{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5e0e68fb",
   "metadata": {},
   "source": [
    "# Logistisk Regresjon\n",
    "\n",
    "La oss fortsette med det klassiske datasettet som inneholder data om størrlsen (lende og bredde) av begerbladene (engelsk: sepal) (de ytre bladene i en blomst) og kronbladene (engelsk: petal) til tre ulike type Iris (setosa, versicolor og virginica) - på norsk hhv.: vill iris, praktiris og blått flagg iris). Vi skal bruke dette datasettet til å se nærmere på logistisk regresjon. Først må vi importere noen pakker og lese inn datasettet.\n",
    "\n",
    "Dette er helt identisk med det vi gjorde for lineær regresjons!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ff3ba579",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "83611939",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression, LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.special import expit\n",
    "from scipy.stats import expon\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "247e2fed",
   "metadata": {},
   "source": [
    "Datasettet er tilgjengelig direkte fra ScikitLearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3ad6dbbe",
   "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",
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       "    }\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>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \\\n",
       "0                5.1               3.5                1.4               0.2   \n",
       "1                4.9               3.0                1.4               0.2   \n",
       "2                4.7               3.2                1.3               0.2   \n",
       "3                4.6               3.1                1.5               0.2   \n",
       "4                5.0               3.6                1.4               0.2   \n",
       "\n",
       "   target  \n",
       "0     0.0  \n",
       "1     0.0  \n",
       "2     0.0  \n",
       "3     0.0  \n",
       "4     0.0  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "df = pd.DataFrame(data= np.c_[iris['data'], iris['target']],\n",
    "                     columns= iris['feature_names'] + ['target'])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c01e1416",
   "metadata": {},
   "source": [
    "Nå er typen iris lagret som 0, 1 og 2. Vi vil gjerne oversette dette til faktiske navn slik at vi ikke glemmer hva de ulike tallene betyr. Dette kan vi gjøre på flere måter, men en mulighet er å bruke såkalte lambda-funksjoner som utfører en test av hvert enkelt element in en kolonne. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f5642189",
   "metadata": {},
   "outputs": [],
   "source": [
    "df['species'] = df['target'].apply(lambda x: \"setosa\" if x == 0.0 else (\"versicolor\" if x == 1.0 else \"virginica\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "32430c31",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "      <th>target</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)  \\\n",
       "145                6.7               3.0                5.2               2.3   \n",
       "146                6.3               2.5                5.0               1.9   \n",
       "147                6.5               3.0                5.2               2.0   \n",
       "148                6.2               3.4                5.4               2.3   \n",
       "149                5.9               3.0                5.1               1.8   \n",
       "\n",
       "     target    species  \n",
       "145     2.0  virginica  \n",
       "146     2.0  virginica  \n",
       "147     2.0  virginica  \n",
       "148     2.0  virginica  \n",
       "149     2.0  virginica  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93a4b039",
   "metadata": {},
   "source": [
