Neural_Nets.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Einführung in Neuronale Netze\n",
        "\n",
        "<img src=\"https://upload.wikimedia.org/wikipedia/commons/3/3d/Neural_network.svg\" alt=\"Ein Neuronales Netz (vereinfacht)\" width=\"400px\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Inhaltsverzeichnis \n",
        "\n",
        "1. Einleitung\n",
        "2. einzelnes Neuron\n",
        "3. Einfaches Neuronales Netz\n",
        "4. Feedforward\n",
        "5. Backpropagation\n",
        "6. Hyperparameter \n",
        "7. Verbessern des Modells\n",
        "8. Ausblick\n",
        "9. Quellen"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Einleitung\n",
        "\n",
        "> A single neuron in the brain is an incredibly complex machine that even today we don't understand. A single 'neuron' in a neural network is an incredibly simple mathematical function that captures a minuscule fraction of the complexity of a biological neuron. - Andrew Ng\n",
        "\n",
        "Ein Neuronales Netz kann zu Beginn, wenn man es noch nicht versteht sehr komplex und abstrakt wirken. Je mehr man jedoch in die Materie einsteigt, desto klarer wird, dass es nur eine Menge mathematischer Operationen sind, die darauf abzielen einen bestimmten Wert zu minimieren. Trotz dieser eigentlichen Einfachheit setzen viele globale Player wie Apple, Microsoft, Google auf Neuronale Netze und implementieren diese gekonnt in Ihrem Unternehmen zur Klassifizierung, Recommendation-System und für viele weitere Bereiche.\n",
        "\n",
        "Daher freuen wir uns besonders in unserer Ausarbeitung und Präsentation das Thema vorzustellen. Um einen kurzen Ausblick zu geben, was wir behandeln werden: Wir werden den grundsätzlichen Aufbau eines Neuronalen Netzes beleuchten, die Hyperparameter wie Kostenfunktionen und Optimizer vorstellen und in einigen Punkten darauf eingehen wie man diese richtig und passend für sein Model bestimmt. Das Erreichen wir zum Teil durch Text-Beschreibungen und Erklärungen und zum anderen haben wir uns Bilder-, Text- und Code-Beispiele überlegt, mit welchen die Themen leichter verständlich gemacht werden sollen.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Das einzelne Neuron\n",
        "<img src=\"https://miro.medium.com/max/856/1*O7YSSqlOdQuNgMrH7J_3dg.png\" alt=\"Das einzelne Neuron\" />\n",
        "\n",
        "Ein Neuronales Netz besteht aus vielen Neuronen, die miteinander verbunden sind. Dabei sind die Neuronen denen im Gehirn nachempfunden, welche untereinander verbunden sind und die aufeinander reagieren. Bei künstlichen Neuronalen Netzen hat jedes Neuron eine oder mehrere Eingaben $x_1...x_n$ und eine Ausgabe $o$. Die Eingaben werden mit Gewichten $w_1...w_n$ multipliziert und anschließend addiert ($ net = \\displaystyle\\sum_{i=1}^{n} (x_i \\cdot w_i) $). Des Weiteren gibt es einen Bias $b$, meist hat jedes Neuron einen eigenen Bias, oft gibt es aber auch einen Bias pro Schicht. Dieser wird auf diese Summe drauf addiert ($ net = \\displaystyle\\sum_{i=1}^{n} (x_i \\cdot w_i) + b $).Das Ergebnis wird dann in eine Aktivierungsfunktion $\\sigma$  gegeben, welche das Ergebnis in die Ausgabe des Neurons umwandelt $o = \\sigma(net)$ und die dann ein Eingabewert (ein anderes $x$) der nächsten Neuronen ist (oder die Ausgabe des Neuronalen Netzes darstellt, wenn das Neuron an der hintersten Ebene ist)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Einfaches Beispiel (Feedforward)\n",
        " \n",
        "Wir nehmen an wir haben ein Neuronales Netz mit zwei Inputs, welches die Sigmoid Funktion als Aktivierungsfunktion verwendet.(Auf die Aktivierungsfunktion werden wir im weiteren Verlauf genauer eingehen. In unserem Beispiel wird mit der Sigmoid Funktion erreicht, dass kleine Werte unter 0 richtig 0 konvergieren, der Wert 0 ergibt 0,5 und Werte über Null Richtung 1 konvergieren.). Die folgenden Parameter sind gegeben:\n",
        "\n",
        "$ w = [0, 1] == w_1 = 0\\ und\\ w_2 = 1 \\\\\n",
        "$ b = 4\n",
        "\n",
        "Nun geben wir den Neuronen ein input x mit x = [2, 3]\n",
        "\n",
        "$$\n",
        "(w \\cdot x)+b = ((w_1 \\cdot x_1) + (w_2 \\cdot x_2)) + b \n",
        "        = 0 \\cdot 2 + 1 \\cdot 3 + 4\n",
        "        = 7\n",
        "y = f(w \\cdot x + b) = f(7) = 1 / (1 + e^(-7)) = 0.999       \n",
        "$$  \n",
        "\n",
        "Für den Input x = [2, 3] bekommen wir einen Output von 0,999. Dieser Prozess in welchem man inputs eingibt, um ein Output zu bekommen ist bekannt als **feedforward** "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Programmierung eines Neurons\n",
        "\n",
        "Um das Neuron zu programmieren importieren wir Numpy. Numpy ist eine beliebte Python Library, um mit Zahlen zu rechnen. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "0.9990889488055994\n"
          ]
        }
      ],
      "source": [
        "#Wir importieren numpy als np um numpy nicht immer ausschreiben zu müssen\n",
        "import numpy as np\n",
        "\n",
        "\n",
        "def sigmoid(x):\n",
        "  # Unsere Aktivierungsfunktion: f(x) = 1 / (1 + e^(-x))\n",
        "  return 1 / (1 + np.exp(-x))\n",
        "\n",
        "class Neuron:\n",
        "  def __init__(self, weights, bias):\n",
        "    self.weights = weights\n",
        "    self.bias = bias\n",
        "\n",
        "  def feedforward(self, inputs):\n",
        "    # Gewichtsinputs, Addiere Gewichte und dann nutze die Aktivierungsfunktion\n",
        "    # np.dot ist eine Funktion um zwei Arrays zu multiplizieren \n",
        "    total = np.dot(self.weights, inputs) + self.bias\n",
        "    return sigmoid(total)\n",
        "\n",
        "weights = np.array([0, 1]) # w_1 = 0, w_2 = 1\n",
        "bias = 4                   # b = 4\n",
        "n = Neuron(weights, bias)\n",
        "\n",
        "x = np.array([2, 3])       # x1 = 2, x2 = 3\n",
        "print(n.feedforward(x))    # 0.9990889488055994"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wie man sieht, kommen wir mit unserem selbstgecodeten Neuron auf dasselbe Ergebnis, wie zuvor nur mit Mathe. Es sind zwei verschiedene Möglichkeiten, um auf dasselbe Ergebnis zu kommen.\n",
        "In der Praxis benutzt man für das Trainieren von Neuronalen Netzen vorgefertigte Bibliotheken wie Tensorflow, da diese sehr perfomant sind und viele Funktionen eingebaut haben, von denen man sich nur bedienen muss."
      ]
    },
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      "cell_type": "markdown",
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      "source": [
        "## Einfaches Neuronales Netz \n",
        "\n",
        "Ein neuronales Netz ist im Endeffekt nur eine Verbindung vieler einzelner Neuronen. So kann ein einfaches Neuronales Netz aussehen:\n",
        "\n",
        "![https://victorzhou.com/77ed172fdef54ca1ffcfb0bba27ba334/network.svg](attachment:network.svg)\n",
        "\n",
        "Dieses Neuronale Netz hat zwei Eingabewerte ($x_1$ und $x_2$) in der Eingabeschicht, eine versteckte Schicht (Hidden-Layer) mit zwei Neuronen ($h_1$ und $h_2$) und eine Ausgabeschicht mit einem Neuron ($o_1$). \n",
        "\n",
        "Der Input für $o_1$ sind die Outputs von $h_1$ und $h_2$, jeweils mit ihren Gewichten multipliziert und dann aufaddiert.\n",
        "\n",
        "Ein Hiddenlayer ist jedes Layer zwischen dem ersten Layer dem Inputlayer und dem letzten Layer dem Outputlayer. Es kann mehrere Hiddenlayer geben.\n",
        "\n",
        "### Beispiel für Feedforward\n",
        "\n",
        "Wir benutzen das Netzwerk von oben und nehmen an, dass alle Neuronen die selben Gewichte haben $w = [0, 1]$, dasselbe gilt für den Bias $b=0$ und die selbe Aktivierungsfunktion Sigmoid. Nun schauen wir uns die Outputs für den Input $x = [2, 3]$ an. Die Hiddenlayer bekommen den Output des Input-Layers als Input. Der Output des Neuronalen Netzes ergibt sich im Output Layer welcher den Output des Hiddenlayers als Input bekommt.\n",
        "\n",
        "$$\n",
        "h_1 = h_2 = \\sigma(w\\cdot x+b) \\\\ \n",
        "        = \\sigma((0 \\cdot 2) + (1 \\cdot 3) + 0) \\\\ \n",
        "        = \\sigma(3) \\\\ \n",
        "        = 0.9526\n",
        "$$\n",
        "\n",
        "$$\n",
        "o1 = \\sigma(w \\cdot [h_1, h_2] + b) \\\\\n",
        "= \\sigma((0 \\cdot h_1) + (1 \\cdot h_2) + 0) \\\\\n",
        "= \\sigma(0.9526) \\\\\n",
        "= 0.7216\n",
        "$$\n",
        "\n",
        "Der Output für den Input $x = [2,3]$ ist $0.7216$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Ein künstliches Neuronales Netz\n",
        "<img src=\"https://1.cms.s81c.com/sites/default/files/2021-01-06/ICLH_Diagram_Batch_01_03-DeepNeuralNetwork-WHITEBG.png\" alt=\"Ein neuronales Netz\" width=\"400px\" />\n",
        "\n",
        "### Aufbau eines neuronalen Netzes\n",
        "\n",
        "Ein neuronales Netz besteht immer aus mindestens drei Schichten mit jeweils mindestens einem Neuron. Die zu verarbeitenden Daten werden in die erste Schicht Neuronen gegeben (Input-Layer), wird dann durch das Netz verarbeitet und in der letzte Schicht bildet ein oder mehr Neuronen die Ausgabe (die Anzahl von Neuronen pro Schicht – vor allem bei der Ein- und Ausgabeschicht – wird vom Anwendungsfall bestimmt). Meistens sind alle Neuronen einer Schicht mit den Neuronen der nächsten Schicht verknüpft, das heißt die Ausgaben aller Neuronen einer Schicht sind Eingaben für die Neuronen der nächsten Schicht (das ist aber nicht zwingend so!). Bevor die Eingabewerte jedoch addiert werden und ihren Weg durch die Aktivierungsfunktion gehen, wird jede Ausgabe eines Neurons zu einem anderen mit einem eigenen Gewicht multipliziert. Dabei hat jede Verbindung ein eigenes Gewicht. Die Gewichte werden beim Training des neuronalen Netzes angepasst, sodass das Netz besser lernt, und eben diese Gewichte gilt es so zu wählen, dass das Neuronale Netz die besten Ausgaben gibt. Am Anfang werden diese Gewichte meist mit einem zufälligen Wert initialisiert (ist auch der Standardwert in den meisten Frameworks)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Backpropagation\n",
        "\n",
        "Backpropagation ist die bekannteste Methode, wie die Gewichte eines neuronalen Netzes beim überwachten Lernen angepasst werden. Dabei wird der Fehler der Ausgabe mit der gewünschten Ausgabe verglichen und die Gewichte so angepasst, dass der Fehler möglichst klein wird. Wie groß der errechnete Wert des Fehlers ist, hängt davon ab, welche Loss Function / Kostenfunktion man benutzt (wird später noch genauer erklärt). Die Backpropagation erhielt ihren Namen, weil die Gewichte \"rückwärts\" von der letzten Schicht bis hin zum Anfang des Netzes angepasst werden."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Hyperparameter\n",
        "\n",
        "Hyperparameter sind Parameter, die vor der Durchführung des gewählten Ansatzes an das Modell übergeben werden. Diese definieren damit die Eigenschaften des gewählten Modells.\n",
        "\n",
        "Vorgestellte Hyperparameter:\n",
        "* Anzahl der Schichten\n",
        "* Anzahl der Neuronen pro Schicht\n",
        "* Aktivierungsfunktion\n",
        "* Lernrate\n",
        "* Batchgröße\n",
        "* Anzahl der Epochen\n",
        "* Kostenfunktion\n",
        "* Optimierer"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Anzahl der Schichten\n",
        "\n",
        "Ein Neuronales Netz besteht immer aus mindestens drei Schichten: Input, Output und Hidden Layer.\n",
        "\n",
        "#### Eingabeschicht / Input Layer\n",
        "Das Input Layer ist die erste Schicht im Netz, die Trainingsdaten werden in diese Schicht eingegeben. Die Anzahl der Neuronen in dieser Schicht entspricht der Anzahl der Features, die das Modell verarbeiten soll. Im Beispiel von MNIST werden 28x28=784 Pixel eingegeben, dementsprechend besteht die Eingabeschicht aus 784 Neuronen, jedes Neuron nimmt den Hell-Dunkel-Wert eines Pixels entgegen.\n",
        "\n",
        "#### Ausgabeschicht / Output Layer\n",
        "Die Ausgabeschicht ist die letzte Schicht im Netz, sie bildet die Ausgabe des Modells. Im Falle der Klassifizierung entspricht die Anzahl der Neuronen in dieser Schicht der Anzahl der Klassen, die das Modell erkennen soll (es ist auch möglich Klassifizierung mit z.B. nur einem Neuron in der Ausgabeschicht durchzuführen, das wird hier aber nicht weiter behandelt). Im Beispiel von MNIST besteht die Ausgabeschicht aus 10 Neuronen, jedes Neuron steht für eine Ziffer und gibt die Wahrscheinlichkeit an, dass das Bild eine bestimmte Zahl darstellt. Wenn jedes Neuron für eine Klasse steht, dann wird als Aktivierungsfunktion für diese Schicht Softmax verwendet (wird später noch genauer erklärt).\n",
        "\n",
        "#### Versteckte Schichten / Hidden Layer\n",
        "Die versteckten Schichten sind alle Schichten zwischen der Eingabe- und der Ausgabeschicht. Anders als diese beiden Schichten ist sowohl die Anzahl der versteckten Schichten als auch die Anzahl der Neuronen pro Schicht frei wählbar. Je mehr versteckte Schichten man verwendet, desto komplexere Sachverhalte können verstanden werden, allerdings dauert dann das Training länger und es werden mehr Daten gebraucht, um das Netz gut zu trainieren. Dasselbe gilt für die Anzahl der Neuronen pro Schicht. Am besten ist es also, so wenig versteckte Schichten und so wenig Neuronen pro Schicht wie möglich, aber so viele wie nötig zu verwenden, um das Modell möglichst einfach zu halten. Je komplexer jedoch das zu lernende Problem, desto mehr Schichten und Neuronen werden benötigt."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Aktivierungsfunktionen\n",
        "\n",
        "#### Warum gibt es Aktivierungsfunktionen?\n",
        " Aktivierungsfunktionen werden verwendet, um dem neuronalen Netzwerk eine nicht lineare Eigenschaft zu verleihen. Auf diese Weise kann das Netz komplexere Beziehungen und Muster in den Daten modellieren. \n",
        "#### Beispiele für Aktivierungsfunktionen\n",
        "<img src=\"https://assets-global.website-files.com/5d7b77b063a9066d83e1209c/60d244bb0e12c94fb442c01e_pasted%20image%200%20(4).jpg\" alt=\"Lineare Aktiverungsfunktion\" height=\"300px\" />\n",
        "<img src=\"https://assets-global.website-files.com/5d7b77b063a9066d83e1209c/60d24547f85f71e3bd2339f8_pasted%20image%200%20(5).jpg\" alt=\"Sigmoid-Aktiverungsfunktion\" height=\"300px\" />\n",
        "<img src=\"https://assets-global.website-files.com/5d7b77b063a9066d83e1209c/60d24d1ac2cc1ded69730feb_relu.jpg\" alt=\"ReLu-Aktiverungsfunktion\" height=\"300px\" />\n",
        "\n",
        "* Die Lineare Aktivierungsfunktion ist die einfachste Aktivierungsfunktion und ist eine Gerade. Sie ist nicht sehr gut für die meisten Modelle geeignet, da sie nur lineare Beziehungen zwischen den Inputs und Outputs modellieren kann.\n",
        "* Die Sigmoid-Funktion wird oft für Hiddenlayer und die Ausgabe des Neuronalen Netzes verwendet, da sie einen Wert zwischen 0 und 1 ausgibt. Sie ist sehr populär, jedoch hat sie an Beliebtheit verloren, da sie die Gradienten \"töten\" kann, wenn der Input sehr große Werte annimmt. Dies kann dazu führen, dass das Neuronale Netz nicht mehr lernt. \n",
        "* Die ReLu-Funktion ist eine weitere sehr beliebte Aktivierungsfunktion. Man könnte meinen dass sie ähnlich wie die lineare Funktion ist, da sie auch eine Gerade für $x>0$ ist. Jedoch ist sie nicht linear, da sie für $x<0$ eine Null ausgibt. Sie beschleunigt die Konvergenz des Gradientabstiegs in Richtung des globalen Minimums und kann so genutzt werden, um oft schneller zu lernen. Besonders bei der ReLu-Funktion muss man jedoch darauf achten, dass Neuronen nicht \"tot\" sind, also immer eine Null ausgeben. \n",
        "* **Softmax-Funktion**: Zur Softmax-Funktion gibt es keinen Graphen zu zeigen, da sie eine Funktion ist, die auf alle Neuronen einer Schicht angewendet wird. Sie wird oft für die Ausgabe des Neuronalen Netzes verwendet, da sie einen Wert zwischen 0 und 1 für jede Klasse ausgibt (wie die Sigmoid-Funktion), jedoch auch dafür sorgt, dass die Summe aller Werte 1 ergibt. Daher eignet sie sich super für Klassifikationsprobleme wie das Erkennen von Ziffern (MNIST) oder das Erkennen von Tieren (CIFAR-10), da der Output dann eine Wahrscheinlichkeit für jede Klasse ausgibt."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Epochen-Anzahl\n",
        "\n",
        "Die Anzahl der Epochen beschreibt, wie oft das Netz mit den kompletten Daten lernt (ein Epochen-Durchlauf = einmal alle Daten gesehen). Eine einzige Epoche reicht aber nicht aus, deswegen werden mehrere Epochen durchgeführt. Die optimale Anzahl der Epochen sorgt dafür, dass das Netz sehr gut auf den Daten gelernt hat, jedoch nicht zu sehr übertrainiert ist (Under- oder Overfitting). Wie viele Epochen am besten sind, kann man nicht pauschal sagen. Am einfachsten ist es, man trainiert das Modell so viele Epochen lang, bis man erkennt, dass das Netz nicht mehr lernt beziehungsweise die Kostenfunktion wieder ansteigt."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Vergleich zwischen meherern Modellen mit unterschiedlicher Epochen-Anzahl\n",
        "from mnist_model import get_trained_mnist_model, plot_accuracy_by_total_epochs\n",
        "\n",
        "# Trainiere 3 Modelle mit unterschiedlichen Epochen-Anzahlen\n",
        "models = [\n",
        "    get_trained_mnist_model(epochs=5),\n",
