyYMGCvO2XLl0q6GeKQCDA/p9IJEgwGCR+v59d6+/vZ/8fGhoi09PTxO12k66uLhKPxwkhhOzbt4+8+uqrOfzIf/7q1avJY489RqxWK7Hb7cTtdpNEIkEee+wx8uCDDxJCCPnJT35CrrzySrJz507S3d1NXC6XgOZUKkWi0SgJhUJkfHycHD16lPT19ZGBgQHS3d1NDh06RE6ePCng98HBwTnHeqY+pti6dSvZvHkzaW1tnbHNr3/9a7Jt2zaya9euvP2cDbvdTo4ePUo8Hk/Od8PDw+TUqVOkp6dHcP2WW26Zk+7zwd69e8ndd9/N/s6WcxSxWIz09/eT1157jVitVpJKpQT3yUc7IYT88pe/JF1dXezvhoaGHDr/8z//k/j9fhIIBIjb7SbJZJIQQsihQ4fIvn37BPfL/ptPM5/egYEBkkgkGO1TU1NkYGCADA0NkZ6eHnLw4EEBv0ciEXLixAnyyCOPCO79xBNPzMkT+fohX/vbbruN/OY3vyH79+9nfJHvMy8PlIa9dDodKisrIZPJoFAoWAVWvnVuFoslr4czPT0tcPH5a3Go1UtBqzdDoRBisRgLJ9psNuzfv39OummZP93Gju7MEo1G84ZECCFYsmQJS5rbbDZm1Wd7JRs2bMChQ4fw9NNPs9/Sf+l2XXRt47lz59gmC9mglc2EEMRisZzlBecLv9/PrCkALORhMpkQi8WwZcsWnDx5cl73fPLJJ7Fp0ybccsst+Pd///e8bUpLS5mXmEgkoFKpWIXqpZdeipKSEvbeoVAI3d3dSKVSOTtNDQ8P49VXX8X999/Pro+OjuKpp57C3/7t385I4+joKF5++WXce++9OWP66KOP4mtf+5rgGj9kHgqFMDw8jImJCVaBTYs+CCGCNX8VFRXQ6XSCnXf6+vrwuc99bs5+BIBPfvKTjEcmJyfR29sLl8uFwcHBvO27u7vzXs/e2iw7fE6fAYBVKyoUChbWBTIhrEgkwrzc48eP53jPx44dw7Fjx3Dvvfey3Ojw8DAOHz4MhUKBr371q/jRj34EAHjrrbdw11134T/+4z8E9+BvvScWixEOh9k6X71ej1gshqKiIkFokO/JzIXS0lK2FpGPr3/963P+9h//8R8BgG3rSJFvz10gEzGh672z165WVlYKqnAptFotJicnUV1dPWO0Zy7wf/fAAw/Meg+6N284HMb4+DjEYrGgP7O9/L6+Phw6dAhbt27FgQMHUFNTg8HBQbbOl4/vfve7OH78OJ599llWF6LT6ZhcBjKyjC41PJ+9faPRKJxOJyorK+F2uxEIBJjXTzdx4b+f1+uF3+/P2Wzj7/7u72Z9TjYkEgm2b9+e97tt27YhmUwKliDlxUyaNd/n0ksvJYODg+TgwYM52txqtZJf/vKX5NFHHyUPP/ww+d73vkfsdjv7vre3l2zdupWsXLmS/OEPf8j5/cMPPzyr5Z7Pa+vs7MzbdibLLB8ikQg5evQoOXjwIOnq6iLDw8M5bdrb2/P+diZaT548SQgh5MorryThcHjW5xOS8dbMZjMhhGDhwoVkZGSEWXYUd999N1mzZg0BQB544AHy1ltvEZfLRc6cOUOOHDlCjh8/nteyPH78eM61L3/5y/PyQGf5CCx2q9VKHnnkEfLKK6+Q6enpvO/60EMPkS1btpDHHntM4LEODg6Su+++WxCJyPfJxpNPPsn6Za7Pu2PWTghBU1MT84h/+9vfku3bt5NTp06Rt956K4cHZrLYb7vttgvuu+uvv57cf//9zAufTz9nw+fzEYfDQaampti1aDRKxsfHyeTkZN7f2Gw2cvr0abJjxw7yT//0Txf8HkePHs251tPTc17e3HvB888/z57X0dGRl0fmw0fvtm8nhKC1tZWMjIyQeDxOwuEwCYfDJBqNCtp2dnaSffv2ka6uLnLgwAGBx0/R29tLnnrqqQuiJYuuvO35cm758uU5vwuFQmTXrl3kwIEDxOl0Cr4Lh8PkhRdeuOBxJyTDYxMTEznPve2228iNN95ICCHkf//3f8mmTZtyaObzRTAYJFarlXR3dwuiVNlIp9Pk2LFjOdd/8YtfnDfNfHg8njl/8+KLLzK+yPeZlwKlLz1byDYUCpHe3l7y8ssvC4To6dOn87r0Vqv1vAft2muvJT/+8Y/JHXfcMWu7mRToiRMnyJEjR0hnZ6eABrvdTjo7O8mZM2fIqVOn2CC2t7eThx9+WND2fGldtWoV+00sFiNvvPEGCQaD5J133snbvqqqipB3J+/Y2Fjevk0mkwIhyb/OD3EQkmHKoaEhEolEyJNPPkn+7u/+jkSjUVJRUXHBk+Z8BPu+ffvIvn37yIkTJ8jWrVvJ4cOHBXTdcccdgr/vuusuYjab5z155zse9HeU5sbGRsJxXN5+5iORSDBDMBaLkc2bN5Pvfe9772cfzvppa2vL28+EEJJKpUhfX5/gGj/dMBPmMlbf6+f06dN5aZ7JEJkv5sMfhBDys5/9bM52fr+f0VxXV8eMYJfLRUZHR0lnZ2cO/alUihw9enRWebhy5cp500uxZcuWWdvz5dyyZctIOp2etd/S6TSZnp4m/f39JBwOk56eHrJ8+fILGmM+XnzxRfb/7u7uvCHzH/7whwKaz8ewGhoaYvJucnKSdHR0CAzCD3ru/fjHPyaHDh1ifJHvc0F74RYXF8Pj8bClC/y1jhqNBi0tLSgvL2dbLxUVFQnW5fGRXaAzG3bu3ImdO3deCMkAMqGsqakpuFwuwfZhdB2YRqNhoWWNRoPNmzfDarXiW9/6Fv7mb/4GL7zwwnk/ix8SojsRabXaGRds88NENBRON6Wna+SkUqmgEImCboHIx+joKDo7O6HX6/HWW2/hrbfewo4dO2Cz2c77HS4Ea9euzTCWVIqnn34asVgMq1atYu/EXw7xhS98Ac8999y8n/FeNlinmGufWbvdDpfLxXaAOXv2LH71q1/h1Vdffc/Png+uv/76nKUswWAQIpGIFXzwQdd0zoZvf/vb7zOVQszE43R3r2z66K5e54M//vGP86bnBz/4Qd4iIX5okJ9CopsaAH/dtjIUCuHw4cOoqqrC8uXLAYBV2mdX4FLceeed53V6zq9+9St84xvfEFz7y1/+wipCs9He3i44RAMA2/Yx3+YYFE6nMyfUnb0pzvli//79bEOIAwcOYMOGDYhEIrj11lvR29ub0/6nP/3pjAVeM6G3txdisRjFxcXwer3weDzo6enBtm3bWOHgB4WHHnoIGzdunLvYcCbNmu+TbTWcOHFCEA686qqrBKHWw4cPkx/96Ec5nic+YMthrhCux+Mhr776Knn11VfJsWPHyLFjx1hhBSEZr/grX/nKe6ZjJuRrS0O4S5YsYZbksWPHyKuvvkp+97vfsd92dXWRHTt2kGeeeYY8+uijpLOzk7hcLhKLxci5c+eYd93b28s8depB0aKc9+Pz7nucV5hu7969gr+ffPLJD5wH8n1KSkoYzVVVVYJClUgkQnw+HyuMu+2228hPfvITcs8995Abb7zxotCbr5+TySTp6uoip0+fzlsA98Ybb+Qdg/MJV71fn3f5TMAbr732Gtm7dy85d+7cnJ5SPjz44IPvad7N9Ruv18toNplMZPfu3YQQQhwOB7Hb7SQQCJDdu3eTU6dOzUqn2+2+YH6hKY3zbc+Xc62trYKUGR+Tk5Nk+/bt5P777yd79uwhhGQihV/84hffl/Gez32yPdBYLEa6urrIf/3Xf5GlS5eSN998k0VRent7yaFDh1jKcGxs7EOde0899RQZGhpifJHvc0EKNLvKjI/p6WkWVurs7CT79+8nU1NT5Gtf+9qH9uLvVljOqECj0Sg5ePAg6e7uzvnuwxyg7A95N89MMTIykpNL3L17Nzly5AgL86ZSKRKJRARt+MbAB/Vu794vR4HSymU+tm/fTu67776L2re8TzshBAaDgXz7298mW7duJXK5nCiVSnLJJZeQm266iZSXl19sGmfs54mJCbJ//37S0dFBurq6SG9vLwmHwyQYDJKJiYm8yuli9jPlDRoSvVB8UHTee++9/Ge0E0JQXFzMcm1er5dViM40ryi+/e1vf6h9zFegDQ0N5J133iGTk5PEarXm0MbP6+/bt++i8fPSpUsJIZkVHV1dXaSzs5OEQiHS399PXnjhBfLyyy+TQ4cOMSWaSqXIH//4x4tCK80r4/0O4fb29go2T+fjtddew+OPPw61Wo3PfvazqKysxLlz5/Doo49eyKMuCF1dXbN+Txco8xcyd3V15WwOcTHAD0+WlJTkLCKnR2fRiki6d2t2m4uB06dP5+z+8lFFIBDAww8/LLh27tw5nDt37iJRNDfo8