    "Det er keitete å ha kolonnenavn som inneholder mellomrom så la oss lage nye enklere navn. Når vi setter *inplace=True* betyr det at data-framen df automatisk blir oppdatert med de nye kolonnenavnene. Hvis ikke må man bruke *df = df.rename()* for at endringene skal bli oppdatert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3a044934",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\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>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>target</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width  target species\n",
       "0           5.1          3.5           1.4          0.2     0.0  setosa\n",
       "1           4.9          3.0           1.4          0.2     0.0  setosa\n",
       "2           4.7          3.2           1.3          0.2     0.0  setosa\n",
       "3           4.6          3.1           1.5          0.2     0.0  setosa\n",
       "4           5.0          3.6           1.4          0.2     0.0  setosa"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.rename({'sepal length (cm)': 'sepal_length'}, axis='columns',inplace=True)\n",
    "df.rename({'sepal width (cm)': 'sepal_width'}, axis='columns',inplace=True)\n",
    "df.rename({'petal length (cm)': 'petal_length'}, axis='columns',inplace=True)\n",
    "df.rename({'petal width (cm)': 'petal_width'}, axis='columns',inplace=True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04a0b1e0",
   "metadata": {},
   "source": [
    "## Forberedelser til logistisk regresjon\n",
    "\n",
    "I eksempelet med lineær regresjon så vi på om det var en lineær sammenheng mellom lengden og bredden til de to ulike typene blader for en type iris. I dette eksempelet skal vi se om vi ut fra målinger av bredde og/eller lengde til bladene kan avgjøre hvilken type iris vi ser på. Det betyr at responsen ikke lengre er kvantitativ (dvs. lengde/bredde til bladene) men kvantitative/kategoriske (dvs. blomsten er enten iris setosa, versicolor eller virginica). For kategoriske data er logistisk regresjon en egnet metode. \n",
    "\n",
    "Før vi setter igang med å lage modellen la oss se på dataene og vurdere om modellen vår vil klare å skille mellom de ulike typene iris basert på størrelsen til bladene. En fin måte å vurdere dette på er ved bruk av såkalte [box-plot](https://en.wikipedia.org/wiki/Box_plot). Feks. kan vi se på fordelingen av bredde og lengde på begerbladene for de tre ulike typene iris.\n",
    "\n",
    "Boxplot gir et godt overblikk over spredningen i målingene vi har i datasettes vårt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4520dc5b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = df.groupby(\"species\").boxplot(column=[\"sepal_length\",\"sepal_width\",\"petal_length\",\"petal_width\"],layout=(1,3),return_type=\"axes\")\n",
    "# La oss forkorte navnene slik at plottene blir mer leselig\n",
    "labels = [\"sl\",\"sw\",\"pl\",\"pw\"]\n",
    "for a in ax:\n",
    "    a.set_xticklabels(labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56d1e19a",
   "metadata": {},
   "source": [
    "Siden vi ønsker å lage en modell som kan predikere hvilken type iris vi har med å gjøre ønsker vi at fordelingen til variablene for de ulike irisiene er så forksjellig som mulig. Det beste vil selvsagt være å bruke alle målingene og det skal vi se på senere, men la oss først bruke kun en variabel. Jeg velger å se på *petal width (pw)* \n",
    "\n",
    "\n",
    "La os se på et scatter-plot for lengde og bredde på kronbladene for de ulike typene iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "087d1b8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd277134b50>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "colors = {'setosa': 'red', 'versicolor': 'blue', 'virginica': 'yellow' }\n",
    "for t in df['species'].unique():\n",
    "    df[df[\"species\"] == t].plot.scatter(x=\"petal_length\",y=\"petal_width\",c=colors[t],ax=ax,label=t)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "320999e0",
   "metadata": {},
   "source": [
    "Ved første øyekast ser det ut disse to variablene er ganske forskjellig for alle de tre ulike typene iris.\n",
    "\n",