        "    get_trained_mnist_model(epochs=10),\n",
        "    get_trained_mnist_model(epochs=15),\n",
        "]\n",
        "\n",
        "# Plotten der Ergebnisse\n",
        "plot_accuracy_by_total_epochs(models)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Batch-Größe\n",
        "\n",
        "Die Batch-Größe beschreibt, wie viele Daten gleichzeitig in das Netz eingegeben werden. Der komplette Datensatz kann meistens nicht gleichzeitig in das Netz eingegeben werden, da das zu viel Speicherplatz benötigt. Deswegen werden die Daten in Batches aufgeteilt und einzeln in das Netz eingegeben. Nach jeder Batch (auch Mini-Batch genannt) finden die Parameter-Updates / Regulierung der Gewichte statt. Ist eine Batch-Größe von 1 gewählt, so wird jedes Mal nur ein Datensatz in das Netz eingegeben. Ist die Batch-Größe gleich der Anzahl der Daten, so wird der komplette Datensatz gleichzeitig in das Netz eingegeben. Eine Batch-Größe von 32 ist sehr häufig gewählt, da sie eine gute Balance zwischen Speicherplatz und Lerngeschwindigkeit bietet (32 ist auch der Standardwert in Keras). Ist die Batch-Größe zu groß, so kann es passieren, dass das Netz nicht mehr lernt, da die Parameter-Updates zu ungenau sind. Ist die Batch-Größe zu klein, so kann es passieren, dass das Netz zu lange braucht, um zu lernen."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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MuLGmJ6b6eJg+TIprhWghisOB22rFXVmFYq3yPq5EsVpxV1k9x6qqah5Xes7xHLfirqpCqfK+r6qK8OuuJeLGG9vt+0gAEp2Gy61wrLiK/QXlNb063luZteFhoNhQA6mxITW3GM99TKihacMVLgdY8iEvt6a3pvyk3pryHKgqbvqX0Yd6Q0wDwSYswRNsdKamXzNATrfTL7TUro1psGfGXkp5IAGuHiatqSak6M2EGcJ8IaZOuKkVbHRtGPKE6GwUp7ORQFLlOVZZhdta5XvdXVWJUmX1BpKax4r3PSc/xnmaw+0ncYwa2aLXC5QEINHhVNfn1A44BwoqOFhgweasf3qRWgXJkUG+cNPbG3Z6x4RgNjXyi7PyBJRm14SYsnrCTUUBNLXnQmtspLem+hYHhtDAfzCNKLWVUlRVVKdXpjrYnNwzc7o1MgDBuuA6oaX285PrZ6qP6TX6FvrWQnROisOBu6LCc6usxF1Rgav6eUVlzWv13SorvYGkqlZ4qQJHG652rVajNplQmUyojcYGH6tMRtSmIP/HJiMq73n6Hj3brs31kAAk2k1z6nP0WjW9ooN94aa6V6dndHDjw1OKAmXHIGcL5GyF3K2ex2XHmtZYtRZC4mt6bcIS6w86xnBopSLYUlspR8qOcKTsCNnl2X73ZfayZl83VBfq1wtTXStzcqDxHff22shsJNFVKG63L6g0dnP5PW/4fMUe4BpYgVCp/ANJkAmV8VSB5KRzTd4g432sMhpRB1W/z4RKpzsjiv0lAIlWdbr1Oam1Qk5qbAhJEUGeQuLGuN1w4oAn4FQHnZytUHWi/vND4mr1zjTQexMU1WrTtWsrsZaQVZ7VrJATpvcPLb6C33p6ZqoDTag+FK1a/hoQZxZFUTzDPLXDicXi1+Nyyp6WigpclZ7zlMrKVmmnSqdDHRx8iluQ77EmOBhVUJAnuAR5Q43RVPPYZEKl158R4aQtyN98okW43ApHiyu9w1VtWJ/jtEPBbv+gk7cd7PUM76i1ENMfEoZA/BBIGArxg1p8OKoxiqJ4enLKj5BVlkVWeZbn3vv4VCEn1hRL97DunltozX1yaDJBuqA2+hZCtLzaw0IuS0PDPw31uNQNM7hbYTNZjaZOMNFUPw86KbgEBTUaajTBwaj0MhzcniQAiYC53Ao/7M5n+/FSX8g5VFjR8vU5J7NXQN4Ob9Dx9u7k7wJXPd3JWpMn3FQHnYQhEDsAtIZmfuumUxSFEltJTbip7tEpy+ZI+ZFTFhHHBsXSPbQ7KWEpJIcm++4l5IiOxDMsVFUrdFg65LBQ40Gk/l6Whs5TGZr4DzPRKUgAEgHZl1fOjE+38ltWSZ3Xqutzep80dHXK+pz6VJ7w9urUqtcp2g9KPSHLaK4VdIZ6Hkf3adUF+hoKOdWPAwk5tXtzkkKSJOSINqE4nbjKynCVluIuLcVVWup5XlKKq6y05nhZeYPFuK1BpdefMqhoQkLqvnZyD0xwsKempQ2GrkXnJAFINInd6ea1Nft59Yf9OFwKoQYtYwfF+w1bJUc2oT7nZIrimWl1cr1OaVb954fE+w9hJQyB8JRWKTyuDjm163BqB56mhJyUsBS/oSoJOaIlKYqCUlnpCzJ1wkup93hpreMlnqDjtpzeLEAftbrhoFJfSPELL3XPU+mkuF60DQlA4pR+yypm5qfb2JPn+YU/pn8sT08cRII5wDVq3G4oPuQfdHK3eqeZ1yOiR92endC40/syJ1EUhWJbcb31OFllWZQ7Gg85cUFxfuEmJTSF5DDPcJVJ23pr+IgzS6O9Md7wUjfQeB6f7vRndUgImrAw1OFmNGYzmjDvvdmMxhyGOjTME05C6h8eUhmNMiwkTklRFJx2Nw6by3czBusIiWj9soSGSAASDaq0O3nx2728+79DKApEBet5csJArh6ScOq/8FxOKNxz0rTzrfWvgqxSQ3SapzenOujED/Zs5dDCHG4Hu4t2syl/E7/m/crm/M2U2EoafU/tkFO7RycpNElCjvCjKAru8nKceXk4i060XW+MTlcTWsLCasKLuVaoCa95XW02owkPRxMaikorvwZEDUVRcDsVHDYXdpsTp606tDj9wsvJN+dJz+0nH7O76iyndtaVPciY0Kt9vigSgEQDftpXyKzPtpJ9wrMz9nXDujHn6gFEBNcza8FRBXk7IWdzTdDJ2wGueqa5awwQN8C/Zyd2AOhbZ0jI6rSyrXAbv+b9yqa8TWwp2FLvbt9xQXF+RccScsTJ3FYrzvx8nPn5OPLycOYXeIJO9THvvWINYA+3k6hDQnxBRm0OQ2MOrwk13gCjDqs+HuY7V2WSTVi7IrfLjcPuxmH1BBRPD4sTu7VWMLF7H1v9w8jJx2qf526JnZ8boTVo0Bk0aLTtW58lAUj4Ka108MyXO/lk41EAuoWb+Nu1g7g4LbbmJKcNflsK2Rs8PTyFe0Fx1b2YPtTTk1NdqxM/BGLSWnXfqjJ7GZvzN7MxbyMb8zayo2gHzpN2Sw/VhzIidgTD44YzPG44aRFpGLXGVmuT6NgUpxNnUZEnyOTleYJMXr4v2Djz83DkF+AuLW3yNTVmM5qoKE8vS3WPTHjt8GL2CzBqs1l6Y7oop8OFrcKJtcKBrdKBtfpxhRNrpQNbhQNrhee4rdJzvDrEuBytMNW/Fo1OjU7vCSs6o/feoEF78jF9zWt1jvnep0Wr91xPFWitaCuR/9uEz9fbcpjzrx0UWmyoVHD7OT2YPjaNEEOtPyaVJ2D5rXDkf/5vDor2H8JKGAoRPVt98cDCqkI25m1kU94mNuZtZG/x3jobbsaaYhkeN5wRcZ7QkxqeKjt9dwGKouAqKakVZKp7bk4KOEVFTV4zRmU0oo2LRRcbhzY21nOLi0UXG4s2znssJga1UQJ1V1Jd31I7xFQHF1tldaBxYK10YrX4n+NsgRCjUqvQG08KJ6cIKLXP87zXG1AMWs85ejVqzZn996QEIEF+mZU5/9rONzvyAOgdE8zzvxvCiJRI/xNPHIQPfu+Zjq4PhXMegMR0T9gJTWi1LSCqKYrCUctRX9jZlL+JI2VH6pzXPbS7L+yMiBtBUkiSDA+cYdyVlTXDUN5eGk/AyfcLPE1eW0ajQRsTUxNmagUcXVx10IlDHRIif5bOYIqi4LC6/IJLfSHGL9xYHFgrHbidzR82UqlVGIO1GIJ0nvtgHcYgHYZgLcZgnd9xQ5AWvS+keAKMWquSP5fNIAGoC1MUhY9/zeaZL3dRbnWiVav448W9eeDSVAzak9bQyVoPy26CyiIIS4JbPoa4ga3aPrfi5kDJAb8envyqfL9zVKjoG9G3pocndjgxQTGt2i7RehSHA2dBQT1hxn9oKpCiYU1kpDfMxKCLi0MbU9Nz4wk4cWgiI2W9mDOEoig4HW7slU5sVU7sVU5slU5sVY6aoSa/4SWnt0fGc/x06l/UGpUnvATr6g009YUbY7AOnVEjAaYdSADqoo4UVTBrxTbWHigCYEiSmecmDaF/Qljdk7evgM/u8xQ1JwyFm5ZDWEKLt8nhdrCraJdfD8/JW0No1VoGRg1kRNwIRsSNID02nTB9PW0WHZartBR79lEc2Vne+2zsR7NxZB/FkZMDrnrqyeqhDg6uOwx1Us+NJiYGtWw30Km43QoOa3VoqQkw9qpaz6ucdQJO7eOnW8Sr0aprwor3ZgjWNtgrY/T2zOgMEmQ6EwlAXYzLrfDuT4d48bs9WB1ujDo1D1+WxpTzeqA9ebxXUeCn/weZcz3P+14Bv3sH9MEt0pYqZxXbCrZ5CpbzN7K1YGudGVomrYmhMUMZHjecs+LOYlD0IJmV1cEpDgeO3FxPsKkTdI7iLjvFzvU6HbqYmJqamtrDULUCjiakZf4cipblcrjr9LzYq1zYKr33VQ5PeLHWH2Ls1qYF4FNRqUAfpMVg0qI3aTEEVQcY/+BSX6jR6ltvFXnRcUgA6kJ25ZQx89OtbDnqmc1yTq8o5k8aTEpUPb9IXA74chps+j/P84z7YOyzp7W9RKmt1DNDK98zQ2tn0c46M7TMBjPDY2uGs/pF9UOnlpVhOxpXWRn2rGwcR7OxZ3t7b45me441oRdHGxODLjkZfXISuqRkdMlJ6Lt3R5eUhDY6Woaj2pGiKNirnFSVe2cfWRz19rTYKp3YrXV7X1wN7AkYKK1O7QsuepM3yNR+7L03nHzM+1x6Y8SpSADqAmxOF698v5/X1xzA6VYINWqZfVV/rj8ruf6/IKyl8PHtcPAHzyKFY+fB2fcF/LkFlQWesJPrGc7aV7yv7gytoFjPcFasZ0irV3gvmaHVAShOZ00vji/o1OrFOcWUcJXBgC4pCX1ysl/Q8dwnoTZJL15bcbncnkJdi4OqcjtVtR5bLQ6qLA6qLN7H5Z7XWmIdGL1Ji96kwWDSNRhSagcZv94akxaNTv4eEK2r3QPQq6++yt///ndyc3MZOnQo//jHPxg1alS95zocDubNm8d7773HsWPHSEtL47nnnmPcuHG+c5588knmzp3r9760tDR2797dqt+jo9p45ASPfrqN/fmeotGxA+N46ppBxIU1ME23JBs+vB7yd4IuCH73LqRdccrPURSFo+VHPQsO5m9iU94mssrr7ufVI6yHb4bW8NjhdAvpJv9KayeusrK6vTfVQef48VP24mhiotFX994kJaPrnuwJPEnJaGOkF6c1KIpnhd7qsOILLhYHVovde6zmcfVMpebQGTSYQj3DQoagekJKUN1eGM9xHXpDx1nrRYiGtGsAWr58OdOmTWPRokVkZGSwcOFCxo4dy549e4iNja1z/uzZs1m6dClvvfUW/fr145tvvuHaa69l7dq1DBs2zHfewIEDWb16te+5tgsuLlZhc/L3b/bw3rrDKApEhxh4+pqBXDG4keLl47/BhzeAJQ9C4uDm5ZA4rN5T3YqbfcX7fGFnY95GCqr89/RSoaJfZD9f2BkeN5xoU3RLfk3RCL9eHG/QqS42tmdnn7oXR69Hl5TkCTjJ3T29N8nJnp6dpCTUQbKh6+lyuxVsFQ0HGN9jX6+No1lDTCoVGEM8NS+mUD3GEB2mEO/jYB2mUB2mEO/xUB3GEB1andTBiDObSlGU1l3zuhEZGRmMHDmSV155BQC3201ycjJ/+tOfmDlzZp3zExMTeeyxx3jggQd8xyZNmoTJZGLp0qWApwfo888/Z/PmzU1uh81mw2ar2bahrKyM5ORkSktLCQvrfDOM1uzJ57HPtnOsxFNQ/PsRSTx2VX/CgxqZDbP7K/j0TnBUQuxAT/gJT6731I15G3nkx0fqBB6dWseg6EG+Gp702HRC9aEt9r1EXYqi4Dh2HNvuXdgPH/YbpnIcPw7Oxv/1r4mORp+U5D9M1d0zbKWNiZFenAC53QpV5XYqy+ye4SbvkFJVdYg5udemwlFnf6Sm0OjUNQGmOsycFGBMIXrfY0OQDrX0yIg2pCgKTpsNa4UFq6Xcc19hwWaxeI9ZSB4wmJQh6S36uWVlZZjN5ib9/m63rhG73c7GjRuZNWuW75harWbMmDGsW7eu3vfYbDaMJ62wajKZ+Omnn/yO7du3j8TERIxGI+eccw7z5s2je/fuDbZl3rx5dYbNOqPiCjtPr9zJit+OAZAUYWLedYO5oM8p1sX5eRGsmgko0PtS+P17YKz/D86uol1MzZyKxWHBpDUxLHaYr3dncPRg2VKiFSlOJ7aDB7Ht2oV15y6su3dj3b270Z4clU7n6cXpnlwzXOUdptIndUMdLDOpTqV62Kmy1E5lmY2KUk/AqSyzU1lqq/XYE3qa809KQ5DWrzfm5ADje+ztwdHq1TJ0LNqEw26rFVrKsVZUYPMGmOpjNm+4OTnguF2N/wNMUdwtHoAC0W4BqLCwEJfLRVxcnN/xuLi4But1xo4dy4IFC7jwwgvp3bs3mZmZrFixAletWoWMjAyWLFlCWloaOTk5zJ07lwsuuIDt27cTGlp/b8SsWbOYNm2a73l1D1BnoSgKK7fm8OQXOyiqsKNSwZRzezJ9bF+C9I38J3a7YNUs2PCG5/nw2+GqFxvcq+tw6WHuW30fFoeFEXEjeH3M6zIlvZW4Kyux7tmDddcubLt2e+737q1/ZWOdDkNqKoZevXxBx9eLExsrvTgNcLncVJU5qCyzecON3fe4whtoKss8AcdpD2DYSQWmUD1BoQ0HmNpDUIZgLZozfMsB0b6cDkfDocViwVpRXhNcfAHH02vjcjhO67PVGg2G4BCMIaEYg4MxBod4n4eQ2LdfC33D5ulUxTEvvfQSd999N/369UOlUtG7d2+mTJnCu+++6zvniitqCnaHDBlCRkYGKSkpfPzxx9x55531XtdgMGAwGFq9/a0hp7SKOZ9vZ/UuzwrJfeNCmD9pCMO7RzT+RnsF/PNO2Pu15/mYJ+G8vzS4nUVuRS73fHcPJ6wn6B/Zn39c+g8JPy3EWVyMdedOv54d+6FD1NeVoA4KwtC/P0bfrR+G1FRUstgf4PnHgK3SWW/vTGWZnYpax6yWwP5i1xk1BIXpCQrTE2w2eB6b9d5jBt9jU4jujN9DSbQ9t8tV0wtTJ7RYTgo4Fr+A47TbTv0BjVCp1Z7QEhzsDTLeEOMNMsbgEAzee6M37FSHHJ3B2GF7K9stAEVHR6PRaMjLy/M7npeXR3x8fL3viYmJ4fPPP8dqtVJUVERiYiIzZ86kV69eDX5OeHg4ffv2Zf/+/S3a/vbmdit89EsW87/aTbnNiU6j4oFLUvnjxanotaf4y7c81zPTK2cLaAxw3Rsw8NoGTz9hPcE9391DTkUOPcJ6sOiyRVLb0wyeep1jnrCze7cn7OzahfOk/weqaWKiPSGnX3+MAzyBR5ec3CV7dJwOV50wUzvgVNTqrQlkTya1WoXJG2qCzHqCw/QEVYcb33HPc51BioLF6XPYbTUhxlJeK9Cc9LxW0LFaLNirKk/vg1UqjEHBNUGlOqR4e2Vqh5bqgGPyHtObTB02xJyOdgtAer2eESNGkJmZycSJEwFPEXRmZiZTp05t9L1Go5Fu3brhcDj49NNPuf766xs812KxcODAAW677baWbH67OlRYwcxPt7L+0AkAhnUP57lJQ+gb14RQkrcDPrgeyo5CUBTctAyS6192AMBit3D/6vs5VHqI+OB43rzsTSKNkQ2eLzwUhwPbwUNYd/n37LjLy+s9X5fSHWP/AZ7AM6A/xn790MZ0jT3NbJUOygqtlBVVUVZopaLE5jccVVlmD3gqtyFIW6uHpqZ3Jrh2b41ZjzFIJ9O1RcA8i0VW+kJKVa3gYqvwf+4LNd76GKejiRv0NkBvCvL1wpzc+1I7tFS/Xh1qDKagLvmPp8a06xDYtGnTuP322znrrLMYNWoUCxcupKKigilTpgAwefJkunXrxrx58wBYv349x44dIz09nWPHjvHkk0/idruZMWOG75rTp09n/PjxpKSkcPz4cZ544gk0Gg033XRTu3zHluR0uXnrv4dYuHovNqcbk07DI2PTuP3cHmia8pf4/kzPAof2cojq49nQNLLh3jOr08qfvv8TO4t2EmGI4M3L3iQhpOX3AOvs3BUVWPfsxbp7ly/s2Pbta7hep0+qX8+OIa3fGb2tg8PuorxWwCkrqvI9Ly+yNjncqLUqgmuFmZN7aGoflyncoin8h5XqBpa6vTTlVHlDjuJu/orXKrXaE2JCQjGGeEJLTZDxHDeFhPidYwwJxRAUjFojf7ZbSrsGoBtuuIGCggIef/xxcnNzSU9PZ9WqVb7C6KysLNS1EqvVamX27NkcPHiQkJAQrrzySt5//33Cw8N95xw9epSbbrqJoqIiYmJiOP/88/n555+J6eT/mt5+rJRHP93KjuOefZQu6BPNs9cOJjmyiWuxbFwCK6eB4oKU8+GG9yGo4Z4ch9vBIz8+wq95vxKsC2bRZYvoae7ZAt+kc3MWFWHdtbumZ2fXbuyHD9dfrxMSgrFfv5qanQH9MfTqdcbV67hcbiwnrJ5wU1hFWZGVcu99WZGVqrJT/4vXFKojLNpEWJSR4AgjweZavTfeUGMI0p6R3fCi5bicDipKSqgsKaaitISKkmLv42IqS0tbfFhJqzf4wonRF15CavXQ+AeYM31IqbNp13WAOqpA1hFobVaHi5cy9/Hmfw7iciuYTTrmXD2AScObuIKy2+3ZzPR/Cz3Ph9wIE14GbcNF327FzeyfZvPvg//GoDHw+pjXGRk/smW+UCehKAqOo0e9Q1e7sFXX6+Tn13u+NiYGg7dOp7pnR5eUdEZ0OStuhYpSm98wVU3AqaKi2HbKqd96k5awaCOhkUZP0Ik2EhZlItR7L/U1oiFutwtreTkVJcV+t8rSYk/Y8d5XlBRjtdQ/xHwqhqDgWkEm1DuU1HCQqe6t0ek75+SZM1mnWAdInNqGQyeY+elWDhZWAHDV4ASemDCA2NAmrrXjqILP7oOdn3ueXzwLLnq0wZle4PnF/9yG5/j3wX+jUWl48aIXz/jw46nXOegtSt7pCTu7d+O2WOqerFKhT0nB0L9fTc1O/35oozvvCteKomC11K7D8e/FKT9hPWVhsUanJizKSGhUTbgJi/aEndAoI8Zg2dBW1PDM1quo6aEpOSnMlBb7XqssLUVRmj7cpNZoCAqPINgcTnB4BEHmCO+92TPUVCvkVNfQyLBS1yQBqAMqtzp4btVulv7s2UsrNtTA0xMHMXZg/bPj6lVRCB/dBEc3gFoHE/4B6aeug1q0ZREf7v4QgGfOf4aLki9q1nfoyBRFwbZ3L+WZmVjW/Iht1y6Ueta6UOl0GPr0qenZ6d8fQ9+0TlmvY69y1tTgVAeboprHTlvj+36p1CpCIw0NBpygML106QscNquvN6Z2z0z1MFRN701JYOvLqFSYQsMIDveEmWBzuCfknPw4PAJjcMgZ0fMqWp8EoA4mc1cesz/fTk6pFYCbRiUz84r+mE0B/Au6cB988DsoPgxGM9zwAfS84JRv+2DXB7y25TUAZo2axdW9rm7OV+iQFKeTyk2bsGRmUp75PY6jR/1eV4eGeut1vD071fU6us7Rc+FyuP0CTnmRf9GxreLUhcbBZr0n0NQOON5hqpBwg6xt00W5nE4qy0qo9IYZ/2Go2mGnGHtVVUDXNgQFe8NLOMHmCIK899VhpjrYBIWZpZdGtDgJQB1EkcXG3H/v5IstxwFIiQpi3nWDObd3gEMrh3+CZbeAtQTCU+CWf0JM31O+7d8H/s38DfMBeCD9AW7uf3OgX6HDcVdWYvnf/7Bkfo/lhx9w1doyQmUwEHzuuYSOvpSgjAxPvU4n6cGoLLNTmF1O4VELhUctFB2zUJxbieJufJjKGKzz1OHU6r0Ji/Lch0QaZOZUF6IoCtYKS63hp2Iqik/4Coere20sJcVYy8sCurZWpyc4IqLeYShfsDGHExQeLjU0ol1JAGpniqLwr83HmfvvHRRXOlCr4K4LevHQmL6Y9AH+QtqyHP71ALgdkDQSbvwIQk49++2HrB+Y8785ANza/1buHXJvc75Kh+AsKsLyww+UZ35Pxdq1KLU2udWYzYRccgkhoy8l5LzzOvxu5m6Xm+K8Soq8Qaf61tCsKp1B4x9wThqm0hvlf/czndNurwk0pd4QU1zPEFRJMa5TbJRbm1qjISjM7DfUVBNsqntvPMdkhpPoLORvxHZ0rKSKxz7bxpo9nl3V+8WH8vzvhjAkKTywCykK/PgcrPGsl8SAa+DaN0B36q0qfsn9hek/TseluJjQewKPjHyk0/3lZT98mPLM7ynPzKTqt9/8pqTrkpIIHX0pIaNHEzR8OCptx/wjb6t0UHTMG3KyPfcnjlfgctZT/KmC8NggopNCiEoKITophOikUILDpQ7nTKS43VRZyj09NCfNgvKFG2/AsVVUBHRtY3BInVBTe/gpxHtvCgmVuhpxxumYvw3OcG63wtL1R3ju691U2F3oNWoeHJ3KvRf1RhdonYXTDv9+ELZ85Hl+3p9h9JPQhL+sdhTu4E/f/wm7284lyZcw99y5qFUd/y85xe3Gun075aszKf8+E/v+A36vGwcMIGTMaEJHj8bQt2+HCgWKW6GsyErRUQsFR8t9vTvlRdZ6z9cZNER184acZE/giUoMkWnjZwCH1UpFSTGWkhN+M6E89ydqFQ+XBLTonkan8xYHe0NMRN0hqGDvMW0nqXETojVIAGpj+/MtzPx0K78eKQZgREoEz00aTGpsM/bWqiqG5bfB4f+CSuPZyf2sKU1668GSg9y3+j4qHBWMih/F3y/6O1p1x/3j4LbbqVy/3jNzK/N7nAUFNS9qtQSPGknI6NGEXnopuoSOsVq1w+7ixLEKCquDjreHx2Gtf8ZVSKSB6KRQb4+OJ+yYo02yVUMn47BaKcnPpbyowBtiahcPn/AFHYc1sIJhU5jZbxZUcERkTaGwuSbYGIKCO1ToF6Kj6ri/8c5A7/50iPlf78buchOs1zBjXD9uOzsFdXN+wZ045NnQtHAv6EPh+iWQOqZJbz1uOc49391Dia2EQVGDePnSlzFoOl4xoqusDMuP/6H8+0wq/vNf3LW699VBQQRfdCGhl44m5KIL0bTjgpWKolBZavfW6HiKk4uOWijJq6x3gUC1VkVUonf4qltN2JG1cjoHRVGoKCmmNC+XkrwcSvNzKcnL9T2vLC1p8rW0BgMh4ZE1M6HCIwgOjzxpKCqcoLBwNB10+FaIzkr+j2pDQXoNdpebi9Ni+Nu1g+kWfuoanXpl/wIf3QiVhRDWDW7+GOIHNemtRVVF3PPdPeRV5tHL3IvXxrxGsK7jrGvjyMmh/PvvsWRmUrHhF6hVqKmNiSHk0ksJHTOaoIwM1O2wpYTL5aYkt9Jbq1Pum4VVVV7/miamUJ034NT07ITHB6GRKeUdmtPhoDQ/1xNucr33eTmU5uVSmp+H025r9P3G4BBCY2J9NTT+wSbcF270po5diC/EmUwCUBu6YWQycWYjF/eNaX4X9Y7P4bN7wWmF+CGe8BPWtCGfcns5962+jyNlR0gMTuSNy94gwhjRvHa0EM+ihPsoz1yNJfN7rDt2+L2uT+1N6KWjCR0zGuOgQW1aiGmtcNSageUJOydyKupdFVmlgvC4IG+tTqivOFkWCOyYFEWhqrysTu9N9XPLiaJ693erplKpCY2OITwuDnNcAubYeMLjEgiPi8ccG48xJKQNv40QojkkALUhlUrFJWmxzXuzosDal+G7xz3P+46DSe+AoWl/0VY5q5iaOZXdJ3YTaYzkzcvfJD44gJWlW1DNooSemVt+ixKqVJiGDSN09GhCR1+KvkeP1m+PW6G0oMrXm1Pdu2Mprv9f+XqjxhtwQn3DV1GJwWgDXbZAtCqX00l5UaGv5+bk4apTbYSpM5oIj/UGnDhvwImNwxyfQFh0DBqtDFkK0ZlJAOoMXE74ajpsXOx5PuoeGDcf1E37hetwO3h4zcNsyt9EqC6UNy57g5SwlFZscF1+ixKuWYOrpMT3Wu1FCUMuvrhN9tWyVjjYvzGf/b/mkX+kHEcDW0GERRtrzcLyBJ7QKKP06nQQtsrKmmCTWyvg5OdSVpB/ytlTIRGRmKt7buLiCY+N9z03hZnlv7MQZzAJQB2dtQz+OQX2rwZUMG4enH1/k9/uVtw89tNj/PfYfzFqjLwy+hX6RfZrvfbW4iwqwrJmDeWrM+tflPDiiwkZM7rNFiV0udxkbS9iz/pcDm0t9BvK0ujURCUG1+nZMZjkf5H2pLjdlJ8oojQvh5L86qGqXO/zvFOuUqzR6bzDU3UDTlhsnKxELEQXJn+7d2SlR+HDGyBvO+iCYNLb0O+qJr9dURSeXf8sXx/6Gq1Ky4KLFzA8bngrNhjsR4541+f5nqpNm9p9UUJFUSjIKmf3z7ns+yUPq6WmWDkqKYR+Z8fTfUAU4XEm2euqnSiKQkXxCYqOZlN0LIvinOO+gFOWn3vKFYtNYWZvsKkOOgme5/HxhIRHygJ+Qoh6SQDqqHK2eMJPeQ6ExMFNy6BbYOHllc2vsHzPclSoePaCZ7kg6dQbogbKtyhh5veUZ67uMIsSlp+wsndDLnt+zqU4t6bWIyhMT99RcaSdHU90UjPWXhLNpigK5UWFnDiaRdGxbIqOZvlCT2MrGKs1GsKiY+sGHG/BsaGDb2kihOiYJAB1RHtWwT//AI4KiOkPt3wM4d0DusR7O97jza1vAjD77Nlc0fOKFm1ixYYNlH31FZbvf8CZn1/zQvWihJeOJvTSS9AlJrbo5zbGbnVycHMBe37O5eieYvB2Pml0anqlx5B2djzJ/SKkp6eVKW43ZYUFFB3zBpyjWRQdzeLEsewGdwtXqdSExycQlZRMREI3wn2Fx/GERsXITuBCiBYnAaijWf8mrHoUFDf0ugSufw+M5oAu8dm+z3jh1xcA+PPwP3N92vUt2sSyVas49peHfM/VQUEEX3ghoaPbflFCt1vh2J5i9vycy4Hf8nHaa4peE/uEk3Z2PKnDY9FLLU+Lc7tdlOXn1wSd7COenp1j2Tht9c+gU2s0hMcnEpWUTFRSd6K6ee4jErqhbYd1nYQQXZf8Vugo3C74djb8/Jrn+fDJcNUC0AQ21TbzSCZPrnsSgDsG3sGdg+5s0WYqLhcFL/8DgJBLLyXiphvbZVHCE8cr2LM+hz3r86goqflla4410e/sePqOiicsupkLTQo/bpeLkrxcT9DJ9vTmFB3LpvjYUZyO+nemV2u0RCZ2I9IbcqKTuxOV1J3w+ASZPi6E6BAkAHUE9gpYcQ/sXul5PvoJOP8hz+p6Afg552ce+c8juBU31/W5jmkjprV4zU35d99hP3gQdVgYic8/h6YNF3yrKrez95c89vycS0FWue+4IUhLn7M8dT1xPcNk6nIzuZxOSnJzKDp6pGbo6lg2xcePNliIrNHpiExM8vTmJHX39eyExyXIsJUQokOTANTeyvPgoxvg+G+gMcC1r8OgSQFfZmvBVh78/kEcbgeXpVzG42c/3uJBQHG7KXx9EQCRt93WJuHH6XBxeKtn6nrW9iLcbk9hj1qtImVwFGlnx9NjUDQandT1NJXT4aA455ivCLm6KLk45xhuV/3rIWkNBs9wVbdkT6+ON+yYY+NQN3E9KiGE6EgkALWn/F3wwe+hNBtMkXDTR9D97IAvs794P3/M/CNVzirOTjib+RfMR9MKv5Qsa9Zg27MHdXAwkbfd2uLXr6YoCrkHy9jzcw77N+Zjq6zpfYhNCSXt7AT6jIzFFCI1I41x2G0UH68JOtU9OiW5xxtcIFBnNHl6cbrV9OZEJSUTFh0r08mFEGcUCUDt5cAP8PFksJVBVKpnT6+o3gFf5mj5Ue797l5KbaUMiR7CS5e8hF7T8sFAURQKX3sdgIibb0YTHt7in1FaUMXeDbns/jmXsoKa2UIhEQb6ZsSTlhFPZELH2bi1o1Dcbgqzj1Bw5JAv5BRlZ1GSn9vgflaGoGAiawWd6KTuRCZ1JzQqWoYQhRBdggSg9rDpfVj5F3A7ofu5cOMHEBQZ8GUKqwq557t7yK/KJzU8ldfGvEaQrnXWRKn46X9Yt29HZTQSOeWOFruurcrJgY357P45h5z9pb7jOoOG3sNjSMuIp1vfCFRq+aVcTVEUinOOk71jC1nbtpC1c1uDKyIbg0OISu7uCTrV90nJBEdEStARQnRpEoDaktsNPzwD/33R83zw9XDNK6ANfDn+Ulsp9353L9nl2XQL6cYbl72B2RDYdPmmUhSFwte9vT833IA2MvCwVpvb5SZr5wnPlhSbC3E5vcMxKkjuH0laRjy90mPQGaS2pFp5USFZ27d4bju2Yikq9HtdZzAS1zuVqKQUvyGsIHO4BB0hhKiHBKC29PUj8MvbnscXPQoXzwp4phdApaOSqZlT2Vu8l2hTNG9d9haxQc3cZb4pn7fhF6o2bUKl1xP5hz806xqKolCYbWHP+lz2bsilqrxmS4rIxGDSzo6n78h4QiJkbyaAyrJSsnds8/TybN9Ccc5xv9c1Wi2JffuTPGgI3QelE9+7D5o22FpECCHOFPI3ZlsafD1sWQ5XPg/pNzfrEg6Xg2lrprG5YDOhes/O7slhyS3cUH/VvT/hv5uELi6woFVRYmOPd0uKE8drtjswheroOzLesyVFckiX76WwVVZybPcOsrZvJmv7VgqOHPJ7XaVSE9c7le4DPYEnMa0fOoOxnVorhBCdnwSgttQ9A/6ytVn1PgAut4tZP83if8f/h0lr4rXRr9E3om8LN9Jf5abfqPz5Z9Bqibrrria9x2FzebakWJ/L0V0nfHW4Gq2ankOjPVtSDIhE04W3pHDa7Rzfu4us7VvJ2rGF3P1768zMik5OofugoSQPGkrygEEYgqQAXAghWooEoLbWzPCjKArPrH+Gbw5/g1atZeHFC0mPTW/ZttWjcJGn98c88ZpG9/VS3ArH9pWw5+ccDmwqwGGrWU8mIdVMWkY8qSNiMQR1zVWA3S4XuQf2kb1jK1nbN3Nszy5cDoffOeFxCd4hraEkDxhMcHhEO7VWCCHOfBKAOomXNr3EP/f+E7VKzXMXPMe53c5t9c+s2r6Div/8F9Rqou+5p95zinMr2PNzLns25GI5UbMlRVi0kbSzE0jLiMMc0/V2666eml5duHx01/Y6G4EGR0TSfdBQ77DWUMJiWq+OSwghhD8JQJ3Au9vf5Z3t7wDw+NmPc3mPy9vkc6t7f8Kuvgp995rd6N1uhZ0/HWfX2hzyD9dMv9abtKSeFUu/jHjie5u7VF2PoiiU5B73DGlt30L2jq1UnTQ13RgcQvLAIb5ensjEpC71MxJCiI5EAlAH98+9/+T/bfx/AEwbMY1JfQPfJqM5rHv2YlmdCSoV0ffe6/favl/y+PHDPQCo1CpSBkaSdnYCPYZEodV1nanr5ScKydq2xTustZXyogK/17UGA0n9B/l6eWJ69JRtI4QQooNo9wD06quv8ve//53c3FyGDh3KP/7xD0aNGlXvuQ6Hg3nz5vHee+9x7Ngx0tLSeO655xg3blyzr9mRfXv4W57++WkA7hx0J1MGTWmzzy56w7PnV+jYsRh6+69QfWiLZw2avqPiOO93fQgK6xpbUlSWlXJ05zZfL09xzjG/1zVaLQl9+9F94FCSBw0hIbWv7HwuhBAdVLsGoOXLlzNt2jQWLVpERkYGCxcuZOzYsezZs4fY2Lr1ELNnz2bp0qW89dZb9OvXj2+++YZrr72WtWvXMmzYsGZds6Nae3wtj/73UdyKm9/1/R1/Hv7nNvts28FDlH29CoDo++/ze83tcpO96wQAgy9JOqPDj72qkqO7d3hWW96xlYLDB/1eV6nUxPXqTfKgoXQfNJRuaf1laroQQnQSKkVpYLOgNpCRkcHIkSN55ZVXAHC73SQnJ/OnP/2JmTNn1jk/MTGRxx57jAceeMB3bNKkSZhMJpYuXdqsawLYbDZstpoC3rKyMpKTkyktLSUsLKzFvm9Tbc7fzD3f3UOVs4qxPcby3AXPtcrmpg05/uhMSv/1L0IuvZTk1171f21fCZ+9uAljsI4pfz8f9Rm0RYVnavpusnds4cj2+qemRyV1p/vgoXQfOJSkAYMwBoe0U2uFEEKcrKysDLPZ3KTf3+3WA2S329m4cSOzZs3yHVOr1YwZM4Z169bV+x6bzYbR6P8vbJPJxE8//dTsawLMmzePuXPnns7XaTF7i/fyQOYDVDmrOK/becw7f16bhh97djalK1cCdXt/AI5sLwKg+8DIMyL85B3cz+Etm8javoXje3bhdNj9XjfHxftmaSUPHCJT04UQ4gzRbgGosLAQl8tFXFyc3/G4uDh2795d73vGjh3LggULuPDCC+nduzeZmZmsWLECl8vV7GsCzJo1i2nTpvmeV/cAtbXs8mzu/e5eyuxlpMeks+CiBeg0bVtDUvTmW+ByEXz++ZgGD67zenUAShkU1abtakmKonB4yybWf/Yxx3bv8HstODyC5IFDfL085ti4Bq4ihBCiM2v3IuhAvPTSS9x9993069cPlUpF7969mTJlCu++++5pXddgMGAwtO8eVPmV+dz97d0UVhXSN6Ivr4x+pdV2dm+IIyeHks8/ByD6j/fXed1SbKPomMWzaemA09sQtT243S72rV/Lhs//Sf7hAwCoNVp6DT/LM1NrUDqR3WRquhBCdAXtFoCio6PRaDTk5eX5Hc/LyyM+Pr7e98TExPD5559jtVopKioiMTGRmTNn0qtXr2ZfsyOo3tn9mOUYyaHJrbqze2OK3n4HHA6CRo0iaPjwOq9n7fD0/sT1CMMU0nmKn11OBzv/8wO/fPFP36aiOoORIWPGMeLqiYRGRrdzC4UQQrS1dgtAer2eESNGkJmZycSJEwFPwXJmZiZTp05t9L1Go5Fu3brhcDj49NNPuf7660/7mu2l0lHJHzP/yP6S/cSaYnnzsjeJNrX9L2RnQQEln3wC1N/7A51v+MthtbI18xt+XbkCywlP243BIQy7YgLDxl2NKbTtC9yFEEJ0DO06BDZt2jRuv/12zjrrLEaNGsXChQupqKhgyhTPejeTJ0+mW7duzJs3D4D169dz7Ngx0tPTOXbsGE8++SRut5sZM2Y0+Zodid1l5y8//IWtBVsxG8y8cdkbJIUmtUtbit5djGK3Y0pPJygjo87rLmfN9PeOHoCqLOVsXrWSTav+jdW7GnNIRCQjrr6WIWPGoTea2rmFQggh2lu7BqAbbriBgoICHn/8cXJzc0lPT2fVqlW+IuasrCzU6podw61WK7Nnz+bgwYOEhIRw5ZVX8v777xMeHt7ka3YULreLmf+dybqcdZi0Jl4f/TqpEant0hZncTHFy5YBnt6f+mpgcg6U4rC5MIXqiEkObesmNoml+AQbv/ycLd99jcPq2XcrPD6BkRMmMeDC0Wh1siihEEIIj3ZdB6ijCmQdgeZQFIUn1z3Jin0r0Kl1vDbmNc5OOLvFP6ep8v/fQoreeAPjwIH0+Ocn9Qag/326n83fZdHv7HhG3zGgHVrZsJLcHH754lN2/Lgal9MJQExKT0ZN/D19zz5Ptp8QQoguolOsA9RVKYrCgo0LWLFvBWqVmr9f+Pd2DT+u0lKKvYtIRt9/X4MzoHzr/3Sg4a+CI4fY8K9/smftf1EUz4KF3foNYNTE39Mz/SyZzSWEEKJBEoDa2Dvb32HJjiUAPHnOk4xOGd2u7TmxdCnuigoMffoQcuml9Z5TVlRFcU4FKrWK5P7tP/392J5dbPj8Yw5u+sV3rGf6CEZN/D1J/Qe1Y8uEEEJ0FhKA2tDHez7mpU0vAfDIWY9wbZ9r27U9LksFJ/7vfcDb+1Or3qq2rB2e4uf4XmEYg9unjkZRFI5s2cT6zz/h6K7tnoMqFX3PPp9R1/yOuJ69G7+AEEIIUYsEoDakKAoqVNw95G4mD5zc3s2h+KMPcZeWou/Zk9CxYxs8rz2nv3sWL1zHhs8/8Vu8cOBFlzJywiQiErq1eZuEEEJ0fhKA2tAN/W5gQNQABkW3/zCNu6qKE4uXABB17z2oNPUXCjsdLo7ubvvp7y6ng53//YFf/vUpxTnHANAaDAwdM44RV11LaJQsXiiEEKL5JAC1scExdffXag8lH3+M68QJdElJmK+6qsHzcvaV4rS7CTbrierW+jufO6xWtn3/Db+s/AxLUSFQvXjheIaNGy+LFwohhGgREoC6ILfNRtE7nv3Tou65G1Uj6+PUnv3VmrOqrBYLv33zbzZ9XbN4YXBEJGddNdGzeKGpbfdFE0IIcWaTANQFla5YgTM/H218PGbvliENObKjdet/6l28MM67eOFFsnihEEKI1iEBqItRHA4K33oLgKi77kKtb3hT09KCSkryKlGrVST3a9np7yV5ufzyxT/Z8WMmLocDgJjuPbyLF56PuoGaJCGEEKIlSADqYkq/+ALn8Rw00dGE/25So+ce2e4pfk5INaM3tcwflYKsw2z4/BO/xQsT0waQMfH39BwmixcKIYRoGxKAuhDF6aTwzTcBiPrDH1AbjY2e35KrPx/fu4v1n3/CwY0bfMd6pI8gQxYvFEII0Q4kAHUhZV9/jeNIFprwcCJuuL7Rc512F8f2FgPNr//xLV74r084urPW4oUZ5zFq4u9l8UIhhBDtRgJQF6G43RQuegOAyDvuQB0c3Oj5x/aW4HK4CYkwEJnQ+Lknc7td7N+wjvWff0L+oZrFCwdc6Fm8MDJRFi8UQgjRviQAdRHl336H/cAB1GFhRNxy8ynPr736c1PrclxOB7v+u4YNX3xK8fGjgGfxwiGjx3HW1bJ4oRBCiI5DAlAXoCgKhYsWARB5661oQkNPef6R7Z5FCJsy/OWwWdn2/bf8+u/PKC8qAMAQHMywcZ7FC4PCzKf5DYQQQoiWJQGoC7D8sAbb7t2og4KInHzbKc8vyaukrNCKWquiW1pEg+dZLRY2f7OSTV9/QVWtxQtHXDWRobJ4oRBCiA5MAtAZrnbvT8QtN6MJDz/le6p3f09MDUdvrPtHRHG7+d/HH/Dbqi+wV3kWLzTHxTNy/CQGXjQabSNrCwkhhBAdgQSgM1zF/9Zi3boVldFI5B13NOk9pxr+2v2/H1n/2XIAor2LF6bJ4oVCCCE6EQlAZ7jCRa8DEHHD9WijTl3PY7c6ObavBGg4AGXv8kxpHzJmHGPuekAWLxRCCNHpqNu7AaL1VGzYQNWvG1HpdET+4Q9Nes+xPcW4nQph0UbC4+qv4cndtweAHkOHS/gRQgjRKTWpB+i6665r8gVXrFjR7MaIllXkrf0x/24Suri4Jr3niLf+J2Vg/dPf7dYqCrOzAEhITWuhlgohhBBtq0kByGyWacydTdXmzVSsXQdaLdF33dWk99Se/t7Q9hd5B/ahKG5CoqIJiWydHeKFEEKI1takALR48eLWbodoYYWve3t/rpmArlvTVl4+kVOB5YQNjU7d4PT3nP17AUhI7dsyDRVCCCHaQbNqgJxOJ6tXr+aNN96gvLwcgOPHj2OxWFq0caJ5qnbswPLjj6BWE33PPU1+X5Z39/dufcPR6euf0ZXjrf+R4S8hhBCdWcCzwI4cOcK4cePIysrCZrNx2WWXERoaynPPPYfNZmORt+5EtJ8i755fYVddhT4lpcnvO7Kj8enviqKQs98bgPpIABJCCNF5BdwD9Oc//5mzzjqL4uJiTCaT7/i1115LZmZmizZOBM66dy/l330HKhXR9za998de5SRnXykA3QfWH4DKiwqpKD6BSq0mrldqi7RXCCGEaA8B9wD997//Ze3atehPWu23R48eHDt2rMUaJpqn6I03AQi9/HIMqU0PKdm7T+B2K4THBREe28D0d2/vT3T3HugMxtNvrBBCCNFOAu4BcrvduFyuOsePHj1K6Ck22RSty3boEGVffw1A9H33BvTeLO/u790HRjZ4jhRACyGEOFMEHIAuv/xyFi5c6HuuUqmwWCw88cQTXHnllS3ZNhGgojfeBLebkEsuwdi/f5Pf55n+7glAje3+LgXQQgghzhQBD4G9+OKLjB07lgEDBmC1Wrn55pvZt28f0dHRfPTRR63RRtEE9qNHKf33vwGIvv++gN5bdMxCRakdrV5NYp/wes9xu1zkHdwPQEKffqfVViGEEKK9BRyAkpKS2LJlC8uWLWPr1q1YLBbuvPNObrnlFr+iaNG2it58C1wugs87D9OQIQG9t7r3JyktAq2u/unvBVmHcdptGIKCiUxs2rpCQgghREfVrHWAtFott956K88//zyvvfYad911V7PDz6uvvkqPHj0wGo1kZGSwYcOGRs9fuHAhaWlpmEwmkpOTeeihh7Barb7Xn3zySVQqld+tX78zu8fCkZtLyWefAYH3/gBNGv6qLoCO690HlVq2kBNCCNG5NakH6IsvvmjyBSdMmNDkc5cvX860adNYtGgRGRkZLFy4kLFjx7Jnzx5iY2PrnP/hhx8yc+ZM3n33Xc4991z27t3LHXfcgUqlYsGCBb7zBg4cyOrVq33Ptdoze9P7orffAYeDoJEjCTrrrIDea61wkHuwDGh4+jtAzr7qAmip/xFCCNH5NSkZTJw40e+5SqVCUZQ6x4B6Z4g1ZMGCBdx9991MmTIFgEWLFvHll1/y7rvvMnPmzDrnr127lvPOO4+bb74Z8Ey9v+mmm1i/fr3feVqtlvj4+Ca3ozNzFhRQ8sknQPN6f7J3nUBxK0QkBBMW3XAvXs0CiDIDTAghROfXpLEMt9vtu3377bekp6fz9ddfU1JSQklJCV9//TXDhw9n1apVTf5gu93Oxo0bGTNmTE1j1GrGjBnDunXr6n3Pueeey8aNG33DZAcPHuSrr76qM/ts3759JCYm0qtXL2655RaysrIabYvNZqOsrMzv1lkULV6CYrNhGjqUoHPOCfj9WTu8w1+NTH+3VVZw4vhRQHqAhBBCnBkCHhv6y1/+wqJFizj//PN9x8aOHUtQUBD33HMPu3btatJ1CgsLcblcxMXF+R2Pi4tj9+7d9b7n5ptvprCwkPPPPx9FUXA6ndx333389a9/9Z2TkZHBkiVLSEtLIycnh7lz53LBBRewffv2BtcpmjdvHnPnzm1SuzsSZ3ExxcuWARB1/32+XrimUtwKR3Z49v9qvP5nHygK5tg4gszhzW6vEEII0VEEXM164MABwsPD6xw3m80cPny4BZrUsDVr1vDss8/y2muvsWnTJlasWMGXX37J008/7Tvniiuu4Pe//z1Dhgxh7NixfPXVV5SUlPDxxx83eN1Zs2ZRWlrqu2VnZ7fq92gpJ957D6WyEsOA/oRcdFHA7y/ILqeqzI7OoCEhNbzB83L2eQJpvPT+CCGEOEME3AM0cuRIpk2bxvvvv+/rvcnLy+ORRx5h1KhRTb5OdHQ0Go2GvLw8v+N5eXkN1u/MmTOH2267jbvuuguAwYMHU1FRwT333MNjjz2Gup7ZSeHh4fTt25f9+/c32BaDwYDBYGhy2zsCV1kZxUs/ACD6vsB7f6Bm9ldy/0g02oazsK/+RwKQEEKIM0TAPUDvvvsuOTk5dO/endTUVFJTU+nevTvHjh3jnXfeafJ19Ho9I0aM8NtA1e12k5mZyTkN1LJUVlbWCTkajWfdmpOLsqtZLBYOHDhAQkJCk9vWGZxYuhS3xYKhTyqhteqoAlFd/9PY9heeHeC9M8CkAFoIIcQZIuAeoNTUVLZu3cp3333nq9Xp378/Y8aMCbgXYtq0adx+++2cddZZjBo1ioULF1JRUeGbFTZ58mS6devGvHnzABg/fjwLFixg2LBhZGRksH//fubMmcP48eN9QWj69OmMHz+elJQUjh8/zhNPPIFGo+Gmm24K9Kt2WC5LBcXv/R8AUffe16x1eaosdnIPeYq9G6v/KSvIo6qsFLVGS2yP3s1rsBBCCNHBNGuBHJVKxeWXX87ll19+Wh9+ww03UFBQwOOPP05ubi7p6emsWrXKN7SWlZXl1+Mze/ZsVCoVs2fP5tixY8TExDB+/Hj+9re/+c45evQoN910E0VFRcTExHD++efz888/ExMTc1pt7UhKln2Eq7QUfUoKYVeMa9Y1sneeAAWiuoUQEtHwzu7V+3/F9uiJVq9v1mcJIYQQHY1KaWjsqBE//vgjL7zwgm/G14ABA3jkkUe44IILWryB7aGsrAyz2UxpaSlhYWHt3Rw/7qoq9o+5DFdREQnPPkv4ddc26zrfLd7B3vV5DB/bnXOuTW3wvB+WvMmmr78gfezVjP5D4OsMCSGEEG0lkN/fAY+dLF26lDFjxhAUFMSDDz7Igw8+iNFoZPTo0Xz44YfNbrRompJPPsFVVISuWzfM469u1jXcboWsJkx/h9oLIEoBtBBCiDNHwENgf/vb33j++ed56KGHfMcefPBBFixYwNNPP+1bpVm0PLfd7tn2Aoi6+25UOl2zrpN/pAyrxYHepCWul7nB81xOB/mHDwKQkCoF0EIIIc4cAfcAHTx4kPHjx9c5PmHCBA4dOtQijRL1K12xAmd+Ptq4OMzNHPqCk6a/axr+I1Bw+BAuhwNjSCjh8YnN/jwhhBCiowk4ACUnJ/tNXa+2evVqkpOTW6RRoi7F4aDozbcAiLrzTtSnUZCc5dv9veHp71B7/Z++zVpnSAghhOioAh4Ce/jhh3nwwQfZvHkz5557LgD/+9//WLJkCS+99FKLN1B4lH7xbxzHj6OJiiL8+t83+zqVZXbyj5QDje/+DjUzwGQFaCGEEGeagAPQ/fffT3x8PC+++KJve4n+/fuzfPlyrrnmmhZvoADF5aLwzTcAiPrDFNTGhqetn0rWTk/vT0z3UILNja9+LQXQQgghzlTNWgfo2muv5dprm1+DIgJT9tXXOI5koTGbibjxxtO6VvXwV2OrPwNUlZdRkpsDQLwUQAshhDjDNCsAVbNYLLjdbr9jHW3dnM5OcbspfGMRAJF33I46OLjZ13K73GTtrJ7+Ht3oubne7S8iErphCglt9mcKIYQQHVHARdCHDh3iqquuIjg4GLPZTEREBBEREYSHhxMREdEabezSyr9bjX3/AdShoUTceutpXSvvUBm2SieGYC1xPRsPqrULoIUQQogzTcA9QLfeeiuKovDuu+8SFxcns4NakaIoFC7y9P5E3HoLmtDT64mpnv7efUAUanXj/918BdBS/yOEEOIMFHAA2rJlCxs3biQtTX4xtjbLmjXYdu1CFRRE5OTJp329I97d31NOUf+jKIpvCCxBZoAJIYQ4AwU8BDZy5Eiys7Nboy2iFr/en5tuRHuaw4sVJTYKsy2gguQBjU9/L845jrXCgkanIyalx2l9rhBCCNERBdwD9Pbbb3Pfffdx7NgxBg0ahO6k7RiGDBnSYo3ryirWrsW6ZSsqg4GoKVNO+3rVvT+xKWEEhTW+iGKut/4ntmdvNNrmbbchhBBCdGQBB6CCggIOHDjAlFq/lFUqFYqioFKpcLlcLdrArqrodU/vT/j116ONbnzGVlPUrP7ceO8P1BRAJ0r9jxBCiDNUwAHoD3/4A8OGDeOjjz6SIuhWUvnLL1T++isqnY6oO/9w2tdzudxk7/JOfz/F6s8AOfs89T+yArQQQogzVcAB6MiRI3zxxRekpqa2RnsEUOjt/TFfdx26+PjTvl7ugVLsVhemUB2xKY3PJHPYbRQcqd4BXgKQEEKIM1PARdCXXnopW7ZsaY22CKBqyxYq1q4FrZaou+9ukWvWnv6uOsX09/xDB3G7XASZwwmLiW2RzxdCCCE6moB7gMaPH89DDz3Etm3bGDx4cJ0i6AkTJrRY47oiX+/PhAnok7q1yDWzvAXQ3U+x+zvUFEDHyw7wQgghzmABB6D77rsPgKeeeqrOa1IEfXqsO3diWbMG1Gqi72mZ3p/yE1aKjlWgUkH3/k2p/6kugO7XIp8vhBBCdEQBB6CT9/4SLadwkWfH97Arr0Tfo0eLXLO69yeupxljyKmntOfsry6Ali0whBBCnLkCrgESrcO2bx/l334LQPS997TYdY8EMP29oqSYsoI8UKmI7y0BSAghxJlLAlAHUfjGmwCEXn45hj59WuSaLoebo7uLgaau/+Pp/YnqlowhKKhF2iCEEEJ0RBKAOgD74cOUffUVANH33dti1z1+oASHzUVQmJ7opJBTnl+7AFoIIYQ4k0kA6gAK33wL3G5CLr4Y44ABLXZd3/T3Qaee/g5SAC2EEKLraFIAmjZtGhUVFQD85z//wel0tmqjuhL70WOUfvEFANH339ei1/Ztf9GE1Z/dbhe5B6QAWgghRNfQpAD0j3/8A4vFAsAll1zCiRMnWrVRXUnR22+B00nwuediGjq0xa5bVlhFcW4lKrWK5P6n3kn+xLGj2Kuq0BoMRCentFg7hBBCiI6oSdPge/Towcsvv8zll1+OoiisW7eOiIj6f6leeOGFLdrAM5kjL4/ST1cALd/7Uz38ldDbjCGoKdPfvfU/vfqg1mhatC1CCCFER9OkAPT3v/+d++67j3nz5qFSqbj22mvrPU8WQgxM0TvvoDgcBJ11FkEjR7botY/saPr0d4DcfTL8JYQQoutoUgCaOHEiEydOxGKxEBYWxp49e4iNlX2iToezsJCS5R8DENXCvT9Oh4tj3unv3ZtQ/wM1PUBSAC2EEKIrCGgl6JCQEH744Qd69uyJVhvwItKilhNLlqDYbBiHDiH43HNb9NrH95bgdLgJDjcQ1S34lOc7rFYKs44AEN9HeoCEEEKc+QJOMRdddBEul4tPP/2UXbt2ATBgwACuueYaNFI70iTO4mJOfPgRANH33dfim47WXv25KdfOPbgPRXETEhlFaGR0i7ZFCCGE6IgCDkD79+/nqquu4ujRo6SlpQEwb948kpOT+fLLL+ndu3eLN/JMU/z++yiVlRj69yfk4otb/PqBbH8BNev/JKSmtXhbhBBCiI4o4IUQH3zwQXr16kV2djabNm1i06ZNZGVl0bNnTx588MGAG/Dqq6/So0cPjEYjGRkZbNiwodHzFy5cSFpaGiaTieTkZB566CGsVutpXbMtucrLOfH+UqB1en9K8iopLahCrVGR1O/U098BcmUDVCGEEF1MwAHoxx9/5PnnnycyMtJ3LCoqivnz5/Pjjz8GdK3ly5czbdo0nnjiCTZt2sTQoUMZO3Ys+fn59Z7/4YcfMnPmTJ544gl27drFO++8w/Lly/nrX//a7Gu2teIPPsBdXo4+tTehl41p8etXz/5KSA1Hb2xaB58UQAshhOhqAg5ABoOB8vLyOsctFgt6vT6gay1YsIC7776bKVOmMGDAABYtWkRQUBDvvvtuveevXbuW8847j5tvvpkePXpw+eWXc9NNN/n18AR6zbbkrqjgxJL3AIi+9z5U6pbfiSQrwOGv8qJCLCeKUKnVxPVKbfH2CCGEEB1RwL+Br776au655x7Wr1+PoigoisLPP//Mfffdx4QJE5p8HbvdzsaNGxkzpqYXRK1WM2bMGNatW1fve84991w2btzoCzwHDx7kq6++4sorr2z2NQFsNhtlZWV+t9ZQvGw5rpIS9CkphF15RYtf32F3cWxvCdC07S+gpvcnOjkFndHY4m0SQgghOqKAA9DLL79M7969OeecczAajRiNRs477zxSU1N56aWXmnydwsJCXC4XcXFxfsfj4uLIzc2t9z0333wzTz31FOeffz46nY7evXtz8cUX+4bAmnNN8BRxm81m3y05ObnJ3yMQ2photIkJRN1zD6pWmDF3bE8xLqeb0EgjEQlBTXqPFEALIYToigKeBRYeHs6//vUv9u/f75sG379/f1JTW3/4ZM2aNTz77LO89tprZGRksH//fv785z/z9NNPM2fOnGZfd9asWUybNs33vKysrFVCkHnCBMLGjYNWGPqCwKe/Q60CaFn/RwghRBfS7NUMU1NTTyv0REdHo9FoyMvL8zuel5dHfHx8ve+ZM2cOt912G3fddRcAgwcPpqKignvuuYfHHnusWdcET12TwWBo9ncJhCrAOqmmUhQl4OnvbpeL3IP7ACmAFkII0bW0TldEE+j1ekaMGEFmZqbvmNvtJjMzk3POOafe91RWVqI+qfekevFFRVGadc0zRUleJeVFVtRaFd3Smjb9vTD7CE6bDb0piMjEpFZuoRBCCNFxtOt+FtOmTeP222/nrLPOYtSoUSxcuJCKigqmTJkCwOTJk+nWrRvz5s0DYPz48SxYsIBhw4b5hsDmzJnD+PHjfUHoVNc8U1X3/nTrG4HO0LT6It/wV+8+rTIjTQghhOio2jUA3XDDDRQUFPD444+Tm5tLeno6q1at8hUxZ2Vl+fX4zJ49G5VKxezZszl27BgxMTGMHz+ev/3tb02+5pnKN/zVxNlfAMf37QYgoY8UQAshhOhaVIqiKO3diI6mrKwMs9lMaWkpYWFh7d2cU7Jbnbzz8H9xuxRumXs24XFNmwG25OE/UnQ0i2semUPqWRmt3EohhBCidQXy+zvgcY8ePXrw1FNPkZWV1ewGipZ1dHcxbpdCWIwJc6ypSe+xVVZSdCwbgATZAkMIIUQXE3AA+stf/sKKFSvo1asXl112GcuWLcNms7VG20QTVW9/EdD09wN7QVEIi4kjOLxpRdNCCCHEmaJZAWjz5s1s2LCB/v3786c//YmEhASmTp3Kpk2bWqONohGKogS8/QXUFEBL748QQoiuqNlTf4YPH87LL7/M8ePHeeKJJ3j77bcZOXIk6enpvPvuu0hpUds4cbwCS7ENjU5Ntz7hTX6fFEALIYToypo9C8zhcPDZZ5+xePFivvvuO84++2zuvPNOjh49yl//+ldWr17Nhx9+2JJtFfWonv2VlBaBVt+06e+KotRMgZctMIQQQnRBAQegTZs2sXjxYj766CPUajWTJ0/m//2//0e/fjUrCV977bWMHDmyRRsq6hfo6s8AZQX5VJaWoNZoiO3Zq7WaJoQQQnRYAQegkSNHctlll/H6668zceJEdDpdnXN69uzJjTfe2CINFA2zVTnJPVAKQPcA1v+p3gE+JqUXOn3bbAEihBBCdCQBB6CDBw+SkpLS6DnBwcEsXry42Y0STXN01wncboXwuCDMMU2b/g6Q6w1ACbIBqhBCiC4q4CLo/Px81q9fX+f4+vXr+fXXX1ukUaJpmjP8BXB8nzcASf2PEEKILirgAPTAAw+QnZ1d5/ixY8d44IEHWqRR4tQURfFb/6epXE4H+YcOAFIALYQQousKOADt3LmT4cOH1zk+bNgwdu7c2SKNEqdWeNRCZakdrUFDYmp4k99XcOQwLocDY3AIEQmJrddAIYQQogMLOAAZDAby8vLqHM/JyUGrbde9VbuU2tPfNbqm/2esLoCO75PW5FWjhRBCiDNNwAHo8ssvZ9asWZSWlvqOlZSU8Ne//pXLLrusRRsnGtac1Z8Bcn31P1IALYQQousKuMvmhRde4MILLyQlJYVhw4YBsHnzZuLi4nj//fdbvIGiLmuFg9yDngAaaACq7gGSAmghhBBdWcABqFu3bmzdupUPPviALVu2YDKZmDJlCjfddFO9awKJlpe96wSKApGJwYRGGpv8vipLOcU5xwGIlx4gIYQQXVizinaCg4O55557Wrotool8098DWPwQajZADY9PwBQa1uLtEkIIITqLZlct79y5k6ysLOx2u9/xCRMmnHajRMMUt0JWM6a/A+RU1//06XeKM4UQQogzW7NWgr722mvZtm0bKpXKt+t79Ywil8vVsi0Ufgqyy6kqd6AzaohPNQf0Xt8K0DL8JYQQoosLeBbYn//8Z3r27El+fj5BQUHs2LGD//znP5x11lmsWbOmFZooaqse/kruH4lG0/T/fIqikOMdApMCaCGEEF1dwD1A69at4/vvvyc6Ohq1Wo1areb8889n3rx5PPjgg/z222+t0U7h1dztL0pyj2O1lKPR6Yjp0bM1miaEEEJ0GgH3ALlcLkJDQwGIjo7m+HHPrKKUlBT27NnTsq0TfqrK7eQdLgMCL4Cu7v2J7dELjVZm6wkhhOjaAu4BGjRoEFu2bKFnz55kZGTw/PPPo9frefPNN+nVq1drtFF4Ze08AQpEJYUQHG4I6L1SAC2EEELUCDgAzZ49m4qKCgCeeuoprr76ai644AKioqJYvnx5izdQ1Gju8BdIAbQQQghRW8ABaOzYsb7Hqamp7N69mxMnThARESF7S7Uit1sha2fzApDTbif/8CEAEvpIAbQQQggRUA2Qw+FAq9Wyfft2v+ORkZESflpZ/uEybBVODEFa4nsGtohh/uEDuF1OTGFmwmLiWqmFQgghROcRUADS6XR0795d1vppB7Wnv6sDmP4OkLOvevp7XwmqQgghBM2YBfbYY4/x17/+lRMnTrRGe0QDTqf+x7cBqhRACyGEEEAzaoBeeeUV9u/fT2JiIikpKQQHB/u9vmnTphZrnPCoKLVRkFUOQPcAp79D7QJoqf8RQgghoBkBaOLEia3QDNGY7J2e3raY7qEEhekDem9laQml+XmgUhGf2qc1mieEEEJ0OgEHoCeeeKI12iEa0RLDX5GJSRiCgk9xthBCCNE1BFwDJNqW2+X2LIBIMwPQPtn/SwghhDhZwD1AarW60ZlEMkOsZeUeLMNe5cQYrCO2R2DT36F2AbQEICGEEKJawD1An332GStWrPDdli9fzsyZM0lISODNN99sViNeffVVevTogdFoJCMjgw0bNjR47sUXX4xKpapzu+qqq3zn3HHHHXVeHzduXLPa1t6O7PBOfx8QiVod2BR2xe0mt3oHeAlAQgghhE/APUDXXHNNnWO/+93vGDhwIMuXL+fOO+8M6HrLly9n2rRpLFq0iIyMDBYuXMjYsWPZs2cPsbGxdc5fsWIFdrvd97yoqIihQ4fy+9//3u+8cePGsXjxYt9zgyGwvbM6itOp/zlx/Bj2qkq0BgPRySkt3TQhhBCi02qxGqCzzz6bzMzMgN+3YMEC7r77bqZMmcKAAQNYtGgRQUFBvPvuu/WeHxkZSXx8vO/23XffERQUVCcAGQwGv/MiIiKa9b3ak6XYRtFRC6ig+8DIgN+fs283AHE9U1FrNC3dPCGEEKLTapEAVFVVxcsvv0y3bt0Cep/dbmfjxo2MGTOmpkFqNWPGjGHdunVNusY777zDjTfeWGc9ojVr1hAbG0taWhr3338/RUVFDV7DZrNRVlbmd+sIqvf+iusRhikksOnvIPU/QgghREMCHgI7edNTRVEoLy8nKCiIpUuXBnStwsJCXC4XcXH++1PFxcWxe/fuU75/w4YNbN++nXfeecfv+Lhx47juuuvo2bMnBw4c4K9//StXXHEF69atQ1NPT8i8efOYO3duQG1vC6cz/AWQI/U/QgghRL0CDkD/7//9P78ApFariYmJISMjo82Hmd555x0GDx7MqFGj/I7feOONvseDBw9myJAh9O7dmzVr1jB69Og615k1axbTpk3zPS8rKyM5Obn1Gt4ELqeb7F3Nn/7usFkpzDoMyBR4IYQQ4mQBB6A77rijxT48OjoajUZDXl6e3/G8vDzi4+MbfW9FRQXLli3jqaeeOuXn9OrVi+joaPbv319vADIYDB2uSDrnQCkOqwtTqI6Y5NCA3593cD+K201IRCShUdGt0EIhhBCi8wq4Bmjx4sV88skndY5/8sknvPfeewFdS6/XM2LECL/iabfbTWZmJuecc06j7/3kk0+w2Wzceuutp/yco0ePUlRUREJCQkDta09Z3uGv7gOjUAU4/R0gZ5+n/ideen+EEEKIOgIOQPPmzSM6um6PQmxsLM8++2zADZg2bRpvvfUW7733Hrt27eL++++noqKCKVOmADB58mRmzZpV533vvPMOEydOJCrKf3jIYrHwyCOP8PPPP3P48GEyMzO55pprSE1NZezYsQG3r71Ur//T/PofKYAWQgghGhLwEFhWVhY9e/asczwlJYWsrKyAG3DDDTdQUFDA448/Tm5uLunp6axatcpXGJ2VlYVa7Z/T9uzZw08//cS3335b53oajYatW7fy3nvvUVJSQmJiIpdffjlPP/10hxvmakj5CSsnjlegUkFy/8Cnv4MUQAshhBCNCTgAxcbGsnXrVnr06OF3fMuWLXV6Y5pq6tSpTJ06td7X1qxZU+dYWloaiqLUe77JZOKbb75pVjs6iurZX/G9zRiDdQG/33KiCEtRISqVmrheqS3dPCGEEKLTC3gI7KabbuLBBx/khx9+wOVy4XK5+P777/nzn//sN/tKNN+RWvU/zVE9/BWd3B290dRi7RJCCCHOFAH3AD399NMcPnyY0aNHo9V63u52u5k8eXKzaoCEP5fDzdHdzZ/+DjXDX/Ey/CWEaCFut9tvGyIh2oNOp6t3Pb/mCDgA6fV6li9fzjPPPMPmzZsxmUwMHjyYlBTZa6olHN9XgtPuJsisJzoppFnXqN4CQ9b/EUK0BLvdzqFDh3C73e3dFCEIDw8nPj7eb03C5gg4AFXr06cPffr0Oa0PF3X5Zn8NjGrWf1y320Xegf0AJKT2bdG2CSG6HkVRyMnJQaPRkJycXGdSihBtRVEUKisryc/PBzjtpW0CDkCTJk1i1KhRPProo37Hn3/+eX755Zd61wgSTXe6218UZWfhsFnRm0xEJrXvatZCiM7P6XRSWVlJYmIiQUFB7d0c0cWZTJ661vz8fGJjY09rOCzgKP+f//yHK6+8ss7xK664gv/85z/NboiA0oJKSvIqUatVJDV7+rt3AcTefVCrZQd4IcTpcblcgKf8QYiOoDqIOxyO07pOwAHIYrHU+z+CTqfrMLuod1ZHtnuKnxNSzRhMzRudzNnnLYCW+h8hRAs63XoLIVpKS/1ZDDgADR48mOXLl9c5vmzZMgYMGNAijeqqsnac3vR3kAJoIYQQoikC7maYM2cO1113HQcOHODSSy8FIDMzk48++kjqf06D0+7i6J5ioPn1P7bKSoqOZQOyArQQQrSXJUuW8Je//IWSkpIWud7hw4fp2bMnv/32G+np6S1yTdGMHqDx48fz+eefs3//fv74xz/y8MMPc/ToUVavXs3EiRNboYldw7G9JbgcbkIiDEQmBjfrGnkH94GiEBYTS3B4RAu3UAghOo877rgDlUrlu0VFRTFu3Di2bt0a0HWefPLJdg8dycnJ5OTkMGjQoDb93G+++Yazzz6b0NBQYmJimDRpEocPH27TNrSmZs1nvOqqq/jf//5HRUUFhYWFfP/991x00UVs3769pdvXZVRPf+8+qHnT30F2gBdCiNrGjRtHTk4OOTk5ZGZmotVqufrqq9u7WQHTaDTEx8f7Fh9uC4cOHeKaa67h0ksvZfPmzXzzzTcUFhZy3XXXtVkbWttpL+hQXl7Om2++yahRoxg6dGhLtKnLURSFI9sKAc/6P83l2wBV1v8RQggMBgPx8fHEx8eTnp7OzJkzyc7OpqCgwHfOo48+St++fQkKCqJXr17MmTPHN7toyZIlzJ07ly1btvh6kpYsWQJASUkJ9957L3FxcRiNRgYNGsTKlSv9Pv+bb76hf//+hISE+MJYQ4qLi7nllluIiYnBZDLRp08fFi9eDHiGwFQqFZs3bwbq9m5V36r3zrTZbEyfPp1u3boRHBxMRkZGvftqNmbjxo24XC6eeeYZevfuzfDhw5k+fTqbN28+7dlXHUWz4+R//vMf3n77bVasWEFiYiLXXXcdr776aku2rcsoza+irNCKWqMiqV/zhq4URZECaCFEq1MUhSqHq10+26TTNLuH3GKxsHTpUlJTU/027g4NDWXJkiUkJiaybds27r77bkJDQ5kxYwY33HAD27dvZ9WqVaxevRoAs9mM2+3miiuuoLy8nKVLl9K7d2927tzptyZNZWUlL7zwAu+//z5qtZpbb72V6dOn88EHH9Tbvjlz5rBz506+/vproqOj2b9/P1VVVfWe+9JLLzF//nzf8/nz5/PRRx/Rr18/wLPB+M6dO1m2bBmJiYl89tlnjBs3jm3btvkWMFapVCxevJg77rij3s8YMWIEarXad47FYuH9999nzJgx6HSBb9LdEQUUgHJzc1myZAnvvPMOZWVlXH/99dhsNj7//HOZAXYaqhc/TOwTjt7YvExaXlhAZWkJao2G2F69W7J5QgjhU+VwMeDxb9rls3c+NZYgfdP/jly5ciUhIZ4thSoqKkhISGDlypV+q1nPnj3b97hHjx5Mnz6dZcuWMWPGDEwmEyEhIWi1WuLj433nffvtt2zYsIFdu3bRt6+nx71Xr15+n+1wOFi0aBG9e3v+Pp46dSpPPfVUg23Nyspi2LBhnHXWWb62NMRsNmM2mwFYsWIFb7zxBqtXryY+Pp6srCwWL15MVlYWiYmJAEyfPp1Vq1axePFi356daWlpvmvUp2fPnnz77bdcf/313HvvvbhcLs455xy++uqrBt/T2TR5CGz8+PGkpaWxdetWFi5cyPHjx/nHP/7Rmm3rMnzbXzRz9hfULIAYk9ITnd7QIu0SQojO7JJLLmHz5s1s3ryZDRs2MHbsWK644gqOHDniO2f58uWcd955xMfHExISwuzZs8nKymr0ups3byYpKckXfuoTFBTkCz/g2baheguH+tx///0sW7aM9PR0ZsyYwdq1a0/5/X777Tduu+02XnnlFc477zwAtm3bhsvlom/fvoSEhPhuP/74IwcOHPC9d/fu3Vx77bUNXjs3N5e7776b22+/nV9++YUff/wRvV7P7373OxRFOWXbOoMmR+mvv/6aBx98kPvvv1/2AGtBDpuLY3tPb/o7SAG0EKJtmHQadj41tt0+OxDBwcGkpqb6nr/99tuYzWbeeustnnnmGdatW8ctt9zC3LlzGTt2LGazmWXLlvHiiy823g7vdgyNOXmYSKVSNRocqoPZV199xXfffcfo0aN54IEHeOGFF+o9Pzc3lwkTJnDXXXdx5513+o5bLBY0Gg0bN26ss01EdW9YU7z66quYzWaef/5537GlS5eSnJzM+vXrOfvss5t8rY6qyQHop59+4p133mHEiBH079+f2267jRtvvLE129YlHN1TjNupEBZtJDyu+fvsSAG0EKItqFSqgIahOhKVSoVarfbV1qxdu5aUlBQee+wx3zm1e4fAswVI9XYg1YYMGcLRo0fZu3dvo71AgYqJieH222/n9ttv54ILLuCRRx6pNwBZrVauueYa+vXrx4IFC/xeGzZsGC6Xi/z8fC644IJmt6WysrLOxrfVgcrtdjf7uh1Jk4fAzj77bN566y1ycnK49957fcVVbreb7777jvLy8tZs5xkra/vp7f4O4HI6yT/o3QFeFkAUQgjAMxsqNzeX3Nxcdu3axZ/+9CcsFgvjx48HoE+fPmRlZbFs2TIOHDjAyy+/zGeffeZ3jR49enDo0CE2b95MYWEhNpuNiy66iAsvvJBJkybx3XffcejQIb7++mtWrVrV7LY+/vjj/Otf/2L//v3s2LGDlStX0r9//3rPvffee8nOzubll1+moKDA9x3tdjt9+/bllltuYfLkyaxYsYJDhw6xYcMG5s2bx5dffum7Rr9+/ep819quuuoqfvnlF5566in27dvHpk2bmDJlCikpKQwbNqzZ37MjCXgafHBwMH/4wx/46aef2LZtGw8//DDz588nNjaWCRMmtEYbz1iKovgKoLufxvBXYdZhnA47huBgIuITW6p5QgjRqa1atYqEhAQSEhLIyMjgl19+4ZNPPuHiiy8GYMKECTz00ENMnTqV9PR01q5dy5w5c/yuMWnSJMaNG8cll1xCTEwMH330EQCffvopI0eO5KabbmLAgAHMmDGjTk9RIPR6PbNmzWLIkCFceOGFaDQali1bVu+5P/74Izk5OQwYMMD3/RISEnx1Q4sXL2by5Mk8/PDDpKWlMXHiRH755Re6d+/uu8aePXsoLS1tsD2XXnopH374IZ9//jnDhg1j3LhxGAwGVq1a1aQhwM5ApbRANZPL5eLf//437777Ll988UVLtKtdlZWVYTabKS0tJSwsrNU+58TxCj56aj0arZo7F1yATt+83ds3f/Mlme++To+hw5n014ZnGQghRKCsViuHDh2iZ8+eGI3G9m6OEI3+mQzk9/dpL4QInnHBiRMnnhHhpy1V9/50SwtvdviBmhlgUgAthBBCNE2LBCDRPEdaYPd3qFUA3UcKoIUQQoimkADUTuxVTnL2lwCnN/3darFQfPwoAPG9JQAJIYQQTSEBqJ0c3V2M26VgjjURHtv86e+53uGv8LgEgsIaXtVTCCGEEDUkALWTI9u9m5+eRu8P1B7+kvofIYQQoqkkALUDRVE4suMEcHq7v4MUQAshhBDNIQGoHRQdq6CixIZWpyaxb3izr6MoihRACyGEEM0gAagdVA9/JfWLQBvg3ja1leblYi0vQ6PVEpPS69RvEEIIIQQgAahdZFUPf51u/c++3QDE9uiN9qSN94QQQgjRMAlAbcxW6SDngGf58ZZb/0fqf4QQoqNYsmQJ4eHhLXa9w4cPo1Kp2Lx5c4tdU0gAanPZu4pR3AoR8UGERZ/efiq+AmgJQEII4eeOO+5ApVL5blFRUYwbN46tW7cGdJ0nn3yS9PT01mlkEyUnJ5OTk8OgQYPa7DP37NnDJZdcQlxcHEajkV69ejF79mwcDofvnLfeeosLLriAiIgIIiIiGDNmDBs2bGizNp4uCUBtrKWmvzsdDgoOHwQgQWaACSFEHePGjSMnJ4ecnBwyMzPRarVcffXV7d2sgGk0GuLj49FqtW32mTqdjsmTJ/Ptt9+yZ88eFi5cyFtvvcUTTzzhO2fNmjXcdNNN/PDDD6xbt47k5GQuv/xyjh071mbtPB0dIgC9+uqr9OjRA6PRSEZGRqMJ8uKLL/ZL9dW3q666yneOoig8/vjjJCQkYDKZGDNmDPv27WuLr9Ioxa346n9OZ/d3gILDB3E5nZhCwzDHxrVE84QQ4oxiMBiIj48nPj6e9PR0Zs6cSXZ2NgUFBb5zHn30Ufr27UtQUBC9evVizpw5vl6OJUuWMHfuXLZs2eL7XbNkyRIASkpKuPfee309JIMGDWLlypV+n//NN9/Qv39/QkJCfGGsIcXFxdxyyy3ExMRgMpno06cPixcvBuoOgZ3cu1V9W7NmDQA2m43p06fTrVs3goODycjI8L3WVL169WLKlCkMHTqUlJQUJkyYwC233MJ///tf3zkffPABf/zjH0lPT6dfv368/fbbuN1uMjMzA/qs9tJ2cbIBy5cvZ9q0aSxatIiMjAwWLlzI2LFj2bNnD7GxsXXOX7FiBXa73fe8qKiIoUOH8vvf/9537Pnnn+fll1/mvffeo2fPnsyZM4exY8eyc+fOdt3NuPCohcoyOzqDhsTe4ad1reoC6IQ+aahUqhZonRBCNIGigKOyfT5bFwTN/PvOYrGwdOlSUlNTiYqq+QdoaGgoS5YsITExkW3btnH33XcTGhrKjBkzuOGGG9i+fTurVq1i9erVAJjNZtxuN1dccQXl5eUsXbqU3r17s3PnTjSamlm9lZWVvPDCC7z//vuo1WpuvfVWpk+fzgcffFBv++bMmcPOnTv5+uuviY6OZv/+/VRVVdV77ksvvcT8+fN9z+fPn89HH31Ev379AJg6dSo7d+5k2bJlJCYm8tlnnzFu3Di2bdtGnz59AFCpVCxevJg77rijST+//fv3s2rVKq677roGz6msrMThcBAZGdmka7a3dg9ACxYs4O6772bKlCkALFq0iC+//JJ3332XmTNn1jn/5B/ssmXLCAoK8gUgRVFYuHAhs2fP5pprrgHg//7v/4iLi+Pzzz/nxhtvrHNNm82GzWbzPS8rK2ux71db7envGt3pdb75CqBl+EsI0ZYclfBsYvt89l+Pgz64yaevXLmSkJAQACoqKkhISGDlypWo1TV//86ePdv3uEePHkyfPp1ly5YxY8YMTCYTISEhaLVa4uPjfed9++23bNiwgV27dtG3r2cNtl69/JcicTgcLFq0iN69ewOeUPLUU0812NasrCyGDRvGWWed5WtLQ8xmM2azZ+ujFStW8MYbb7B69Wri4+PJyspi8eLFZGVlkZjo+e80ffp0Vq1axeLFi3n22WcBSEtL812jMeeeey6bNm3CZrNxzz33NPodHn30URITExkzZswpr9sRtOsQmN1uZ+PGjX4/LLVazZgxY1i3bl2TrvHOO+9w4403Ehzs+Z/i0KFD5Obm+l3TbDaTkZHR4DXnzZvn+wNlNptJTk4+jW/VsJjuYaSOiKX38Lo9W4GSAmghhGjcJZdcwubNm9m8eTMbNmxg7NixXHHFFRw5csR3zvLlyznvvPOIj48nJCSE2bNnk5WV1eh1N2/eTFJSki/81CcoKMgXfgASEhLIz89v8Pz777+fZcuWkZ6ezowZM1i7du0pv99vv/3GbbfdxiuvvMJ5550HwLZt23C5XPTt25eQkBDf7ccff+TAgQO+9+7evZtrr732lJ+xfPlyNm3axIcffsiXX37JCy+8UO958+fPZ9myZXz22WftOtISiHbtASosLMTlchEX51/DEhcXx+7du0/5/g0bNrB9+3beeecd37Hc3FzfNU6+ZvVrJ5s1axbTpk3zPS8rK2uVEJQyKOq0i58BKstKKc3zfJf43n1O+3pCCNFkuiBPT0x7fXYAgoODSU1N9T1/++23MZvNvPXWWzzzzDOsW7eOW265hblz5zJ27FjMZjPLli3jxRdfbPS6JtOpZ/DqTlqbTaVSoShKg+dXB7OvvvqK7777jtGjR/PAAw80GDhyc3OZMGECd911F3feeafvuMViQaPRsHHjRr8hOcDXGxaI6t+FAwYMwOVycc899/Dwww/7XfuFF15g/vz5rF69miFDhgT8Ge2l3YfATsc777zD4MGDGTVq1Gldx2AwYDAYWqhVrS/XO/wVmZiEMTjwP9BCCNFsKlVAw1AdiUqlQq1W+2pr1q5dS0pKCo899pjvnNq9QwB6vR6Xy+V3bMiQIRw9epS9e/c22gsUqJiYGG6//XZuv/12LrjgAh555JF6A5DVauWaa66hX79+LFiwwO+1YcOG4XK5yM/P54ILLmixtgG43W4cDgdut9sXgJ5//nn+9re/8c033/iG7zqLdg1A0dHRaDQa8vLy/I7n5eX5jbfWp6KigmXLltUZj6x+X15eHgkJCX7XbO+1HFpK7QJoIYQQ9bPZbL6e/+LiYl555RUsFgvjx48HoE+fPmRlZbFs2TJGjhzJl19+yWeffeZ3jR49enDo0CHfsFdoaCgXXXQRF154IZMmTWLBggWkpqaye/duVCoV48aNa1ZbH3/8cUaMGMHAgQOx2WysXLmS/v3713vuvffeS3Z2NpmZmX4z2iIjI+nbty+33HILkydP5sUXX2TYsGEUFBSQmZnJkCFDfDOm+/Xrx7x58xocBvvggw/Q6XQMHjwYg8HAr7/+yqxZs7jhhht8vVvPPfccjz/+OB9++CE9evTw/ayrh906unatAdLr9YwYMcJvylz1FLpzzjmn0fd+8skn2Gw2br31Vr/jPXv2JD4+3u+aZWVlrF+//pTX7CyqC6BlB3ghhGjYqlWrSEhIICEhgYyMDH755Rc++eQTLr74YgAmTJjAQw89xNSpU0lPT2ft2rXMmTPH7xqTJk1i3LhxXHLJJcTExPDRRx8B8OmnnzJy5EhuuukmBgwYwIwZM+r0FAVCr9cza9YshgwZwoUXXohGo2HZsmX1nvvjjz+Sk5PDgAEDfN8vISHBVze0ePFiJk+ezMMPP0xaWhoTJ07kl19+oXv37r5r7Nmzh9LS0gbbo9Vqee655xg1ahRDhgxh7ty5TJ06lbffftt3zuuvv47dbud3v/udXzsaGrbraFRKY4OSbWD58uXcfvvtvPHGG4waNYqFCxfy8ccfs3v3buLi4pg8eTLdunVj3rx5fu+74IIL6NatW71/QJ577jnmz5/vNw1+69atTZ4GX1ZWhtlsprS0lLCwsBb7ri1Bcbt59c6bsFVWcOv8l4jr2fvUbxJCiGayWq0cOnSInj17dpriVnFma+zPZCC/v9u9BuiGG26goKCAxx9/nNzcXNLT01m1apWviDkrK8tvyiJ4kutPP/3Et99+W+81Z8yYQUVFBffccw8lJSWcf/75rFq16oz4n/dEzjFslRVo9QZiuvdo7+YIIYQQnVK79wB1RB25B2jHj5mseu3/0a3fAG6c+3x7N0cIcYaTHiDR0bRUD1CH2ApDNF11AbTU/wghhBDNJwGok8nZJytACyGEEKdLAlAn4rBZKcg6BMgUeCGEEOJ0SADqRPIOHUBxuwmOiCQ0Krq9myOEEEJ0WhKAOpHcfZ79vxJS+8oO8EIIIcRpkADUicgCiEIIIUTLkADUieT4eoAkAAkhhBCnQwJQJ2EpPkF5UQEqlZr43qmnfoMQQoh2sWTJEsLDw1vseocPH0alUrF58+YWu6aQANRp5Oz39P5EJXdHbwpq59YIIUTHdscdd6BSqXy3qKgoxo0bx9atWwO6zpNPPtnuG2knJyeTk5PDoEGD2vRzFUXhhRdeoG/fvhgMBrp168bf/va3es/93//+h1arbfefVSAkAHUStQughRBCnNq4cePIyckhJyeHzMxMtFotV199dXs3K2AajYb4+Hi02rbdverPf/4zb7/9Ni+88AK7d+/miy++YNSoUXXOKykpYfLkyYwePbpN23e6JAB1ElIALYQQgTEYDMTHxxMfH096ejozZ84kOzubgoIC3zmPPvooffv2JSgoiF69ejFnzhwcDgfgGcqaO3cuW7Zs8fUkLVmyBPD80r/33nuJi4vDaDQyaNAgVq5c6ff533zzDf379yckJMQXxhpSXFzMLbfcQkxMDCaTiT59+rB48WKg7hDYyb1b1bc1a9YAYLPZmD59Ot26dSM4OJiMjAzfa021a9cuXn/9df71r38xYcIEevbsyYgRI7jsssvqnHvfffdx8803c8455wT0Ge2t3TdDFafmdrvIPbAPkAUQhRDtS1EUqpxV7fLZJq2p2UuAWCwWli5dSmpqKlFRUb7joaGhLFmyhMTERLZt28bdd99NaGgoM2bM4IYbbmD79u2sWrWK1atXA2A2m3G73VxxxRWUl5ezdOlSevfuzc6dO9FoNL7rVlZW8sILL/D++++jVqu59dZbmT59Oh988EG97ZszZw47d+7k66+/Jjo6mv3791NVVf/P+aWXXmL+/Pm+5/Pnz+ejjz6iX79+AEydOpWdO3eybNkyEhMT+eyzzxg3bhzbtm2jT58+AKhUKhYvXswdd9xR72f8+9//plevXqxcuZJx48ahKApjxozh+eefJzIy0nfe4sWLOXjwIEuXLuWZZ55pwn+JjkMCUCdQdDQbh7UKndFEVFJyezdHCNGFVTmryPgwo10+e/3N6wnSNb0GcuXKlYSEhABQUVFBQkICK1euRK2uGfyYPXu273GPHj2YPn06y5YtY8aMGZhMJkJCQtBqtcTHx/vO+/bbb9mwYQO7du2ib19PWUKvXr38PtvhcLBo0SJ69+4NeELJU0891WBbs7KyGDZsGGeddZavLQ0xm82YzWYAVqxYwRtvvMHq1auJj48nKyuLxYsXk5WVRWJiIgDTp09n1apVLF68mGeffRaAtLQ03zXqc/DgQY4cOcInn3zC//3f/+FyuXjooYf43e9+x/fffw/Avn37mDlzJv/973/bfHiuJXS+FndB1dPf43v3Qa3WnOJsIYQQAJdccgmvv/464Blieu2117jiiivYsGEDKSkpACxfvpyXX36ZAwcOYLFYcDqdp9xFfPPmzSQlJfnCT32CgoJ84QcgISGB/Pz8Bs+///77mTRpEps2beLyyy9n4sSJnHvuuY2247fffuO2227jlVde4bzzzgNg27ZtuFyuOm2z2Wx+PV+7d+9u9Nputxubzcb//d//+a71zjvvMGLECPbs2UNqaio333wzc+fObfTn0JFJAOoEcvdLAbQQomMwaU2sv3l9u312IIKDg0lNrVk25O2338ZsNvPWW2/xzDPPsG7dOm655Rbmzp3L2LFjMZvNLFu2jBdffLHxdphO3Q6dTuf3XKVSoShKg+dfccUVHDlyhK+++orvvvuO0aNH88ADD/DCCy/Ue35ubi4TJkzgrrvu4s477/Qdt1gsaDQaNm7c6DckB/h6w5oiISEBrVbrF2769+8PeHqr4uLi+PXXX/ntt9+YOnUq4AlNiqKg1Wr59ttvufTSS5v8ee1BAlAn4CuAlvofIUQ7U6lUAQ1DdSQqlQq1Wu2rrVm7di0pKSk89thjvnOOHDni9x69Xo/L5fI7NmTIEI4ePcrevXtbtPcjJiaG22+/ndtvv50LLriARx55pN4AZLVaueaaa+jXrx8LFizwe23YsGG4XC7y8/O54IILmt2W8847D6fTyYEDB3w9WXv3en4XpaSkEBYWxrZt2/ze89prr/H999/zz3/+k549ezb7s9uKBKAOzl5VSWG2539IWQFaCCGazmazkZubC3iGwF555RUsFgvjx48HoE+fPmRlZbFs2TJGjhzJl19+yWeffeZ3jR49enDo0CHfsFdoaCgXXXQRF154IZMmTWLBggWkpqaye/duVCoV48aNa1ZbH3/8cUaMGMHAgQOx2WysXLnS1+NysnvvvZfs7GwyMzP9ZrRFRkbSt29fbrnlFiZPnsyLL77IsGHDKCgoIDMzkyFDhnDVVVcB0K9fP+bNm8e1115b72eMGTOG4cOH84c//IGFCxfidrt54IEHuOyyy3yh7+R1iWJjY30z4joDmQbfweUe2A+KQmh0DCERkad+gxBCCABWrVpFQkICCQkJZGRk8Msvv/DJJ59w8cUXAzBhwgQeeughpk6dSnp6OmvXrmXOnDl+15g0aRLjxo3jkksuISYmho8++giATz/9lJEjR3LTTTcxYMAAZsyYUaenKBB6vZ5Zs2YxZMgQLrzwQjQaDcuWLav33B9//JGcnBwGDBjg+34JCQmsXbsW8MzMmjx5Mg8//DBpaWlMnDiRX375he7du/uusWfPHkpLSxtsj1qt5t///jfR0dFceOGFXHXVVfTv37/BNnVGKqWxQckuqqysDLPZTGlp6SmL4Vrb+s8/4aeP3qPv2ecz/qGZ7doWIUTXY7VaOXToED179sRoNLZ3c4Ro9M9kIL+/pQeog5MCaCGEEKLlSQDqwBRFqZkCLwXQQgghRIuRANSBlRcVUFFSjEqtJq5n71O/QQghhBBNIgGoA8vZ55lyGJPSE51Bxt6FEEKIliIBqAPL8dX/yPCXEEII0ZIkAHVgvgJoqf8RQgghWpQEoA7K5XSSd/AAAPEyA0wIIYRoURKAOqjC7CM47TYMQcFEJnRr7+YIIYQQZxQJQB2Ub/p7al9UavnPJIQQQrQk+c3aQUn9jxBCdE5LliwhPDy8xa53+PBhVCoVmzdvbrFrCglAHVZ1D5DMABNCiMDdcccdqFQq3y0qKopx48axdevWgK7z5JNPkp6e3jqNbKLk5GRycnLadJPRNWvWcM0115CQkEBwcDDp6el88MEHfucsWbLE72esUqnq3S5l165dTJgwAbPZTHBwMCNHjiQrK6utvkqDJAB1QNYKCyeOHwWkAFoIIZpr3Lhx5OTkkJOTQ2ZmJlqtlquvvrq9mxUwjUZDfHw8Wq22zT5z7dq1DBkyhE8//ZStW7cyZcoUJk+ezMqVK/3OCwsL8/2Mc3JyOHLkiN/rBw4c4Pzzz6dfv36sWbOGrVu3MmfOnA6xr5wEoA4o98A+AMxx8QSFmdu5NUIIUUNRFNyVle1yC3TvboPBQHx8PPHx8aSnpzNz5kyys7MpKCjwnfPoo4/St29fgoKC6NWrF3PmzMHhcACeHo65c+eyZcsWXw/HkiVLACgpKeHee+8lLi4Oo9HIoEGD6oSDb775hv79+xMSEuILYw0pLi7mlltuISYmBpPJRJ8+fVi8eDFQdwjs5N6t6tuaNWsAsNlsTJ8+nW7duhEcHExGRobvtab661//ytNPP825555L7969+fOf/8y4ceNYsWKF33kqlcr3M46PjycuLs7v9ccee4wrr7yS559/nmHDhtG7d28mTJhAbGxsQO1pDW0XJxvw6quv8ve//53c3FyGDh3KP/7xD0aNGtXg+SUlJTz22GOsWLGCEydOkJKSwsKFC7nyyisBT3fl3Llz/d6TlpbG7t27W/V7tKScfZ62yvCXEKKjUaqq2DN8RLt8dtqmjaiCgpr1XovFwtKlS0lNTSUqKsp3PDQ0lCVLlpCYmMi2bdu4++67CQ0NZcaMGdxwww1s376dVatWsXr1agDMZjNut5srrriC8vJyli5dSu/evdm5cycajcZ33crKSl544QXef/991Go1t956K9OnT68zjFRtzpw57Ny5k6+//pro6Gj2799PVVVVvee+9NJLzJ8/3/d8/vz5fPTRR/Tr1w+AqVOnsnPnTpYtW0ZiYiKfffYZ48aNY9u2bfTp0wfwBJfFixdzxx13NPlnWFpaSv/+/ev8XFNSUnC73QwfPpxnn32WgQMHAuB2u/nyyy+ZMWMGY8eO5bfffqNnz57MmjWLiRMnNvlzW0u7BqDly5czbdo0Fi1aREZGBgsXLmTs2LHs2bOn3nRot9u57LLLiI2N5Z///CfdunXjyJEjdYrNBg4c6PvDCrRpt2FLyN3v2QJDCqCFEKL5Vq5cSUhICAAVFRUkJCSwcuVK1LVm1s6ePdv3uEePHkyfPp1ly5YxY8YMTCYTISEhaLVa4uPjfed9++23bNiwgV27dtG3r6dMoVevXn6f7XA4WLRoEb17e/ZxnDp1Kk899VSDbc3KymLYsGGcddZZvrY0xGw2YzZ7RgdWrFjBG2+8werVq4mPjycrK4vFixeTlZVFYmIiANOnT2fVqlUsXryYZ599FvB0DFRfoyk+/vhjfvnlF9544w3fsbS0NN59912GDBlCaWkpL7zwAueeey47duwgKSmJ/Px8LBYL8+fP55ln/n979x5WVZ0ucPy7ubq5uA3ksvHCRUDwgpISB0k9Hj0KmYrDzFhDik6aOVBeBm8ZXsq8ZOAlC1NH8BkzpizKQcNRNDuljh4TxYOXVBJLEUoDQdngZp0/GPe046IQsLH9fp5nPY97rd/6rXftvWu//H7vWmspK1euJCsri9/85jccOHCAwYMHP/DxW4JJM4Pk5GSmTJnCpEmTANiwYQO7du1iy5YtzJs3r1b7LVu2cOPGDQ4dOoS1tTVQ95fk51/W+9HpdOh0OsPr0tLSRp5J8/npE+BlBEgI0dao1Gq6f3XcZMdujCFDhpCSkgLUTDG9/fbbREZGcvToUTw9PYGaP8TXrVvHxYsXKSsr4+7du7Rv377BfnNycujcubMh+amLnZ2dIfkB0Gq1FBUV1dt+2rRpREdH89VXXzF8+HCioqIYMGBAg3GcOHGC8ePHs379esLDwwHIzc1Fr9fXik2n0xmNfDVmVuTAgQNMmjSJTZs2GUZ3AMLCwggLCzO8HjBgAIGBgbzzzju8+uqrVFdXAzBmzBhmzpwJQN++fTl06BAbNmwweQJkshqgyspKjh8/zrBhw/4djIUFw4YN4/Dhw3Xus3PnTsLCwoiLi8PNzY1evXqxbNky9Hq9Ubuvv/4aDw8PfHx8iImJuW+1+fLlyw0ZtUajoUuXLr/8BJuopOg6d26VYmllhYuXz/13EEKIVqRSqbCwszPJolKpGhWrvb09vr6++Pr6EhISwubNmykvL2fTpk0AHD58mJiYGJ544gkyMzM5ceIECxYsoLKyssF+1Q+QiN37I/2n71tDNUyRkZFcvnyZmTNncvXqVYYOHUpCQkK97QsLCxk9ejSTJ0/m2WefNawvKyvD0tKS48ePk5OTY1jOnDnD2rVr7xv3zx08eJBRo0axevVqJkyY0GBba2trgoODuXDhAgAdO3bEysqKHj16GLULDAw076vAvv/+e/R6fa2CKTc3NwoLC+vc59KlS+zYsQO9Xs/u3btJTEwkKSmJpUuXGtqEhoaSlpZGVlYWKSkp5OfnM3DgQG7dulVvLPPnz6ekpMSwXLlypXlOsgnuPQDVxcsHq5/9BySEEKLpVCoVFhYWhtqaQ4cO4enpyYIFC+jfvz9+fn61rmKysbGp9Ud2UFAQ3377LefPn2/W+FxcXIiNjWXbtm2sWbOGjRs31tmuoqKCMWPGEBAQQHJystG24OBg9Ho9RUVFhuTv3tKYmRGouRR+5MiRrFy5kueee+6+7fV6Pbm5uWi1WqDmvQsJCeHcuXNG7c6fP28YgTOlh6o4prq6GldXVzZu3IilpSX9+vXju+++Y9WqVSxatAioyaLvCQoKIjQ0FE9PT95//32jLPmnbG1tsbW1bZVzuB8pgBZCiOah0+kMf1DfvHmT9evXU1ZWxqhRowDw8/OjoKCA9PR0QkJC2LVrFxkZGUZ9eHl5kZ+fb5j2cnR0ZPDgwQwaNIjo6GiSk5Px9fXl7NmzqFQqIiIimhTrwoUL6devHz179kSn05GZmVmr4PieqVOncuXKFbKzs42uaHNycsLf35+YmBgmTJhAUlISwcHBFBcXk52dTVBQECNHjgQgICCA5cuXM3bs2DqPceDAAZ588kmmT59OdHS04X20sbHByckJgFdeeYX/+I//wNfXlx9//JFVq1Zx+fJlJk+ebOhn9uzZjBs3jkGDBjFkyBCysrL4+9//3uir0lqCyUaAOnbsiKWlJdevXzdaf/369XqzVK1Wi7+/v1GlfWBgIIWFhfUOWXbo0AF/f3/DkFxbV/i1FEALIURzyMrKQqvVotVqCQ0N5dixY3zwwQf853/+JwCjR49m5syZxMfHG2pTEhMTjfqIjo4mIiKCIUOG4OLiwnvvvQfAhx9+SEhICE8//TQ9evRgzpw5tUaKGsPGxob58+cTFBTEoEGDsLS0JD09vc62Bw8e5Nq1a/To0cNwflqtlkOHDgGQmprKhAkT+POf/0z37t2Jiori2LFjdO3a1dDHuXPnKCkpqTeerVu3cvv2bZYvX250jN/85jeGNjdv3mTKlCkEBgbyxBNPUFpayqFDh4ymvMaOHcuGDRt4/fXX6d27N5s3b+bDDz/k8ccfb/J71VxUSmNvrNCMQkNDeeyxx3jzzTeBmhGerl27Eh8fX2cR9EsvvcT27du5dOmSoYp/7dq1rFy5kqtXr9Z5jLKyMrp27crixYt58cUXHyiu0tJSNBoNJSUl9y2Ga053q6pYP/F36O/e5dm1m+jgrm21YwshRF0qKirIz8/H29u7Tdy8ToiGvpON+f026Y0QZ82axaZNm9i6dStnzpxh2rRplJeXG64KmzBhAvPnzze0nzZtGjdu3GD69OmcP3+eXbt2sWzZMuLi4gxtEhISOHjwIN988w2HDh1i7NixWFpa8vTTT7f6+TVW8eVL6O/eRe3YHo1b4+ZqhRBCCPHgTFoDNG7cOIqLi1m4cCGFhYX07duXrKwsQ2F0QUGB0f0aunTpwp49e5g5cyZBQUF06tSJ6dOnM3fuXEObb7/9lqeffpoffvgBFxcXHn/8cY4cOYKLi0urn19jXfvX9Je7r3+jr3YQQgghxIMzeRF0fHw88fHxdW6rq0gqLCyMI0eO1NtffXOmDwMpgBZCCCFahzwLrA2RO0ALIYQQrUMSoDbidmkJP16veVCePAFeCCGEaFmSALURhRdrRn8e8ehMO3sHE0cjhBBC/LpJAtRG3CuA1srojxBCCNHiJAFqIwovyANQhRBCiNYiCVAboFRXG54BJgXQQgghRMuTBKgNuFl4FV15OVbWNnTs6mXqcIQQQvwCaWlpdOjQodn6++abb1CpVOTk5DRbn0ISoDbh2tc1oz+uPr5YWpn81kxCCPHQmzhxIiqVyrA4OzsTERHBqVOnGtXP4sWL6du3b8sE+YC6dOnCtWvX6NWrV6sd817S9fPlp/fh+7//+z+io6Px8vJCpVKxZs2aWv0sX76ckJAQHB0dcXV1JSoqqtbT4U1FEqA24NoFKYAWQojmFhERwbVr17h27RrZ2dlYWVnx5JNPmjqsRrO0tMTd3R0rE/yBvG/fPsN7eO3aNfr162fYdvv2bXx8fFixYkW9DzE/ePAgcXFxHDlyhL1791JVVcXw4cMpLy9vrVOolyRAbUCh1P8IIR4SiqJQpdObZGnss7ttbW1xd3fH3d2dvn37Mm/ePK5cuUJxcbGhzdy5c/H398fOzg4fHx8SExOpqqoCaqaylixZwsmTJw0jIGlpaQD8+OOPTJ06FTc3N9q1a0evXr3IzMw0Ov6ePXsIDAzEwcHBkIzV5+bNm8TExODi4oJarcbPz4/U1FSg9hTYz0e37i33np6g0+lISEigU6dO2NvbExoaWueTFR6Es7Oz4T10d3fH2trasC0kJIRVq1bx1FNPYWtrW+f+WVlZTJw4kZ49e9KnTx/S0tIoKCjg+PHjTYqnOcl8i4lVVeoovpwPSAIkhGj77lZWs3H6QZMc+7m1g7G2tWzSvmVlZWzbtg1fX1+cnZ0N6x0dHUlLS8PDw4Pc3FymTJmCo6Mjc+bMYdy4cZw+fZqsrCz27dsHgEajobq6msjISG7dusW2bdvo1q0beXl5WFr+O7bbt2/zxhtv8Ne//hULCwueeeYZEhISePfdd+uMLzExkby8PD799FM6duzIhQsXuHPnTp1t165dy4oVKwyvV6xYwXvvvUdAQABQ84ipvLw80tPT8fDwICMjg4iICHJzc/Hz8wNApVKRmprKxIkTG3zfRo8eTUVFBf7+/syZM4fRo0ff/81uQElJCQBOTk6/qJ/mIAmQiRVduki1Xo99h0dwdG77D2wVQoiHRWZmJg4ONTeWLS8vR6vVkpmZafSQ7Zdfftnwby8vLxISEkhPT2fOnDmo1WocHBywsrIymuL5xz/+wdGjRzlz5gz+/jWlCz4+PkbHrqqqYsOGDXTr1g2oSUpeeeWVemMtKCggODiY/v37G2Kpj0ajQaPRAPDRRx/xzjvvsG/fPtzd3SkoKCA1NZWCggI8PDwASEhIICsri9TUVJYtWwZA9+7dDX3UxcHBgaSkJMLDw7GwsODDDz8kKiqKjz/+uMlJUHV1NTNmzCA8PLxV65nqIwmQid27/N3dt7s8AV4I0eZZ2Vjw3NrBJjt2YwwZMoSUlBSgZorp7bffJjIykqNHj+Lp6QnA3/72N9atW8fFixcpKyvj7t27tG/fvsF+c3Jy6Ny5syH5qYudnZ0h+QHQarUUFRXV237atGlER0fz1VdfMXz4cKKiohgwYECDcZw4cYLx48ezfv16wsPDAcjNzUWv19eKTafTGY18nT17tsG+O3bsyKxZswyvQ0JCuHr1KqtWrWpyAhQXF8fp06f54osvmrR/c5MEyMSkAFoI8TBRqVRNnoZqbfb29vj6+hpeb968GY1Gw6ZNm1i6dCmHDx8mJiaGJUuWMGLECDQaDenp6SQlJTXYr1qtvu+xf1orAzXvW0M1TJGRkVy+fJndu3ezd+9ehg4dSlxcHG+88Uad7QsLCxk9ejSTJ0/m2WefNawvKyvD0tKS48ePG03JAYbRsKYKDQ1l7969Tdo3Pj6ezMxMPv/8czp37vyL4mgukgCZmBRACyFE61CpVFhYWBhqaw4dOoSnpycLFiwwtLl8+bLRPjY2Nuj1eqN1QUFBfPvtt5w/f77BUaDGcnFxITY2ltjYWAYOHMjs2bPrTIAqKioYM2YMAQEBJCcnG20LDg5Gr9dTVFTEwIEDmy02qBn50mq1jdpHURReeOEFMjIy+Oyzz/D29m7WmH4JSYBMqPzHm5QWF4FKhXs3P1OHI4QQvyo6nY7CwkKgZgps/fr1lJWVMWrUKAD8/PwoKCggPT2dkJAQdu3aRUZGhlEfXl5e5OfnG6a9HB0dGTx4MIMGDSI6Oprk5GR8fX05e/YsKpWKiIiIJsW6cOFC+vXrR8+ePdHpdGRmZhIYGFhn26lTp3LlyhWys7ONrmhzcnLC39+fmJgYJkyYQFJSEsHBwRQXF5OdnU1QUBAjR44EICAggOXLlzN27Ng6j7F161ZsbGwIDg4GamqNtmzZwubNmw1tKisrycvLM/z7u+++IycnBwcHB8PIW1xcHNu3b+eTTz7B0dHR8HloNJoHGklrUYqopaSkRAGUkpKSFj3O10cPK2/8fqSS9uc/tehxhBCiqe7cuaPk5eUpd+7cMXUojRIbG6sAhsXR0VEJCQlRduzYYdRu9uzZirOzs+Lg4KCMGzdOWb16taLRaAzbKyoqlOjoaKVDhw4KoKSmpiqKoig//PCDMmnSJMXZ2Vlp166d0qtXLyUzM1NRFEVJTU016kNRFCUjI0Np6Cf31VdfVQIDAxW1Wq04OTkpY8aMUS5duqQoiqLk5+crgHLixAlFURTF09PT6NzuLQcOHFAURVEqKyuVhQsXKl5eXoq1tbWi1WqVsWPHKqdOnTIc76fnUpe0tDQlMDBQsbOzU9q3b6889thjygcffGDU5l5cP18GDx5sdJy6loaOfT8NfScb8/ut+leA4idKS0vRaDSUlJTctxjul/if97Zy9OMP6DVkOCOef7HFjiOEEE1VUVFBfn4+3t7etGvXztThCNHgd7Ixv99yI0QT+nf9jxRACyGEEK1JEiATqa7WU3jxawC0vlIALYQQQrQmSYBM5Ma3V6i8cwdr23Y4d+lq6nCEEEIIsyIJkIncu/+Pezc/LCwejntqCCGEEL8WkgCZiOEO0HL/HyGEEKLVSQJkIoVf/6sAWu4ALYQQQrQ6SYBMoLLiDt9fKQCkAFoIIYQwBUmATOD6xa9RlGocnV1wcHK+/w5CCCGEaFaSAJmAPABVCCGEMC1JgEzg2tdSAC2EEL9WaWlpdOjQodn6++abb1CpVOTk5DRbn0ISIJMw3AFaRoCEEKJFTJw4EZVKZVicnZ2JiIjg1KlTjepn8eLF9O3bt2WCfEBdunTh2rVr9OrVq9WOWVFRwcSJE+nduzdWVlZERUXV2e6zzz7j0UcfxdbWFl9fX9LS0oy2L1++nJCQEBwdHXF1dSUqKopz587V2ZeiKERGRqJSqfj444+b94TqIAlQK7v1w/eU3byBysICNx9fU4cjhBC/WhEREVy7do1r166RnZ2NlZUVTz75pKnDajRLS0vc3d2xsrJqtWPq9XrUajUvvvgiw4YNq7NNfn4+I0eOZMiQIeTk5DBjxgwmT57Mnj17DG0OHjxIXFwcR44cYe/evVRVVTF8+HDKy8tr9bdmzRpUKlWLndPPSQLUyu7d/6djVy+sbeXBgkKIh4uiKFRVVJhkaeyzu21tbXF3d8fd3Z2+ffsyb948rly5QnFxsaHN3Llz8ff3x87ODh8fHxITE6mqqgJqprKWLFnCyZMnDSNJ90Y4fvzxR6ZOnYqbmxvt2rWjV69eZGZmGh1/z549BAYG4uDgYEjG6nPz5k1iYmJwcXFBrVbj5+dHamoqUHsK7OejW/eWzz77DACdTkdCQgKdOnXC3t6e0NBQw7YHZW9vT0pKClOmTMHd3b3ONhs2bMDb25ukpCQCAwOJj4/nt7/9LatXrza0ycrKYuLEifTs2ZM+ffqQlpZGQUEBx48fN+orJyeHpKQktmzZ0qg4f4nWSyfr8dZbb7Fq1SoKCwvp06cPb775Jo899li97X/88UcWLFjARx99xI0bN/D09GTNmjU88cQTTe6zNd2r//GQ+h8hxEPork7HutjfmuTYL27dgXUTn0hfVlbGtm3b8PX1xdn531ffOjo6kpaWhoeHB7m5uUyZMgVHR0fmzJnDuHHjOH36NFlZWezbtw8AjUZDdXU1kZGR3Lp1i23bttGtWzfy8vKwtPz3Xf1v377NG2+8wV//+lcsLCx45plnSEhI4N13360zvsTERPLy8vj000/p2LEjFy5c4M6dO3W2Xbt2LStWrDC8XrFiBe+99x4BAQEAxMfHk5eXR3p6Oh4eHmRkZBAREUFubi5+fn4AqFQqUlNTmThxYpPeT4DDhw/XGh0aMWIEM2bMqHefkpISAJycnAzrbt++zR/+8AfeeuutepOtlmDSBOhvf/sbs2bNYsOGDYSGhrJmzRpGjBjBuXPncHV1rdW+srKS//7v/8bV1ZUdO3bQqVMnLl++bFRs1tg+W5uhAFru/yOEEC0qMzMTBwcHAMrLy9FqtWRmZmJh8e/Jj5dfftnwby8vLxISEkhPT2fOnDmo1WocHBywsrIy+mH+xz/+wdGjRzlz5gz+/jW1nD4+PkbHrqqqYsOGDXTr1g2oSUpeeeWVemMtKCggODiY/v37G2Kpj0ajQaPRAPDRRx/xzjvvsG/fPtzd3SkoKCA1NZWCggI8PDwASEhIICsri9TUVJYtWwZA9+7dDX00VWFhIW5ubkbr3NzcKC0t5c6dO6jVaqNt1dXVzJgxg/DwcKN6ppkzZzJgwADGjBnzi+JpLJMmQMnJyUyZMoVJkyYBNcNpu3btYsuWLcybN69W+y1btnDjxg0OHTqEtbU1UPtL0tg+W1O1Xs/1/AuA3ABRCPFwsrK15cWtO0x27MYYMmQIKSkpQM0U09tvv01kZCRHjx7F09MTqPmjed26dVy8eJGysjLu3r1L+/btG+w3JyeHzp07G5KfutjZ2RmSHwCtVktRUVG97adNm0Z0dDRfffUVw4cPJyoqigEDBjQYx4kTJxg/fjzr168nPDwcgNzcXPR6fa3YdDqd0cjX2bNnG+y7JcTFxXH69Gm++OILw7qdO3eyf/9+Tpw40erxmCwBqqys5Pjx48yfP9+wzsLCgmHDhnH48OE699m5cydhYWHExcXxySef4OLiwh/+8Afmzp2LpaVlk/qEmi+GTqczvC4tLW2GM6zt+yuXuavTYWtnj5NHpxY5hhBCtCSVStXkaajWZm9vj6/vvy822bx5MxqNhk2bNrF06VIOHz5MTEwMS5YsYcSIEWg0GtLT00lKSmqw35+PbNTl3h/p96hUqgZrmCIjI7l8+TK7d+9m7969DB06lLi4ON5444062xcWFjJ69GgmT57Ms88+a1hfVlaGpaUlx48fN5qSAwyjYc3F3d2d69evG627fv067du3r/UexcfHk5mZyeeff07nzp0N6/fv38/Fixdr3TYgOjqagQMHNrp2qTFMlgB9//336PX6OofP6stML126xP79+4mJiWH37t1cuHCBP/3pT1RVVbFo0aIm9Qk1l+ktWbLkl5/Ufdyb/nLr5ofKQurPhRCiNalUKiwsLAy1NYcOHcLT05MFCxYY2ly+fNloHxsbG/R6vdG6oKAgvv32W86fP9/gKFBjubi4EBsbS2xsLAMHDmT27Nl1JkAVFRWMGTOGgIAAkpOTjbYFBwej1+spKipi4MCBzRZbXcLCwti9e7fRur179xIWFmZ4rSgKL7zwAhkZGXz22Wd4e3sbtZ83bx6TJ082Wte7d29Wr17NqFGjWi542kARdGNUV1fj6urKxo0bsbS0pF+/fnz33XesWrWKRYsWNbnf+fPnM2vWLMPr0tJSunTp0hwhG6kou4WVja0UQAshRCvQ6XQUFhYCNVNg69evp6yszPDD6ufnR0FBAenp6YSEhLBr1y4yMjKM+vDy8iI/P98w7eXo6MjgwYMZNGgQ0dHRJCcn4+vry9mzZ1GpVERERDQp1oULF9KvXz969uyJTqcjMzOTwMDAOttOnTqVK1eukJ2dbXRFm5OTE/7+/sTExDBhwgSSkpIIDg6muLiY7OxsgoKCGDlyJAABAQEsX76csWPH1htTXl4elZWV3Lhxg1u3bhmuQrt3X6Tnn3+e9evXM2fOHP74xz+yf/9+3n//fXbt2mXoIy4uju3bt/PJJ5/g6Oho+Dw0Gg1qtdpwld7Pde3atVay1OwUE9HpdIqlpaWSkZFhtH7ChAnK6NGj69xn0KBBytChQ43W7d69WwEUnU7XpD7rUlJSogBKSUnJA+/zoPR37yq6O7ebvV8hhGgJd+7cUfLy8pQ7d+6YOpRGiY2NVQDD4ujoqISEhCg7duwwajd79mzF2dlZcXBwUMaNG6esXr1a0Wg0hu0VFRVKdHS00qFDBwVQUlNTFUVRlB9++EGZNGmS4uzsrLRr107p1auXkpmZqSiKoqSmphr1oSiKkpGRoTT0k/vqq68qgYGBilqtVpycnJQxY8Yoly5dUhRFUfLz8xVAOXHihKIoiuLp6Wl0bveWAwcOKIqiKJWVlcrChQsVLy8vxdraWtFqtcrYsWOVU6dOGY7303OpT33H+akDBw4offv2VWxsbBQfH59afda1//2ODdT6Hf+phr6Tjfn9Vv3rYCYRGhrKY489xptvvgnUjPB07dqV+Pj4OguWX3rpJbZv386lS5cMVfxr165l5cqVXL16tUl91qW0tBSNRkNJScl9i+GEEOLXrKKigvz8fLy9vWn3kNT+iF+3hr6Tjfn9NmkhyqxZs9i0aRNbt27lzJkzTJs2jfLycsMVXBMmTDAqaJ42bRo3btxg+vTpnD9/nl27drFs2TLi4uIeuE8hhBBCCJPWAI0bN47i4mIWLlxIYWEhffv2JSsry1DEXFBQYHS/hi5durBnzx5mzpxJUFAQnTp1Yvr06cydO/eB+xRCCCGEMOkUWFslU2BCCFFDpsBEW/OrmAITQgghhDAFSYCEEELcl0wWiLaiub6LkgAJIYSo1727CVdWVpo4EiFq3L59G6h9t+3GeqhuhCiEEKJ1WVlZYWdnR3FxMdbW1kYXpgjRmhRF4fbt2xQVFdGhQ4daj/poLEmAhBBC1EulUqHVasnPz6/1mAghTKFDhw513j26sSQBEkII0SAbGxv8/PxkGkyYnLW19S8e+blHEiAhhBD3ZWFhIZfBi18VmcwVQgghhNmRBEgIIYQQZkcSICGEEEKYHakBqsO9myyVlpaaOBIhhBBCPKh7v9sPcrNESYDqcOvWLaDm4atCCCGEeLjcunULjUbTYBt5GGodqquruXr1Ko6OjqhUKlOH0yaVlpbSpUsXrly5Ig+MbQPk82hb5PNoW+TzaFta8vNQFIVbt27h4eFx35t2yghQHSwsLOjcubOpw3gotG/fXv6H0obI59G2yOfRtsjn0ba01Odxv5Gfe6QIWgghhBBmRxIgIYQQQpgdSYBEk9ja2rJo0SJsbW1NHYpAPo+2Rj6PtkU+j7alrXweUgQthBBCCLMjI0BCCCGEMDuSAAkhhBDC7EgCJIQQQgizIwmQEEIIIcyOJEDigS1fvpyQkBAcHR1xdXUlKiqKc+fOmTos8S8rVqxApVIxY8YMU4di1r777jueeeYZnJ2dUavV9O7dm//93/81dVhmSa/Xk5iYiLe3N2q1mm7duvHqq68+0HOixC/3+eefM2rUKDw8PFCpVHz88cdG2xVFYeHChWi1WtRqNcOGDePrr79utfgkARIP7ODBg8TFxXHkyBH27t1LVVUVw4cPp7y83NShmb1jx47xzjvvEBQUZOpQzNrNmzcJDw/H2tqaTz/9lLy8PJKSknjkkUdMHZpZWrlyJSkpKaxfv54zZ86wcuVKXn/9dd58801Th2YWysvL6dOnD2+99Vad219//XXWrVvHhg0b+Oc//4m9vT0jRoygoqKiVeKTy+BFkxUXF+Pq6srBgwcZNGiQqcMxW2VlZTz66KO8/fbbLF26lL59+7JmzRpTh2WW5s2bx5dffsn//M//mDoUATz55JO4ubnxl7/8xbAuOjoatVrNtm3bTBiZ+VGpVGRkZBAVFQXUjP54eHjw5z//mYSEBABKSkpwc3MjLS2Np556qsVjkhEg0WQlJSUAODk5mTgS8xYXF8fIkSMZNmyYqUMxezt37qR///787ne/w9XVleDgYDZt2mTqsMzWgAEDyM7O5vz58wCcPHmSL774gsjISBNHJvLz8yksLDT6/5ZGoyE0NJTDhw+3SgzyMFTRJNXV1cyYMYPw8HB69epl6nDMVnp6Ol999RXHjh0zdSgCuHTpEikpKcyaNYuXXnqJY8eO8eKLL2JjY0NsbKypwzM78+bNo7S0lICAACwtLdHr9bz22mvExMSYOjSzV1hYCICbm5vRejc3N8O2liYJkGiSuLg4Tp8+zRdffGHqUMzWlStXmD59Onv37qVdu3amDkdQ84dB//79WbZsGQDBwcGcPn2aDRs2SAJkAu+//z7vvvsu27dvp2fPnuTk5DBjxgw8PDzk8xAyBSYaLz4+nszMTA4cOEDnzp1NHY7ZOn78OEVFRTz66KNYWVlhZWXFwYMHWbduHVZWVuj1elOHaHa0Wi09evQwWhcYGEhBQYGJIjJvs2fPZt68eTz11FP07t2b8ePHM3PmTJYvX27q0Myeu7s7ANevXzdaf/36dcO2liYJkHhgiqIQHx9PRkYG+/fvx9vb29QhmbWhQ4eSm5tLTk6OYenfvz8xMTHk5ORgaWlp6hDNTnh4eK1bQ5w/fx5PT08TRWTebt++jYWF8c+cpaUl1dXVJopI3OPt7Y27uzvZ2dmGdaWlpfzzn/8kLCysVWKQKTDxwOLi4ti+fTuffPIJjo6OhnlajUaDWq02cXTmx9HRsVb9lb29Pc7OzlKXZSIzZ85kwIABLFu2jN///vccPXqUjRs3snHjRlOHZpZGjRrFa6+9RteuXenZsycnTpwgOTmZP/7xj6YOzSyUlZVx4cIFw+v8/HxycnJwcnKia9euzJgxg6VLl+Ln54e3tzeJiYl4eHgYrhRrcYoQDwioc0lNTTV1aOJfBg8erEyfPt3UYZi1v//970qvXr0UW1tbJSAgQNm4caOpQzJbpaWlyvTp05WuXbsq7dq1U3x8fJQFCxYoOp3O1KGZhQMHDtT5mxEbG6soiqJUV1criYmJipubm2Jra6sMHTpUOXfuXKvFJ/cBEkIIIYTZkRogIYQQQpgdSYCEEEIIYXYkARJCCCGE2ZEESAghhBBmRxIgIYQQQpgdSYCEEEIIYXYkARJCCCGE2ZEESAghhBBmRxIgIYR4ACqVio8//tjUYQghmokkQEKINm/ixImoVKpaS0REhKlDE0I8pORhqEKIh0JERASpqalG62xtbU0UjRDiYScjQEKIh4KtrS3u7u5GyyOPPALUTE+lpKQQGRmJWq3Gx8eHHTt2GO2fm5vLf/3Xf6FWq3F2dua5556jrKzMqM2WLVvo2bMntra2aLVa4uPjjbZ///33jB07Fjs7O/z8/Ni5c2fLnrQQosVIAiSE+FVITEwkOjqakydPEhMTw1NPPcWZM2cAKC8vZ8SIETzyyCMcO3aMDz74gH379hklOCkpKcTFxfHcc8+Rm5vLzp078fX1NTrGkiVL+P3vf8+pU6d44okniImJ4caNG616nkKIZtJqz50XQogmio2NVSwtLRV7e3uj5bXXXlMURVEA5fnnnzfaJzQ0VJk2bZqiKIqyceNG5ZFHHlHKysoM23ft2qVYWFgohYWFiqIoioeHh7JgwYJ6YwCUl19+2fC6rKxMAZRPP/202c5TCNF6pAZICPFQGDJkCCkpKUbrnJycDP8OCwsz2hYWFkZOTg4AZ86coU+fPtjb2xu2h4eHU11dzblz51CpVFy9epWhQ4c2GENQUJDh3/b29rRv356ioqKmnpIQwoQkARJCPBTs7e1rTUk1F7Va/UDtrK2tjV6rVCqqq6tbIiQhRAuTGiAhxK/CkSNHar0ODAwEIDAwkJMnT1JeXm7Y/uWXX2JhYUH37t1xdHTEy8uL7OzsVo1ZCGE6MgIkhHgo6HQ6CgsLjdZZWVnRsWNHAD744AP69+/P448/zrvvvsvRo0f5y1/+AkBMTAyLFi0iNjaWxYsXU1xczAsvvMD48eNxc3MDYPHixTz//PO4uroSGRnJrVu3+PLLL3nhhRda90SFEK1CEiAhxEMhKysLrVZrtK579+6cPXsWqLlCKz09nT/96U9otVree+89evToAYCdnR179uxh+vTphISEYGdnR3R0NMnJyYa+YmNjqaioYPXq1SQkJNCxY0d++9vftt4JCiFalUpRFMXUQQghxC+hUqnIyMggKirK1KEIIR4SUgMkhBBCCLMjCZAQQgghzI7UAAkhHnoyky+EaCwZARJCCCGE2ZEESAghhBBmRxIgIYQQQpgdSYCEEEIIYXYkARJCCCGE2ZEESAghhBBmRxIgIYQQQpgdSYCEEEIIYXb+H5co/BRsdA+cAAAAAElFTkSuQmCC",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Vergleich zwischen meherern Modellen mit unterschiedlicher Batch-Größe\n",
        "from mnist_model import get_trained_mnist_model, plot_accuracy_by_batch_size\n",
        "\n",
        "# Trainiere 6 Modelle mit unterschiedlichen Batch-Größen\n",
        "models = [\n",
        "    get_trained_mnist_model(batch_size=8),\n",
        "    get_trained_mnist_model(batch_size=32),\n",
        "    get_trained_mnist_model(batch_size=64),\n",
        "    get_trained_mnist_model(batch_size=256),\n",
        "    get_trained_mnist_model(batch_size=512),\n",
        "    get_trained_mnist_model(batch_size=1024)\n",
        "]\n",
        "\n",
        "# Plotten der Ergebnisse\n",
        "plot_accuracy_by_batch_size(models, [8, 32, 64, 256, 512, 1024])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wie man erkennt, ergibt sich bis zu einer Batch-Size von 64 so gut wie keine Veränderung in der Genauigkeit, jedoch wird die Lerngeschwindigkeit deutlich erhöht!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Lernrate\n",
        "<div style=\"display:flex; justify-content: center;\">\n",
        "<div>Die Lernrate bestimmt, wie stark die Parameter bei jeder Batch angepasst werden. Kleine Lernraten sorgen dafür, dass das Netz nicht so schnell lernt, konvergiert dafür aber reibungsloser. Große Lernraten beschleunigen den Lernprozess, jedoch kann es passieren, dass das Netz nicht mehr lernt, da die Parameter-Updates zu ungenau sind (Siehe Bild). Die Lernrate sollte also so gewählt werden, dass das Netz schnell lernt, jedoch nicht zu schnell lernt. Meistens ist es am besten, zuerst eine Lernrate von 0,1 oder 0,01 zu wählen und zu beobachten, wie gut das Modell damit trainiert. Dementsprechend kann die Lernrate angepasst werden.</div>\n",
        "\n",
        "<img src=\"https://miro.medium.com/max/1276/0*FA9UmDXdzYzuOpeO.jpg\" alt=\"Lernrate Veranschaulichung\" width=\"350px\" style=\"margin: 20px\" />\n",
        "</div>\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Vergleich zwischen meherern Modellen mit unterschiedlicher Batch-Größe\n",
        "from mnist_model import get_trained_mnist_model, plot_loss_by_learning_rate\n",
        "from keras.optimizers import Adam\n",
        "\n",
        "# Trainiere 5 Modelle mit unterschiedlichen Batch-Größen\n",
        "# In diesem Beispiel wird der \"Adam\" Optimizer verwendet.\n",
        "# Dieser und weitere Optimizer werden im nächsten Kaptiel behandelt.\n",
        "models = [\n",
        "    get_trained_mnist_model(\n",
        "        10, batch_size=64, optimizer=Adam(learning_rate=0.001)),\n",
        "    get_trained_mnist_model(\n",
        "        10, batch_size=64, optimizer=Adam(learning_rate=0.005)),\n",
        "    get_trained_mnist_model(\n",
        "        10, batch_size=64, optimizer=Adam(learning_rate=0.01)),\n",
        "    get_trained_mnist_model(\n",
        "        10, batch_size=64, optimizer=Adam(learning_rate=0.015)),\n",
        "    get_trained_mnist_model(\n",
        "        10, batch_size=64, optimizer=Adam(learning_rate=0.02)),\n",
        "    get_trained_mnist_model(\n",
        "        10, batch_size=64, optimizer=Adam(learning_rate=0.03)),\n",
        "    get_trained_mnist_model(\n",
        "        10, batch_size=64, optimizer=Adam(learning_rate=0.05)),\n",
        "]\n",
        "\n",
        "# Plotten der Ergebnisse\n",
        "plot_loss_by_learning_rate(\n",
        "    models, [0.001, 0.005, 0.01, 0.015, 0.02, 0.03, 0.05])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Dem Graphen ist zu entnehmen, dass die Modelle mit einer Lernrate von 0.001-0.01 ähnlich gut performen. Ab einer Lernrate von 0.015 lässt sich erkennen, dass das Modell ab einer bestimmten Epochen keinen Fortschritt mehr macht,\n",
        "da die Kostenfunktion nicht mehr sinkt. Bei einer Lernrate ab 0.03 fällt die Kostenfunktion gar nicht, da sich das Model nicht dem globalen Minimum nähern kann, da die Schritte zu groß sind (Siehe Grafik)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Loss Functions/ Kostenfunktion"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Was ist eine Kostenfunktion?\n",
        "\n",
        "Eine Kostenfunktion ist eine mathematische Formel. Sie gibt wieder, wie gut ein gegebenes Modell zu bestimmten Daten performed. Wir werden uns im Verlauf drei solcher Kostenfunktionen ansehen. Die wohl bekannteste Kostenfunktion unter Laien ist die Mean Squared Error (MSE) Funktion, da Sie oft schon in der Schule behandelt wird. Wir werden aber auch kurz auf die Sparse Categorical Crossentropy (SCCE) Funktion und die Categorical Crossentropy (CCE) Funktion eingehen. Das Ergebnis jeder Kostenfunktionen sind die Kosten, welche wir möglichst klein halten wollen. Je kleiner die Kosten desto besser passt unser Modell zu den Daten. Wir müssen nur aufpassen, dass wir nicht overfitten."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Mean Squared Error\n",
        "$$\n",
        "m = vorhergesagten \\; Zielwerte \n",
        "$$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "$$\n",
        "y = tatsächliche \\; Zielwerte \n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "$$\n",
        "MSE = \\frac{1}{n}\\sum_{i=1}^{n}(m-y)^2\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Caterogical Cross Entropy\n",
        "Im deutschen bekannt als Kreuzentropie.\n",
        "$$\n",
        "P = Wahrscheinlichkeit\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "$$\n",
        "CCE = -\\sum_{i=1}P^*(i) \\log_{P(i)}\n",
        "$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Kostenfunktionen am Beispiel vom MNIST Datensatz\n",
        "Da der MNIST Datensatz von vorherigen Gruppen schon behandelt wurde, werden wir nicht weiter darauf eingehen, sondern werden uns voll und ganz den Kostenfunktionen widmen."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
            "11490434/11490434 [==============================] - 8s 1us/step\n"
          ]
        }
      ],
      "source": [
        "import tensorflow as tf\n",
        "from tensorflow import keras\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "# Laden des MNIST Datensatzes\n",
        "(train_images, train_labels), (test_images, test_labels) = keras.datasets.mnist.load_data()\n",
        "\n",
        "# Normalisieren der Pixelwerte  \n",
        "train_images = train_images / 255.0\n",
        "test_images = test_images / 255.0\n",
        "\n",
        "def get_model():\n",
        "  return keras.Sequential([\n",
        "    keras.layers.Flatten(input_shape=(28, 28)),\n",
        "    keras.layers.Dense(128, activation='relu'),\n",
        "    keras.layers.Dense(10, activation='softmax')\n",
        "  ])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "model_mse = get_model() # Modell mit Mean Squared Error Loss\n",
        "model_cce =  get_model() # Modell mit Categorical Crossentropy\n",
        "model_scce = get_model() # Modell mit Sparse Categorical Crossentropy\n",
        "\n",
        "optimizer = 'sgd'\n",
        "\n",
        "model_mse.compile(\n",
        "    optimizer=optimizer,\n",
        "    loss='mean_squared_error',\n",
        "    metrics=['accuracy']\n",
        ")\n",
        "model_cce.compile(\n",
        "    optimizer=optimizer,\n",
        "    loss='categorical_crossentropy',\n",
        "    metrics=['accuracy']\n",
        ")\n",
        "model_scce.compile(\n",
        "    optimizer=optimizer,\n",
        "    loss='sparse_categorical_crossentropy',\n",
        "    metrics=['accuracy']\n",
        ")\n",
        "  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Trainiern der Modelle\n",
        "\n",
        "Dabei werden die Trainigsergebnisse in der Liste \"history\" gespeichert. \n",
        "\n",
        "Für das Training mit der Sparse Categorical Crossentropy müssen die Daten nicht geändert weden. Deswegen kann hier schon mit `model.fit()` trainiert werden. Dabei wird gleich ein Validierungsdatensatz auch bekannt als Testdatensatz festgelegt.\n",
        "\n",
        "Die anderen beiden Modell werden der Liste \"models\" hinzugefügt, um diese Trainieren zu können. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch 1/15\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1870/1875 [============================>.] - ETA: 0s - loss: 0.6582 - accuracy: 0.8357\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch 2/15\n",
            "1875/1875 [==============================] - 15s 8ms/step - loss: 0.3388 - accuracy: 0.9054 - val_loss: 0.2935 - val_accuracy: 0.9176\n",
            "...\n",
            "Epoch 15/15\n",
            "1875/1875 [==============================] - 14s 8ms/step - loss: 0.1286 - accuracy: 0.9646 - val_loss: 0.1298 - val_accuracy: 0.9611\n"
          ]
        }
      ],
      "source": [
        "epochs=15 # Festlegung von 15 Trainigsepochen\n",
        "history = [model_scce.fit(\n",
        "    train_images,\n",
        "    train_labels,\n",
        "    epochs=epochs,\n",
        "    validation_data=(test_images, test_labels),\n",
        "    verbose=True)\n",
        "]\n",
        "models = [model_mse, model_cce]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Umwandlung der Labels in Categorical Labels \n",
        "\n",
        "\n",
        "Diese werden für das Training für die Categorical Cross Entropy Loss Function benötigt. Etwas weiter unten wird noch erklärt, wie diese Umwandlung aussieht."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch 1/15\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1871/1875 [============================>.] - ETA: 0s - loss: 0.0849 - accuracy: 0.3290\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch 2/15\n",
            "1875/1875 [==============================] - 13s 7ms/step - loss: 0.0187 - accuracy: 0.8907 - val_loss: 0.0174 - val_accuracy: 0.8993\n",
            "...\n"
          ]
        }
      ],
      "source": [
        "_train_labels = keras.utils.to_categorical(train_labels, 10)\n",
        "_test_labels = keras.utils.to_categorical(test_labels, 10)\n",
        "\n",
        "# Trainieren der anderen beiden Modelle\n",
        "history += [model.fit(train_images, _train_labels, epochs=epochs, validation_data=(test_images, _test_labels), verbose=True) for model in models]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Plotten der Ergebnisse mit Matplotlib\n",
        "\n",
        "Über `plt.plot` werden die einzelnen Ergebnisse der Modelle in verschiedenen Farben eingebunden."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def plot_learning_curve(ylim=0.6):\n",
        "    plt.figure()\n",
        "    plt.title(\"accuracy comparison\")\n",
        "    axes = plt.gca()\n",
        "    axes.set_ylim([ylim, 1])\n",
        "    plt.xlabel(\"Epoch\")\n",
        "    plt.ylabel(\"Accuracy\")\n",
        "    train_sizes = np.arange(1, 1 + len(history[0].history['accuracy']))\n",
        "    plt.ylim((0,1))\n",
        "    plt.grid()\n",
        "    plt.plot(\n",
        "        train_sizes,\n",
        "        history[0].history['accuracy'],\n",
        "        'o-',\n",
        "        color=(177/255, 6/255, 58/255),\n",
        "        label=\"scce\"\n",
        "    )\n",
        "    plt.plot(\n",
        "        train_sizes,\n",
        "        history[1].history['accuracy'],\n",
        "        'o-',\n",
        "        color=(246/255, 168/255, 0),\n",
        "        label=\"mse\")\n",
        "    \n",
        "    plt.plot(\n",
        "        train_sizes,\n",
        "        history[2].history['accuracy'],\n",
        "        'o-',\n",
        "        color='green',\n",
        "        label=\"cce\"\n",
        "    )\n",
        "\n",
        "    plt.legend(loc=\"best\")\n",
        "    return plt\n",
        "\n",
        "plot_learning_curve()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "- scce = Sparse Categorical Crossentropy\n",
        "- cce = Categorical Crossentropy\n",
        "- mse = Mean Squared Error"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Wann sollte man Categorical Cross Entropy nutzen und wann Sparse Categorical Cross Entropy und wann Mean Squared Error?\n",
        "\n",
        "für `Categorical Cross Entropy` müssen die Labels als Array mit einer 1 am Index der zugehören Klasse vorliegen (one hot encoding).\n",
        "\n",
        "\n",
        "für `Sparse Categorical Cross Entropy` müssen die Labels mit Bezeichnung der Ausgangsklasse vorliegen.\n",
        "\n",
        "fur  `Mean Squared Error` eignen sich Probleme mit linearer Regression. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Test labels categorical:\n",
            "[[0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]]\n",
            "Verwendung der categorical_crossentropy gefordert\n",
            "\n",
            "\n",
            "Test labels non categorical:\n",
            "[7 2]\n",
            "Verwendung der sparse_categorical_crossentropy gefordert\n"
          ]
        }
      ],
