RegressionKISSplustext.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.5"
    },
    "colab": {
      "name": "RegressionKISSplustext.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Bogula/KISS/blob/main/RegressionKISSplustext.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bFro0XtO-tWt"
      },
      "source": [
        "#Lineare Regression\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9ChFncE0o_TR"
      },
      "source": [
        "Dieses Notebook ist die Umsetzung der Lektion 6 aus dem OER KISS*\n",
        "\n",
        "https://blogs.hoou.de/oerkiss/courses/kiss/1130/"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xmb6JLev-tWu"
      },
      "source": [
        "#Import der benötigten Module\n",
        "\n",
        "import numpy as np\n",
        "from sklearn.linear_model import LinearRegression"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5AHDd4pL-tWv"
      },
      "source": [
        "#Eingabe der X Werte und Y Werte\n",
        "\n",
        "x = np.array([3,6,9,15,18,21,3,9,18])\n",
        "\n",
        "y = np.array([400,350,310,200,175,150,370,280,199])"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v2FHwPidfULF"
      },
      "source": [
        "#Die Eingabe in unser ML Modell muss immer aus einem ARRAY von Zahlen in eckigen Klammern sein\n",
        "#also so aussehen: [ [1][5][3] ]. \n",
        "\n",
        "#Um aus einem einfachen ARRAY ein ARRAY von ARRAYS zu machen nutzen wir den Befehl:\n",
        "x2 = x.reshape((-1, 1))"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PkyqdIiZAVHN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "606aa64e-f9d1-4213-eb81-ae7850b2d24c"
      },
      "source": [
        "#Nun haben wir genau das Format, das wir brauchen \n",
        "x2"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 3],\n",
              "       [ 6],\n",
              "       [ 9],\n",
              "       [15],\n",
              "       [18],\n",
              "       [21],\n",
              "       [ 3],\n",
              "       [ 9],\n",
              "       [18]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bbsiw-jU-tWw"
      },
      "source": [
        "#Wir erzeugen unser Modell\n",
        "model = LinearRegression()"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TFkaSi9P-tWw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b6bb3d7b-34f0-4195-999d-75002146f3d9"
      },
      "source": [
        "#Wir trainieren unser Modell mit den Trainingsdaten: \n",
        "model.fit(x2, y)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jUPcJZKZgW4g"
      },
      "source": [
        "Nach dem Training gibt das Modell uns mehrere Daten:\n",
        "\n",
        "model.intercept_   sagt, wo die Gerade die y Achse schneidet\n",
        "\n",
        "model.coef_. sagt wie die Steigung der Geraden ist\n",
        "\n",
        "Zur Erinnerung eine Gerade ist beschrieben als:\n",
        "\n",
        "y = a*x + b\n",
        "\n",
        "wobei a, die Steigung ist und b der Schnitt mit der y-Achse"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WphSJgwf-tWx",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c7fb1cda-ac43-4862-b7cc-2ebc84ddf79c"
      },
      "source": [
        "Schnittpunkty = model.intercept_\n",
        "print('Schnitt mit der y Achse:', Schnittpunkty)\n"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Schnitt mit der y Achse: 421.45454545454544\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-axInldX-tWy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d37e9cdd-0ecd-4f17-f6f7-900b185e8827"
      },
      "source": [
        "#Achtet mal drauf, dass hier keine reine Zahl wieder gegeben wird, sondern ein Wert in eckigen Klammern\n",
        "print('Steigung:', model.coef_)"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Steigung: [-13.32442068]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I1NMmRLgicyB",
        "outputId": "f51c977f-e329-46d0-f4da-5c531f167c0b"
      },
      "source": [
        "#Um den Wert aus der Klammer rauszuholen gibt es die Funktion item()\n",
        "\n",
        "SteigungWert = model.coef_.item()\n",
        "print(SteigungWert)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "-13.324420677361852\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kFkD3ohPi7KC"
      },
      "source": [
        "So als nächstes machen wir die Graphik\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z5cPxL7p-tWz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 613
        },
        "outputId": "977b2bbf-664a-423d-9666-d7df8554f6e5"
      },
      "source": [
        "#Wir laden das Grafikmodul\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "#Wir sagen, wie groß die Grafik sein soll\n",
        "plt.figure(figsize=(15,10))\n",
        "\n",
        "#Wir malen alle x,y als Punkte mit der Größe 22pixel\n",
        "plt.scatter(x, y, s=22)\n",
        "\n",
        "#Wir machen ein schönes Gitter in den Hintergrund\n",
        "plt.grid()\n",
        "#Wir zeigen das ganze an\n",
        "plt.show()"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 1080x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zV8E-CABjWzo"