    "Tenk deg at du skulle tegnet tre vertikale streker som skulle definere de ulike områdene for de tre iris-typene. Det er mulig å plassere strekene slik at vi får relativt høy overvekt av en bestemt type iris i området definert av hver strek. Type noe slikt (enda bedre om vi hadde brukt y-aksen i tillegg - altså effektivt en 2-dimensjonal logistisk regresjon):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bbd1f184",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd276fa4a90>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "colors = {'setosa': 'red', 'versicolor': 'blue', 'virginica': 'yellow' }\n",
    "for t in df['species'].unique():\n",
    "    df[df[\"species\"] == t].plot.scatter(x=\"petal_length\",y=\"petal_width\",c=colors[t],ax=ax,label=t)\n",
    "plt.axvline(x = 2.5,color=\"green\")\n",
    "plt.axvline(x = 5.0,color=\"green\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b29cd4cc",
   "metadata": {},
   "source": [
    "La oss avslutte denne seksjonen med å beskrive problemet vi ønsker å undersøke. Vi vil altså finne ut sannsynligheten for at irisen er av typen versicolor eller setosa gitt lengden på kronbladet, eller\n",
    "\n",
    "$$P(Y = versicolor | \\text{lengde på kronblad})$$\n",
    "\n",
    "Dette er altså en sansynlighet for at blomsten er en iris versicolor. Det betyr at P må ha verdier mellom 0 og 1. Det er ganske åpenbart at lineær regresjon ikke fungerer godt i slike tilfeller. La oss bare kjapt illustrere dette ved å bruke lineær regresjon (dette burde være godt kjent fra tidligere).\n",
    "\n",
    "Når vi skal starte med å lage en modell som kan si om en blomst er iris setosa eller iris versicolor bare basert på lengden til kronbladene (petal). Vi trekker derfor ut dette som Y (respons) og X (predikator) til modellen vår. \n",
    "\n",
    "Vi bruker *target* kolonnen som sier at hvis det er en **iris setosa er target 0** mens **target lik 1 betyr versicolor**. Dette betyr at respons-vektoren vår kan ta to verdier, 0 dersom  blomstent er av type setosa og 1 dersom blomsten er av typen versicolor. Matematisk kan vi representere dette slik\n",
    "\n",
    "\n",
    "$$Y = \\begin{cases}\n",
    "    1, & \\text{hvis } \\texttt{versicolor}.\\\\\n",
    "    0, & \\text{hvis } \\texttt{setosa}.\n",
    "  \\end{cases}$$\n",
    "\n",
    "Vi henter dette ut fra pandas dataframen vår direkte og konverterer til numpy-arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d28cce0f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Trekk ut målingene til lengden av kronbladene til hhv. iris setosa og iris versicolor\n",
    "X = df[(df[\"target\"] == 0) | (df[\"target\"] == 1)].petal_length.to_numpy()\n",
    "Y = df[(df[\"target\"] == 0) | (df[\"target\"] == 1)].target.to_numpy()\n",
    "X = X[:, np.newaxis]\n",
    "Y = Y[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "551806f6",
   "metadata": {},
   "source": [
    "Definer en lineær regresjonsmodell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "611fdeaa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficient = 0.34\n",
      "Intercept = -0.46\n",
      "Score/R^2 = 0.94\n"
     ]
    }
   ],
   "source": [
    "\n",
    "#Y = Y[:, np.newaxis]\n",
    "clf = LinearRegression().fit(X,Y)\n",
    "print(\"Coefficient = %.2f\"%clf.coef_)\n",
    "print(\"Intercept = %.2f\"%clf.intercept_)\n",
    "print(\"Score/R^2 = %.2f\"%clf.score(X,Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b2b92bfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Definer en x-vektor som dekker datapunktene (i dette tilfellet mellom 4 og 7 cm)\n",
    "X_plot = np.linspace(0, 6, 300)\n",
    "# Lag så responsfunksjonen ved å bruke parameterne fra modellen vår\n",
    "fit = clf.intercept_[0] + clf.coef_[0]*X_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3bd75572",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd277016ad0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(8, 4))\n",
    "plt.clf()\n",
    "plt.scatter(X, Y,label=\"Iris Data\")\n",
    "plt.plot(X_plot, fit, label=\"Linear Regression Model\", color=\"red\", linewidth=3)\n",
    "plt.xlabel(\"lengde til kronblad\")\n",
    "plt.ylabel(\"sannsynlighet for iris versicolor\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0edcbb2",
   "metadata": {},
   "source": [