      "source": [
        "_test_labels = keras.utils.to_categorical(test_labels, 10)\n",
        "\n",
        "print('Test labels categorical:')\n",
        "print(_test_labels[:2])\n",
        "print('Verwendung der categorical_crossentropy gefordert')\n",
        "print('\\n')\n",
        "print('Test labels non categorical:')\n",
        "print(test_labels[:2])\n",
        "print('Verwendung der sparse_categorical_crossentropy gefordert')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Umwandlung in Categorical Werte:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "_test_labels = keras.utils.to_categorical(train_labels, 10)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Optimizer"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "**\"Der richtige Optimizer Algorithmus kann die Trainingszeit exponentiell verringern.\"**\n",
        "\n",
        "Der Optimizer in einem Neuronalen Netz beschreibt wie das Neuronale Netz lernt. \n",
        "Optimization: Optimizer sind Algorithmen, welche mithilfe der Veränderung der Attribute im Neuronalen Netz wie z.B. die Gewichte oder die Learning Rate versuchen die Kosten zu verringern. Folgende Grafik hilft bei der Veranschaulichung:\n",
        "\n",
        "<img src=\"https://miro.medium.com/max/1156/1*65Mxg_Yfq-L7AvaS0K5aGA.png\" alt=\"Learned Optimizer\" width=\"400px\" />\n",
        "\n",
        "Das Ziel mithile des Optimizers ist es, das globale Minimum zu finden und dadurch die Kosten auf ein Minimum zu bringen. \n",
        "\n",
        "Nun werden wir mithilfe von Tensorflow ein Neuronales Netz programmieren und uns ein paar Beispiele zu Optimizern anschauen.\n",
        "Wir verwenden zum Trainieren und zum Testen den MNIST Datensatz. Der MNIST Datensatz wird von einer vorangegagenen Gruppe schon erklärt, daher benutzen wir diesen ohne weitere Erklärung, um was es sich dabei handelt."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [],
      "source": [
        "model_sgd = get_model() # Modell mit Stochastic Gradient Descent Optimizer\n",
        "model_adam = get_model() # Modell mit Adam Optimizer\n",
        "model_rmsprop = get_model() # Modell mit RMSProp Optimizer\n",
        "\n",
        "model_adam.compile(\n",
        "    optimizer='adam',\n",
        "    loss='mean_squared_error',\n",
        "    metrics=['accuracy']\n",
        ")\n",
        "model_rmsprop.compile(\n",
        "    optimizer='rmsprop',\n",
        "    loss='mean_squared_error',\n",
        "    metrics=['accuracy']\n",
        ")\n",
        "model_sgd.compile(\n",
        "    optimizer='sgd',\n",
        "    loss='mean_squared_error',\n",
        "    metrics=['accuracy']\n",
        ")\n",
        "\n",
        "models = [model_adam, model_rmsprop, model_sgd]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch 1/15\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "1869/1875 [============================>.] - ETA: 0s - loss: 0.0119 - accuracy: 0.9233\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "...\n",
            "Epoch 15/15\n",
            "1875/1875 [==============================] - 19s 10ms/step - loss: 9.0414e-04 - accuracy: 0.9948 - val_loss: 0.0035 - val_accuracy: 0.9779\n"
          ]
        }
      ],
      "source": [
        "_train_labels = keras.utils.to_categorical(train_labels, 10)\n",
        "_test_labels = keras.utils.to_categorical(test_labels, 10)\n",
        "\n",
        "#15 Epochen lang werden nun die einzelnen Modelle trainiert\n",
        "epochs=15\n",
        "history = [model.fit(train_images, _train_labels, epochs=epochs, validation_data=(test_images, _test_labels), verbose=True) for model in models] "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Genauigkeiten verschiedener Optimizer\n",
        "\n",
        "Das Ergebnis des Lernens plotten wir nun auf einen Graphen."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def plot_learning_curve(ylim=0.6):\n",
        "    plt.figure()\n",
        "    plt.title(\"accuracy comparison\")\n",
        "    axes = plt.gca()\n",
        "    axes.set_ylim([ylim, 1])\n",
        "    plt.xlabel(\"Epoch\")\n",
        "    plt.ylabel(\"Accuracy\")\n",
        "    train_sizes = np.arange(1, 1 + len(history[0].history['accuracy']))\n",
        "\n",
        "    plt.grid()\n",
        "\n",
        "    plt.plot(\n",
        "        train_sizes,\n",
        "        history[0].history['accuracy'],\n",
        "        'o-',\n",
        "        color=(177/255, 6/255, 58/255),\n",
        "        label=\"Adam\"\n",
        "    )\n",
        "    plt.plot(\n",
        "        train_sizes,\n",
        "        history[1].history['accuracy'],\n",
        "        'o-',\n",
        "        color=(246/255, 168/255, 0),\n",
        "        label=\"RmsProp\"\n",
        "    )\n",
        "    \n",
        "    plt.plot(\n",
        "        train_sizes,\n",
        "        history[2].history['accuracy'],\n",
        "        'o-',\n",
        "        color='green',\n",
        "        label=\"Sgd\"\n",
        "    )\n",
        "\n",
        "    plt.legend(loc=\"best\")\n",
        "    return plt\n",
        "\n",
        "plot_learning_curve()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wir sehen, dass Adam und RMSProb ziemlich schnell gute Ergebnisse liefern. Stochastic Gradient Descent braucht ein bisschen länger, nähert sich aber auch langsam dem Optimum"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Gradient Descent\n",
        "\n",
        "Durch seine Einfachheit ist der Gradient Descent der meistebenutzte Optimizer. Vor allem findet er Anwendung bei Problemen mit Linearer Regression oder Klassifikation.\n",
        "Für Backpropagation in Neuronalen Netzen wird ebenfalls Gradient Descent verwendet.  \n",
        "\n",
        "\"Unter Gradient Descent versteht man einen Optimierungsalgorithmus, der das Minimum einer Funktion findet, indem er sich schrittweise in Richtung des stärksten Gefälles bewegt. Dies kann man sich anschaulich wie eine blinde Person vorstellen, die auf einem Berg steht, und einen im Tal gelegenen Kiosk erreichen möchte\"\n",
        "\n",
        "Um es in der Praxis anzuwenden, wählen wir zu Beginn einfach eine zufällige Position in unserer Kostenfunktion als Startposition und würden dann nach dem stärksten Gefälle suchen. Bei einer  Funktion mit zwei inputs, kann man das gut nachvollziehen. Wir würden einfach schauen, ob die Steigung m in y = mx + b negativ oder positiv ist. Ist die Steigung positiv bewegen wir uns nach links und wenn Sie negativ ist umgekehrt. Wir bewegen uns in der Schrittweite unserer Learning Rate. An der neuen Position, wiederholen wir das Ganze mit der Anzahl an Epochen die wir angegeben haben.\n",
        "Im Bild ist ein Beispiel zu sehen, wo das globale Minimum mit Erfolg erreicht wird. \n",
        "\n",
        "<img src=\"https://1.cms.s81c.com/sites/default/files/2021-01-06/ICLH_Diagram_Batch_01_04-GradientDescent-WHITEBG_0.png\" alt=\"Einfaches Beispiel Gradient Descent\" width=\"400px\" />\n",
        "\n",
        "\n",
        "\n",
        "**Zu beachten:** \n",
        "Es ist nicht schwer ein Minimum mit dem Gradient Descent Verfahren zu finden, jedoch muss man beachten, dass nicht immer das globale Minimum gefunden wird, sondern je nach Startposition man in einem lokalen Minimum landet oder sogar in einem Sattelpunkt und diese Punkte oft nicht zufriedenstellende Resultate liefern. Das kann man umgehen, wenn man theoretisch n-viele verschiedene Startpositionen hat. Dann wird sich mit Sicherheit irgendwann eine Startposition finden, bei welcher das globale Minimum erreicht werden kann. Jedoch ist dieser Prozess sehr zeitaufwendig bei komplexen Problemen kann das auch unter Umständen nie zu einem zufriedenstellendem Ergebnis führen\n",
        "\n",
        "**Vorteile:**\n",
        "- Einfach auszurechnen\n",
        "- Einfach anzuwenden\n",
        "- Einfach zu verstehen\n",
        "- Gut für kleine Datensätze\n",
        "\n",
        "**Nachteile:**\n",
        "- Kann im lokalen Minimum oder Sattelpunkten stecken bleiben\n",
        "- Die Gewichte werden nach jedem Durchlauf im gesamten Datensatz angepasst, das kann bei großen Datensätzen zu einem großen zeitlichen Aufwand führen.\n",
        "- Benötigt viel Speicher um den Gradienten auf dem gesamten Datenset zu errechnen. Das fällt wieder bei großen Datensätzen ins Gewicht. \n",
        "\n",
        "Es gibt drei Arten von Gradient Descent Verfahren, welche wir uns nun genauer ansehen.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Batch Gradient Descent\n",
        "\n",
        "Beim Batch Gradient Descent gehen wir durch alle Datensätze im Datensatz und berechnen am Ende der Epoche die Gesamtkosten. Die Gesamtkosten ergeben sich aus der Summe von den Kosten für jeden Datensatz. Das schauen wir uns genauer an einem Beispiel mit Hauspreisen an.\n",
        "\n",
        "<table>\n",
        "  <tr>\n",
        "    <th>area</th>\n",
        "    <th>bedrooms</th>\n",
        "    <th>price</th>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td>2600</td>\n",
        "    <td>3</td>\n",
        "    <td>550000</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td>3000 </td>\n",
        "    <td>4</td>\n",
        "    <td>565000</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td>3200</td>\n",
        "    <td>3</td>\n",
        "    <td>610000</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td>3600</td>\n",
        "    <td>3</td>\n",
        "    <td>595000</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td>4000</td>\n",
        "    <td>5</td>\n",
        "    <td>760000</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td>4100</td>\n",
        "    <td>6</td>\n",
        "    <td>810000</td>\n",
        "  </tr>\n",
        "</table>\n",
        "\n",
        "Im Bild zu sehen ist ein Datensatz mit 3 Spalten (Fläche, Schlafzimmer und Preis) und mit 6 Datensätzen. Unser Ziel ist es den Preis vorherzusagen. Dafür haben wir folgende Formel:\n",
        "$$ \\hat{p} \\ ist \\ der \\ vorhergesagte\\ Preis $$\n",
        "$$ p \\ ist \\ der \\ tatsächliche\\ Preis $$\n",
        "$$w_1, \\ w_2 \\ sind \\ die \\ Gewichte $$\n",
        "$$b \\ ist \\ der \\ Bias $$\n",
        "$$f \\ ist \\ die \\ Fläche $$ \n",
        "$$s \\ ist \\ die \\ Anzahl \\ an \\ Schlafzimmern $$\n",
        "$$\\hat{p} = w_1 \\cdot f + w_2 \\cdot s + b$$\n",
        "\n",
        "In unserem Beispiel bestimmen wir einfach $$w_1,w_2,b = 1$$\n",
        "und rechnen nun für alle Datensätze die vorhergesagten Preise aus:\n",
        "$$\\hat{p_1} = 1 * 2600 + 1 * 3 + 1 = 2604$$ \n",
        "$$\\hat{p_2} = 1 * 3000 + 1 * 4 + 1 = 3005$$\n",
        "Das System ist nicht schwer zu erkennen, daher hören wir mit der Kalkulation an der Stelle auf, aber normalerweise würden wir das für alle Datensätze im Datensatz machen.\n",
        "Parallel zum errechnen der Preise, erechnen wir für jeden einzelnen Datensatz die Kosten. Das erfolgt mit dieser Formel:\n",
        "$$k \\ sind \\ die\\ Kosten$$\n",
        "$$k = (p_1 - \\hat{p_1})^2$$\n",
        "\n",
        "Nun können wir mit der Formel die Kosten berechnen.\n",
        "\n",
        "$$k_1 = (550000 - 2604)^2$$\n",
        "$$k_2 = (565000 - 3005)^2$$\n",
        "\n",
        "Das machen wir für alle Datensätze. Wenn das Geschehen ist, sind wir am Ende der 1. Epoche. Als letzten Schritt ziehen wir die Summe von allen Kosten. \n",
        "\n",
        "$$Gesamtkosten = \\sum_{i=1}^{6}k_i$$\n",
        "$$mse\\ ist \\ Mean Sqaured Error$$\n",
        "$$mse = \\frac{Gesamtkosten}{Menge\\ an\\ Datensätzen\\ (6)}$$\n",
        "\n",
        "Bevor wir mit der nächsten Epochen starten, passen wir die Gewichte an.\n",
        "\n",
        "$$w_1 = w_1 - learning rate * \\frac{\\partial{(mse)}}{\\partial{w_1}}$$\n",
        "\n",
        "$$b = b - learning rate * \\frac{\\partial{(mse)}}{\\partial{b}}$$\n",
        "\n",
        "$$\\frac{\\partial{(mse)}}{\\partial{w_1}}= \\frac{1}{n}\\sum_{i=1}^{n}\\frac{\\partial{}}{\\partial{w_1}}(pi-(w_1*f+w_2*s+b))^2$$\n",
        "\n",
        "Die Ableitung von $$\\frac{\\partial{}}{\\partial{w_1}}$$ ist durch die Kettenregel wie folgt:\n",
        "\n",
        "$$\\frac{\\partial{}}{\\partial{w_1}} = 2(p_i-(w_1*f+w_2*s+b))*(-f) \\\\= \\frac{1}{n}\\sum_{i=1}^{n}(-2f)*(p_i-(w_1*f+w_2*s+b)) \\\\= -\\frac{2f}{n}\\sum_{i=1}^{n}(p_i-(w_1*f+w_2*s+b))$$\n",
        "\n",
        "$$\\frac{\\partial{}}{\\partial{w_2}} = -\\frac{2s}{n}\\sum_{i=1}^{n}(p_i-(w_1*f+w_2*s+b))$$\n",
        "\n",
        "$$\\frac{\\partial{}}{\\partial{b}} = -\\frac{2}{n}\\sum_{i=1}^{n}(p_i-(w_1*f+w_2*s+b))$$\n",
        "\n",
        "Nun setzen wir die Werte in die Formeln ein, um die neuen Gewichte auszurechnen\n",
        "\n",
        "$$w_1 = 1 - (-50) = 51$$\n",
        "\n",
        "$$w_1 = 1 - (-8) = 9$$\n",
        "\n",
        "$$b = 1 - (-20000) = 20001$$\n",
        "\n",
        "$$\\hat{p_1} = 51 * 2600 + 9 * 3 + 20001 = 152610$$ \n",
        "\n",
        "Wir sehen, dass unser vorhergesagter Preis dem tatsächlchen Preis schon näher kommt und unsere Kosten auf jeden Fall kleiner sein werden in der zweiten Epochen. Wir führen das ganze so oft durch bis ein Minimum der Kostenfunktion erreicht wird. In unserem Beispiel hören wir an dieser Stelle auf, da es uns wichtig war das Konzept zu übermitteln und nicht es von vorne bis hinten einmal durchzuspielen.\n",
        "\n",
        "$$w_i = w_i - learning rate * \\frac{\\partial{(mse)}}{\\partial{w_i}}$$\n",
        "\n",
        "Diese Formel wenden wir für alle Gewichte an. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Stochastic Gradient Descent\n",
        "\n",
        "Bei Stochastic Gradient Descent wählen wir ein zufälliges Gewicht, rechnen die Kosten für dieses Gewicht aus und passen danach mit den Kosten alle Gewichte und den Bias an. Damit ist eine Epoche beendet und wir wiederholen diesen Prozess.\n",
        "\n",
        "**Zu beachten:** \n",
        "Kann manchmal mehr Epochen zum konvergieren brauchen als andere Optimizer, da das Gewicht welches zum optimieren verwendet wird, per Zufall gewählt wird. \n",
        "\n",
        "**Vorteile:**\n",
        "- Gut bei großen Datensätzen, wenn wir nicht zu viel rechnen möchten.\n",
        "- Konvergiert schneller, da die Model Parameter öfter angepasst werden.\n",
        "- Braucht weniger Speicher, da wir die Werte von der Kostenfunktion nicht speichern müssen\n",
        "- Kann neue Minimas finden\n",
        "\n",
        "**Nachteile:**\n",
        "- Kann nach Erreichen des gloabeln Minimums wieder herauskommen, da es per Zufall den nächsten Referenzwert wählt.\n",
        "- Hohe Varianz in den Model Parametern\n",
        "- Um die selbe Konvergenz wie Batch Gradient Descent zu bekommen, müssen wir langsam mit der Zeit die Learning Rate verringern\n",
        "- Kann in Sattelpunkten und lokalen Minimas stecken bleiben."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Mini-Batch Gradient Descent\n",
        "\n",
        "Mini-Batch Gradient Descent ist ähnlich zu Stochastic Gradient Descent, statt ein zufälligen Datensatz zu wählen, wählen wir ein zufälliges Bündel an Datensätzen (Mini-Batch), auf welchem wir das Batch Gradient Descent Verfahren anwenden. \n",
        "\n",
        "Beispiel: WIr haben ein Datensatz mit 20 Datensätzen, dann könnten wir zum Beispiel ein Bündel von 5 Datensätzen wählen und dafür den Feedforward durchführen und die Gesamtkosten berechnen. Das ist dann unsere Epoche, wir passen die Gewichte an und danach wählen wir zufällig die nächsten 5 Datensätze. \n",
        "\n",
        "**Vorteile:**\n",
        "- Updated regelmäßig die Modell Parameter und hat weniger Varianz.\n",
        "- Braucht moderate Speicherkapazität\n",
        "\n",
        "**Zusammenfassend können wir sagen, dass alle Gradient Descent Verfahren ihre Herausforderungen haben:**\n",
        "\n",
        "Die optimale Learning Rate wählen. Wenn die Learning Rate zu klein ist, braucht das Model zu lange zum konvergieren. <br>\n",
        "Manche Parameter bleiben dauerhaft konstant, wir würden Sie aber lieber mit der Zeit anpassen. Z.B. Learning Rate<br>\n",
        "Kann im lokalen Minmum oder im Sattelpunkt stecken bleiben.\n",
        "\n",
        "<img src=\"https://1.cms.s81c.com/sites/default/files/2020-10-27/Local%20Minimum_SaddlePoints.jpg\" alt=\"Mögliche Probleme in der Konvergenz von Gradient Descent\" width=\"400px\" />\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Coding Beispiel Gradient Descent mit sklearn\n",
        "\n",
        "wir importieren unsere selbsterstellte csv-Datei mit Pandas und schauen uns diese einmal an. Unser Dataframe besteht aus drei Spalten und 14 Zeilen."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>area</th>\n",
              "      <th>bedrooms</th>\n",
              "      <th>price</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>200</td>\n",
              "      <td>3</td>\n",
              "      <td>550000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>300</td>\n",
              "      <td>4</td>\n",
              "      <td>680000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>100</td>\n",
              "      <td>2</td>\n",
              "      <td>400000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>200</td>\n",
              "      <td>5</td>\n",