      },
      "source": [
        "Als nächstes wollen wir die Regressionsgrade malen\n",
        "\n",
        "Wir haben ja die Steigung und den Schnittpunkt mit der y Achse\n",
        "und wir wissen auch wie die Formel für einen Gerade ist:\n",
        "\n",
        "y = a * x + b\n",
        "\n",
        "a ist SteigungWert\n",
        "\n",
        "b ist Schnittpunkty\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-oRvZLPXCsOG",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "outputId": "a43e39d8-21d9-4f51-9353-841850528fb8"
      },
      "source": [
        "#Wir machen eine Liste von 10 x-Werten zwischen 0 und 25\n",
        "xg = np.linspace(0,25,num=10)\n",
        "\n",
        "#Wir berechnen zu jedem x aus der Liste oben den dazugehörigen y Wert\n",
        "yg = SteigungWert* xg + Schnittpunkty\n",
        "\n",
        "#Wir malen die Gerade mit xg, yg der Farbe rot und dem Label \"Preisnäherung\"\n",
        "plt.plot(xg, yg, '-r', label='Preisnäherung')\n",
        "#Wir setzen das Label oben rechts in die Ecke\n",
        "plt.legend(loc='upper right')\n",
        "\n",
        "plt.title('Handy-Preise')\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yg5gnKOamEE0"
      },
      "source": [
        "So jetzt wo wir gesehen haben wir man die Werte als Punkte auf die Grafik packt und wie die Gerade, fügen wir beides in einem Schaubild zusammen. Also nix neues sondern die letzten beiden Zellen in einer zusammen\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 627
        },
        "id": "xE_QlAqgmTak",
        "outputId": "20c8079a-dd94-45ac-d5f1-71143c23a454"
      },
      "source": [
        "#Wir laden das Grafikmodul\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "#Wir sagen, wie groß die Grafik sein soll\n",
        "plt.figure(figsize=(15,10))\n",
        "\n",
        "#Wir malen alle x,y als Punkte mit der Größe 22pixel\n",
        "plt.scatter(x, y, s=22)\n",
        "\n",
        "#Wir machen ein schönes Gitter in den Hintergrund\n",
        "plt.grid()\n",
        "\n",
        "#Wir machen eine Liste von 10 x-Werten zwischen 0 und 25 \n",
        "xg = np.linspace(0,25,num=10)\n",
        "\n",
        "#Wir berechnen zu jedem x aus der Liste oben den dazugehörigen y Wert\n",
        "yg = SteigungWert* xg + Schnittpunkty\n",
        "\n",
        "#Wir malen die Gerade mit xg, yg der Farbe rot und dem Label \"Preisnäherung\"\n",
        "plt.plot(xg, yg, '-r', label='Preisnäherung')\n",
        "#Wir setzen das Label oben rechts in die Ecke\n",
        "plt.legend(loc='upper right')\n",
        "\n",
        "plt.title('Handy-Preise')\n",
        "\n",
        "#Wir zeigen das ganze an\n",
        "plt.show()"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAA20AAAJOCAYAAAAkve/mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdd5RV1cGG8WcPIChgQwQNFtSIDL2LFYQoNsCCsUtQLFiILXaNvReIiL1rULH3go4ERQWUOgQQxYiKURSlCAKzvz/O1Q8JyAD3zrkz8/zWmuXMafedeEJ4s8/ZO8QYkSRJkiTlp4K0A0iSJEmSVs7SJkmSJEl5zNImSZIkSXnM0iZJkiRJeczSJkmSJEl5zNImSZIkSXnM0iZJqpBCCH8PITycBzkmhRA6pZ1DklR+WdokSWUmhDAjhNB1uW29Qwgj0sq0IpmcP4UQ5oUQvg4h3B9CqLUm14oxNokxFmU5oiSpErG0SZK0YvvHGGsBrYG2wIXLHxBCqFrmqSRJlY6lTZKUN0II54YQpocQ5oYQikMIByyzr3cIYUQI4YYQwvchhE9DCHsvs79hCOHtzLmvA5sss+/FEMKpy33W+GWvvzIxxi+Al4GmmfNiCOHkEMI0YFpm234hhLEhhDkhhHdDCM2X+ZxfRxdDCO1DCKNDCD9mRvBuWua4HTPnzgkhjPORSknSLyxtkqR8Mh3YFdgAuBR4OISw2TL7OwBTSArZdcA9IYSQ2fcoMCaz73LgmGXOewA48pcfQggtgD8AL64qUAhhC2Af4KNlNvfMZCkMIbQC7gVOAOoAdwDPhRCqr+ByA4ABMcb1gW2BxzOf8UuWK4CNgbOAJ0MIdVeVT5JU8VnaJEll7ZnMaNKcEMIc4LZfdsQYn4gxfhljLIkxPkYyktV+mXM/izHeFWNcSlLENgPqhRC2BNoBF8UYF8UYhwPPL3Pec8D2IYQ/Zn4+CngsxvjzqnICI4C3gauW2Xd1jPG7GONPwPHAHTHG92OMS2OMDwCLgB1XcM3FwHYhhE1ijPNijO9lth8JvBRjfCnzu78OjCYpi5KkSs7SJkkqaz1jjBv+8gX0+2VHCOHoZR4znEPySOImy5w765dvYowLMt/WAjYHvo8xzl/m2M+WOXYh8BhwZAihADgMeCjzmS9nJhyZF0I4YgU5t4ox9ssUtF98vsz3WwFnLldEt8hkWt6xwPbAv0MIo0II+y1zjV7LXWMXklIqSarkfIFakpQXQghbAXcBXYCRMcalIYSxQPj9MwH4CtgohFBzmeK2JRCXOeYBkqI2AlgQYxwJEGPcm9W37HU/B66MMV65ypNinAYclimOBwJDQwh1Mtd4KMbYdw2ySJIqOEfaJEn5oiZJGfoGIITwFzKTf6xKjPEzkscJLw0hrBNC2AXYf7ljRgIlwI1kRtmy5C7gxBBCh5CoGULYN4RQe/kDQwhHhhDqxhhLgDmZzSXAw8D+IYS9QghVQgg1QgidQggNsphTklROWdokSXkhxlhMUqhGAl8DzYB3VuMSh5NMDvIdcAnw4AqOeTBz3awtuh1jHA30BW4Fvgc+Bnqv5PBuwKQQwjySSUkOjTH+FGP8HOgBnE9SWj8Hzsb/nZYkASHGuOqjJEmqAEIIRwPHxxh3STuLJEml5f+DJ0mqFEII65FMenJn2lkkSVodljZJUoUXQtiL5LHDr0nWc5Mkqdzw8UhJkiRJymOOtEmSJElSHsuLddo22WSTuPXWW6cd43/Mnz+fmjVrph1DFZT3l3LNe0y55P2lXPL+Ui7l6/01ZsyYb2OMdVe0Ly9K29Zbb83o0aPTjvE/ioqK6NSpU9oxVEF5fynXvMeUS95fyiXvL+VSvt5fIYTPVrbPxyMlSZIkKY9Z2iRJkiQpj1naJEmSJCmP5cU7bZIkSZLW3OLFi5k5cyYLFy5MO0re22CDDZg8eXJqn1+jRg0aNGhAtWrVSn2OpU2SJEkq52bOnEnt2rXZeuutCSGkHSevzZ07l9q1a6fy2TFGZs+ezcyZM2nYsGGpz/PxSEmSJKmcW7hwIXXq1LGw5bkQAnXq1FntEVFLmyRJklQBWNjKhzX592RpkyRJkqQ8ZmmTJEmStNaqVKlCy5Ytadq0Kb169WLBggWlPvfLL7/k4IMPXqPP/eXc4uJijjvuuF+39+7dm6FDh67RNfONpU2SJEnSWlt33XUZO3YsEydOZJ111uH222//zf4lS5as9NzNN998jQvWL+cWFhZy9913r9E1lhdjpKSkJCvXygZLmyRJkqSs2nXXXfn4448pKipi1113pXv37hQWFrJ06VLOPvts2rVrR/PmzbnjjjsAmDFjBk2bNgVg0qRJtG/fnpYtW9K8eXOmTZvGjBkzaNy4MX379qVJkybsueee/PTTTwDcfvvttGvXjhYtWnDQQQf9ZoRv+PDh7LTTTmyzzTa/KYXXX3/9