XfhcBj19fWIRqOYnp7G2bNn2fmT/DXT/f39s64F/jBBN0qZL86ePZtTlf9+4sc//nHONf6c4p+pOdNuS9PT0/iHf/gHvPHGGx8YnXMhlUphdHQUfr8fEokECoWChZaDwSB7n0Qigauuuuqi0dnf3w8gUzk+OjrKUmdNTU1oampiJxJNT0+jubkZO3fuxPe///2LQuvp06fnbHNBCnTXrl346le/OuMuKRTns8Tkw8DExATefPNNtLW1IRaLweVyYf/+/eA4DsXFxbjvvvsuNokMsVgMAwMDkEgkgtyy0+mE2WzG1VdfDavVij179sDj8bBlB0NDQ/jv//5vVFVV5eR73o+cYTb4udjz2YHoowYyS/7zowT+JE6n01AqlaitrWUGVEtLC7797W8jHA6jtbWVLXT/qIDm2LJ3+KL4zW9+w7arpEsKVq1ahePHjyMYDH6gynOmfKFKpYLP54PT6URHRwfWr18/46HQH7SCP18kk0ns2LEDIyMjuPHGG9kWi2vWrLngPOcHAXpMGV26xN/SEshsoH/XXXfh8OHDF4O8eWPeClSlUs3rvLSLjXynvH+UQbenC4fDTIFarVYcOXIEV199NUwmE0QiEbRaLdatW4fJyUl0dHTg1ltvxRNPPJGTqP+gFBu/UGQuj7+AC8d3v/td9n+ZTJZ3d6T//u///hApmh/oZvU1NTX46U9/iuLiYqxdu5YVFd5xxx2srVQqxbZt23DixIkPxSDLPgeSQiKR4Pnnn8eePXsQj8dRW1uLJUuW4OTJk6xwa+XKlXj99dc/cBrPF4lEAoFAAHK5nBUfDQ4OfqSUJx9erxd33nkngsGg4BzbjxvmrUA/TsoTyHhuHyfQLbiopeZyufD222+jo6MDjY2NMJlM7BQatVqNnp4evPjii/B6vYKK5o+KZVzAe0P2tonZ+POf//whUXJh8Pv9OH36NCoqKvDQQw+hvr4eHMehurpacIoOAHz/+9/Htm3bLhKlf4VYLMYTTzyBQCAAIFPRTreFo/goKE/+ST30nFm+p3wh53B+WIhEIh/pdMl5Y6bkaL4PLlLi+UI+H1ea8xU9HTlyhBw7doxs27aNbNy4kbW/7777WJt77rnnYtDc/nHr448zzStWrLjYdFxQP19//fWEECLYJu79rAh/Lx8+KM2VlZUXna550J8j52688UZSVVV10WmbjeaLTcN8+APvdxFRAR8sAoEA/H4/lEolPB4PwuEwrr76auzevVuw/unmm2/Oe5xTAf83Md8tGD8qeOONNz6yOfJ8W/L5/f6LRM37g5dffvlik/B/Br///e9n/b6gQD9i8Hg8+OlPf4oTJ06gvr4eNTU1bPOBbAG6aNGij6xgKqCAjwNWrlyJoaEhwTX+8VwF/P+Nr371q7M3mE8Id8WKFSQQCFx0t3quz7vrdz4WIdzLLrvsYxnaePfDQovV1dUXm5Z50fwRoKNA80fkQ9da42MWKpdKpR8bOcf/fNzoxSwh3LkPRcyCTqfDsWPHsHbt2vn+9END9mHFH0UsX74cu3btmvu8uY8JJiYmLjYJc4J/lmABBVBkH3r9cQH/hBWtVjvnFo4XCzOtn71YyFPbc8GYlwJNp9Pw+XywWCz4n//5n7wa2e12z7hmaj7Ytm0bu2dXVxcOHTo0n2InBr1en/dA1Xxobm6el0f+xhtvYOfOnTh8+DC+//3vC47mmgunT5/Gpz/96f9TIdjs/vnlL395sUli2Lp1K3bs2MH+5h/iOxuuvPLKvLx1xx134JFHHsHatWvR0tICQkjew9wL+HggezOSUCj0gTxnfHwc3/rWtwBkKqjdbvd5rRTI5sEbbrhBsGFKOp1GTU0Nmpub2SHhdM9ePt4P2TxfJBKJnGsNDQ34j//4D3z5y18WvNsvfvGL9/XZdPnRbAqTXr/yyiuxfPnynOrwWTEfhZF9sPH27duZm1tXV5dzysm3vvWtWV1juVwu+Lu5uZkd/3MhAEA+8YlPkJaWFkJpXrx4MfF4PITjODI4OEi2b99OPve5z13skIDgc8kll9BDo3GxaZnnp50QggULFrB9OI8ePUoOHDhATpw4IRgbu91ODh06RLZv3z7r1n5Go5GYzWZSXl5OqqqqSFtbG9Hr9QTInHBTX18vaHv77beT7u5uMj4+TrZs2ULuvvtucs8995BDhw6R+++/n9xyyy3kpptuYnubIs/2gx+hbQZzPiMjI4zmj1N1KD5GIVwAdK9dxhulpaXvy30JyZyMxP+bkMzh1bfffjuxWCzv9f4gJHMM4j/8wz9c9H48X5pXrFhBHnroISKXy8nNN99MPvWpT5Ha2lry3e9+N+8RjBSPPfZY3uvf+ta3yCWXXEJEIpHgWc8//zxrc/jwYTIwMJCjM7I/mzdvZt9zHMf4It9nXkVE2VvE8V1zjuNyvKmHH36YbZfW3t6Oo0ePYteuXZBKpSgvL8evf/1rpNNpdHR04LnnnkNLS0vOzhTZGBsbQ3V1NSKRCDQaDcRiMUKhEH73u98BAA4fPoz6+nrWPp1Osyq7xsZGNDY2YuPGjTAajYhEImhsbMTbb7+NQ4cOzacr3jcsXrwY99xzD372s59dlOe/H5DJZBgYGMCJEydw6NAhqFQqVFdXC06MKCsrg06ng1arRXNzM8RiMa688kp0dXXB7XajpqYG9fX1MJvNcLvdqKysRGVlJdLpNLq6unD06FH80z/9E1wuF9566y0Amd1tli9fzk7y+Md//Ec4HA4QQtDY2IhgMMhO1sj2MPi45557cP311+eccHGx8Y1vfEMQ1aioqIDVagUAvPrqq/j617/O/v4o4fHHH8edd94JAKivr8ddd92FsbEx/Od//ueHSkdVVdV59w/f4+Q4DmazOe8h3fMBPUCevx3n9u3bMTQ0hAceeICd9HOh4J/ApFQqsWTJEtTW1sLtdn9kC6H4h2tv3LgRdrsdFRUVCAQCsFgs+OEPfyjYYjUb2Qe+U3zzm9/E1772NRgMBuzduxcHDhzAnj17BCfDJBIJvPPOO6ipqcHrr7+edwOSG2+8Ed/85jfZ33OdxiIi84gBr1y5ksx1PM+//Mu/4Fe/+hWATG7h+uuvx6ZNm/Dggw/izJkzgrYqlQpGoxEGgwE1NTVQKpUQi8XndWSU0WhEa2srli5dimPHjqGvrw/RaBS//e1v8eijj6K9vV00G83JZJLtcflRwMqVK9He3i7S6XTkgwoffQA4SQhZSft4cHAQFRUVmJiYwOnTp7F48WL4fD4cOXIEnZ2dGBwcxNGjR9Ha2oq6ujqsXLkSu3fvht1ux1e+8hUMDQ1hZGQEXV1duPXWW3HrrbfC4/Ggo6MD77zzDq655hqEw2H09vbCYrHAbrfjlVdewcaNG1FaWopUKoWamhqUl5dj+fLlOHjwIIaGhmCxWLBq1SosXrwYRqNRQPNf/vIXfOpTnwKQOX7q8ccfn1cHRCIRPPnkk4Iddehey3zs378fCoUC1dXV89oXdnBwEE1NTScJISsXL15MPuhdn9xuN9tDdf/+/fjkJz8JILOHKTVYk8kkpFIpNBrNjMJOJBKxfn7wwQexceNGwfd8uUMN75aWFvT19X0AbzU3zGYznE4no/mZZ57BxMQErrzySkG7l19+GTfddNP7+uzrr79+XvvoHj9+HKtWrWIyA8jIuRdffBEDAwO45JJLMDAwgH379uH06dMIBAJsdzNCCORyOdxuN/x+P3w+H6RSKaRSqWCTnLq6OshkMnAch5GREXZdp9OhqqoKixYtwttvvw0g45jU1dUhEolgz549kEgkkEgkUKvVuOKKK7By5Urceuut0Gg02LBhA06ePCk6H13y1FNPYcuWLRgdHcUbb7yBVCqF9evXC9pYLBY8/PDD+NznPpfz+1deeQU33ngjqqur8corr8BisaCvrw9btmzBSy+9JGh7yy234Jvf/CZWrFiRcx/Ky/lovOBlLG+++SY0Gg0WLFggiBnfd999+PznP4/jx4+jqKgIRUVFaGtrw2OPPYZgMAi3241gMAi/34/Dhw/jqquuwqZNm1BXV4fJyUl0d3fjm9/8JqxWK06dOoVgMIi6ujrcfPPN+MEPfgC3240vfvGLuPrqq1FTU4NYLIaJiQn4fD6YzWa0tbXNuHH966+/joULF6KxsfEjoTxTqRQ4jhPsydnS0sLOEPzOd76D//qv/7pY5M2I1atX4+jRo4KIQ39/P4aHh7FgwQK0traitbUVvb294DgONTU1+PSnP42SkhKUlJRgdHQUkUgECoUCmzZtAiEEGzZsQHd3NwYHB+Hz+dDW1oYlS5ZAKpXimmuuQWdnJ+x2O0wmE26//XZUVlaCEIKrrroKFRUVKCoqwoIFC8BxHKRSKbRaLcrLyzE1NYV0Og2LxZJX2NMdnwDMuHPTSy+9xIRmPB4XjJdarRYoS6fTiWeffRaVlZVYunQpampqIJfLmSLKxkxnYfb29uL48ePo7u5m12QyGWw2G7xeL6anp2GxWGbMu0ciEUxMTEAqlaKxsZFd7+npQVNTE6RSKQghmJ6ehtvthkajQTweRzQahUwmg1QqxcqVK5FKpTAxMYE9e/YIFKjX64XX60V3dzcikQi0Wi3uv/9+lJeX5/TzNddcI1CYw8PDeP3112G32zEwMMCuU+XZ1NQkuL5u3TpYLBZwHIenn36aXb/77rsxPj6OPXv2QKVSvact4VpbW1ku0ul0IhaLCZTniRMnUFRUhPr6erz44oss0nLdddfh5z//+Yw7QtXW1uLLX/4ytm7dikAgAEIIdu/ejU9/+tN47LHHcPXVV6OxsVEwlzQaDYqKimYszLviiitw9913CzzYVCoFo9GItWvXQqPRQKlUQi6X4wtf+ALEYjE4jmPeWGNjI/x+P+LxOGKxGEpLS6FWqxGJRBAKhRCNRsFxHHQ6HQwGA0pLSzE5OYne3l4kk0lYLBasWbMGvb298Pl88Pl8WLx4MRQKBaamphCPx5FIJOB2u9HY2IjKykpWqJWv5iMUCiGRSLBtSimuvPJKJJNJjIyMwGKxoKioCL///e9hNpvBcRyeeOIJPPDAA3kPNjl79iy8Xi9uvvlmfP3rX2eK8fLLL4dOp8M///M/o6enB1u2bMG//Mu/YN26dXnnv8vlyjsGFBesQEOhENRqdc5pIUVFRVi/fj1Wr14Nq9WKRCIBnU6HsrIyKJVK5sJTZl22bBmrlG1oaIBcLmcnSmzevBl9fX0oKSmBxWLBHXfcAYfDgWXLlmHhwoUAMuERk8mUiUdLZ38djuNywiY2mw1arVYQDqETqKioiIVhKLq6ulBcXIyysjImOP1+f17hPDAwgKmpKZhMppyTXqLRKOx2O6xWq0DA8bFlyxZs2bIFO3fuRDKZxHXXXQepVDrvw73ngsViQX9//wUbFdQQUKvVgutGoxHJZBLpdBqNjY3s+6amJsRiMbbPKL2+aNEi1o8qlYptRaZSqbB69Wp0d3dDq9WisrISQGYybty4EbFYLGcMgUyVIn2n7O8o+Jucz3SoM7XUjUYjgsEgUqmUgC/4BqRYLGa8Tk9Ome2Un+HhYbjdbmi1WpSWlsLpdMLj8aCvrw/j4+Nwu92srUgkgkgkQjqdRiwWg9/vByFEIHRGR0dhs9kQDAYhlUpzNgmYmJhAcXExSktLMT09Db/fj1gsJhi7VCoFmUwGtVoNh8MBt9vNvAoa0tLr9eA4DqlUCna7HYlEAk8//TSuuOKKOU/kaWhowAsvvICpqamcENmdd96JW265Bd/4xjewatUqXHLJJbj55psRCAQwMDDAFOiyZcuwefNmBAIBrF69GqWlpXjkkUdyttw7X3ziE59gaRyO43L2yfV6vZDJZKiqqsKyZcuwadMmxgPr1q0DAPz85z+HUqmESCSCzWaDQqGA0WjE7bffjhtvvBFTU1MAgE2bNuGKK65gYW4AeP7555FIJLBixQpotVo4nU4899xz+NOf/sQUqUKhQEVFBUZHR+HxeHL2uVWr1YzfjUYjqqqqBNEOWkDU0NCAeDyOVCqFdDqdMzfC4TDC4TA0Gg17x5qaGlRXV8PtdsNsNkOv1+Oyyy4Dx3GYmppiz2loaGD78lKDV6/Xs3vni3ju3r0boVAIOp1O4N2XlJTg0ksvRUtLC4qLiyGTyfDZz36WRUhSqVRe5dnR0YFoNIrW1lZEo1Fccsklgu+bm5uxePFiXH311dDr9Vi1ahVqa2shl8sRjUaRTCah1+sRjUZx9OjRnPsLMFNyNN+nubmZHDt2jPT29pJYLJaTyH322WfzHuo6MDBAenp68p4VOT4+Tg4fPkxeeukldo7obBgeHiYvv/wycblchBBC+vr6iMPhIBzHsTbvnqkJQjIHVM+Fjo4OweHEfr+fTE1NkcHBQTIyMiJom0gkiN1uJ319faS3t5cEAgFCCCHJZJKdG8jHnj17yNNPP01GR0dzvvN6vez+9Gy/hoYG8oc//IH88Y9/nJPup59+Ou/13//+93P+9v0A8hTk2O124vf7Be18Ph+x2Wzs3NJIJELGxsby9gmF1Wolb7zxRt4zGM+cOUOOHDlCJiYm2P2npqZy2oVCIeJ2uwkhmXMFrVZrXpop6IHGhBDy+OOPkzfffJOcO3eOpFIpdj0ajZJnnnmG/M///A9JpVIkFAoxHshGX18feeWVV0h7ezshhJAdO3YInkFI/vNTKdrb28nWrVsZzTPxcjKZJMlkkhCSOY83e25Go1EyNDRE2tvbyY4dO4jT6SSEEBIOh3Pu5fP52P/Hx8fJyZMnSWdnJ3G73TOehxmPx8nIyAgbD0L+yhtNTU1k37595J133iFTU1PE4XCQyclJ8vOf/5y89NJLgvt8/vOfF/ztcrnI0NAQGRgYEMxvinzFJk6nU9DW5XKRaDRKCMmcScovKskGpbmlpYXs2rWLvPLKK4x/snHo0CGybds2sn37dtLV1TVjO3oO5zvvvEPuvvtuQkhmPM6dO0cIyRx2/eyzz+b9rd/vJ+FwmDgcDvLkk0+y8zK3bdtGxsfHBeeB8s8RpsimyefzEY/HQ+LxOOMZyjcUiURCwAN83ickc8B4V1cXefPNN/PSTGGz2ci5c+fIyZMnyalTp9h7tLW1EUKEB2qHQiESiURIIpEQ0BMMBgX3TKfTgu0gHQ4HO/9227Zteeehy+UiR48eZXP26aefnvHgcfq+9DzVyclJ8uc///n9KyJSq9VYtWrVjG64yWQSWPGxWAyhUAg1NTWIRqNIpVIIBAICi6SmpgZVVVXsFBKPxwO1Ws2spXQ6jWg0ing8LjgHk1oher0ecrkciUQCSqUSNptNUBAgFouRSqUE3un09DQ4jmNeS2trKyuISiaT4DgO5eXlSCQSSCQS7CgxIBNGKysrE7xnPB5HMplEIpFAJBJBeXk5e97atWths9lyrMVYLAa73Q6tVotIJMKuGwwG+Hw+/OpXv4LL5YLRaIRMJsNXvvKVnD6fydK/7bbb8l7/MFBWVoZEIgG73c6sRoPBgHg8junpaeh0OkilUlRWVgrGpKenB2KxGFqtFlVVVaisrGSeEB/pdBqVlZVIJpNsDFQqFeLxeE54lW9BA/nDRzQ0bDAYBCedrF27FtFoFHK5XBCiVSqVWLduHYaGhjA5OQmFQgGJRAKv15tz6k9zczNbLhOJRLBixQokk0mMjY0hHA5DrVYLjqzLRnFxsWCupNNpOBwO6HQ65jHS4/mATFEfrSPgY2pqCsXFxaitrRX0+fj4OCoqKgTRE35/mUwmlJeXg+M4hMNh5oUVFRUJ7i+Xy6HRaDAxMZGzHlGv1+fkEQHgS1/6Uk7EiO+R7du3DxUVFTAajSx0nI1oNJqzFV9JSQn8fj/C4TAbGypL+FEQPsbHx2Gz2djfWq0WmzZtAgAcOXIEZWVlaGhoYJEChUKBdevWYd26dYhGoxgfH4fdbodGo8k5Io0W8yxevJjxn1KpRF1dHYDMfLniiitY+76+PhQXF0Mul4MQArVaDbVajb/9278FIYSNd748OpWxkUgESqVS0C8ejwd6vR4ikQjRaDQncghk+Ivm72mEiOM4wXiXlpZCoVAwD1YqlTL5p1ar2TiVl5ejvLychYnpPKJ9wHEc+vv7MT09zTz47H5zuVzwer0oKyuDXC6HSCQSLD9LpVKIx+NQKpWCPvR4PIxmqVSKRYsWYfXq1Uin0yyKMxMCgQAikQgikYgg+jMT5l2Fm/1wOnmpC85HMBhkOT6FQoFUKoXx8XGBUAD+WumkUCgwPj7OQnRARqF5PB5MTEzg8ssvh0QiEeR9FAoFxGIxC/e5XC6BshKJRIwRKHPTpDohBDqdTsD0lOFFIhGj2+v1IhKJ5J18AFj4khCCRCIBj8fDYv5arRb19fWw2Wzw+/2MiTmOg0wmg1KpZKEU2hcmkwkcx+HPf/4zIpEIY/7Pfvazgud+FPK4+RCPx+HxeCASiZiS0+v1LC9SWlqaIzwdDgc7XJeChgmBzOSmYcSSkhIEg0HGN1SAU+NHLpfn3J/juLzho1AoBKvVCoVCITCKamtr4XK5BMolnU5DLBajqqqKTUaxWAxCCMbGxqDX62dczE5zTUBGSHZ3d6OoqChvDpMaAtkpBJFIBI/Hg/HxcZbHTKfTSKfTIIQgmUyipKSE5SmpUQdk+DC7sCkcDsPv90OtVsPn80GtVgueJ5PJ2IfmR/P1IZAZK2rsns