              "      <td>500000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>400</td>\n",
              "      <td>2</td>\n",
              "      <td>650000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>200</td>\n",
              "      <td>2</td>\n",
              "      <td>480000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>250</td>\n",
              "      <td>5</td>\n",
              "      <td>600000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>100</td>\n",
              "      <td>2</td>\n",
              "      <td>450000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>600</td>\n",
              "      <td>7</td>\n",
              "      <td>800000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>550</td>\n",
              "      <td>5</td>\n",
              "      <td>725000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>300</td>\n",
              "      <td>3</td>\n",
              "      <td>625000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>400</td>\n",
              "      <td>6</td>\n",
              "      <td>780000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>280</td>\n",
              "      <td>2</td>\n",
              "      <td>450000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>50</td>\n",
              "      <td>1</td>\n",
              "      <td>200000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    area  bedrooms   price\n",
              "0    200         3  550000\n",
              "1    300         4  680000\n",
              "2    100         2  400000\n",
              "3    200         5  500000\n",
              "4    400         2  650000\n",
              "5    200         2  480000\n",
              "6    250         5  600000\n",
              "7    100         2  450000\n",
              "8    600         7  800000\n",
              "9    550         5  725000\n",
              "10   300         3  625000\n",
              "11   400         6  780000\n",
              "12   280         2  450000\n",
              "13    50         1  200000"
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "import pandas as pd \n",
        "df_housing = pd.read_csv('housing_prices.csv')\n",
        "df_housing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Als nächstes importieren wir sklearn und betreiben preprocessing auf dem Datensatz, dadurch werden alle Datensätze zwischen 0 und 1 skaliert. Wobei 0 der kleinste Wert des Datensatzes ist und 1 der größte. Wenn wir unser Dataframe anschauen, dann haben wir immer bei Index 8 unseren den größten Datensatz und bei Index 13 den kleinsten Datensatz. Wir werfen die Spalte 'price' aus dem df (Dataframe) damit wir nur unsere Features haben."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.27272727, 0.33333333],\n",
              "       [0.45454545, 0.5       ],\n",
              "       [0.09090909, 0.16666667],\n",
              "       [0.27272727, 0.66666667],\n",
              "       [0.63636364, 0.16666667],\n",
              "       [0.27272727, 0.16666667],\n",
              "       [0.36363636, 0.66666667],\n",
              "       [0.09090909, 0.16666667],\n",
              "       [1.        , 1.        ],\n",
              "       [0.90909091, 0.66666667],\n",
              "       [0.45454545, 0.33333333],\n",
              "       [0.63636364, 0.83333333],\n",
              "       [0.41818182, 0.16666667],\n",
              "       [0.        , 0.        ]])"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from sklearn import preprocessing\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "sx = preprocessing.MinMaxScaler()\n",
        "sy = preprocessing.MinMaxScaler()\n",
        "\n",
        "scaled_X = sx.fit_transform(df_housing.drop('price',axis='columns'))\n",
        "scaled_X  # sclaed_X besteht nun aus den zwei Spalten area und bedrooms und ist skaliert"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0.58333333],\n",
              "       [0.8       ],\n",
              "       [0.33333333],\n",
              "       [0.5       ],\n",
              "       [0.75      ],\n",
              "       [0.46666667],\n",
              "       [0.66666667],\n",
              "       [0.41666667],\n",
              "       [1.        ],\n",
              "       [0.875     ],\n",
              "       [0.70833333],\n",
              "       [0.96666667],\n",
              "       [0.41666667],\n",
              "       [0.        ]])"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "scaled_y = sy.fit_transform(df_housing['price'].values.reshape(df_housing.shape[0],1))\n",
        "scaled_y"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Nun sind unsere Dataframes für x und y so angepasst, damit wir damit arbeiten können. Als nächsten Schritt implementieren wir eine Funktion für den Batch Gradient Descent. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch: 0, Weights: [0.99657554 0.99639105], Bias: -0.004603896103896102, Cost: 0.15450126262626254\n",
            "Epoch: 50, Weights: [0.88808603 0.87879232], Bias: -0.10757744909845124, Cost: 0.0693104390033905\n",
            "Epoch: 100, Weights: [0.83503757 0.81698297], Bias: -0.10494193855931723, Cost: 0.05522885717119274\n",
            "Epoch: 150, Weights: [0.79830448 0.7718876 ], Bias: -0.07923795124766368, Cost: 0.04706495473383574\n",
            "Epoch: 200, Weights: [0.76805309 0.73366181], Bias: -0.05036092250994574, Cost: 0.040616279530338306\n",
            "Epoch: 250, Weights: [0.74163244 0.69963109], Bias: -0.022929357800431028, Cost: 0.035378119917097314\n",
            "Epoch: 300, Weights: [0.7181707 0.6688988], Bias: 0.002146442331722147, Cost: 0.031113793872064848\n",
            "Epoch: 350, Weights: [0.69725273 0.64102636], Bias: 0.02484065224121092, Cost: 0.027641144681393722\n",
            "Epoch: 400, Weights: [0.67859488 0.61570856], Bias: 0.045324226308928746, Cost: 0.02481261166105806\n",
            "Epoch: 450, Weights: [0.66196359 0.59269214], Bias: 0.06379879772861098, Cost: 0.022508193587355695\n",
            "Die Gewichte w1 und w2: [0.64743329 0.57215366], der Bias b: 0.08014124621790815, die Kosten: 0.02066419129335206\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "def batch_gradient_descent(X, y_true, epochs, learning_rate = 0.01):\n",
        "\n",
        "    number_of_features = X.shape[1] # Das gibt uns die Anzahl an Features zurück in unserem\n",
        "    #Beispiel sind es zwei (area,bedrooms) daher ist number_of_features = 2\n",
        "    \n",
        "    w = np.ones(shape=(number_of_features)) # Nun brauchen wir einfach Startgewichte, diese können\n",
        "    # zufällig gewählt sein. In unserem Beispiel nehmen wir die 1 als w_1 und w_2\n",
        "    b = 0  # bias fängt bei uns bei 0 an da können wir, aber auch nehmen was wir wollen.\n",
        "    total_samples = X.shape[0] # Anzahl an Reihen in X\n",
        "    \n",
        "    cost_list = []\n",
        "    epoch_list = []\n",
        "    \n",
        "    for i in range(epochs):     \n",
        "        y_predicted = np.dot(w, X.T) + b # y = w_1 * area + w_2 * bedrooms + bias\n",
        "        # X.T taucht Spalten in Reihen bedeutet wenn wir \n",
        "        '''\n",
        "        e = example_list\n",
        "        vorher e     naher e.T\n",
        "                    [[1,4],\n",
        "        [[1, 2,     [2,4],\n",
        "        2, 2,       [2,5],\n",
        "        3, 3],      [2,5],\n",
        "        [4, 4,      [3,6],\n",
        "        5, 5,       [3,6]]\n",
        "        6, 6]]      \n",
        "        '''\n",
        "        w_grad = -(2/total_samples)*(X.T.dot(y_true-y_predicted)) \n",
        "        b_grad = -(2/total_samples)*np.sum(y_true-y_predicted)\n",
        "        \n",
        "        w = w - learning_rate * w_grad # Anpassung der Gewichte\n",
        "        b = b - learning_rate * b_grad # Anpassung vom Bias \n",
        "        # Formel ist oben beim Batch Gradient Descent nochmal erklärt\n",
        "        \n",
        "        cost = np.mean(np.square(y_true-y_predicted)) # MSE (Mean Squared Error)\n",
        "        # Bei jeder 10. Epoche fügen wir die Kosten und die Epoche den jeweiligen Listen hinzu\n",
        "        if i%50==0:\n",
        "            print(f\"Epoch: {i}, Weights: {w}, Bias: {b}, Cost: {cost}\")\n",
        "            cost_list.append(cost)\n",
        "            epoch_list.append(i)\n",
        "        \n",
        "    return w, b, cost, cost_list, epoch_list\n",
        "\n",
        "# Wir weisen den Output der Funktion den fünf unten angezeigten w,b,cost.. Variablen zu.\n",
        "w, b, cost, cost_list, epoch_list = batch_gradient_descent(scaled_X,scaled_y.reshape(scaled_y.shape[0],),500)\n",
        "print(f'Die Gewichte w_1 und w_2: {w}, der Bias b: {b}, die Kosten: {cost}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Jede 50. Epoche haben wir ausgegeben, damit wir uns die Ouputs bisschen genauer anschauen können. In der letzten Zeile ist unser Resultat nach 500 Epochen. Wir können gut sehen wie die Kosten mit steigender Epochenzahl sinken und die Gewichte und der Bias so angepasst werden, damit es bestmöglich zu den Daten passt. Nun plotten wir noch die Kosten abhängig von der Epochenzahl"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.xlabel(\"epoch\")\n",
        "plt.ylabel(\"cost\")\n",
        "plt.plot(epoch_list,cost_list)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Was ist nun unser Mehrwert von unserem Modell? Wir können zum Beispiel nun Vorhersagen tätigen. Dazu impementieren wir eine Funktion."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 42,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "525674.4730270626"
            ]
          },
          "execution_count": 42,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "def predict(area,bedrooms,w,b):\n",
        "    scaled_X = sx.transform([[area, bedrooms]])[0]\n",
        "    # hier w_1 = w[0] , w_2 = w[1] und bias ist b\n",
        "    # Gleichung für den Preis ist w_1*area + w_2*bedrooms + bias\n",
        "    # scaled_X[0] ist die Fläche\n",
        "    # scaled_X[1] sind die Schlafzimmer\n",
        "    scaled_price = w[0] * scaled_X[0] + w[1] * scaled_X[1] + b\n",
        "    # sobald wir die Schätzung des Preises bekommen müssen wir es zurück scalen, da der Ouput in Wert zwischen 0 uznd 1 ist. \n",
        "    # Daher sy.inverse_transform. Das List Inhdexing wird gebraucht, da der Ouput eine zwei dimensionalle Liste mit einem Value in der ersten Liste an erster Stelle hat.[0][0]\n",
        "    return sy.inverse_transform([[scaled_price]])[0][0]\n",
        "\n",
        "predict(200,4,w,b)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "976276.4285353697"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "predict(1000,2,w,b)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "481872.8278011883"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "predict(300,2,w,b)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Dassselbe können wir nun auch für Stochastic Gradient Descent machen. Dazu implementieren erst einmal eine Funktion."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 74,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch: 0, Gewichte: [0.99989953 0.99995996], Bias: -0.00024025974025974008, Kosten: 0.0282851239669421\n",
            "Epoch: 10000, Gewichte: [0.59856555 0.49986206], Bias: 0.13864497918543328, Kosten: 0.01927746939554222\n",
            "Epoch: 20000, Gewichte: [0.54680631 0.38762119], Bias: 0.2101334118738257, Kosten: 0.0210781381974647\n",
            "Epoch: 30000, Gewichte: [0.5456287  0.35105867], Bias: 0.2276639191197257, Kosten: 0.01342235936574492\n",
            "Epoch: 40000, Gewichte: [0.56105847 0.33949188], Bias: 0.2298490863926534, Kosten: 0.009440429586545764\n",
            "Epoch: 50000, Gewichte: [0.57098328 0.32914983], Bias: 0.23079048525312415, Kosten: 0.00970760116446844\n",
            "Epoch: 60000, Gewichte: [0.57446977 0.3162039 ], Bias: 0.2299736817898741, Kosten: 0.011325923346318007\n",
            "Epoch: 70000, Gewichte: [0.5770861  0.31368936], Bias: 0.2380085405879184, Kosten: 0.056810264494889476\n",
            "Epoch: 80000, Gewichte: [0.58765092 0.31771205], Bias: 0.22999441511128058, Kosten: 0.018479679449992792\n",
            "Epoch: 90000, Gewichte: [0.58097528 0.31108064], Bias: 0.2279168060761999, Kosten: 0.007876769124251375\n",
            "Die Gewichte w1 und w2: [0.58235898 0.30559441], der Bias b: 0.2319467890800801, die Kosten: 0.012085338323854928\n"
          ]
        }
      ],
      "source": [
        "import random\n",
        "def stochastic_gradient_descent(X, y_true, epochs, learning_rate = 0.01):\n",
        " \n",
        "    number_of_features = X.shape[1]\n",
        "    # numpy array mit 1 Spalte und Zeilen gleich der Anzahl von Features. In \n",
        "    # unserem Fall number_of_features = 2 (area, bedrooms)\n",
        "    w = np.ones(shape=(number_of_features)) \n",
        "    b = 0\n",
        "    total_samples = X.shape[0]\n",
        "    \n",
        "    cost_list = []\n",
        "    epoch_list = []\n",
        "    \n",
        "    for i in range(epochs):    \n",
        "        random_index = random.randint(0,total_samples-1) # random index from total samples\n",
        "        sample_x = X[random_index]\n",
        "        sample_y = y_true[random_index]\n",
        "        \n",
        "        y_predicted = np.dot(w, sample_x.T) + b\n",
        "    \n",
        "        w_grad = -(2/total_samples)*(sample_x.T.dot(sample_y-y_predicted))\n",
        "        b_grad = -(2/total_samples)*(sample_y-y_predicted)\n",
        "        \n",
        "        w = w - learning_rate * w_grad\n",
        "        b = b - learning_rate * b_grad\n",
        "        \n",
        "        cost = np.square(sample_y-y_predicted)\n",
        "        \n",
        "        if i%10000==0: # at every 100th iteration record the cost and epoch value\n",
        "            print(f\"Epoch: {i}, Gewichte: {w}, Bias: {b}, Kosten: {cost}\")\n",
        "            cost_list.append(cost)\n",
        "            epoch_list.append(i)\n",
        "        \n",
        "    return w, b, cost, cost_list, epoch_list\n",
        "\n",
        "w_sgd, b_sgd, cost_sgd, cost_list_sgd, epoch_list_sgd = stochastic_gradient_descent(scaled_X,scaled_y.reshape(scaled_y.shape[0],),100000)\n",
        "print(f'Die Gewichte w_1 und w_2: {w_sgd}, der Bias b: {b_sgd}, die Kosten: {cost_sgd}')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Was hier direkt auffällt ist, dass wir viel mehr Epochen haben, aber der Code nur bisschen länger braucht zum ausführen. Das liegt daran, dass Batch Gradient Descent bei allen Gewichten die Kosten ausrechnet und Sie dann angepasst werden und bei Stochastic Gradient Descent wird nur ein zufälliges Gewicht ausgewählt, anhand von den Kosten werden alle Gewichte angepasst. Dadurch verläuft die Kostenfunktion viel volatiler und es ist nicht unüblich, dass wir aus dem Minimum wieder herausfallen. Eine Lösung dafür wäre, dass wir das Trainieren abbrechen, sobald wir einen bestimmten Kostenwert erreicht haben. Nun plotten wir noch die Kosten abhängig von der Epochenzahl und schauen uns auch hier anschließend ein paar Vorhersagen an. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 76,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.xlabel(\"epoch\")\n",
        "plt.ylabel(\"cost\")\n",
        "plt.plot(epoch_list_sgd,cost_list_sgd)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Wir sehen es verläuft um einiges sprunghafter als der Batch Gradient Descent und teilweise waren die Kosten schon nach sehr wenigen Iterationen teilweise sehr niedrig sind, aber sind dann wieder hochgegangen. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 54,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "789095.3330091073"
            ]
          },
          "execution_count": 54,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "predict(600,4,w_sgd, b_sgd) "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 55,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "363710.8720732219"
            ]
          },
          "execution_count": 55,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "predict(100,2,w_sgd, b_sgd)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 63,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "834767.1400292962"
            ]
          },
          "execution_count": 63,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "predict(500,3,w_sgd, b_sgd)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Die Implementierung vom Code um abbzubrechen, wenn die Kosten einen bestimmten Wert erreichen. In unserem Fall haben wir uns für 0.0000005 entschieden. Der Code wurde mehrfach ausgeführt. Einige Male war das Lernen schon nach weniger als 100 Epochen vollendet und einmal hat es 4000 Epochen gebraucht. Was dadurch klar wird, ist, dass ein Abbruch, sobald ein bestimmter Kostenwert erreicht ist, beim Stochastic Gradient Descent sinnvoll ist, sofern man die Konvergenz einschätzen kann und einen guten Kostenwert für das jewilige Modell einschätzen kann. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 61,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Epoch: 0, Gewichte: [0.9995427  0.99940115], Bias: -0.0007186147186147185, Kosten: 0.2530394857667584\n",
            "Epoch: 100, Gewichte: [0.9761839  0.97484648], Bias: -0.03001671465610849, Kosten: 0.03831990463251462\n",
            "Epoch: 200, Gewichte: [0.96241895 0.95910777], Bias: -0.049191800303372155, Kosten: 0.00877533782674041\n",
            "Die Gewichte w1 und w2: [0.96241918 0.95910794], der Bias b: -0.04919128689315384, die Kosten: 1.2915912560952912e-07\n"
          ]
        }
      ],
      "source": [
        "def stochastic_gradient_descent(X, y_true, epochs, learning_rate = 0.01):\n",
        " \n",
        "    number_of_features = X.shape[1]\n",
        "    # numpy array mit 1 Spalte und Zeilen gleich der Anzahl von Features. In \n",
        "    # unserem Fall number_of_features = 2 (area, bedrooms)\n",
        "    w = np.ones(shape=(number_of_features)) \n",
        "    b = 0\n",
        "    total_samples = X.shape[0]\n",
        "    \n",
        "    cost_list = []\n",
        "    epoch_list = []\n",
        "    \n",
        "    for i in range(epochs):    \n",
        "        random_index = random.randint(0,total_samples-1) # random index from total samples\n",
        "        sample_x = X[random_index]\n",
        "        sample_y = y_true[random_index]\n",
        "        \n",
        "        y_predicted = np.dot(w, sample_x.T) + b\n",
        "    \n",
        "        w_grad = -(2/total_samples)*(sample_x.T.dot(sample_y-y_predicted))\n",
        "        b_grad = -(2/total_samples)*(sample_y-y_predicted)\n",
        "        \n",
        "        w = w - learning_rate * w_grad\n",
        "        b = b - learning_rate * b_grad\n",
        "        \n",
        "        cost = np.square(sample_y-y_predicted)\n",
        "        \n",
        "        if i%100==0: # at every 100th iteration record the cost and epoch value\n",
        "            print(f\"Epoch: {i}, Gewichte: {w}, Bias: {b}, Kosten: {cost}\")\n",
        "\n",
        "        cost_list.append(cost)\n",
        "        epoch_list.append(i)    \n",
        "        if cost <= 0.0000005:\n",
        "            break    \n",
        "        \n",
        "    return w, b, cost, cost_list, epoch_list\n",
        "\n",
        "w_sgd, b_sgd, cost_sgd, cost_list_sgd, epoch_list_sgd = stochastic_gradient_descent(scaled_X,scaled_y.reshape(scaled_y.shape[0],),10000)\n",
        "print(f'Die Gewichte w_1 und w_2: {w_sgd}, der Bias b: {b_sgd}, die Kosten: {cost_sgd}')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 64,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.xlabel(\"epoch\")\n",
        "plt.ylabel(\"cost\")\n",
        "plt.plot(epoch_list_sgd,cost_list_sgd)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Die Code Implementierung vom Mini-Batch Gradient Descent lassen wir aus, da es einfach die Kombination aus Batch Gradient Descent und Stochastic Gradient Descent ist. Die Theorie dahinter ist weiter oben erklärt. Auf die restlichen Optimizer werden wir im weiteren Verlauf nur oberflächlich eingehen. Viel mehr konzentrieren wir uns auf das grundsätzliche Verständnis, wann welcher Optimizer benutzt werden sollte und was die Vor- und Nachteile sind. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Momentum\n",
        "\n",
        "Momentum ist eine Optimierungsfunktion, welche einen weiteren Hyperparameter ß benötigt als der Batch Gradient Descent Optimizer. ß wird mit den Datenpunkten multipliziert, wodurch wir den exponentiell gewichteten Durchschnitt bekommen. Bekannt als exponentially weighted moving average. Das bedeutet, dass neue Daten stärker gewichtet werden als alte, in dem jeder Datenpunkt mit einer Variable ß multipliziert wird. Jeder Datenpunkt der ganz neu ist, wird ohne jegliche Multiplikation mit ß angenommen. Ein Datenpunkt der eine Iteration alt ist, wird mit ß multiplizert. ß ist ein Wert zwischen 0 und 1. Normalerwise wird ß auf 0.9 gesetzt. Ein zwei Iterationen alter Datenpunkt wird mit ß^2 multipliziert. Daraus schließen wir, dass alte Datenpunkte nicht mehr in die Gewichtung mit reinfallen, da der Exponent immer größer wird und somit das Ergebnis der Multiplikation gegen null geht. Ein Problem, dass der Momentum Optimizer angeht, ist, dass er schneller und weniger volatil in die relevante Richtung konvergiert, wie es zum Beispiel der Mini-Batch Gradient Descent Optimizer oft macht. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Adam\n",
        "\n",
        "Adam ist der beliebteste Optimizer. Das liegt daran, dass er oft sehr schnell gute Ergebnisse liefert. Adam ist eine Kombination aus Momentum und RMSProb. Da wir RMSProb und Momentum nicht in der Tiefe in unserer Ausarbeitung behandelt haben, werden wir auch auf Adam nicht in der Tiefe eingehen.\n",
        "\n",
        "**Vorteile:**\n",
        "- Findet schnell gute Lösungen \n",
        "\n",
        "**Nachteile:**\n",
        "- Kann über das Minimum hinaus schießen."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "<img src=\"https://miro.medium.com/max/1200/1*_osB82GKHBOT8k1idLqiqA.gif\" alt=\"Various Optimizers\" width=\"400px\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "#### Abschluss\n",
        "\n",
        "Es nicht leicht zu sagen, welcher Optimizer der beste ist. Es ist immer problemabhängig und oft kann man durch ein wenig probieren herausfinden, welcher geeignet ist. Adam oder Stochastic Gradient Descent sind gute Optimizer zum anfangen. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Verbessern des Modells\n",
        "<!-- \n",
        "Aufzeigen, wie das Lernen verbessert und beschleunigt werden kann\n",
        "\n",
        "* Hyperparameter verbessern\n",
        "* Daten verbessern\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Overfitting / Underfitting\n",
        "\n",
        "Overfitting ist ein Problem, welches bei jedem Modell auftreten kann. Es ist ein Phänomen, bei dem das Modell zu stark an die Trainingsdaten angepasst wird. Dadurch wird das Modell nicht mehr in der Lage sein, neue Daten zu erkennen. Das Modell lernt die Trainingsdaten zu gut und kann diese nicht mehr richtig einordnen. Das Modell wird zu spezifisch.\n",
        "\n",
        "Underfitting ist das Gegenteil von Overfitting. Das Modell ist nicht in der Lage, die Trainingsdaten richtig zu erkennen. Das Modell ist zu allgemein und kann die Trainingsdaten nicht richtig einordnen. Dadurch werden Entscheidungen eher willkürlich getroffen.\n",
        "\n",
        "<img src=\"https://miro.medium.com/max/1400/1*i_lp_hUFyUD_Sq4pLer28g.png\" alt=\"Over- / Underfitting Example\" height=\"300px\" />\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "### Automatisch die besten Werte finden\n",
        "\n",
        "Von Hand die einzelnen Hyperparameter zu ändern und zu gucken, welcher Wert am besten ist, ist sehr zeitaufwendig. Deswegen gibt es sogenannte Hyperparameter-Tuning-Tools. Diese Tools können die besten Hyperparameter automatisch finden. Ein bekanntes Tool ist zum Beispiel GridSearchCV von Scikit-Learn. Hier kann man eine Matrix (Grid) mit verschiedenen Hyperparametern erstellen und das Tool trainiert verschiedene Modelle mit allen möglichen Kombinationen. Das Tool gibt dann die besten Hyperparameter zurück. Damit Scikit-Learn die Modelle von Tensorflow/Keras versteht, wird das Paket `scikeras` benötigt, welches dann eine abstrakte Klasse von Keras für Scikit-Learn erstellt."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "{'batch_size': 64, 'epochs': 15}\n"
          ]
        }
      ],
      "source": [
        "from scikeras.wrappers import KerasClassifier\n",
        "from sklearn.model_selection import GridSearchCV\n",
        "from mnist_model import get_compiled_model\n",
        "from keras.datasets import mnist\n",
        "\n",
        "# Can also have more hyperparameters\n",
        "param_grid = {\n",
        "    'epochs': [5, 10, 15],\n",
        "    'batch_size': [32, 64, 128]\n",
        "}\n",
        "\n",
        "kc = KerasClassifier(get_compiled_model, verbose=0)\n",
        "\n",
        "gs = GridSearchCV(\n",
        "    estimator=kc,\n",
        "    param_grid=param_grid,\n",
        "    cv=10, # 10-fold cross validation\n",
        "    n_jobs=-1, # use all available cores\n",
        "    scoring='accuracy',\n",
        "    verbose=0 # suppress output\n",
        ")\n",
        "\n",
        "# Load MNIST data\n",
        "(X_train, y_train), (X_test,  y_test) = mnist.load_data()\n",
        "\n",
        "# Normalize data\n",
        "X_train = X_train / 255.0\n",
        "X_test = X_test / 255.0\n",
        "\n",
        "gs.fit(X_train, y_train)\n",
        "\n",
        "print(gs.best_params_)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Ausblick\n",
        "\n",
        "Wir möchten an dieser Stelle einen Ausblick gewähren, welche Themen wir nicht behandelt haben und welche Sie sich selbstständig noch aneignen können. \n",
        "Im Rückblick haben wir uns mit dem Aufbau eines einfachen Neuronalen Netzes beschäftigt und sind dabei auf die Hyperparameter (Lernrate, Epochen, Batch-Größe, Aktivierungsfunktionen, Anzahl der Schichten, Kostenfunktion und Optimizer) eingegangen. \n",
        "Dabei haben wir bei einzelnen Themen auch Coding Beispiele eingebaut, die Ihnen zum leichteren Verständnis dienen sollen.\n",
        "\n",
        "### Spannende Themen im Umfeld Neuronale Netze\n",
        "Das Einsatzgebiet von Neuronalen Netzen ist riesig, es kann verwendet werden zum Erkennen von Brustkrebs, dem autonomen Landen von Raketen und das Erkennen oder auch das fälschen von Gesichtern und Stimmen in Videos (Deep Fakes).\n",
        "Wir haben Ihnen zwei Themenfelder ausgewählt, in denen Sie sich selbst noch vertiefen können.\n",
        "\n",
        "#### Convolutional Neural Networks\n",
        "Wir haben in dieser Arbeit den MNIST-Datensatz verwendet, um Ziffern auf Bildern zu erkennen. Dabei haben wir das Feed-Forward Verfahren benutuzt. \n",
        "Sehr beliebt, vor allem in der Bilderkennung, aber auch zum Beispiel beim verarbeiten von Sprache, sind Convolutional Neural Networks (CNN). \n",
        "Diese heißen so, da sie sogenannte Convolutional Layers (faltbare Schichten) verwenden. Eine schöne Einführung (auf Englisch) finden Sie in dem Artikel [\"A Comprehensive Guide to Convolutional Neural Networks\"](https://towardsdatascience.com/a-comprehensive-guide-to-convolutional-neural-networks-the-eli5-way-3bd2b1164a53).\n",
        "\n",
        "#### Reinforcment Learning\n",
        "Komplett anders und sehr spannend ist auch die Anwendung des Reinforcement Learning (verstärktes Lernen). Anstatt Datensätze zu benutzen, dessen richtige Ausgaben bereits bekannt sind und so dem Modell beigebracht werden, benutzt das Reinforcement Learning einen \"Agent\", der mittels Belohnung / Bestrafung lernt. So kann zum Beispiel ein Auto lernen autonom einzuparken, indem es zuerst zufällige Bewegungen ausführt, jedoch mittels der Belohnungen beziehungsweise Bestrafungen lernt die Werte der Abstandssensoren und der Geschwindigkeit richtig zu verstehen. Die Bewegungen wirken immer weniger zufällig, bis das Auto in viele verschiedene Parklücken einparken kann (dafür sind jedoch mehrere tausend bis millionen von Durchläufen nötig, welche oft in einem Unfall enden werden, weshalb es ratsam ist das Auto hauptsächlich in einer Simulation zu trainieren und erst am Ende in der realen Welt zu testen). Eine Einführung (auf Englisch) bietet der Artikel [\"Introduction to Reinforcement Learning for Beginners\"](https://www.analyticsvidhya.com/blog/2021/02/introduction-to-reinforcement-learning-for-beginners/)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Quellen\n",
        "\n",
        "\n",
        "1. <a href=\"https://towardsdatascience.com/machine-learning-for-beginners-an-introduction-to-neural-networks-d49f22d238f9\">Machine Learning for Beginners an Introduction to Neural Networks</a>\n",
        "2. <a href=\"https://learn.microsoft.com/de-de/training/modules/intro-machine-learning-keras/\">Coding Beispiel eines Neuronalen Netzes von Microsoft</a>\n",
        "3. <a href=\"https://open.hpi.de/courses/neuralnets2020/overview\">Online Kurs von OpenHPI zu Neuronalen Netzen</a>\n",
        "4. <a href=\"https://towardsdatascience.com/write-markdown-latex-in-the-jupyter-notebook-10985edb91fd\">Learn to write LaTeX in Jupyter Notebook</a>\n",
        "5. <a href=\"http://neuralnetworksanddeeplearning.com/\">Buch: Einführung in Neuronale Netze und Deep Learning</a>\n",
        "6. <a href=\"https://www.youtube.com/watch?v=aircAruvnKk\">Video: What is a Neural Network</a>\n",
        "7. <a href=\"https://www.youtube.com/watch?v=IHZwWFHWa-w\">Video: Gradient descent, how neural networks learn</a>\n",
        "8. <a href=\"https://www.youtube.com/watch?v=Ilg3gGewQ5U\">Video: What does Backpropagation do?</a>\n",
        "9. <a href=\"https://de.wikipedia.org/wiki/Kreuzentropie\">Wikipedia: Kreuzentropie</a>\n",
        "10. <a href=\"https://vitalflux.com/keras-categorical-cross-entropy-loss-function/#:~:text=categorical_crossentropy%3A%20Used%20as%20a%20loss%20function%20for%20multi-class,converted%20into%20categorical%20encoding%20using%20keras.utils%20to_categorical%20method.\">Article: Cross Entropy Loss Function </a>\n",
        "11. <a href=\"https://www.grund-wissen.de/informatik/latex/mathematischer-formelsatz.html#:~:text=Das%20Summenzeichen%20kann%20im%20Mathe-Modus%20mittels%20sum%20gedruckt,Syntax%20genutzt%20und%20somit%20sum_%20%7B%7D%5E%20%7B%7D%20geschrieben%3A\">Artikel: Mathematischer Formelsatz LaTeX</a>\n",
        "12. <a href=\"https://neuroforge.de/wie-optimiere-ich-ein-neuronales-netz/\">Artikel: Wie optimiere ich ein Neuronales Netz</a>\n",
        "13. <a href=\"https://towardsdatascience.com/optimizers-for-training-neural-network-59450d71caf6\">Article: Which is the best optimzer?</a>\n",
        "14. <a href=\"https://towardsdatascience.com/overview-of-various-optimizers-in-neural-networks-17c1be2df6d5\">Article: Overview of various Optimizers</a>\n",
        "15. <a href=\"https://methpsy.elearning.psych.tu-dresden.de/mediawiki/index.php/Gradient_Descent#:~:text=Unter%20Gradient%20Descent%20versteht%20man%20einen%20Optimierungsalgorithmus%2C%20der,und%20einen%20im%20Tal%20gelegenen%20See%20erreichen%20m%C3%B6chte.\">Artikel: TU Dresden zu Gradient Descent</a>\n",
        "16. <a href=\"https://towardsdatascience.com/epoch-vs-iterations-vs-batch-size-4dfb9c7ce9c9\">Artikel: Epochen vs Iterations vs Batchsizes</a>\n",
        "17. <a href=\"https://towardsdatascience.com/what-are-hyperparameters-and-how-to-tune-the-hyperparameters-in-a-deep-neural-network-d0604917584a\">Artikel: What are Hyperparameters and how to tune the hyperparameters in a deep neural network</a>\n",
        "18. <a href=\"https://www.youtube.com/watch?v=IU5fuoYBTAM&t=8s\">Video: Difference Batch-,Stochastic- and Mini-Batch Gradient Descent</a>\n",
        "19. <a href=\"https://www.youtube.com/watch?v=cT4pQT5Da0Q\">Video: Derratives for Deep Learning</a>\n",
        "20. <a href=\"https://www.youtube.com/watch?v=oCPT87SvkPM\">Video: Backpropagation</a>\n",
        "21. <a href=\"https://www.alexanderthamm.com/de/data-science-glossar/backpropagation/\">Artikel: Backpropagation</a>\n",
        "22. <a href=\"https://github.com/codebasics/deep-learning-keras-tf-tutorial\">Github Repo: Deep Learning Keras Tutorial</a>\n",
        "23. <a href=\"https://www.youtube.com/watch?v=Vce8w1sy0e8\">Video: Momentum Optimizer</a>\n",
        "24. <a href=\"https://machinelearningjourney.com/index.php/2020/12/01/momentum-optimizer/#:~:text=The%20momentum%20optimizer%20is%20a%20set%20of%20equations.,terms%20in%20order%20to%20update%20a%20networks%20parameters.\">Article: Momentum Optimizer</a>\n",
        "25. <a href=\"https://www.youtube.com/watch?v=JXQT_vxqwIs\">Video: Adam Optimizer</a>\n",
        "26. <a href=\"https://www.youtube.com/watch?v=mdKjMPmcWjY\">Video: Optimizers explained</a>\n",
        "27. <a href=\"https://www.bmc.com/blogs/deep-neural-network/\">Artikel: Whats a Deep Neural Nework</a>\n",
        "28. <a href=\"http://www.neuronalesnetz.de/aktivitaet.html\">Website: Einführung in Neuronale Netze</a>\n",
        "29. <a href=\"https://www.youtube.com/watch?v=s-V7gKrsels\">Video: Activation Function explained</a>\n",
        "\n",
        "\n",
        "### Dokumentation benutzter Libraries\n",
        "\n",
        "1. <a href=\"https://www.tensorflow.org/api_docs/python/tf/keras\">Keras</a>\n",
        "2. <a href=\"https://numpy.org/doc/stable/user/index.html#user\">Numpy</a>\n",
        "3. <a href=\"https://matplotlib.org/stable/api/pyplot_summary.html\">Matplotlib</a>\n",
        "4. <a href=\"https://www.tensorflow.org/api_docs/python/tf\">Tensorflow</a>\n",
        "5. <a href=\"https://scikit-learn.org/stable/\">Scikit-Learn</a>\n",
        "6. <a href=\"https://www.adriangb.com/scikeras/stable/\">SciKeras</a>\n",
        "\n",
        "### Empfehlungen bei zusätzlichem Literatur-/Informationsbedarf\n",
        "\n",
        "1. <a href=\"https://towardsdatascience.com/\">Towards Data Science Blog</a>\n",
        "2. <a href=\"https://www.udemy.com/course/the-data-science-course-complete-data-science-bootcamp/\">Online Kurs zu ML und Data Science auf Udemy in Englisch</a>\n",
        "3. <a href=\"https://youtube.com/playlist?list=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi\">Youtube Videos über Neuronale Netze auf Englisch</a>"
      ]
    }
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