rxkuueSSXzM0atSIo48+mqZNm/L5559Tq1atX88ZOnQovXv3BpJRvNNOO+1/rl1SUkK/fv3YYYcd+NOf/sQ+++yTldE+p/yXJEmSKpK//hXGjs3uNVu2hFtuKdWhS5Ys4eWXX6Zbt24AfPjhh0ycOJGGDRty5513ssEGGzBq1CgWLVrEzjvvzJ577vmbyTluv/12+vfvzxFHHMHPP//M0qVL+frrr5k2bRr//Oc/ueuuuzjkkEN48sknOfLII+nVqxcnnngiABdeeCH33HMPp556KgBfffUVI0aM4N///jfdu3fn4IMPZtiwYUybNo0PPviAGCPdu3dn+PDhbLnllkybNo0HHniAHXfccZW/54qu/dRTTzFjxgyKi4v573//S+PGjenTp8/q/qf9PyxtkiRJktbaTz/9RMuWLYFkpO3YY4/l3XffpX379r+uSfbaa68xfvz4X0effvjhB6ZNm8b222//63U6duzIlVdeycyZMznwwAP54x//CEDDhg1/vX6bNm2YMWMGABMnTuTCCy9kzpw5zJs3j7322uvXa/Xs2ZOCggIKCwv5+uuvAXjzzTd57bXXaNWqFQDz5s1j2rRpbLnllmy11ValKmwru/aIESPo1asXBQUF1K9fn86dO6/Rf5bLs7RJkiRJFUkpR8Sy7Zd32pZXs2bNX7+PMfKPf/zjN8UK+LWAARx++OF06NCBF198kX322Yc77riDbbbZhurVq/96TJUqVX59PLJ3794888wztGjRgvvvv5+ioqJfj1v2nBjjr/8877zzOOGEE/4nw7JZ4bfT8y+/ttqKrp0rvtMmSZIkqUzstddeDB48mMWLFwMwdepU5s+f/5tjPvnkE7bZZhtOO+00evTowfjx43/3mnPnzmWzzTZj8eLFPPLII6vM0KVLF+69917mzZsHwBdffMF///vfFR5br149Jk+eTElJCU8//fQqr73zzjvz5JNPUlJSwtdff/2bArk2HGmTJEmSVCaOO+44ZsyYQevWrYkxUrduXZ555pnfHPP444/z0EMPUa1aNerXr8/555/Pjz/+uNJrXn755XTo0IG6devSoUMH5s6d+7sZunTpwmeffUbHjh0BqFWrFg8//DBVqlT5n2OvueYa9ttvP+rWrUvbtm1/LXorc9BBBzFs2DAKCwvZYostaN26NRtssMHvnlMaIddDeaXRtm3bOHr06LRj/I+ioiI6deqUdgxVUN5fyjXvMeWS95dyyftr9U2ePJnGjRunHaNcmDt3LrVr187Z9efNm0etWrWYPXs27du355133qF+/fq/OWZF/75CCGNijG1XdE1H2iRJkiQpS/bbbz/mzJnDzz//zEUXXfQ/hW1NWNokSZIkKUuy9R7bspyIRJIkSaoA8uG1J63amvx7srRJkiRJ5VyNGjWYPXu2xS3PxRiZPXs2NWrUWK3zfDxyZWIkLF2adgpJkiRplRo0aMDMmTP55ptv0o6S9xYuXLjapSmbatSoQYMGDVbrHEvbytx7L62vvRYeewwyq6VLkiRJ+ahatWo0bNgw7RjlQlFREa3K2d/vfTxyZTbdlHVmz4Z27eD882G5FdAlSZIkqSxY2lZm//0Zdf/9cPTRcPXV0LIlvPNO2qkkSZIkVTKWtt+xpHZtuPdeePXVZKRt113h1FNhFausS5IkSVK2WNpKY889YeLEpLANGgRNmyZFTpIkSZJyzNJWWrVqwYABMGIErLcedOsGvXvDd9+lnUySJElSBWZpW1077QQffQQXXACPPAKFhfDkk2mnkiRJklRBWdrWRI0acMUVMGoU/OEPcPDBcNBB8NVXaSeTJEmSVMFY2tZGy5bw/vtwzTXw4ovJqNt994Er0UuSJEnKEkvb2qpaFc45B8aPh2bNoE8f2GsvmDEj7WSSJEmSKgBLW7Zsvz0UFcFtt8HIkckMkwMHwtKlaSeTJEmSVI5Z2rKpoABOOgkmTYLddoP+/ZO13SZPTjuZJEmSpHLK0pYLW26ZvOP20EMwZUry7tuVV8LixWknkyRJklTOWNpyJQQ48shklK1nT7jwQmjbFsaMSTuZJEmSpHLE0pZrm24Kjz0GTz8N33wDHTrAuefCTz+lnUySJElSOWBpKys9e0JxMfTuDddeCy1awPDhaaeSJEmSlOcsbWVpww3h7rvhjTdgyRLYfXc4+WT48ce0k0mSJEnKU5a2NHTpAhMmwOmnw+DByfIAL72UdipJkiRJecjSlpaaNeGmm+Ddd6F2bdh3XzjqKPj227STSZIkScojlra07bgjfPghXHwxDBkChYXw+OMQY9rJJEmSJOUBS1s+qF4dLr00WQ5gq63gz3+GAw6AL79MO5kkSZKklFna8knz5jByJFx/Pbz6ajLqds89jrpJkiRJlZilLd9UrQpnnZVMVNKyJRx3HHTtCp98knYySZIkSSmwtOWr7baDN9+EO+6AUaOSGSZvvhmWLk07mSRJkqQyZGnLZwUFcPzxyaLce+wBZ5wBO+8MkyalnUySJElSGbG0lQcNGsDzz8Ojj8L06dCqFVx2Gfz8c9rJJEmSJOWYpa28CAEOOywZdevVCy65BNq2TR6dlCRJklRhWdrKm7p14ZFH4Lnn4LvvknXezj4bFixIO5kkSZKkHLC0lVf775+829a3L9xwQ7JcQFFR2qkkSZIkZZmlrTzbYAO4/fZklkmAzp3hhBPghx/SzSVJkiQpa0pd2kIIVUIIH4UQXsj83DCE8H4I4eMQwmMhhHUy26tnfv44s3/r3ETXrzp3hvHjk/Xd7r4bmjSBF15IO9VqmTJrLq9MnMWUWXPTjiJJkiTlldUZaesPTF7m52uBm2OM2wHfA8dmth8LfJ/ZfnPmOOXaeuvB9dfDyJGw0UbJ45OHHw7ffJN2slUa8MZUegwawVlPjKPHoBEMHDY17UiSJElS3ihVaQshNAD2Be7O/ByAPYChmUMeAHpmvu+R+ZnM/i6Z41UW2reHMWPg0kth6FAoLIR//hNiTDvZCk2ZNZfBb09n4eIS5i1awsLFJdxWNN0RN0mSJCkjxFL8ZT6EMBS4GqgNnAX0Bt7LjKYRQtgCeDnG2DSEMBHoFmOcmdk3HegQY/x2uWseDxwPUK9evTZDhgzJ2i+VLfPmzaNWrVppx1hj6336KTtcfz3rT57Mtx07Mu3001lUt27asX7jx4VLmPndApYucx9WCYEGG6/H+jWqppgs98r7/aX85z2mXPL+Ui55fymX8vX+6ty585gYY9sV7Vvl34pDCPsB/40xjgkhdMpWqBjjncCdAG3bto2dOmXt0llTVFREPuYqtU6d4OijYeBANrngAjY59tjkEcq+faEgP+agmTJrLn8bNIKFi0t+3VajWgHPntyBRvVrp5gs98r9/aW85z2mXPL+Ui55fymXyuP9VZq/ue8MdA8hzACGkDwWOQDYMITwS+lrAHyR+f4LYAuAzP4NgNlZzKzVUaUKnH46TJwI7drBiSdCly7w8cdpJwOgUf3anLT7ttSoVkCt6lWpUa2Afp22rfCFTZIkSSqtVZa2GON5McYGMcatgUOBN2OMRwBvAQdnDjsGeDbz/XOZn8nsfzOW5hlM5dY228Abb8Bdd8GHH0KzZsn6bkuWpJ2M/l2359mTd+GGXi149uRdOK3L9mlHkiRJkvLG2jwjdw5wRgjhY6AOcE9m+z1Ancz2M4Bz1y6isiYEOO44KC6GPfeEs8+GnXaCCRPSTkaj+rXp1rS+I2ySJEnSclartMUYi2KM+2W+/yTG2D7GuF2MsVeMcVFm+8LMz9tl9n+Si+BaC3/4AzzzDDz2GMyYAa1bwyWXwKJFaSeTJEmStJz8mI1CZS8EOOQQmDwZDj0ULrssKW/vvZd2MkmSJEnLsLRVdnXqwEMPwYsvwo8/Jo9LnnEGzJ+fdjJJkiRJWNr0i332gUmTktklb745mahk2LC0U0mSJEmVnqVN/2/99eG22+Dtt6FqVejaNVnTbc6ctJNJkiRJlZalTf9rt91g3Dg45xy47z4oLIRnn131eZIkSZKyztKmFVt3XbjmGnj/fdh0U+jZE/78Z/j667STSZIkSZWKpU2/r00bGDUKrrgiWSagsBAefhhcL12SJEkqE5Y2rVq1anDBBTB2LDRqBEcdBfvuC//5T9rJJEmSpArP0qbSa9wY/vUvGDAgmaykSRMYPBhKStJOJkmSJFVYljatnipV4LTTYOJE6NgR+vWDTp1g6tS0k0mSJEkVkqVNa6ZhQ3j11WR2yQkToEULuO46WLIk7WSSJElShWJp05oLAXr3huJi2HvvZImADh2S5QIkSZIkZYWlTWtvs83gqadg6FD44gto2xYuvBAWLkw7mSRJklTuWdqUPQcdlIy6HXEEXHkltGoF776bdipJkiSpXLO0Kbs23hjuvx9eeQUWLIBddoH+/WHevLSTSZIkSeWSpU25sddeyQyTJ58M//gHNG0Kr72WdipJkiSp3LG0KXdq104K2/DhUKNGUuT+8hf4/vu0k0mSJEnlhqVNubfLLjB2LJx3Hjz0EBQWJhOXSJIkSVolS5vKRo0acNVVMGoU1K+fTFpy8MEwa1baySRJkqS8ZmlT2WrVCj74IClwL7yQjLo98ADEmHYySZIkKS9Z2lT2qlVLHpUcOzYpbb17J4tzf/ZZ2skkSZKkvGNpU3p22CGZpOTWW+Gdd6BJk+T7kpK0k0mSJEl5w9KmdBUUJMsCTJyYTFhy6qmw227w73+nnUySJEnKC5Y25YettoKXX07ebysuhhYtkvfeFi9OO5kkSZKUKkub8kcIcPTRMHkydO8OF1wA7dvDRx+lnUySJElKjaVN+adePXjiCXjyyWRJgHbtkolLFi5MO5kkSZJU5ixtyl8HHpg8Knn00XDNNckjkyNGpJ1KkiRJKlOWNuW3jTaCe++F116Dn3+GXXeFU06BuXPTTiZJkiSVCUubyoc//QkmTID+/eG226BpU3j11bRTSZIkSTlnaVP5UasW3HJLsqZbzZrQrRsccwzMnp12MkmSJClnLG0qfzp2TGaUvPBCePRRKCyEoUMhxrSTSZIkSVlnaVP5VL06XH45jB4NW2wBvXrBQQfBV1+lnUySJEnKKkubyrcWLeC99+Daa5PFuQsL4b77HHWTJElShWFpU/lXtSr87W8wbhw0bw59+sCee8Knn6adTJIkSVprljZVHNtvD2+9BYMHw/vvJzNMDhwIS5emnUySJElaY5Y25YUps+byysRZTJm1luuvFRTAiSfCpEmw++7JEgG77gqTJ2cnqCRJklTGLG1K3YA3ptJj0AjOemIcPQaNYOCwqWt/0S22gBdfhIcfhqlToWVLuOIKWLx47a8tSZIklSFLm1I1ZdZcBr89nYWLS5i3aAkLF5dwW9H0tR9xAwgBjjgCiovhgAPgoougbVsYM2btry1JkiSVEUubUvXpt/OpWvDb27BqQQGffjs/ex+y6aYwZAg88wx88w20bw/nnAM//ZS9z5AkSZJyxNKmVDXcpCZLSkp+s21JSQkNN6mZ/Q/r0SMZdevTB667LlkuYPjw7H+OJEmSlEWWNqWqUf3anLT7ttSoVkCt6lWpUa2Afp22pVH92rn5wA03hLvugjfeSGaV3H136NcPfvwxN58nSZIkraWqaQeQ+nfdnm5NN+PTb+fTcJOauStsy+rSBcaPh4svhltugRdegNtvh332yf1nS5IkSavBkTblhUb1a9Otaf2yKWy/qFkTbrwR3n0XateGffeFo46Cb78tuwySJEnSKljapA4d4MMP4ZJLkglLCgvhsccgxrSTSZIkSZY2CYDq1eHvf0/K21ZbwaGHQs+e8OWXaSeTJElSJWdpk5bVrBmMHAk33ACvvZaMut19t6NukiRJSo2lTVpe1apw5pkwYQK0bAl9+0LXrvDJJ2knkyRJUiVkaZNWZrvt4M034Y47YPRoaNoUbr45WSpAkiRJKiOWNun3FBTA8cfDpEnJMgFnnAE775z8LEmSJJUBS5tUGg0awHPPwaOPwvTp0KoVXHYZ/Pxz2skkSZJUwVnapNIKAQ47DIqLoVevZImANm1g1Ki0k0mSJKkCs7RJq6tuXXjkkWTk7fvvYccd4ayzYMGCtJNJkiSpArK0SWtq//2Td9v69oUbb4TmzaGoKO1UkiRJqmAsbdLa2GADuP32ZJZJgM6d4YQT4Icf0s0lSZKkCsPSJmVD584wfnzymOTdd0OTJvDCC2mnkiRJUgVgaZOyZb314Prr4b33YOONk8cnDz8cvvkm7WSSJEkqxyxtUra1a5csxn3ppTB0KBQWwj//CTGmnUySJEnlkKVNyoV11oGLL4aPPoJtt01G3Lp3h5kz004mSZKkcsbSJuVSkybwzjtw000wbFgy6nbHHVBSknYySZIklROWNinXqlSB00+HiROTRydPPBG6dGHdL75IO5kkSZLKAUubVFa22QbeeCOZXfKjj2jbpw/ccAMsWZJ2MkmSJOUxS5tUlkKAY4+F4mK+b9cOzj4bdtoJJkxIO5kkSZLylKVNSsPmmzPx8svhscdgxgxo3RouuQQWLUo7mSRJkvKMpU1KSwhwyCEweTIceihcdhm0aQPvv592MkmSJOURS5uUtjp14KGH4MUX4YcfoGNHOOMMmD8/7WSSJEnKA6ssbSGEGiGED0II40IIk0IIl2a23x9C+DSEMDbz1TKzPYQQBoYQPg4hjA8htM71LyFVCPvsA5MmJbNL3nwzNGuWLBOQZVNmzeWVibOYMmtu1q8tSZKk7CvNSNsiYI8YYwugJdAthLBjZt/ZMcaWma+xmW17A3/MfB0PDM52aKnCWn99uO02ePttqFoVunaFvn1hzpysXH7AG1PpMWgEZz0xjh6DRjBw2NSsXFeSJEm5s8rSFhPzMj9Wy3zF3zmlB/Bg5rz3gA1DCJutfVSpEtltNxg3Ds45B+67L1mU+9ln1+qSU2bNZfDb01m4uIR5i5awcHEJtxVNd8RNkiQpz4UYf69/ZQ4KoQowBtgOGBRjPCeEcD/QkWQkbhhwboxxUQjhBeCaGOOIzLnDgHNijKOXu+bxJCNx1KtXr82QIUOy91tlybx586hVq1baMVRBlfb+qjVlCjtcfz21pk/nv507M+3UU1m80Uar/Xk/LlzCzO8WsHSZ/85XCYEGG6/H+jWqrvb1lP/8M0y55P2lXPL+Ui7l6/3VuXPnMTHGtivaV6rS9uvBIWwIPA2cCswGZgHrAHcC02OMl5W2tC2rbdu2cfTole5OTVFREZ06dUo7hiqo1bq/Fi+G665LZpisVQsGDIAjjkhmoCylKbPm0mPQCBYuLvl1W41qBTx78i40ql97NdOrPPDPMOWS95dyyftLuZSv91cIYaWlbbVmj4wxzgHeArrFGL/KPAK5CLgPaJ857Atgi2VOa5DZJmlNVasGF1wAY8dCo0Zw1FGw777wn/+U+hKN6tfmpN23pUa1AmpVr0qNagX067SthU2SJCnPrfKZqBBCXWBxjHFOCGFd4E/AtSGEzWKMX4UQAtATmJg55TnglBDCEKAD8EOM8asc5Zcql8aN4V//gkGD4LzzoEmTZATuhBOgYNX/H0z/rtvTrelmfPrtfBpuUtPCJkmSVA6UZqRtM+CtEMJ4YBTweozxBeCREMIEYAKwCXBF5viXgE+Aj4G7gH5ZTy1VZlWqwGmnwcSJsOOO0K8fdOoEU0s3E2Sj+rXp1rS+hU2SJKmcWOVIW4xxPNBqBdv3WMnxETh57aNJ+l0NG8Jrr8H99yeLcbdoAZdemnxf1YlFJEmSKorVeqdNUp4JAf7yFyguhr33TpYI6NAhWS5AkiRJFYKlTaoINtsMnnoKhg6FL76Atm3hootg0aK0k0mSJGktWdqkiuSgg5JRtyOOgCuugJYt4d13004lSZKktWBpkyqajTdO3nN75RVYsAB22QX694d589JOJkmSpDVgaZMqqr32SmaYPPlkGDgQmjWD119PO5UkSZJWk6VNqshq14Z//CNZ2616ddhzT+jTB77/Pu1kkiRJKiVLm1QZ7LILjB0L554LDz4IhYXw9NNpp5IkSVIpWNqkyqJGDbj6ahg1CurXhwMPhF69YNastJNJkiTpd1japMqmVSv44AO46ip4/vlk1O2BByDGtJNJkiRpBSxtUmVUrRqcd17yyGRhIfTunSzO/dlnaSeTJEnScixtUmW2ww4wfHgyWcmIEdCkCdx6K5SUpJ1MkiRJGZY2qbIrKIBTToFJk5IJS049FXbbDaZMSTuZJEmSsLRJ+sVWW8HLLyfvtxUXQ4sWycQlixennUySJKlSs7RJ+n8hwNFHw+TJsP/+cP750L49fPRR2skkSZIqLUubpP9Vrx488QQ8+WSyJEC7dsnEJQsXpp1MkiSp0rG0SVq5Aw9MHpU8+mi45prkkckRI9JOJUmSVKlY2iT9vo02gnvvhddeg59/hl13TSYumTs37WSSJEmVgqVNUun86U8wYQKcdhrcdhs0bQqvvpp2KkmSpArP0iap9GrVggEDkkck11sPunWDY46B2bPTTiZJklRhWdokrb6ddoKxY+HCC+HRR6GwEIYOhRjTTiZJklThWNokrZnq1eHyy2H0aNhiC+jVCw46CL76Ku1kkiRJFYqlTdLaadEC3nsPrr02WZy7sBDuu89RN7mSo6EAACAASURBVEmSpCyxtElae1Wrwt/+BuPGQbNm0KcP7LknfPpp2skkSZLKPUubpOzZfnsoKkpml3z//WSGyYEDYenStJNJkiSVW5Y2SdlVUAAnnQSTJsHuu0P//snabsXFaSeTJEkqlyxtknJjiy3gxRfh4Ydh6lRo1QquuAIWL047mSRJUrliaZOUOyHAEUcko2wHHAAXXQRt28KYMWknkyRJKjcsbZJyb9NNYcgQeOYZ+OYbaN8ezjkHfvop7WSSJEl5z9Imqez06JGMuvXpA9ddlywXMHx42qkkSZLymqVNUtnacEO46y54441kVsndd4d+/eDHH9NOJkmSlJcsbZLS0aULjB8PZ5wBd9wBTZrASy+lnUqSJCnvWNokpadmTbjxRnj3XVh/fdh3XzjySPj227STSZIk5Q1Lm6T0degAH34Il1wCjz0GhYXJP2NMO5kkSVLqLG2S8kP16vD3vyflbaut4NBDoWdP+PLLtJNJkiSlytImKb80awYjR8INN8Drryejbnff7aibJEmqtCxtkvJP1apw5pnJRCWtWkHfvtC1K0yfnnYySZKkMmdpk5S/ttsOhg1LZpccPToZhbvppmSpAEmSpErC0iYpvxUUwPHHw6RJyTIBZ54JO+0EEyemnUySJKlMWNoklQ8NGsBzz8Gjj8Inn0Dr1nDppfDzz2knkyRJyilLm6TyIwQ47DAoLoZevZLZJtu0gVGj0k4mSZKUM5Y2SeVP3brwyCPw/PPw/few445w1lmwYEHaySRJkrLO0iap/Npvv+Rdt7594cYboXlzeOuttFNJkiRllaVNUvm2wQZw++3/X9b22ANOOAF++CHdXJIkSVliaZNUMXTqlKzrdtZZyWLchYXJ45OSJEnlnKVNUsWx3npw/fXw3ntQpw507w6HHw7ffJN2MkmSpDVmaZNU8bRrlyzGfdllMHQoNG6cLBUQY9rJJEmSVpulTVLFtM46cNFF8NFHsN12cMQRycjbzJlpJ5MkSVotljZJFVuTJvDOO3DzzfDmm8m7bnfcASUlaSeTJEkqFUubpIqvShX4619hwgRo3x5OPDGZZXLatLSTSZIkrZKlTVLlsc028PrryeySY8cm67rdcAMsWZJ2MkmSpJWytEmqXEKAY4+F4mLYay84+2zo2DFZLiDLpsyayysTZzFl1tysX1uSJFUeljZJldPmm8PTT8Njj8Fnn0GbNnDJJbBoUVYuP+CNqfQYNIKznhhHj0EjGDhsalauK0mSKh9Lm6TKKwQ45BCYPBkOOyxZIqB162Sdt7UwZdZcBr89nYWLS5i3aAkLF5dwW9F0R9wkSdIasbRJUp068OCD8NJLMHcu7LQTnH46zJ+/Rpf79Nv5VC347R+vVQsK+PTbNbueJEmq3CxtkvSLvfeGiRPhpJPgllugWTMYNmy1L9Nwk5osWW5JgSUlJTTcpGa2kkqSpErE0iZJy1p/fRg0CN5+G6pWha5d4bjjYM6cUl+iUf3anLT7ttSoVkCt6lWpUa2Afp22pVH92jkMLkmSKqqqaQeQpLy0224wbhxcemmyLMBLL8HgwdCjR6lO7991e7o13YxPv51Pw01qWtgkSdIac6RNklZm3XXhmmvg/fdh002hZ0/485/h669LdXqj+rXp1rS+hU2SJK0VS5skrUqbNjBqFFx5JTzzDBQWwkMPQYxpJ5MkSZWApU2SSqNaNTj/fBg7Fho1gqOPhn33hf/8J+1kkiSpgrO0SdLqaNwY/vUvGDgQhg+HJk3gtttgudkiJUmSssXSJkmrq0oVOPXUZHmAjh3h5JOhUyeYOjXtZJIkqQKytEnSmtp6a3j1VbjvPpgwAZo3h2uvhSVL0k4mSZIqEEubJK2NEKB3b5g8OXnH7dxzoUOHZLkASZKkLLC0SVI21K8PTz4JQ4fCF19A27Zw4YWwcGHaySRJUjm3ytIWQqgRQvgghDAuhDAphHBpZnvDEML7IYSPQwiPhRDWyWyvnvn548z+rXP7K0hSHjnoICguhiOOSJYIaNUK3n037VSSJKkcK81I2yJgjxhjC6Al0C2EsCNwLXBzjHE74Hvg2MzxxwLfZ7bfnDlOkiqPjTeG+++HV16BBQtgl13gtNNg3ry0k0mSpHJolaUtJn75m0a1zFcE9gCGZrY/APTMfN8j8zOZ/V1CCCFriSWpvNhrr2SGyZNPhltvhaZN4bXX0k4lSZLKmRBjXPVBIVQBxgDbAYOA64H3MqNphBC2AF6OMTYNIUwEusUYZ2b2TQc6xBi/Xe6axwPHA9SrV6/NkCFDsvdbZcm8efOoVatW2jFUQXl/VS7rT5jADtdfz3qff85X3boxvV8/ltSundPP9B5TLnl/KZe8v5RL+Xp/de7ceUyMse2K9lUtzQVijEuBliGEDYGngR3WNlSM8U7gToC2bdvGTp06re0ls66oqIh8zKWKwfurkunUCfr2hcsvZ7Nrr2WzsWNh0CA48MCcfaT3mHLJ+0u55P2lXCqP99dqzR4ZY5wDvAV0BDYMIfxS+hoAX2S+/wLYAiCzfwNgdlbSSlJ5VqNGMjnJ6NGw2WbJpCUHHwyzZqWdTJIk5bHSzB5ZNzPCRghhXeBPwGSS8nZw5rBjgGcz3z+X+ZnM/jdjaZ7BlKTKomVLeP99uPpqeOEFKCxMJi7xj0pJkrQCpRlp2wx4K4QwHhgFvB5jfAE4BzgjhPAxUAe4J3P8PUCdzPYzgHOzH1uSyrlq1ZKFuMeNgyZN4C9/gW7dYMaMtJNJkqQ8s8p32mKM44FWK9j+CdB+BdsXAr2ykk6SKrpGjeDtt2Hw4KTENW2ajMCdfDIUrNYT7JIkqYLybwSSlLaCgqSkTZwIu+6arOm2227w73+nnUySJOUBS5sk5YuttoKXXoIHH4TJk6FFC7jqKli8OO1kkiQpRZY2SconIcBRR0FxMfToARdcAO3bw4cfpp1MkiSlxNImSfmoXj14/HF46qlkSYD27eG88+Cnn9JOJkmSypilTZLy2QEHJKNuxxwD11yTLBcwYkTaqSRJUhmytElSvttoI7jnHnj9dfj552SyklNOgblz004mSZLKgKVNksqLrl1hwgT461/httuS5QFeeSXtVJIkKccsbZJUntSqBTffDO+8AzVrwt57J49Ozp6ddjJJkpQjljZJKo86doSPPoKLLoJHH4XCQnjiCYgx7WSSJCnLLG2SVF5Vrw6XXQajR8MWW8Ahh8CBB8JXX6WdTJIkZZGlTZLKuxYt4L334LrrknfcGjeGe+911E2SpArC0iZJFUHVqnD22TBuXFLijj2W5mefDZ9+mnYySZK0lixtklSRbL89vPUWDB7M+pMnJzNMDhgAS5emnUySJK0hS5skVTQFBXDiiYy67z7o1ClZImCXXZJFuiVJUrljaZOkCmrRppvCCy/Aww/DtGnQqhVcfnmyQLckSSo3LG2SVJGFAEcckYyyHXggXHwxtGuXzDgpSZLKBUubJFUGm24K//wnPPssfPstdOgAf/sb/PRT2skkSdIqWNokqTLp3h0mTYJjj4Xrr4fmzeHtt9NOJUmSfoelTZIqmw03hDvvhGHDoKQkmazkpJPgxx/TTiZJklbA0iZJldUee8CECXDGGUmJa9IEXnwx7VSSJGk5ljZJqszWWw9uvBHefRc22AD22w+OPDJ5702SJOUFS5sk5ciUWXN5ZeIspsyam3aUVevQAT78EC65BB5/HBo3hiFDIMa0k0mSVOlZ2iQpBwa8MZUeg0Zw1hPj6DFoBAOHTU070qqtsw78/e8wZgw0bAiHHQY9e8IXX6SdTJKkSs3SJklZNmXWXAa/PZ2Fi0uYt2gJCxeXcFvR9PIx4gbQrBmMHJk8Nvn661BYCHfd5aibJEkpsbRJUpZ9+u18qhb89o/XqgUFfPrt/JQSrYEqVZIJSiZMgDZt4PjjoUsXmD497WSSJFU6ljZJyrKGm9RkSUnJb7YtKSmh4SY1U0q0FrbdNlka4M47k8cmmzWDm26CpUvTTiZJUqVhaZOkLGtUvzYn7b4tNaoVUKt6VWpUK6Bfp21pVL922tHWTAjQty8UF0PXrnDmmbDTTjBxYtrJJEmqFKqmHUCSKqL+XbenW9PN+PTb+TTcpGb5LWzL+sMf4Nln4bHH4NRToXVruOACOO+8ZBITSZKUE460SVKONKpfm25N61eMwvaLEODQQ2HyZOjVK5ltsk0b+OCDtJNJklRhWdokSatvk03gkUfg+efh+++hY0c46yxYsCDtZJIkVTiWNknSmttvv+Rdt+OPT5YIaNYM3nor7VSSJFUoljZJ0tpZf30YPBiKiqCgAPbYA044AX74Ie1kkiRVCJY2SVJ27L47jBsHZ58Nd9+dLMr9/PNpp5IkqdyztEmSsme99eC66+D996FOHejeHQ47DL75Ju1kkiSVW5Y2SVL2tW0Lo0fDZZfBk09C48bw6KMQY9rJJEkqdyxtkqTcWGcduOgi+Ogj+OMf4YgjYP/94fPP004mSVK5YmmTJOVWkyYwYgTccksys2STJnD77VBSknYySZLKBUubJCn3qlSB/v1hwgRo3x5OOimZZXLatLSTSZKU9yxtkqSys8028PrrcM89MHYsNG8O118PS5aknUySpLxlaZMkla0QoE+fZFHuvfaCv/0NOnaE8ePTTiZJUl6ytEmS0rH55vD00/D44/Cf/0CbNnDxxbBoUdrJJEnKK5Y2SVJ6QoBevZJRt8MOg8svh1atYOTItJNJkpQ3LG2SpPTVqQMPPggvvQTz5sHOO8Nf/wrz56edTJKk1FnaJEn5Y++9YdIk6NcPBgyApk3hjTfSTiVJUqosbZKk/FK7Ntx6KwwfDtWqwZ/+BMceC3PmpJ1MkqRUWNokSflp111h3Dg491x44AEoLIRnnkk7lSRJZc7SJknKX+uuC1dfDR98APXqwQEHwCGHwNdfp51MkqQyY2mTJOW/1q2T4nbllfDss9C4cTJxSYxpJ5MkKecsbZKk8qFaNTj//OSRycaN4ZhjYJ99kjXeJEmqwCxtkqTyZYcd4F//goEDk382aQKDBkFJSdrJJEnKCUubJKn8KSiAU0+FiROhY0c45RTYfXeYMiXtZJIkZZ2lTZJUfm29Nbz6Ktx3X1LgWrSAa66BxYvTTiZJUtZY2iRJ5VsI0Ls3TJ4M++0H550HHTrARx+lnUySpKywtEmSKob69WHo0OTryy+hXTu44AJYuDDtZJIkrRVLmySpYjnoICguhqOOgquugpYt4Z130k4lSdIas7RJkiqejTdO3nN79dVkpG3XXeG002DevLSTSZK02ixtkqSKa889kwlKTjkFbr0VmjZNipwkSeWIpU2SVLHVqvX/a7qtuy5065ZMXPLdd2knkySpVCxtkqTKYeedkxklL7gAHn4YCgvhySfTTiVJ0ipZ2iRJlUeNGnDFFTB6NGy+ORx8cDJxyVdfpZ1MkqSVsrRJkiqfli3hgw+ShbhffDEZdbv/fogx7WSSJP0PS5skqXKqWhXOOQfGjUsmKPnLX2CvvWDGjLSTSZL0G5Y2SVLl1qgRvP02DBoEI0cmBW7gQFi6NO1kkiQBljZJkqCgAPr1g0mTkjXd+veH3XaDyZPTTiZJkqVNkqRfbbklvPQSPPgg/PvfybtvV14JixennUySVImtsrSFELYIIbwVQigOIUwKIfTPbP97COGLEMLYzNc+y5xzXgjh4xDClBDCXrn8BSRJyqoQ4KijoLgYevaECy+Edu3gww/TTiZJqqRKM9K2BDgzxlgI7AicHEIozOy7OcbYMvP1EkBm36FAE6AbcFsIoUoOskuSlDv16sFjj8HTT8PXX0P79nDuufDTT2knkyRVMqssbTHGr2KMH2a+nwtMBv7wO6f0AIbEGBfFGD8FPgbaZyOsJEllrmfPZNStd2+49lpo0QKGD087lSSpEglxNdakCSFsDQwHmgJnAL2BH4HRJKNx34cQbgXeizE+nDnnHuDlGOPQ5a51PHA8QL169doMGTJkbX+XrJs3bx61atVKO4YqKO8v5Zr3WPZtNGYM2994I+t+9RVf9OjBJ337srRmzbRjpcL7S7nk/aVcytf7q3PnzmNijG1XtK/UpS2EUAt4G7gyxvhUCKEe8C0QgcuBzWKMfUpb2pbVtm3bOHr06NX6pcpCUVERnTp1SjuGKijvL+Wa91iOzJ+fvOc2YAA0aAB33AF77512qjLn/aVc8v5SLuXr/RVCWGlpK9XskSGEasCTwCMxxqcAYoxfxxiXxhhLgLv4/0cgvwC2WOb0BpltkiSVfzVrws03w7vvQu3asM8+cPTRMHt22skkSRVUaWaPDMA9wOQY403LbN9smcMOACZmvn8OODSEUD2E0BD4I/BB9iJLkpQHdtwxmVHyoovgn/+Exo3h8cdhNV47kCSpNEoz0rYzcBSwx3LT+18XQpgQQhgPdAZOB4gxTgIeB4qBV4CTY4xLcxNfkqQUVa8Ol10GY8Yka7z9+c9wwAHw5ZdpJ5MkVSBVV3VAjHEEEFaw66XfOedK4Mq1yCVJUvnRvDm8917y2OTFF0NhIdx4I/Tpk6z7JknSWijVO22SJGkVqlaFs8+G8eOhZUs47jjo2hU++STtZJKkcs7SJklSNv3xj/Dmm3D77TBqFDRrBrfcAkt9U0CStGYsbZIkZVtBAZxwQrIod+fOcPrpsPPOMGlS2skkSeWQpU2SpFxp0ACefx4eeQQ+/hhatUomLvn557STSZLKEUubJEm5FAIcfjhMngwHHQSXXAJt2yaPTkqSVAqWNkmSykLdusl6bs8+myzEveOOycQlCxaknUySlOcsbZIklaXu3ZN33Y47Dm64AVq