+C/urqajYmVKZs2LCBfU+PQKPvk41kMomioiL4/X42D6hSIISwPB7/fQwGA5NRVquVFceEw2GBEctHKBSCTCZDQ0MD/H4/QqEQqqqqGH+pVCpUVVXB5/MhEolALBYzeqLRKKNdq9UKUjUajYalnajRSXPDV111FUpKSpBIJAT8JxKJoFKpBBso8L+jhg4N3/NldTAYZEolmw8oYrEYxGIx5HJ5Dv/wYTAYUFJSglAoJJCvHMflpLKoDCWECJ7LcRwCgcCM1cKhUIjlbu12OzNO+Ss/lEol6+vKykrmlPT396O5uRnl5eWQy+WsAp/PR7FYDKlUKseQoONHaylmkvkU73kvXIVCgdHRURBCBDt6BIPBnEN0pVIpxsbGmGBqaWlh3/n9fvj9/pyXonF//vmTfMbIVuoGg0GgWDiOg8vloutYAWQEQygUgt/vF5zcvnv3bjQ3N+fsTFJbW8s80WQyCZ1OB5VKha6uLjQ2NjKDQKfTQafTYXh4GFNTUwiFQli3bh2kUilqamowMjICj8eD+vp6aDQaNqFSqZRAMNEKVAqHw4ETJ05g//79WLp0KbZu3cqWfhw7dgzBYBCNjY246aab8IlPfAJyuRwdHR344x//iKmpKdxwww247rrrcPbsWaRSKYhEIkxMTMDhcGBsbAyf/vSnAWQE+7/+679CJpPhmWeegUQigUajwaWXXorh4WF4PB60trbmPZOS9vWJEycQj8chFouhUChgNpshFouhVCpZbjsWiwkMEprL4AuGSCSCkZERmM1mlJSU5CwAD4fDzHMsLS1lAmlsbAzJZFKwA5XL5UIikch7NuLll18uWDoVDAZBCIFerxcYepOTkxgcHERtbS3bo5giFosJlMfY2BhKS0sFS2f4k7elpQUcx7HvOY5Dd3c3gsEgMzoaGhqg1+sFc0gul7PcPx/ZBimQEd70fMh8Xm4sFoPJZIJarUY6ncbY2BgsFgtTOFQQ0zExGAxMMQeDQcjlcshkMoHxu2jRIlaclP0sv9+PdDrNDmJPpVKYnp7G1NQUm5tmsxmEEIyMjKCxsVEwhu3t7RgfH8fGjRuh1Wohk8nQ1taGeDyOxx9/XFAFbTQaodPpIJFIMDw8jGg0yo76o/ROT0+jq6sLf/M3f8OKZ/KhoqKCeYs6nQ69vb14+eWXsXnzZrZcTqvVsrxlV1cX6/eioiLBEYNSqVTgMQ8MDEAsFqOiogIajQatra0wGo0oLy+H0+nEr3/9a9x///05Tsvk5GRew4vSoVQqBUYMX5ED+TeNoLxXWlrKlCiNCvb19aG0tFTg0dbV1SEWiyGZTKK0tBQOhwOBQADJZJLRQJFKpSCRSCCVShkdIpEIFotFwM/xeBzBYJB5rXyDw+v1Mjrr6upYoRVFMBhEMpkEIQRtbW3sO/670jHWarXMu9RqtQIjzmAwMCNg0aJFjF9nwrwVKA1rarVaFo4qKyuDyWSCTCaD1+tFIBBgSdxsrFmzhlX5AWATsqioiBE+OjoKiUSC4uJiqNVqSKXSGU8c0ev1iMVizFPhhxEAsLAHv9pSq9WySZEdPuWvIaWwWq1QqVQwGAzMArLb7TlCEsgMUl1dHfOc+aAhkmzwrcVYLIazZ88CANra2gBkFH55eTmCwSAOHjzIBnbt2rWwWq2s0MNsNrOwo1qtxoIFCwRVvNSwkEqlWLZsGVKpFMLhMJqbm+F0OgVLCNavX494PM4O725paYFUKp11jZZEIkFVVRUUCsWM26ONjIywPiaEwOl0IhqN5oS+qEAmhOTdPUWv10MqlQr60263M4szkUiwsaIe6/mcZTs0NASJRJJTkScWi1FaWgqPx5OjkJRKJZuw6XSa8RYhBKOjo5DJZMxIo2hqamLjEQqFmDfZ0NAgiMDMtQ6NguM4eDwepnD1er2gsI7jOFbsJhKJoFQqBe9x6aWXsmeNj4+DEJLD2zqdDul0GuPj45BIJDnjPJO1rlQq2clC1IuXSqUoKipiCo6OjdVqxeDgoKAPKH3ZPAJk5m9paSmSyaSAT6i3o9PpEAwGc34nlUpRVVXFCsB8Pl9e2gcHB+mGLDCbzTCbzairq4PJZEI8HodUKoVEImEeVr60CjWwFAqFQFFrtVrm9ScSCRBCmMFiNptx3XXX5Q03UiUzE/j94HQ6EY/Hc8aGRi4ofygUipzwv0qlglKpBMdxbD0136Pnp8bKysqY0ZUdGaPt+FEQKleyaaWRuOyxNhqNUCqVKCkpgUgkEszvdDqdd/cgvmKkleK0PfDXueXz+ZghkI188pqPeSlQQgj8fj+LSweDQUSjUUGYJRQKweVyCVztcDgsqOzjIxAIwGazCawJh8OBRCKBUCiEBQsWsAGhA0knNu1EmgMFkBO6oP/nHy7LH2CaP4tGozkeczgcxtTUFKLRKAsHUMRiMVRVVbF7+Xw+5t1RRskeEIlEMuOA8HMD4+PjbCkHvVZbW4upqSkMDQ1hw4YNLBdQVVWFqqoqEEJgtVoRDAZhMBigVCpzrFRqbWk0GtTV1QnCnBKJRBDCpJYzx3GIxWI5CmAmmEymnLAIDUmmUimBAKHVpJFIRBD+p2sRZwo1ARlhLZfLBYIvkUhAr9dDJpMhGAwKaKYWMP/ZwWAQ6XRaYBS4XK4chd3f3w+TyYSSkpIZl0qUl5dDJBIhFAoxj9Dr9cLhcMBgMAg8kVgsxp5BBSfd2CO7ajZbgWbncahCSiQSOQaCSqVifZhMJpmnlS/UTJ8Ti8UQCASgUqmg0+ly1kvTkDU1WvlCai5Qj4bKAKVSyVIf9BnU+KbRCv5vi4qKckLz6XQatbW1kEgkCAQCcLlcqKurEyjQWCyWs1xIqVQKctb5ws7U8M4OM9Lfeb1eDA0NsfGcaXvIPXv2oK2tDQ0NDfB4PCzPKJfL2VwZGxuDTCYTzNl8m8rQ/p7tsGw+z3g8HkgkEkF0hxCCQCAAjuOYIUoNomzQeZlMJuHz+QQKVCKRCHhDo9EgFAoJ5m32qgfKKyKRKEfR0voYvoPF/x1f7vOjPul0Oq98crvdKCkpYeFiyneJRELwDFp1TecSBQ1pz4Z5KVCRSITi4mLodDoolUoYDIYcRq+oqEBJSQnzAmjJv9PphMPhYEzm8/nYZKaKgqKhoYElnrPDtVKpFC6XC2NjYxCJRMxyViqViEQiOeEKmUyWE3Kcnp5mQk4kEmFychJKpRKNjY1MyBuNRkSjUSiVyrwb0vOVp9PpZBY7XxHQ/AB9D4vFglAohN7eXpSXl7O8ID8MrVKpcNVVV7F3SKVScLlcWLhwIUpLS7Fs2TJ2f5fLxYp0aH5s//792LBhA1wul4DZ9+zZgzVr1uQN942NjQEAvvKVr7A1mhaLhXnzBw8eRGNjI6qrq/N6GYQQNqGzJwxdp0vXBC9evBgOhwM+nw8VFRWoqanJEcDhcJhNCOq10DwKDQ8aDAZIpVKB5Uk9PyBTyr5q1SooFArs2rULFRUVAiFClZ3T6YRUKkVrayvEYjHUarUgbON2u5FIJJhxxTeKenp6YLFYoFKp2Pc2m42FkgghqK+vZ+vbwuEwE1oU3d3dWLZsGYxGI9uEwuPxsPmT7QVSI1IikSAUCsHtdqOlpQUqlQo1NTXweDxsiVlxcbGgcIXOVZfLxfJE2UgkEmhqamLCdHJyEtFoFHV1dcyApBEEn88Hr9cLo9EIsVgMn8/HDNp8oGtHA4EALrvsMqjVaoHH1tPTA7PZjEWLFgHI8E5nZycuu+wydHZ2Ynh4WLBgnhp2/IMtIpEIAoEA4vE4XC4X2traWPrEarWCEAKXy4XFixfPaqDRPvvSl77E/s5WwiaTCY2Njczo4Ss1fiHL8PAwq1+YmJhANBpFU1MTvF4v5HI59Hq9QMacPHkSUqkUS5cuRXd3N7q6urB8+XI0NzdDJBLNuF6Zgm6OoNVqWdicKgvKO3q9nskYKsfi8bhgTaZSqWQ5zGAwiImJCVaYJ5PJGG/29vaivr5ekA4DMtEEs9k84/67Ho8HiUQCVVVViMViiMVibOyBTIib4zg0NDQgEomwd5LL5UilUqxojo+JiQkolUoWBi4pKckxIDiOE8xjKkM8Hg/i8TgIIWwp2lx7B887hEtzWzNZnlTYAWCeocfjgVgsZmEZWmzDV74DAwPQaDQoLy8XeIK00IGGD+lgUw+ED4VCwSyqbJopaOEQH/ziCerB9vT0wGAwCGgJBAJsgTKlI51OIxQK5Q39SiQS+Hw+VhgEZJiVhk6o4s+mlX9NKpUK7s2vNKXhb1o8Ul1djauuugptbW0YGhpiBV6pVApFRUUCwR0KhaBQKCCTyQSKR6VSscIJIDPhaCXkTIKRWsTpdDrHqlQqlSguLmaVbRqNBmVlZYKoQvZ48e9BjSaFQoFEIgGRSCSgIxAIIJVKCSq3ab85nU7odDqYzWb2Dnya+YUclEcsFgvzCqiVnm3gUUQiEQSDQYGSo4UcZWVlORb92NgYlEqlYByyQ4cqlQoajYZViWf3OQ1/Uo8h29tPJpPM0KXzkyp0+p7Zlb3U0s6mDch4FXSu0dwe7WeaPqF9Rz35mTzS6upqlJWVgeO4vILp5MmTgmrKSCTCoioLFixg+bJUKoXR0VHBvKDeNX/ta3a0w+FwsPTFhYBWn9JxJYQIIgZ+vx9arRZisRh+v58pUH6VqVgsZsK8tLSU9QPdClUsFqO2tpbxlFwuh8lkmtepUtS4lEgkaGlpYePjdrtzvHv+rllUWabTabbFHh1LnU7Hqrhp9SvlPbp+H4AgtMwv8skG1SMAmNOSLQc0Gg0ikQhisVhOhIDyMvVCaT/SFR0ABJv022w2qFSqnEI5vlFkMBjg9/uRTCbnNK7Ye5xXqyyIRCJBoQBNJgOZAeErLJFIhK6uLhbaBDJCOdtTOXDgAN5++23B3oW0LbVcGdFiMTQaTc5kp0Uvs718dmUekBFafEEkkUjQ3d2NVColmOjBYFCQ1ySEMKacCdFoVDCRKZPM54gfPg3RaJSF0YGMkKB7dtJdn4DM8iCFQgGPxwO73Z6TI+jo6EBHRwf8fr/gOp24MpkMqVQKyWQSBoMBGo1m1o0qqMeVb8KYTCYkEgnB5CoqKmJLjLLDUfznSKVS5tXQCjn+M3w+H5xOZ07JuUwmg8/ng8PhYAo025vTaDQwmUwCIVhZWSkIwearOk0mk6xggk5wCqqQspVnMBiE3W4XKExCSE7xilKpZCmA7EIJIDOfaDUyDQHy+4/OP74S4zgO09PTmJycBPBXoUzppV5bNoLBINRqNWtrs9lYtALINfbmWiJAUzg6nS5vaKy/v1/Ql/F4HF6vF263W7BJgM1mw6lTpwTzvLu7G6Ojo4L78qMl6XSaeecXCpVKxcY8HA7n8C3dac3lcgnCvitWrGDLMiQSCTPg+TUV0WiUrVowm81MHtFipPmc2kSX7wBC52F6ejqnLiMej7NlPxRisRiBQADT09MC/qdLeDiOY1XHlEb+/ejuRAqFYka6qSGsUCjYqohs2UGfl2/PYPp+lJaOjg5BZT7w1/BzIpHA9PQ0q7fgw+l0Mp6gS56yT7mZDfPaC1ckEjkBjM3Z8OKjjhBiBj5+NH+M6AUKNH9YKND84eDjRnNBzn04YP2cjXkp0AIKKKCAAgooIIMLCuEWUEABBRRQwP/vKCjQAgoooIACCrgAFBRoAQUUUEABBVwACgq0gAIKKKCAAi4ABQVaQAEFFFBAAReAggItoIACCiiggAtAQYEWUEABBRRQwAWgoEALKKCAAgoo4AJQUKAFFFBAAQUUcAH4f+BNzhjlODRrAAAAAElFTkSuQmCC\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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ICQnxa3XgwZlU+rMVFhbS119/TXfccQcBGJabUqmk7Oxs4mSeNGkSlZSU0I4dO6inp4e8qa2tJSIih8NBAOi9995jxwZzf2++/vpreuKJJ3z2ExFZLBZqbW0ll8tFRUVFRESYMmUKL01PTw8dPnyY/f/DDz+w38eOHWO/tVot+93Z2cl+2+123vU6OzupqqqKt6+lpYU6OjqIiMhoNFJHRwfV19f7yOuZfzabjQAcIiIUFRWRRqOhiooKKi4u5p3jcDjIarXy9jU1NdE333xDb7zxBhER3XfffQHztLu720cWjueff579PnXqFO3bt4/27t1LZrOZl06v11NrayuTeerUqbR//35as2aN3/eXk5NzXsuuPziZJ0+eTPX19VRaWkoHDhwgjUbD8vP999+n2bNns2u98MILtGvXLmpoaPC5nk6no1OnTlF1dbXg/err69m1y8rK6Pjx4+y8w4cP03vvvUcnT54UPNftdtPJkyd5+WwwGEij0VB7ezs1NzfTyZMnyWazsXOcTifp9XoymUzez+2z3XvvvfTMM8/Q/fff7zfNpZdeSmVlZXTq1CmfsudwONjz+MvnX75FRmdnJxUXF9Nrr71GL730Er399ttUWloqdD5vu/DCC+nGG29k///hD3/o8/mE4Ooob7g6Q0jmvu4zFFtSUhJlZGSQkLxff/01LVmyhF5//XXasWMHHThwgB0zm83kdDpJpVLRmjVrePUex/Hjx8npdLL/3W43739v6uvrqampiZeew7P+/CX/DpEfnTigHqjT6URlZSU++OCDgZx2XtFqtbxeoMPhQEdHB9ra2mAymXwcjzizqFQqxYwZM3DjjTf6vfbmzZtx3XXXYd68efjxxx8F0xw/fpzXWl+yZAkaGhoE0zY2NsJisfDMCJ6yA70mqIKCAva/Zy/R0xnFszXlac70HpSPj4/3cUBKSEhg5qrw8HCEh4cLtu49zSUWi4V3rLOzE0eOHEFkZCQbvDebzdDpdD5jTPX19Thx4gSWL1/er1Z0bGwsAN+8AcAbx9FoNJgyZQoiIiJw8uRJ5qB06NAh5iTFYbfb8eyzz+KLL77gXe+yyy6DXC7H9u3b+5TrXHPRRRfh+++/BwDmNOZpRuR6i2q1GtHR0czkt2LFChw8eJB3rY0bN+LUqVOIjIzE3XffzXosJ06cQGpqKqKiolBZWYnk5GQkJSXh+PHjzIGorq4OMTExyM7ORnNzMyIiIjB58mTs3r0bra2tsNvt+OabbzBq1CgsXboUx44dg1qtxrhx43jDCZ5ycx7gUqkUoaGhvHIpkUgQFhaG06dPM2cQf6xfvx5tbW346quv/KZxuVxQKBSQy+XMQ5krZ/4cVfzhcDigUqlQXV2NMWPGIDQ0FHK53MdS8vTTT/P+JyL84x//wKOPPgqg1xrFWcwGyrhx49DQ0IAxY8YM+NyBmnl/Szo6OgRN/Xa7HadPn8axY8ewYcMGNvTAwVnS0tLSMHHiRBiNRpw+fRrx8fGsl+htBRGJRLBYLD4WRM6rXi6XM1lqampgMBgwc+ZMAOi3oxwwQBOu3W7Hrl27mHfjcMVTPpvNhpqaGjQ3N2Py5MmIjY1FSEgIOjo6YLfbeebG0tJS9lvIpMqxcuVKvwo0Ly/Pp6K/88478dJLL+Gaa65hNv62tjbs27cPoaGhPMeGvkwmnsrUs6ISMkf4w9s81d/pCZ5jSd7eey0tLdizZw9mzpyJ5uZm5Ofno6mpCRaLBTExMbxnPHjwIDQajeBYTyC8TeTetLS0MO/Fo0ePIiQkBEqlEtu2bUNubi7PGcFgMPgoTwDYuXPngGQ6l+zduzdghedwOHD69Gl0dHRg5syZbDqYt/IEfh3W0Ov1eOihh3yOjx49GqdP+3Uu7DfPPvss7/+EhAT86U9/4u2z2WwwGo2IiYlhZmfuObmxT4lEgpMnT8JkMmHSpEkB75mSkoJLLrkEgPA46JgxY5CdnY2IiAg23CCXy5kntj/TrxCdnZ2oqanB3r17cdtttwmm2bFjBx5++GGf/Zzy3LNnDy6++GIA/DL84IMP+ow5+ivjn376KRQKBUaNGoWrrrqqT7m9p3MMF4SGftrb21FbW4vm5mYf5enNihUr0N3djbKyMuj1ehQUFDCnO+8pKVqtlqdAueGww4cPM493oLfer6urw8mTJ3lmXqDv+njAPVBuXuZIwWw2Y/fu3aiqqsJdd93FFI1Op4Ner0dPT0+fH6y3Q5RKpRqwHHfffTfvf4vFAqVSiaysLJ4S99c63rBhAxITE7F06VJm009MTGSOUVKpFBqNhs0bq6ioQEtLC6ZNm4bu7m6o1WrodDqMGzcORUVFaGxsZM5Id9xxB4gI1157LZYvX478/Hxer/jEiRO8MUWtVuujQJOSkpCdnY1Fixaxnl9eXh6cTifKysqQmZmJrq4uvP3221i5ciW++eYbv9MTgN6efF5ens9xfxXM+++/z7MeXHHFFWxe7Lp165gjC8dg3uFQ43K5kJKSgqKioj57an1xLpSnEJ2dnTwnKc6r1263Iy4uTrDxZrfbIRaLsXjxYp4zYiC4xuPcuXN9FOj333+PEydOYNq0aayXodfrYbPZ2JQWs9kMrVbLGln+HI0cDgdmz56N3//+94LHa2pqBI95z6HlpnJxShXobXx4K1Du3A8++IDXEPnrX/+KiooKlJWV4csvv0RCQkJAR77hqDz9MW3aNDZunZKSIuiLMGPGDGzZsgVZWVmIjY3F4sWLecf37NmDqqoqnDx5EiEhIZg7dy