    "For små kronbladlengder blir sannsynligheten negativ, og for veldig lange kronblad blir sansynligheten større enn 1! Dette er ikke et unikt eksempel. I alle tilfeller hvor vi prøver å tilpasse en lineær funksjon til en binær (0 eller 1) respons vil vil alltid predikere sannsynligheter $ >1 $ og $ < 0$ - dersom ikke verdiene til x er begrenset på noen måte."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7e30554",
   "metadata": {},
   "source": [
    "## Logistisk funksjon"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6484898f",
   "metadata": {},
   "source": [
    "I logistisk regresjon trenger vi altså en funksjon som gir verdier mellom 0 og 1 for alle verider av $X$. Det er mange funksjoner som oppfyller dette kravet, men i logistisk regresjon bruker vi en såkalt *logistisk funksjon* definert som:\n",
    "\n",
    "$$ p(X) = \\frac{e^{\\beta_0 + \\beta_1 X}}{1+e^{\\beta_0 + \\beta_1 x}} $$\n",
    "\n",
    "som er ett (av mange) eksempler på en *sigmoid*-funksjon. La oss ta en titt på hvordan den ser. Først definerer vi en funskjon i python, ```def logistic()```, som returnerer den *logistisk funksjonen* når vi gir den de to parameterne samt en X-vektor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d9ba5894",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def logistic(beta_0, beta_1, X): \n",
    "    return np.exp(beta_0 + beta_1*X)/(1+np.exp(beta_0 + beta_1*X))\n",
    "\n",
    "x = np.linspace(-5, 5, 100)\n",
    "# beta0 = 2, beta1 = 3\n",
    "y = logistic(2, 3, x)\n",
    "plt.plot(x, y)\n",
    "plt.xlabel(r\"$X$\")\n",
    "plt.ylabel(r\"$p(X)$\")\n",
    "plt.savefig(\"logistic.svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c56e16f0",
   "metadata": {},
   "source": [
    "Som vi ser gir denne funksjonen et tall mellom 0 og 1 for alle $X$. Det er litt mindre intuitivt hvilken effekt $\\beta_0$ og $\\beta_1$ har på denne funksjonen sammenlignet med det vi så for den lineære funksjonen vi brukte i lineær regresjon. La oss derfor se hvordan den logistiske funksjonen endrer seg med parametrene: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2cec7877",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Auto-utforsk\n",
    "beta0s = [-1, 1]\n",
    "beta1s = [1, 2, 3]\n",
    "\n",
    "for beta0 in beta0s: \n",
    "    for beta1 in beta1s:\n",
    "        x = np.linspace(-5, 5, 100)\n",
    "        y = logistic(beta0, beta1, x)\n",
    "        plt.plot(x, y, label=rf\"$\\beta_0 = {beta0}, \\beta_1 = {beta1}$\")\n",
    "plt.legend()\n",
    "plt.xlabel(r\"$X$\")\n",
    "plt.xlabel(r\"$p(X)$\")\n",
    "plt.savefig(\"logistic_variation.svg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c803662a",
   "metadata": {},
   "source": [
    "Eller på en enda morsommere måte:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "f5440478",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "159404bf2785459e82f3448084f6cdcc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='beta0', max=3.0, min=-3.0), FloatSlider(value=0.0, d…"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from ipywidgets import interactive\n",
    "#import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def f(beta0, beta1):\n",
    "    x = np.linspace(-5, 5, num=1000)\n",
    "    plt.plot(x, logistic(beta0, beta1, x))\n",
    "    plt.ylim(-0.1, 1.1)\n",
    "\n",
    "interactive_plot = interactive(f, beta0=(-3.0, 3.0), beta1=(-3, 3, 0.1))\n",
    "interactive_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5668a63f",
   "metadata": {},
   "source": [
    "Basert på disse plottene kan vi gjøre følgende observasjoner:\n",
    "\n",
    "1. $\\beta_0$ flytter vendepunktet (den bratte delen av funksjonen) fram og tilbake langs $x$.\n",
    "1. $\\beta_1$ styrer hvor bratt funksjonen er \n",
    "1. posisjonen til vendepunktet er avhengig av både og $\\beta_0$ og $\\beta_1$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e3791b4",
   "metadata": {},
   "source": [
    "## Forberedelser til logistisk regresjon"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e0705cc",
   "metadata": {},
   "source": [
    "Nå som vi har etablert en passende funksjon til å bruke i logistisk regresjon kan vi starte med å se hvordan vi kan bruke dette til å forutsi hvilken type iris vi har med å gjøre bare basert på lengden på kronbaldene.\n",
    "\n",
    "I likhet med da vi gjorde lineær regresjon må vi gi X-vektoren (predikatoren) vår en ekstra dimensjon for at vi skal kunne bruke scikit-learn sin implementering av LogisticRegression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "26ffb0c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "#X = X[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ab96eb9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/scratch2/eirikgr/anaconda3/lib/python3.11/site-packages/sklearn/utils/validation.py:1184: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(C=100000.0)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(C=100000.0)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(C=100000.0)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg = LogisticRegression(C=1e5)\n",
    "logreg.fit(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "054970be",
   "metadata": {},
   "source": [
    "Siden vi vet hva hver blomst er klassifisert som kan vi sjekke modellen vår og se hvor ofte den klassifiserer riktig og feil. Her antar modellen at alle X som gir $P(X) > 0.5$ betyr at blomsten klassifiseres som *versicolor* mens alle X som gir $P(X) < 0.5$ klassifiseres som *setosa*. Det er kanskje ikke en optimal inndeling. Vi skal diskutere dette mer senere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6ddc0717",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Klassifiserte riktig 100 ganger og feil 0 ganger. Treffprosent = 100%\n"
     ]
    }
   ],
   "source": [
    "pred = logreg.predict(X)\n",
    "correct = 0\n",
    "wrong = 0\n",
    "for i in range(len(pred)):\n",
    "    if pred[i] == Y[i]:\n",
    "        correct += 1\n",
    "    else:\n",
    "        wrong += 1\n",
    "print(\"Klassifiserte riktig %i ganger og feil %i ganger. Treffprosent = %.0f%%\"%(correct,wrong,100.*(correct)/(correct+wrong)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb5954b5",
   "metadata": {},
   "source": [
    "Vi kan hente ut parameterne samt $R^2$ direkte fra modellen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "60a1ed33",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta0 = 16.62\n",
      "beta1 = -41.17\n",
      "Score/R^2 = 1.00\n"
     ]
    }
   ],
   "source": [
    "print(\"beta0 = %.2f\"%logreg.coef_)\n",
    "print(\"beta1 = %.2f\"%logreg.intercept_)\n",
    "print(\"Score/R^2 = %.2f\"%logreg.score(X,Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c58ebdbc",
   "metadata": {},
   "source": [
    "Og vi kan plotte funksjonen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a071d5c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "logfunc = logistic(logreg.intercept_[0],logreg.coef_[0],X_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4e286975",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd276d81f90>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(8, 4))\n",
    "plt.clf()\n",
    "plt.scatter(X, Y,label=\"Iris Data\")\n",
    "plt.plot(X_plot, logfunc, label=\"Logistic Regression Model\", color=\"red\", linewidth=3)\n",
    "plt.xlabel(\"lengde til kronblad [cm]\")\n",
    "plt.ylabel(\"sannsynlighet iris versicolor\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0729389",
   "metadata": {},
   "source": [
    "Vi kan bruke modellen til å se på sannsynligheten for at blomsten er hhv. versicolor og setosa for en gitt måling av lengden på kronbladet ($X$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "5ff6accb",
   "metadata": {},
   "outputs": [],
   "source": [
    "v = np.ones((1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "75d5750c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d30f90d2",
   "metadata": {},
   "source": [
    "F.eks: si at vi måler $x = 2.4$. Hvor sansynlig er det at dette er en iris versicolor. Funksjonen ```predict_proba()``` returnerer sannsynligheten for iris setosa (target = 0) som første element og sannsynligheten for iris versicolor (target = 1) som andre element i en array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "73ab21df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1.]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg.predict_proba(v*5.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ba26cba",