0gKKitFNJkvKYpU2SpLK2wQZwxx3JLJMxJpOVnHgi/PBD2skkSXnI0iZJUlo6d07WdTvzTLjrLmjSBF54Ie1UkqQ8Y2mTJClN662XPCY5ciRstBHsv38ycck336SdTJKUJyxtkiTlg/btYcwY+PvfYehQKCxMJi6JMe1kkqSUWdokScoX66yTLAnw4YewzTbJiFv37jBzZtrJJEkpsrRJkpRvmjaFd9+Fm26CYcOSd93uvBNKStJOJklKgaVNkqR8VKUKnH46TJgAbdrACSdAly7w8cdpJ5MklTFLmyRJ+WzbbZPRtrvuSh6bbNYsmbhkyZK0k0mSyoilTZKkfBdCshh3cTHsuSecfTbstFMyCidJqvAsbZIklRd/+AM88wwMGQIzZkDr1snEJYsWpZ1MkpRDljZJksqTEODPf05G3Q49FC67LHnn7f33004mScoRS5skSeXRJpvAQw/BCy/ADz9Ax45wxhkwf37aySRJWWZpkySpPNt3X5g0CU48EW6+OZmoZNiwtFNJkrLI0iZJUnm3/vpw221QVJQsFdC1K/TtC3PmpJ1MkpQFljZJkiqK3XeH8ePhb3+De++FwkJ49tm0U0mS1pKlTZKkimTddeHaa5OJSerWhZ49kwlL/vvftJNJktaQpU2SpIqobVsYPRouvxyefhoaN4aHH4YY004mSVpNljZJkiqqatXgwgvho49g++3hqKNgv/3g88/TTiZJWg2WNkmSKrrCQhgxAm65JZmspEkTGDwYSkrSTiZJKgVLmyRJlUGVKtC/P0ycCB06QL9+0KkTTJ2adjJJ0ipY2iRJqkwaNoTXXoN77klmmmzRAq67DpYsSTuZJGklLG2SJFU2IUCfPlBcDN26wTnnJKNv48alnUyStAKWNkmSKqvNN4ennoInnoCZM5MZJy+6CBYtSjuZJGkZljZJkiqzEODgg5NRt8MPhyuugFatYOTItJNJkjIsbZIkCerUgQcegJdfhvnzYeed4a9/hXnz0k4mSZWepU2SJP2/bt2SGSb79YMBA6BZM3j99bRTSVKlZmmTJEm/Vbs23HorDB8O66wDe+6ZTFzy/fdpJ5OkSsnSJkmSVmzXXZMZJc87Dx58MFmk++mn004lSZWOpU2SJK1cjRpw1VXwwQdQvz4ceCD06sU6332XdjJJqjQsbZIkadVat06K21VXwfPP065372T0Lca0k0lShWdpkyRJpVOtWvKo5NixLNhySzjmGNh7b/jss7STSVKFZmmTJEmrZ4cd+GjgQPjHP2DECGjaFAYNgpKStJNJUoVkaZMkSauvoABOOSVZHmCnnZLvd9sNpkxJO5kkVTiWNkmStOa23hpeeQXuvx+Ki6FFC7j6ali8OO1kklRhWNokSdLaCSF5v634/9q78/goq3uP458TgkYBC1QFrijulLAL4oYYLqioV8GFinUB94W6VSturVqX4lK4oOKCUpWWi1XrUrWKYBEpLiyCQCgoLq0WFKpVQFFCzv3jGW8plyVAJs/M5PN+vXgleSYZvuh5jXw9z/xOORx9NFx9Ney3H7z1VtrJJKkgWNokSVL1aNoUHnsMnngC/v532HffpMCtXJl2MknKa5Y2SZJUvY47DubNg9NOS26V7NAB/vzntFNJUt6ytEmSpOrXqBGMGgUvvpjstB18MFx4ISxblnYySco7ljZJkpQ9hx2WTJi88MLkWIA2bZIiJ0mqMkubJEnKrvr1Ydiw5Ey3bbeFXr2SwSWffZZ2MknKC5Y2SZJUMw48MJkoec01MGYMtGoFjz+edipJynmWNkmSVHNKSuCmm2DqVGjeHPr2heOPh0WL0k4mSTnL0iZJkmpehw7wxhsweDA89xyUlsKvfw0xpp1MknKOpU2SJKWjuBgGDYK334a2beGMM+Dww+GDD9JOJkk5xdImSZLStffeMHFiMl3ytdeSCZPDh8Pq1Wknk6ScYGmTJEnpKyqCCy6AuXOhWze4+OLkbLd589JOJkmps7RJkqTcscsuyXvcRo+G+fOT977dfDOsWpV2MklKjaVNkiTllhDglFOSXbY+feDaa6FzZ5g+Pe1kkpQKS5skScpNO+4Ijz4KTz4JS5bAfvvBlVfC11+nnUySapSlTZIk5bY+faC8HAYMgFtvhfbtYdKktFNJUo2xtEmSpNzXsCE88ACMHw8VFXDIIcngki+/TDuZJGWdpU2SJOWPHj1g9my49FK4997keIDnn087lSRllaVNkiTll3r1YMgQmDIFGjSAo46CU0+FpUvTTiZJWWFpkyRJ+Wn//WHGDPj5z2HsWCgthd/9DmJMO5kkVStLmyRJyl9bbw033JAcB9CiBZx4Ihx7LPz972knk6RqY2mTJEn5r107eO01uP12ePHFZNftwQfddZNUECxtkiSpMBQXw+WXJ4NKOnSAs86Cnj3hvffSTiZJW8TSJkmSCsuee8LLL8N998HUqdC2LQwdCqtXp51MkjbLRktbCGHnEMKfQgjlIYS5IYSLM9cbhxBeCiG8k/nYKHM9hBCGhxDeDSG8HULYJ9t/CEmSVHPmL17GlysrmL94WdpR1q+oCM45JzmUu3t3+MlP4KCDYO7ctJNJ0iaryk5bBXBZjLEU2B8YGEIoBa4EJsQY9wImZL4GOALYK/PrHOCeak8tSZJSMWz8AnrfPZmPPvuK3ndPZviEBWlH2rDmzeEPf4AxY2DhQujYEX7xC/j227STSVKVbbS0xRgXxRhnZD5fBswDdgJ6Aw9nvu1hoE/m897AIzHxOtAwhNCs2pNLkqQaNX/xMu55ZSErV1WyOkZWrqpkxMSFub3jBhACnHRSsut2wglw3XXQuXNy62SOm794GS/MWZz7/4wlZVWImzBVKYSwKzAJaAP8NcbYMHM9AJ/HGBuGEJ4FBscYJ2cemwAMijFOW+u5ziHZiaNJkyadxo4du+V/mmq2fPly6tevn3YMFSjXl7LNNabq9uXKCj767CtWx0iTbeCTr6FOCDRvvC3blRSnHa/Kvj9lCnsPHcpWn33G3/r25YMBA6gsKUk71v/z6bJvWLLsGwIQgR0abM2ODbZOO1aN8PVL2ZSr66t79+7TY4yd1/VYlV9hQwj1gSeAS2KMXyY9LRFjjCGETZqpG2O8H7gfoHPnzrGsrGxTfrxGTJw4kVzMpcLg+lK2ucZU3eYvXsYVd09m5apKLmtbwa9mF1NSt4inB+5Hy6YN0o5XdWVlMHAgDBrELvfdxy7Tp8PIkcn1HDF/8TLOu3syK1fV+b9rJXUreXpgp/z6Z72ZfP1SNuXj+qrS9MgQQl2SwvbbGOPvM5c/+e62x8zHTzPXPwZ2XuPHm2euSZKkPNayaQPOP2QPSuoWUScESuoWcUHZHvlZIr73Pbj33mTKZIzJsJLzzoMvvkg7GQDvL11BcdG//zWtuKiI95euSCmRpDRVZXpkAB4E5sUYh6zx0DNA/8zn/YGn17h+WmaK5P7AFzHGRdWYWZIkpeTinnvz9MCuNG+8LU8P7MpFPfZOO9KW6d4d3n47Od9t5Eho3RqefTbtVOy2fT0qKiv/7VpFZSW7bV8vpUSS0lSVnbaDgFOB/wwhzMz8OhIYDBwaQngH6Jn5GuB54D3gXWAkcEH1x5YkSWlp2bQB25UU5+cO27psuy3cfju89ho0agRHHw0/+hEsWZJapDV3NetvXZzfu5qStthG39OWGSgS1vNwj3V8fwQGbmEuSZKkmtWlC0yfDoMHw003wUsvwfDh0K9fMoGyhl3cc296tWnG+0tXsNv29SxsUi1Wpfe0SZIk1QpbbQU//znMmAG7757suB1zDHz0USpxWjZtQK82TS1sUi1naZMkSVpbmzYwZQoMGQITJiTvdbv/fljrfWaSVBMsbZIkSetSpw5ceinMmZMcxn3uudCjB7z7btrJJNUyljZJkqQN2X13GD8+mS45Ywa0bQt33AEVFWknk1RLWNokSZI2JgQ46ywoL4fDDoOf/hQOPBBmz047maRawNImSZJUVTvtBE89BWPHwgcfwD77wHXXwTffpJ1MUgGztEmSJG2KEODEE5Ndt3794Be/gE6d4I030k4mqUBZ2iRJkjbH9tvD6NHw3HPwxRdwwAHw9sxn0wAAGnlJREFUk5/AihVpJ5NUYCxtkiRJW+LII2HuXDjvPBg6FNq1g5dfTjuVpAJiaZMkSdpS220HI0bAK68kRwX06AFnnw3//GfaySQVAEubJElSdenWDWbNgiuugFGjoLQUnn467VSS8pylTZIkqTptsw3cemsymGSHHaBPn2Rgyaefpp1MUp6ytEmSJGVD584wbRrceCM8+SS0agW/+Q3EmHYySXnG0iZJkpQtdevCtdfCW29By5Zw6qnwX/8Ff/tb2skk5RFLmyRJUraVlsKrr8KwYTBxIrRuDffcA5WVaSeTlAcsbZIkSTWhTh246CKYMwf22w8uuADKymDBgrSTScpxljZJkqSatNtuMG5cMl1y9mxo3x5uuw0qKtJOJilHWdokSZJqWghw+ulQXg5HHAGDBiW7b7NmpZ1MUg6ytEmSJKWlWTN44gl47DH46KNk4uTPfgbffJN2Mkk5xNImSZKUphDghBNg3jw4+WS46Sbo2BFeey3tZJJyhKVNkiQpFzRuDA89BC+8ACtWwEEHwSWXwPLlaSeTlDJLmyRJUi45/PBkwuTAgckRAW3bwksvpZ1KUoosbZIkSbmmQQO4887kbLett4bDDoMzzoDPP087maQUWNokSZJyVdeuMHMmXHUVPPJIckj3k0+mnUpSDbO0SZIk5bKSErjlFpg6FZo2heOOg759YfHitJNJqiGWNkmSpHzQsSO8+WZS4P7wh2TX7eGHIca0k0nKMkubJElSvqhbN7lVcubMpLQNGJAczv3hh2knk5RFljZJkqR884MfwKRJybCSyZOhdWu46y6orEw7maQssLRJkiTlo6Ii+PGPYe7cZGDJhRdCt24wf37aySRVM0ubJElSjpq/eBkvzFnM/MXL1v9NLVrAH/+YHMxdXg7t28MvfwmrVtVYTknZZWmTJEnKQcPGL6D33ZO5/LFZ9L57MsMnLFj/N4cA/fsnpe3oo+Hqq2G//eCtt2ousKSssbRJkiTlmPmLl3HPKwtZuaqS5d9UsHJVJSMmLtzwjhskRwI89hg88QQsWgT77psUuJUraya4pKywtEmSJOWY95euoLjo3/+aVlxUxPtLV1TtCY47Ltl1O+205FbJ9u2TgSWS8pKlTZIkKcfstn09KtaaBFlRWclu29er+pM0agSjRsG4cfDtt3DwwcngkmUb2a2TlHMsbZIkSTmmZdMGnH/IHpTULaL+1sWU1C3igrI9aNm0waY/2aGHwuzZcNFFMGIEtGkDL75Y/aElZU1x2gEkSZL0/13cc296tWnG+0tXsNv29TavsH2nfn0YNgxOPBHOPBN69UpunRw6FBo3rr7QkrLCnTZJkqQc1bJpA3q1abplhW1NBx6YTJS89loYMwZatYLHH6+e55aUNZY2SZKk2qSkBG68EaZNg513hr59k8ElixalnUzSeljaJEmSaqP27eH11+HWW5PDuUtL4de/hhjTTiZpLZY2SZKk2qq4GK64AmbNgrZt4Ywz4LDD4P33004maQ2WNkmSpNpu771h4sRkuuTrrycTJocPh9Wr004mCUubJEmSAIqK4PzzYe5cOOQQuPji5Gy3efPSTibVepY2SZIk/csuu8Bzz8Ho0bBgAXToADffDKtWpZ1MqrUsbZIkSfp3IcApp0B5ORx7bHJEQOfOMH162smkWsnSJkmSpHXbcUcYOxaeegqWLIEuXWDQIPj667STSbWKpU2SJEkb1rt3sut2xhlw223JcQGTJqWdSqo1LG2SJEnauIYNYeRIGD8eKiqSYSUXXABffpl2MqngWdokSZJUdT16wOzZcOmlcO+9yfEAzz+fdiqpoFnaJEmStGnq1YMhQ2DKFGjQAI46Ck49FZYuTTuZVJAsbZIkSdo8++8PM2bAddclA0tKS+HRRyHGtJNJBcXSJkmSpM239dZw/fVJedt1V+jXD/r0gb//Pe1kUsGwtEmSJGnLtW2b3C55xx0wblyy6/bAA+66SdXA0iZJkqTqUVwMl12WDCrp0AHOPht69oT33ks7mZTXLG2SJEmqXnvuCS+/DPfdB1OnJhMmhw6F1avTTiblJUubJEmSql9REZxzTnIod48e8JOfwEEHwdy5aSeT8o6lTZIkSdnTvDk88wyMGQMLF0LHjvCLX8C336adTMobljZJkiRlVwhw0knJrlvfvskRAZ06JbdOStooS5skSZJqxg47wG9/m+y8ff55cs7b5ZfDV1+lnUzKaZY2SZIk1ayjj07e23b22fCrX0G7djBxYtqppJxlaZMkSVLN+9734N57kymTAN27w7nnwhdfpJtLykGWNkmSJKWne3d4++3kNskHHoDWrfn+a6+lnUrKKZY2SZIkpWvbbeH22+H116FxY9pefTX86EewZEnayaScYGmTJElSbth3X5g2jfcHDIDHH4dWrZKjAmJMO5mUKkubJEmScsdWW/Fh//7w1luw555w8slwzDHw0UdpJ5NSY2mTJElS7mndGv78ZxgyBCZMgNJSuO8+qKxMO5lU4yxtkiRJyk116sCll8KcOcmtk+edBz16wLvvpp1MqlEbLW0hhFEhhE9DCHPWuHZ9COHjEMLMzK8j13jsqhDCuyGE+SGEw7MVXJIkSbXE7rvD+PEwciTMmAFt28Idd0BFRbX9FvMXL+OFOYuZv3hZtT2nVF2qstP2ENBrHdeHxhg7ZH49DxBCKAX6Aa0zPzMihFCnusJKkiSplgoBzjoLysvhsMPgpz+FAw5IjgvYQsPGL6D33ZO5/LFZ9L57MsMnLKiGwFL12WhpizFOAj6r4vP1BsbGGL+JMb4PvAt02YJ8kiRJ0r/stBM89RQ8+ih8+CF06gTXXQfffLNZTzd/8TLueWUhK1dVsvybClauqmTExIXuuCmnhFiFEaohhF2BZ2OMbTJfXw8MAL4EpgGXxRg/DyHcBbweY/xN5vseBP4YY3x8Hc95DnAOQJMmTTqNHTu2Gv441Wv58uXUr18/7RgqUK4vZZtrTNnk+lI2VXV9FX/xBXvefTdNX3qJFS1aMP+KK/iytHSTfq8vV1bw0WdfsXqNvxPXCYHmjbdlu5LiTc6u3Jerr1/du3efHmPsvK7HNre0NQGWAhG4EWgWYzxjU0rbmjp37hynTZtW9T9RDZk4cSJlZWVpx1CBcn0p21xjyibXl7Jpk9fX88/DuefCxx/DJZfAjTdCvXpV+tH5i5fR++7JrFz1r6mUJXWLeHpgV1o2bbCJyZUPcvX1K4Sw3tK2WdMjY4yfxBhXxxgrgZH86xbIj4Gd1/jW5plrkiRJUnYceSTMnZtMlxw6NBlUMmFClX60ZdMGnH/IHpTULaL+1sWU1C3igrI9LGzKKZu15xtCaBZjXJT58ljgu8mSzwBjQghDgP8A9gLe3OKUkiRJ0oZstx2MGAH9+iUDS3r2TD7efjs0bLjBH7245970atOM95euYLft61nYlHM2WtpCCP8DlAHbhxA+Aq4DykIIHUhuj/wAOBcgxjg3hPA7oByoAAbGGFdnJ7okSZK0lm7dYNYsuOGG5FiA556De+6B3r03+GMtmzawrClnVWV65EkxxmYxxroxxuYxxgdjjKfGGNvGGNvFGI9ZY9eNGOPNMcY9YowtY4x/zG58SZIkaS3bbAODB8Mbb8COO0KfPnDiifDJJ2knkzbLZr2nTZIkScp5nTrB1Klw003JMQGlpfCb30AVBvFJucTSJkmSpMJVty5ccw3MnAktW8Kpp8JRR8Ff/5p2MqnKLG2SJEkqfK1awauvwrBh8Mor0Lp18l63ysqN/6yUMkubJEmSaoc6deCii2DOHNh/f7jgAigrgwUL0k4mbZClTZIkSbXLbrvBuHEwahTMng3t2sGtt0JFRdrJpHWytEmSJKn2CQFOPx3Ky5PDua+8EvbbLzkuQMoxljZJkiTVXs2awe9/D48/Dh9/DJ07w7XXwsqVaSeT/o+lTZIkSTr++GTX7eST4eaboWNHmDIl7VQSYGmTJEmSEo0bw0MPwQsvwFdfQdeucPHFsHx52slUy1naJEmSpDUdfngyYXLgQBg+HNq0SQaXSCmxtEmSJElra9AA7rwzOdutpCQpcqefDp9/nnYy1UKWNkmSJGl9unaFmTPhqqtg9GgoLU0Gl0g1yNImSZIkbUhJCdxyC0ydCk2bJkNLTjgBFi9OO5lqCUubJEmSVBUdO8KbbyYF7tlnk123hx+GGNNOpgJnaZMkSZKqqm7d5FbJmTOT0jZgABxxBHz4YdrJVMAsbZIkSdKm+sEPYNKkZFjJ5MnQujXcdRdUVqadTAXI0iZJkiRtjqIi+PGPYe7cZGDJhRdCt27wl7+knUwFxtImSZIkbYkWLeCPf0wO5i4vh/btk/e9rVqVdjIVCEubJEmStKVCgP79k9J2zDFwzTXQpQu89VbayVQALG2SJElSdWnaFB57DJ54IjkSYN99k8ElK1emnUx5zNImSZIkVbfjjkt23U47DQYPTm6ZnDw57VTKU5Y2SZIkKRsaNYJRo2DcOPj2Wzj44GRwybJlaSdTnrG0SZIkSdl06KEwezZcdBGMGAFt2sALL6SdSnnE0iZJkiRlW/36MGxYcovkttsmB3L37w//+EfayZQHLG2SJElSTTnwwGSi5DXXwJgxUFoKjz8OMaadTDnM0iZJkiTVpJISuOkmmDoVmjeHvn3h+ONh0aK0kylHWdokSZKkNHToAG+8AbfemhzOXVqaDC5x101rsbRJkiRJaSkuhiuugFmzoG1bOPNMOOwweP/9tJMph1jaJEmSpLTtvTdMnJhMl3z99WTC5LBhsHp12smUAyxtkiRJUi4oKoLzz4e5c+GQQ+CSS6Br1+SQbtVqljZJkiQpl+yyCzz3HIweDQsWQMeOyeCSVavSTqaUWNokSZKkXBMCnHIKzJsHxx4LP/sZdO4M06ennUwpsLRJkiRJuWrHHWHsWHjqKViyBLp0gUGD4Ouv006mGmRpkyRJknJd797Je9vOOANuuw3atYNXXkk7lWqIpU2SJEnKBw0bwsiRMH58MlWyrCwZXPLll2knU5ZZ2iRJkqR80qMHzJ4Nl14K990HrVvD88+nnUpZZGmTJEmS8k29ejBkCEyZAtttB0cdlQwuWbo07WTKAkubJEmSlK/23x9mzIDrroNHH4XS0uRjjGknUzWytEmSJEn5bOut4frrk/LWogX06wd9+sDHH6edTNXE0iZJkiQVgrZt4bXX4I47YNy4ZNdt5Eh33QqApU2SJEkqFMXFcNllyaCSjh3hnHOSwSULF6adTFvA0iZJkiQVmj33hJdfTqZLTpuW7MINGZIcFaC8Y2mTJEmSClFRUbLTVl6e7LZddhkceCDMmZN2Mm0iS5skSZJUyJo3h2eegTFj4L33YJ994IYb4Ntv006mKrK0SZIkSYUuBDjppGTXrW/fZNpkp07w5ptpJ1MVWNokSZKk2mKHHeC3v0123j7/HA44AC6/HL76Ku1k2gBLmyRJklTbHH00zJ0LZ58Nv/pVMqjkT39KO5XWw9ImSZIk1Ubf+x7ce29S1kKA//xPOPdc+OKLtJNpLZY2SZIkqTYrK4O3305uk3zggeRQ7j/8Ie1UWoOlTZIkSarttt0Wbr8dXn8dvv99OOYY+NGPYMmStJMJS5skSZKk7+y7b3IY9w03wOOPQ6tWyVEBMaadrFaztEmSJEn6l622gp//HN56C/bcE04+ORlc8re/pZ2s1rK0SZIkSfr/WreGP/8Zhg5NhpW0bg333QeVlWknq3UsbZIkSZLWrU4duOQSmD0bunSB885Lpky+807ayWoVS5skSZKkDdt9d3jppWS65MyZ0K4d3HEHVFSknaxWsLRJkiRJ2rgQ4MwzobwcDj8cfvpTOOCA5LgAZZWlTZIkSVLV/cd/wJNPwqOPwocfQqdOyeCSb75JO1nBsrRJkiRJ2jQhwA9/CPPmQb9+cOONsM8+yTlvqnaWNkmSJEmb5/vfh9Gj4bnnYNkyOPBAuPRSWLEi7WQFxdImSZIkacsceSTMmQPnnw///d/Qti1MmJB2qoJhaZMkSZK05bbbDu6+G155BYqLoWdPOOss+Oc/006W9yxtkiRJkqpPt24waxYMGgQPPQSlpfD002mnymuWNkmSJEnVa5ttYPBgeOMN2HFH6NMHTjwRPvkk7WR5ydImSZIkKTs6dYKpU+Gmm+Cpp5Jdt9GjIca0k+UVS5skSZKk7KlbF665BmbOhJYt4bTT