7vvTQ1NaG0tBQOhwOJiYno7u5GXV0d3nnnHRw+fBhutxupqalob29HcnIyO68vT+cBKVCRSPSbfXi/FXa7HVVVVeju7uY5N3CedyaTqc9rPPHEE+z3I488guTkZPzrX//C6tWrBy2XSCSCTCbz60Xpyccff4xbbrkF+fn5WLp0KXbu3Amr1YpZs2ahvr4eRITp06fj5MmTaGlpQWVlJXPyKCwsRGxsLKKjo3HkyBHodDqcPHkSXV1d6O7uRktLC1OGP/zwAyZMmICwsDAUFhYC6DUlHjt2jCnQqqoqqNVqH0eRiIgIxMTE8ByGgN6KjjOjq9VqaLVaHDt2zGfuJsDv5XuawfsDN40H6K20vXvV3qY7oUnfwx0iwujRo3mOFAcOHBhCiYTp7u7m/S+VShEWFibomONyuXy8gPsDN5zgadngqKurw48//ojc3FyWLjQ0FG63mylezpGOC9Dij4yMjIBWgQ0bNvQpa3t7O2pqaiCTybBo0aI+0wO9jjfePfmpU6di6tSp2LNnD3OGEmKkdXI8nb6ElCcAlJWVDajR+PHHH+Pee+8dkBx33XUX7rrrLgBATEwM7rjjjoBe4MAAFahEIuFNdRgJmEwm5t1YWVmJiRMnIjw8HPHx8bDZbFCr1SxtRUWFj5eiJ08//TS+++477NmzB+Hh4X4V6F/+8hc2Ad8fCoWCTWDX6/UBTQXcSzx69Chmz54NlUqFnJwcTJw4Ea+99hpaWlqwcuVKlJaWory8HG1tbZgyZQruuusuXHrppayCWLx4MRwOB/bu3QuFQsE8lDk8x6mA3rHDuro61NbWsrmRU6ZMwcKFC3HZZZfxZIyNjUVCQgKrCLl5bECvt1xFRQWioqKwdu1awdZxINOsN0K90Pnz56OiogIPPvggLBaLoFnzvwFvr9Lf/e53PmmWLFmCOXPmYPXq1RCLxVi6dCnS0tKQkJCAUaNGCTZeBotSqcRbb72Fiy++GPPmzYPVauVZJ0QiEZRKpY9lhYhgs9lgsVh4jRupVMqbguMPTjH6G35YvXo1xo8fj9TUVCQnJ/uYbUNDQ5GYmBhwmhMnfyC8G4xC7Nu3D4cOHUJoaChmzJiBdevWob29HS+++CJuvfVWvPnmmz7nTJw40e/1Fi5cCKPR6Peb4XwGhjslJSVsBsRwo6enB0899RSeeuqpwAn9eRcJbWlpaUPuydXfjZPZc9+OHTsEPbJsNhv985//ZF5wAtcarAx9smLFCvroo4/oF+9bHy/coc5Hf1tSUhLzTuM86r755hsiItq9ezctWrSI56mpVqtp69at3Hn9yqu6urqzyttjx47Rzp076ZNPPvHMz0PkVS5GwHaIiPCLB+OwLBcCnvnMC5fDZrORVqul1tZWMpvNZDKZfDwe+yr7REQqlYr27NlDRESbNm3yK5PVaiW9Xk8Wi4WIej3SdTod6fV6f/dj5bmtrY0qKip4x0tKSmjq1Km8e2RmZp7XfP7b3/5G27dvp5dffpmSk5OJBLxwh7os9LVx8mq1Wnr//feHXJ5+bH69cAcUykLI5l5bWzuQSwwpQubnb7/9FtOnT8f/+3//D4Bwi/O39GTjwt15OlWcj/ueLR0dHT77uB6n3W5Ha2srzzweFhaGgwcPCp7nj7Fjx8JffM++8ubkyZOQSCRITEzEoUOH+gxeMRLoT3zioeLVV18V3O/5nrq6utDV1QWTyeQTNrC/5OfnY/r06VixYgUA/vCKNwqFgheYQSQSscAPnjgcDhiNRva/0+nERx99hJtvvpk3p3fWrFmoqKjgnXsu5oAOhKeffhq///3v8corrwQcAx0JxMTECAa/GVH406yC2lYsFmwReu87V1tGRsZZtXKEehqeTJw48by1Yh599FHBVu8777xD5eXlbE5XWlraiGlJwqsH2tXVxWQ/dOgQ+93S0kIHDhzo6335ZcKECf06x3O+6EsvvcQ7ZrVaqba2lsk8DPJuwPlcUFBAq1atGmpZBlU2iHotAsePH6fOzk5yOBy899PR0UFr166lH374gaqqqmjr1q1nLYPnnGTPnm5XVxdZLBY296+rq4tOnDjBZB47duxQ512/NoVCQeTRA92xY4dPmuFYj3iXi6GWpx+b3x7ogBSon8wY6ofz+5KGY0X52GOP8SqOtrY2Ivp1UrRcLqeHH36YXnzxxSGXtb8Fi/sYuGfx5rPPPuvP+/KhuLh4QOcBoKuvvprq6urooosuohdffJEFC6ipqaG//e1vTOZhkHcDzmdv8+Ew33wUqGcDS4hVq1ZRSkrKgO6zYsWKgHXQRRddRHq9nsrKyngNLKfTSUajkYh6g5B4Nq5iY2OHOu/6tUVFRbF6rqioSDBNoLwZqs27XAy1PP3Yggp0OG1ERNu3b6frrruO1Go1Ef2qQIdatv5u4eHhrGBxHwOnrHQ6Ha1fv54+/vhjuv766/uVH97cdNNN/c7Lvj5EIqJt27bRBRdcwGQWiURDnocD2A7RL+Pjw0CWAcnsL0KOzWZjCozj7rvvDnjNDz/8kPf/xIkT2bmB8ubIkSNUW1tLdXV11Nrays7hxkJ7enqovr6eySyVSoc67/q1jRo1itVzBQUFPsf7+i6GavMuF0Mtj9BWXFxMTz/9NCmVSlYuhLZzshpLIDgvtZE47+63wnNcqKSkpN9z34YTQtN/Pvnkkz7n1AZisGO+fZ0nEokwduxY3nSFkJAQn2hKw52R5gEfiIqKClgsFqSnp7Nl+u6991689NJLgul/aVyyqR233HILdu/ejerqakyaNAkVFRV+y0F7ezubPnLmzBm2bFpkZCR0Oh3cbjcvOpfn9JArrrgCX3755Tl55nONp2fx+R6LHSjc+/P2Ih+uPPDAAygrK+s7oT/NKrRBQFN7xxIdLlsgmYfbFhsbS7m5uTRS5PXYWC+jqanpbN7VoFuiHCEhIX2mUalUTObU1NShzrsB5/Mvvf6RsrGyYbfbyWAw8HqbFouFXC4XEfWadrmYtYHen+fxpKQkksvltHXrVnZsxowZBPSa8QNdwzM+tMlkIrvdTm63m8nsed6oUaOGOh/9bp6xcAPl21DL6SlLfn4+ceViOMnXx3ZuvHCFeP7558/2EmfF9ddfz4scMZJYsmQJgN6J5yPJm1mIF198cdDnvvnmm4PufXK9yP70Jj2Xl/OMtDRS6E/Qj+GAZ0hMoHd+MRd4w2Qyobq6GiEhIcwiEBsb269wkp5LhXGhOGtqati+Cy64AMCvKyl5otPp2G+RSMRi5HIh/vyVv5aWlj7lCtJ/+hs2dKRw1gp0qF2p/YV+GgkMZdzVc8369esHfe6qVasGfW5YWJjgcnB9ER4eDiLC3LlzB33vIMJ4Blp3u92wWCwwm83Ytm0btm/fLjhksXnz5j7foWdwDK4BtHbtWhbjmFvoXAjPcH/d3d3o6emBxWIZ0JqfI43hNA3u3XffRVlZGVs6j2M4yTgYRnzp4VaEDzJ0eIduG24kJibyIk55snnz5hEzLjMSISJIJBJERUVh/PjxCA0N5a12UVJSglmzZvldsciTV155hf32HA/mejWcRUdIQXvHVR4p0XoCMZLG8G+++WaEh4fzgrt7ht8cqYx4BRpk6GlsbBxqEQLiGWvTm/6EYgsyMDyDEhARZDIZoqKikJCQ4JO2uroas2bN6jPAhsPh8Bv7lbsuVyELNapnz54Ns9kMh8Mx4ns9HCPNMdNkMvECZwx3x6f+cFYm3MLCQuZdFeTcQ0R9BjMO0j/8VZqBYh8HGRye68ZKpVJERkb6mEo3b96MPXv24JZbbgHAX9tWCCEfgaioKCQlJaGurg5Ar5K9+uqr8e677/LSrVmzBhKJBDKZDOXl5bxYzE1NTVCpVH4tFMMZobU1vRuLw62XN9DIU0PNp59+GvD4WSnQjRs3ns3p5wXPNSBHIv1dvSHIwNm/fz8qKyuHWoz/avw1sLOyslBUVMT+50JpesOVf259U0/0ej06Ojpw5swZfPfdd5DJZIIORJxSkclkSExM5Cme2NhYSCQSn9WFRgKeTnEc3otBD7deHuc4NtzXlOboc+1Vf+65QhuGsZu0gGwBI3QMt01oGgtRb7D5YZzXIyqqzy/5d4hoZC2MMNLy2VPmwsJCUqvV1NraSgaDwSeEH1FvCMZA74yb/hDofr98P36/EQ5uugwRsVB+Wq2WqqurR1w+C01jGYZ1BG9LTU31qeeG8+ZZZwhtZzUGKhKJcPPNN5/NJYL8gufgOoen2XG4jdsEcswZCZw5c2aoRfiv4ne/+x1++uknn/0SiURw7NNqtaKjowP19fVYuHCh3+v2t9zX1tYGTLt+/XosXLiQWaRMJhP0ej1SUlIQExPT57JmI4XhVk9409rayn5z1onhLnMgznoaC7fwcpD/WwxkVZUg//0IKU9vLBYLHA4HgN5IUAqFAjab7bcWDQCQmZmJ+Ph43sos/VnMPsj/bfoy7Z+VAt2/fz9bwXuoOHbsGPsohPCcaD0SKCoqQnNzM6677rqhFsUv3uNanmNZI4Vg5Xn+OXPmDFQqFRuTTE5OxsyZM/HMM8/85ve+6qqrkJKSAgBwuVwICwv7r+l1AiPTGU7ICWq4sW/fvoDHB61AiQjz5s0b7OnnjLy8vIDBHEbKXKnDhw+z36NGjcLmzZuHUJrAiESiEak0PRkzZsxQi/B/CpvNhrFjxyIrK4uZdF0uF5qamrB69erzKktLSwuamppw6tQpVFRUoLW1FXa7/bzKcC5wuVzst0gkwuOPPz6E0gwci8Uy7M23V155ZcDjg1agL7zwwmBPPaeMtLlQ/hCa4+bZ07viiivOpzh94r2w8EhjJI/fjjTsdrtgQ7anpwdtbW0AwHqH5wNuSotCoYBYLAYRwe12n7f7nyu8g0+M1JCmI5lBK9AHHniAxeYcyrmgZ7P6x3CEGyPi4Ly9vvjiiz69pDdt2oSVK1cOKKze/PnzYTKZ2DW0Wi2sVivvutnZ2T7njcQIUJ6t3aACPX8YDAZetCqNRgOdToeWlhYcO3YMwPldaSY5ORlpaWlIS0vDuHHjkJaWFnAYaLjiPT53xx13DJEk/71cdNFFgROczTSWodoyMjJIoVD05X48rGTuz8bJ67nwLxHRc8895+P6X19fT/v27aNHH32Uli5dOuB7rVixgu6++2668847acmSJTR//nyaPn06rV69mk6cOMG7l9VqpU2bNrFVLu644w6ee3dWVtaQ590AthE1VWEkypyZmclk9lx1o6enhwwGA28Vls8++4yIiHbt2vWbysSh0WioqanJ53vyLM8TJkygRYsWDXk+9vO5QETIzc3l8n3Yb8O5LM+aNYtOnTrF/u/q6mLlQlAnDkSBRkREDPkDAqB169b1u2ANtayDKVizZs1iH/XmzZtJKpWy/99++2267bbb6M9//jPdcMMNNHXqVEpKSgp4XalUSjfccAOtWLGCbrvtNlq7di3t3buXvvvuO/rwww/pqquuovT0dAJAU6ZMobfffluwgmlubqbZs2ezCggjrGL/ZRtSmWtra33yta/3d65lXrVqFTU2Ngq+YyKijo4O3nzJQFx44YX03Xff8fa99dZbTGZvBarT6cjpdBJRrwLdvXs3O/5b5jtHaWkpnT59WvBZvGX+4IMPhrqs9ue5QEQYPXo05eTkDLk8/ZX5XFxn2bJl/Sqjg2Hu3Ln04Ycf8sqF0DageaDR0dG8OJfni+TkZERHRyMtLQ01NTV4+OGHA6b3XGh2pJGYmIgrr7wS7777LiZOnIisrCzs2bOHHR83bhxmzJgBqVQK6u39+ZifTp8+jZ9//hkqlQpXXnklLBYLXC4XJk+eLHjPFStWYP/+/ViwYAEqKyvxP//zPygrK4NarYZEIsGsWbOQm5uL2NhYLFu2LOCqFyOFoqIilJeXD+rcxYsX47PPPuPleyBniCuuuAJ2ux27du0SPO65mlBWVtagosdw00Ly8/PR2tqKxsZGyGQyKJVKqNVqiEQiNtTyxhtv4P333+eNS1osFuaZ7Pn9HDlyBI2NjQgPD0dRURFv4WkAuPXWW3lmrl27duG9994TlDE6Ohp2ux1qtRpGoxF6vf68DP943kOr1WL69Ok+aYSm0/zpT3/CypUrf1PZzhUOh2PERPcBeusxLjzj7bffjquvvtrHXLpx40b8+OOP2LJlC7799ltMnDgR69atw2WXXeazitKpU6fQ2toKo9GIadOm4eDBg/jss8+wZMkSLFiwIKBOcLvd+PTTT6HX63Ho0CFUVlaipKQEiYmJfQ8R+tOsQltoaOiQt14CbQ8++CCtWbOG4uLiWMtsqGUayEa/mGK6urr8toy8zbtEvYsTV1dX+0R50el0RERkNBp5Ziu73U6NjY0+9zl16hR9++23tHnzZnr55Zfpvvvuo3vvvZe2b99O7e3tRNRrAuPACO6BFhUV0dq1awd8/s6dOwV7MP7SZ2dn06pVqyg5OdnvO/WktLSUrrnmGlae6+vrA+bzrFmzaOXKlXTVVVdRYWEhLVy4kKZMmeKTbvTo0TRt2jQCehejXrlyJbun0Wikjo4OstlsRER07Ngx6uzsFJTPYrFQcXEx+9/b3F9aWkpr1qxhMk+dOpW0Wi2dOXOG1Go1bzHr7u5u+uCDD/rMw3PwXTF27tzJftvtdmpra6OOjg7SaDS8svFby3QOnw1EhHHjxtF111035PL0tWVnZxMRYfLkySyP9+zZQ59//jmVlJSwfS0tLWS1Wqm7u5v27t0rWBbr6uqouLiY9u/fL3icQ6/XU319Pe3atYu+/fZbOnLkCO+4wWCg5uZmIuqtAysqKnjHca56oMPdU+3RRx/F119/7XfVhuFITEwMr+UYEhIScKkl7x4A0BvVxWg04syZM4iPj2fBsrk1E7m1L1UqFcxmM3P+cjqdkEqlLF1WVhYLPv3ll1+CiOB0OqFUKpGUlAQAiIuL87l/dHQ0b8HikcLjjz+OOXPm8OIN79q1C2q1mq0XuWjRIkyZMsXnXC7vXC4Xvv76a7/3KCgoQEpKCqxWK3Q6HaKjo3nXaGpqglarRUREBCZMmIAZM2bwFo72JDk52Wft28jISMjlclgsFlitVmg0GthsNsTGxvIcd/Lz8zFu3Dikp6cjMzMTBQUF7FhHRwfi4+Nhs9lgNpvZYtVxcXE+PWuXy4XOzk50d3cjNjYWGRkZvOMhISE8pzMigslkgk6nQ0REBK/8KJXK874eJxfM3Gw2Q6fTwWazQS6XsxitIxWFQoGioiJUVlYKBt4fau688048+eST7FvzzO/p06ejrKwMX375JWbOnAmg18kvPT0dCoWCLZTuzTvvvAOj0Yi4uLiAUyqlUimam5tx/PhxyOVy3qLera2tCAsLY0saDjT4/oBKb1paGk6dOjWgG5xP3nnnHZSWlo6YuZ/0i2lpw4YNbFFpzwpl3bp1SExMxJw5c9DY2IicnBwWisxgMKCqqgoJCQkIDw9HTk4OjEYjWlpaoNPpWEHkiIiIgMFg8Fn1orKyEuHh4UhISOAp5/nz56OwsBBms5lXEbtcLkgkEt41xo4di0OHDvk83z/+8Q9s2LABp0+fHkz2nHO++uorXH755QB6vT4///xz5vWsVquxfv16GAwGJCUlYcaMGZg7dy5rjGg0GqjVauTl5aG9vR2VlZVQKBSQSCQBTcFr1qyB3W5HbW0tHnroIWRmZmLRokUoKiqC3W7H6tWroVQqMWHCBEyYMCGg/GlpaSgrK8Njjz3GzKS7d+8WTHvNNdeguroaQO9ctrvuuktw3dO6ujpUVVWxVX9OnDiBhIQEQeUJ9FbUkydPZoooNDSUheULDQ2Fy+XiTUkRi8VIS0tDamoqrFarj6IKFMbvXPHzzz8zsy0XgD0sLIy9v/8GZDIZli9fjgULFmD69OnYtm0bli9f/pvdb//+/WcVB8BgMGD37t2IiIjA7NmzsXDhQpjNZna8p6cHJpOJt3JOa2sr5HI5K5urVq1CSEgIG0qpq6tDfX09WxeWu49EIsGFF16ICy+8kO1XqVSor69HQ0MDL2jN0aNHUVFRgRtuuAFA73cfiAEpUIVCgcceewwbN24cdlH+Z82ahfvuuw9Ab2EaCfztb3+DWCzGzz//LNgCLiwsRFpaGiZMmACxWMyrALmx6NGjR7Oxq7i4OFgsFjQ2NqKzsxMxMTFwOBws4odQw2Ly5MlobW2FXq+H3W5nPc2oqCjWMzUYDLDZbCAi1NfXIz8/v1/P98gjj+CRRx5h/3/yySe4+uqr+3XuuWDZsmV48cUXWb55N/5cLhezViQmJmLatGnIzc31eT61Wo3a2loWrzg5ORlTpkxhcV4XLFiAJ554wuf+zz77LKZNmwYAmDNnDogIp06dwk8//YSioiKEhYVh/vz5sFqtkEql+PHHH33GdrwZNWoU3n33XWRlZcFsNiMiIgIdHR2QyWSIj4+HRqNBUlISli5ditDQUDgcDjQ0NKCnpwcKhcJnLMizUQb0liGXywUiQltbG1OGR44cwahRoxATE4Ps7GxYLBYYjUZEREQgJCSE9SZTU1MFI/x4hs4zmUyQyWSQy+XnZWHrffv2MQWam5vL9tvt9v+aiFQikQgZGRlQKpXQ6XTIzMzEww8/jHXr1v0m9zt69OhZKVC3242ffvoJtbW1mD17NgCwv4Dv9BGVSoWmpibk5eWxhp2nL4ZOp0NYWBjGjBmDo0ePIjU1FbGxsbyl9TxpaGhAV1cXMjMzeUpao9Hw4vV6KnUhBqRApVIprrzySkybNg1SqRRPPPEESktLB3KJQVNQUIB58+ZBJBJh7969iI2NhUKhgNVqxcUXXwypVIqSkhIAGDHmmHfeeQcSiQRRUVGCSn/s2LGs8k9ISOA5rTgcDkRFRflUAKGhoVAqlbBarWhpaYFWq0VaWhqSk5MFHTbEYjHCw8Oh1+vR1dUFhUKBqKgoXh5GRkZCr9dDo9FAq9X6XEOv16OiogJTpkwJ6Ezzxz/+MaDTyCuvvIK///3vbI5mTk4OOjo6kJubi5kzZ0IqlSImJgZpaWm49tprYbFY8PXXX+Phhx+G0WjEPffcg4iICDgcDpSXl+OTTz4B0NsQycnJ4ZnKRSIRpFIpz9yfl5cn2Av84osvMHr0aN5Ede9J62q1GgcOHEBpaSn27t2LlStX4s477+SlEYlEGDNmDMrKyuBwOCCTyTBjxgx0d3fDaDSiqqqKmVhtNhvP1OTNY489xn63tLRALBYjJSUFGo0GYWFhvMUJYmNjWfSdvhzsoqOjIZfLYTQaoVKpkJSUBIPBgPb2diQkJLD363a7odfr2X1CQ0MhFoshkUj8Vlqe8nKNj/MRTu/TTz/Fgw8+yNtnt9thNpv7VKBXX301Pv74499SvHNKZGQkiouLkZycjH/+85/9UqB79+4VNJMG+pZPnz6Nmpoa5OXlBbz24cOH0dzcLBjRR61WMysJAMFFBzi4Rry/zpHFYkFERAQSEhJw8OBBWK1WmM1mpKen+6R1OBywWCwQi8U+QxBWq5VFpXK73X07ufkbHBXaCgsLqbi4mP7zn/+wAdaysjL66aefqKSkhA4fPkxOp5M6Ojpo/fr1tHbtWtq8eTNL6+18MXfuXPrPf/5DdrudKisrad26dbwpHES9UyeOHDnCc1wQoqWlhQDQuHHjKCUlhTiZCwoKaPLkyUM+eO69XXDBBUz248eP09ixY4m8HBgsFgsvH44fP07t7e1UXV1Nra2tvOfXaDRUWVnpMwDe2trKuw5HeXk5HTt2jEwmk88xk8lEPT09vH06nY5UKpWgE9HEiRNp48aNdM899/DO4eb7ERFVV1fTwYMHecc9HVD8OQKUl5fTli1b6PXXX6enn36aHn74YVq1apVgWo6ffvqJgF/n09544430xhtv8JasmjhxIlVWVvIcFzxpbm6m4uJi2rlzJ3388cds/6ZNm+irr76igwcPktlsFjz3vvvuoz//+c/svgaDQTCdp0MNEVFlZSWVl5fT/v37ac2aNbR9+3ZqampiMnuWDbVazX673W7S6/U8xx+tVkuHDh3iTZvRaDQ8x7Hy8nKqr6+n7u5uamxs9HnnLpeLfvjhBzp+/LiP7MeOHePlXVdXFzmdTjIYDKRWqwVl5ti3bx998cUXtHfvXp5z22/5vXF0d3fT9u3b6YsvvqAffviBJ5eQzMPZcTI9PZ2Ifl22kWPnzp3suz5+/Dh7fx988AE9/fTT9PzzzzOnGX8Euq9MJhM8x2Aw0Nq1a3n7Xn75Zbr00kvZ/F9uCbaCggKqrKz0mQJVVVXFK7Mul4sOHz7MS6PVaqmtrY33/XjWY21tbVRZWUl79uyhxsZGMhqNRESC9SBR7/SqM2fOEBHRoUOHeFOrLBbLuXMiEolEiImJ4Wn16dOno7q6GlKpFOPHj4dIJEJiYiIuv/xyKJVK5jRQXl6O06dP8zT+5ZdfjoKCAshkMhQWFkIsFvus8jFq1CiMGjUK3d3daG1tBRFBoVD4LBybnp6OJUuWYM6cObyFvqVSKe69914899xzOHLkyEAe14dJkybxWkwPPvggcnNzkZycjDVr1rAWeWhoKMLCwhAbG4t9+/ZBoVDghhtuYEGzp02bhu+//55dZ/z48YKRUOx2O3NwkMlkCAkJYTFFufQ2mw0qlQoWiwWpqak8Jw2HwwG32827ttPphEajQXp6uk9vxOVyQSQSISQkxGfleKfTCaPRKBgAWiqVorCw0Cccm1gshkajgdlsRkVFBcaOHcs77hl1KSkpCUTk0+odN24cMjIyEBISAqPRyJbA4jh69KiPyXXOnDm4++672ZjukiVLkJWVxes1ymQyJCQkCMZRpl/Ml8nJyUhISOA5/owePRoFBQVs39GjR3HixAmeadozzGV7ezvr5ZaUlCAuLg45OTlsZRLPFnVMTAyICGFhYRg/fjySkpJ8yoXb7YZWq0VHRwecTifrdbrdbl6PVS6XIzk5mWeeiouLQ0NDA6KioiCVSiEWixEVFQWlUgmlUgm3282cozjZ8/PzWZk6deoUHA4HcnNzeT0Pi8UCk8kEh8MBiUTSpwVo/vz5AY//FvzhD3/AqlWrUFhYiAsuuABut7tfcVh37tzp14llKFm2bJlfZ6HU1FRW5saPHw+Xy4WSkhLk5OTgoosuOquQf1deeSWLeKTT6aDVatlycBERET5OOKmpqZg6dSq6urp4vTmJRIJRo0YJhnDkHPhCQ0PhdrvhcDh430pMTAzzzeCGnJqbmzF+/HgAvdahxMREVg4dDge0Wi1UKhXCw8N9IqtxY/eA7+pifUWoGpQCTUlJgdlsZpUpN2biWSA9x1WAXgeO06dPY9myZWxfUlISz2kmPT2dZ/7RaDRMUcbGxmLLli1Qq9XIycnBzJkzfcZPbr/9dqSlpfFWpReJRFi8eDHy8vJw3333weFwIDU1FTfddBOys7ORkZHBM3cVFxdj3759iIuLw6JFi3wqfX8sXrzYx6PQaDQypfn3v/+dOQoJeXoJmevsdjsbxJbJZBCJRDCbzbyX2tnZiebmZshkMp4i0ev1OHnypI+StFgsUKlUbGyOo62tDVqtFmPGjGExQj1xOp3Me9fbkUgqlWLixImCc6bi4+Pxv//7v7DZbDxZnE4n7xpJSUmorq5GV1cXwsLCmBNUREQEez8RERFITk5GcnIyNm7ciPr6ehw+fBjbt2/3ue/999/PfnPOQJ5lSyKRQKlUwmw2o6enB2FhYZDL5dDr9ejs7IROp0NBQYHPB5SRkcFTqF9++SWeffZZ1NXV4e677+YpLKD3Y9bpdHj33Xdx/PhxpKamYvny5bBarYiIiGDjzNzzSSQSuFwujBs3DomJiT4Nlp6eHmg0GnR3d7M81Gq1kMvlCA8Ph9PphFgshlwuR2pqqo+SMBgMMBqNiImJgVQq5T2LWCyGVqtlY+mdnZ28ucPl5eVwuVy8cUSgd0yTU6KRkZE+edAfiouLB3zOQNi+fTuSkpIwadIkXp73xYIFC0BE2LBhA2655ZZ+n3fPPffg3//+N2+fy+VCXV0dq+iB3u+guLiYObgQEYsRvG/fPsE6iPMcFprPCvR+Sw6Hg32nEokEn3zyCW655Rae8nS73bzvvKOjA0ql0u9auZs3b+Y53OzcuRMnT55EQkICbrvtNgC+dVtycjImT54Mm83GGy4Ri8WCHv0SiQQmkwkqlQo5OTlM6Xqbb8PCwtDa2gqr1QqRSIS2tjakpaWxb9zzuWQyGVQqFVOgUVFRvA6YXC5n39lAncpEnq2CPhOLRJ0AhodLZWBGE1ECMPJkHkHyAkGZzxdBmc8PI03mYD13fmD57M2AFGiQIEGCBAkSpJeR4a4aJEiQIEGCDDOCCjRIkCBBggQZBEEFGiRIkCBBggyCoAINEiRIkCBBBkFQgQYJEiRIkCCDIKhAgwQJEiRIkEEQVKBBggQJEiTIIAgq0CBBggQJEmQQBBVokCBBggQJMgj+P/r17e+5XyG1AAAAAElFTkSuQmCC\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 10 Axes>" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%time highres_pca = PCA(.99).fit(x_train)\n", "highres_data = highres_pca.transform(x_train)\n", "highres_gm = GaussianMixture(150, random_state=42)\n", "%time highres_gm.fit(highres_data[y_train == 1])\n", "draw_gm_sample(highres_gm, highres_pca, n=10)\n", "for i in range(10):\n", " highres_gm.fit(highres_data[y_train == i])\n", " draw_gm_sample(highres_gm, highres_pca, n=10)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 5 }