4Kij4K9/TTtZ3thoaQshjAohfBpCmLPGtcYhhJdCCO9kPjbKXA8hhOEhhHdDCG+HEPbJZnhJkiRJeaJVK3j1VRg+HCZNgtatYcQIqKxMO1nOq8pO20NAr7WuXQlMiDHuBUzIfA1wBLBX5tc5wD3VE1OSJElS3qtTBy68MDke4IADYOBAKCuDBQvSTpbTNlraYoyTgM/WutwbeDjz+cNAnzWuPxITrwMNQwjNqiusJEmSpAKw667w4ovw61/D7NnQrh3ceitUVKSdLCeFWIU3AYYQdgWejTG2yXz9zxhjw8znAfg8xtgwhPAsMDjGODnz2ARgUIxx2jqe8xyS3TiaNGnSaezYsdXzJ6pGy5cvp379+mnHUIFyfSnbXGPKJteXssn1Vbts9Y9/sNewYezw6qss22sv5l9xBcv33DNrv1+urq/u3btPjzF2XtdjxVv65DHGGELY5PEvMcb7gfsBOnfuHMvKyrY0SrWbOHEiuZhLhcH1pWxzjSmbXF/KJtdXLXT88fDEEzQYOJDO552XnPH2s59BSUm1/1b5uL42d3rkJ9/d9pj5+Gnm+sfAzmt8X/PMNUmSJElav+OPh/JyOOUUuOUW6NgRpkxJO1VO2NzS9gzQP/N5f+DpNa6flpkiuT/wRYxx0RZmlCRJklQbNG4MDz0EL7wAX30FXbvCRRfB8uVpJ0tVVUb+/w/wGtAyhPBRCOFMYDBwaAjhHaBn5muA54H3gHeBkcAFWUktSZIkqXAdfngyYXLgQLjrLmjTBsaNSztVajb6nrYY40nreajHOr43AgO3NJQkSZKkWq5BA7jzTjjxRDjrrKTIDRgAQ4ZAo0Zpp6tRm3t7pCRJkiRlX9euMHMmXH01jB4NpaXw+9+nnapGWdokSZIk5baSErj5Zpg2DZo1S4aWnHACLF6cdrIaYWmTJEmSlB86dIA33oBf/hKefTbZdXvoIajC2dP5zNImSZIkKX/UrQtXXgmzZkHr1nD66dCrF3zwQdrJssbSJkmSJCn/tGwJr7ySTJecMiWZMHnnnVBZmXayamdpkyRJkpSfioqSYwHmzIGDD07OdOvWDf7yl7STVStLmyRJkqT81qIFPP88PPIIzJsH7dvDLbfAqlVpJ6sWljZJkiRJ+S8EOPVUKC+H3r3hmmugSxeYMSPtZFvM0iZJkiSpcDRpAr/7XXKW2+LFSXG76ir4+uu0k202S5skSZKkwnPsscmuW//+MHhwclzA5Mlpp9osljZJkiRJhalRI3jwQXjpJfj2Wzj4YPYaNgxWrkw72SaxtEmSJEkqbD17JhMmL7mEegsXJme95ZHitANIkiRJUtbVqwdDhzJr/HgOqVMn7TSbxJ02SZIkSbVGLM6/fStLmyRJkiTlMEubJEmSJOUwS5skSZIk5TBLmyRJkiTlMEubJEmSJOUwS5skSZIk5TBLmyRJkiTlMEubJEmSJOUwS5skSZIk5TBLmyRJkiTlMEubJEmSJOUwS5skSZIk5TBLmyRJkiTlMEubJEmSJOUwS5skSZIk5TBLmyRJkiTlMEubJEmSJOUwS5skSZIk5TBLmyRJkiTlMEubJEmSJOUwS5skSZIk5TBLmyRJkiTlsBBjTDsDIYQlwIdp51iH7YGlaYdQwXJ9KdtcY8om15eyyfWlbMrV9dUixrjDuh7IidKWq0II02KMndPOocLk+lK2ucaUTa4vZZPrS9mUj+vL2yMlSZIkKYdZ2iRJkiQph1naNuz+tAOooLm+lG2uMWWT60vZ5PpSNuXd+vI9bZIkSZKUw9xpkyRJkqQcZmmTJEmSpBxmaVuPEEKvEML8EMK7IYQr086jwhJC+CCEMDuEMDOEMC3tPMpvIYRRIYRPQwhz1rjWOITwUgjhnczHRmlmVH5bzxq7PoTwceZ1bGYI4cg0Myo/hRB2DiH8KYRQHkKYG0K4OHPd1zBViw2ssbx6DfM9besQQqgDLAAOBT4CpgInxRjLUw2mghFC+ADoHGPMxYMdlWdCCN2A5cAjMcY2mWu3AZ/FGAdn/sdToxjjoDRzKn+tZ41dDyyPMd6RZjbltxBCM6BZjHFGCKEBMB3oAwzA1zBVgw2ssR+SR69h7rStWxfg3RjjezHGb4GxQO+UM0nSOsUYJwGfrXW5N/Bw5vOHSf4DJW2W9awxaYvFGBfFGGdkPl8GzAN2wtcwVZMNrLG8Ymlbt52Av63x9Ufk4b9c5bQIjAshTA8hnJN2GBWkJjHGRZnPFwNN0gyjgvXjEMLbmdsnvX1NWySEsCvQEXgDX8OUBWutMcij1zBLm5SOrjHGfYAjgIGZW4+krIjJffDeC6/qdg+wB9ABWAT8Kt04ymchhPrAE8AlMcYv13zM1zBVh3Wssbx6DbO0rdvHwM5rfN08c02qFjHGjzMfPwWeJLklV6pOn2Tu4//ufv5PU86jAhNj/CTGuDrGWAmMxNcxbaYQQl2Sv0z/Nsb4+8xlX8NUbda1xvLtNczStm5Tgb1CCLuFELYC+gHPpJxJBSKEUC/zRlhCCPWAw4A5G/4paZM9A/TPfN4feDrFLCpA3/2FOuNYfB3TZgghBOBBYF6MccgaD/kapmqxvjWWb69hTo9cj8zYz/8G6gCjYow3pxxJBSKEsDvJ7hpAMTDG9aUtEUL4H6AM2B74BLgOeAr4HbAL8CHwwxijgyS0WdazxspIbiuKwAfAuWu8B0mqkhBCV+BVYDZQmbl8Ncl7jnwN0xbbwBo7iTx6DbO0SZIkSVIO8/ZISZIkScphljZJkiRJymGWNkmSJEnKYZY2SZIkScphljZJkiRJymGWNkmSJEnKYZY2SZIkScph/wteM0/GBfuB+wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1080x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DyXaT05w-tWz",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "42a42363-6a9f-4397-d75e-ff37a28c1e9e"
      },
      "source": [
        "#Wenn wir den Preis zu einem bestimmten Alter haben wollen\n",
        "#berechen wir das so, dass wir das Alter als x eingeben und den Preis dann als y erhalten\n",
        "#für das Alter 12 Monate erhalten wir dann\n",
        "\n",
        "preis = SteigungWert * 12 + Schnittpunkty\n",
        "preis"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "261.5614973262032"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hXqQtoLrnHLj",
        "outputId": "5ef8373a-b2b1-4658-d5a5-ad9561016f27"
      },
      "source": [
        "#Wir runden das Ergebnis auf 2 Nachkommastellen\n",
        "gerundet = round(preis,2)\n",
        "print('Der Preis ist ', gerundet, ' Euro.')"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Der Preis ist  261.56  Euro.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FJVSQCQanbsZ"
      },
      "source": [
        "#Bonuswissen\n",
        "#Um zu einem bestimmten Eingabewert den vom Modell berechneten Wert zu kriegen\n",
        "#gibt es die Funktion predict()\n",
        "#immer dran denken, das model will die x Werte immer in doppelten eckigen Klammen\n",
        "#als nicht model.predict(12), sondern model.predict([[12]])"
      ],
      "execution_count": 49,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NiuYo7i7-tW0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a290f1f5-4a55-43e0-dc1c-ea23c6bce5b2"
      },
      "source": [
        "model.predict([[12]])"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([261.56149733])"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8N_yf6qWoBqY",
        "outputId": "6434f01b-7894-4c4c-9a18-253079b638a6"
      },
      "source": [
        "#Auch das Ergebnis des Models ist wieder ein ARRAY mit eckigen Klammern\n",
        "#wir haben die Funkiont item() um die reine Zahl aus dem Array rauszuholen\n",
        "\n",
        "arrayzahl = model.predict([[12]])\n",
        "arrayzahl.item()\n",
        "\n"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "261.5614973262032"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    }
  ]
}