   "metadata": {},
   "source": [
    "La oss plotte alt i samme plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "67b998d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(6, 4))\n",
    "plt.clf()\n",
    "plt.scatter(X[:,0], Y, label=\"iris data\", zorder=20)\n",
    "#plt.scatter(X_train[:,0], y_train, label=\"train data\", color=\"green\",marker='.', zorder=20)\n",
    "X_plot = np.linspace(0, 6, 300)\n",
    "\n",
    "loss = expit(X_plot * logreg.coef_ + logreg.intercept_).ravel()\n",
    "plt.plot(X_plot, logfunc, label=\"Logistic Regression Model\", color=\"red\", linewidth=3)\n",
    "\n",
    "# lineær modell\n",
    "plt.plot(\n",
    "    X_plot,\n",
    "    clf.coef_[0] * X_plot + clf.intercept_[0],\n",
    "    label=\"Linear Regression Model\",\n",
    "    linewidth=1,\n",
    "    color=\"green\"\n",
    ")\n",
    "\n",
    "plt.axhline(0.5, color=\".5\")\n",
    "\n",
    "plt.ylabel(\"Sansynlighet for iris versicolor\")\n",
    "plt.xlabel(\"lengde kronblad [cm]\")\n",
    "plt.xticks(range(0, 6))\n",
    "plt.yticks([0, 0.5, 1])\n",
    "plt.ylim(-0.5, 1.25)\n",
    "plt.xlim(0, 6)\n",
    "plt.legend(\n",
    "    loc=\"lower right\",\n",
    "    fontsize=\"small\",\n",
    ")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a6b078ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "i = 0\n",
    "odds = np.linspace(0, 7, 300)\n",
    "for x in X_plot:\n",
    "    odds[i] = math.exp(loss[i])\n",
    "    #if i > 5: break\n",
    "    i += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "945b7e39",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "abe6e618",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fd276bf0f90>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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swYcffuj9mZFyMchJYVSCIAje7vzNN98gODgYVVVVSElJ6XXMyy+/jLKyMly+fNnZl52djUuXLqG6uhoAkJGRAbvdjpMnTzrHPPXUU5gwYQKKiorcqsVut0Or1cJmsyGQf7jK9rvfAa+/fq/94x8DxcXS1UPkJXdz7b7WyG02GwAgKCiozzHV1dVITU0V9S1fvhwXL17E7du3+x1z/vz5Po/rcDhgt9tFGxEAzshJcbwOckEQkJubiwULFmDmzJl9jrNarQgJCRH1hYSEoKOjA9evX+93jNVq7fO4BoMBWq3WuUVERHh7KiQ3rkHOe8hJ5rwO8k2bNuGTTz5xa+lDpVKJ2ndXc7r39zbGta+7vLw82Gw259bY2OhJ+SRnfM4KKcwYb3bavHkzysrKYDKZEB4e3u/Y0NDQHjPr5uZmjBkzBhMnTux3jOssvTu1Wg21Wu1N+SR3XFohhfFoRi4IAjZt2oTi4mKcOXMGU6dOHXCfpKQkVFRUiPrKy8sxZ84cjB07tt8xycnJnpRH1IVBTgrjUZDr9XocPHgQhw4dgkajgdVqhdVqxffff+8ck5eXh3Xr1jnb2dnZ+Pe//43c3FxcvnwZ7777Lvbv348tW7Y4x+Tk5KC8vBzbt2/H559/ju3bt+P06dN46aWX7v8MSXkY5KQ0ggcA9LodOHDAOSYrK0tYtGiRaL/KykohPj5e8PPzE6ZMmSLk5+f3OPbRo0eF6OhoYezYsUJMTIxgNBo9KU2w2WwCAMFms3m0H8nQlCmCANzbysqkrojIK+7m2n3dRz6S8D5ycpo4Efjuu3vtykpg0SLJyiHy1rDcR0404ggCl1ZIcRjkJC83bwIdHeI+BjnJHIOc5IVvByIFYpCTvDDISYEY5CQvrkHu5wfwi2Mkcwxykhde6CQFYpCTvDDISYEY5CQvfGAWKRCDnOSFM3JSIAY5yQuDnBSIQU7ywiAnBWKQk7zw7UCkQAxykhfOyEmBGOQkLwxyUiAGOckLg5wUiEFO8sIgJwVikJO8MMhJgRjkJC8MclIgBjnJC4OcFMjjIDeZTEhPT0dYWBhUKhWOHTvW7/j169dDpVL12GbMmOEcU1BQ0OuYmzdvenxCpGAdHcD334v7GOSkAB4HeXt7O+Li4rBnzx63xu/atQsWi8W5NTY2IigoCM8++6xoXGBgoGicxWKBv7+/p+WRkrk+MAtgkJMijPF0h7S0NKSlpbk9XqvVQqvVOtvHjh3DjRs38Nxzz4nGqVQqhIaGeloO0T18OxAp1LCvke/fvx9Lly5FZGSkqL+trQ2RkZEIDw/HypUrUVtb2+9xHA4H7Ha7aCOFc/0dUKmAceOkqYVoGA1rkFssFpw8eRLPP/+8qD8mJgYFBQUoKytDUVER/P39MX/+fNTV1fV5LIPB4Jzta7VaREREDHX5NNL1dqFTpZKmFqJhNKxBXlBQgPHjx2P16tWi/sTERKxduxZxcXFYuHAh3nvvPUyfPh1vvvlmn8fKy8uDzWZzbo2NjUNcPY14vGOFFMrjNXJvCYKAd999F5mZmfDz8+t37KhRo5CQkNDvjFytVkPNl+pSdwxyUqhhm5FXVVXh6tWr2LBhw4BjBUGA2WyGTqcbhspINmw2cZuPsCWF8HhG3tbWhqtXrzrb9fX1MJvNCAoKwuTJk5GXl4empiYUFhaK9tu/fz/mzZuHmTNn9jjm1q1bkZiYiKioKNjtduzevRtmsxl79+714pRIsVyDvNvdUkRy5nGQX7x4EYsXL3a2c3NzAQBZWVkoKCiAxWJBQ0ODaB+bzQaj0Yhdu3b1esyWlhZs3LgRVqsVWq0W8fHxMJlMmDt3rqflkZIxyEmhVIIgCFIXMRjsdju0Wi1sNhsCuTaqTJs3A92/qPbCC8C+fdLVQ3Sf3M01PmuF5IMzclIoBjnJh2uQjx8vSRlEw41BTvLBGTkpFIOc5KOlRdxmkJNCMMhJPjgjJ4VikJN8MMhJoRjkJA+C0PMr+gxyUggGOclDeztw5464j0FOCsEgJ3lwvdAJMMhJMRjkJA+u6+MAn35IisEgJ3lwDfIHHwTGDNtTmokkxSAneeAdK6RgDHKSBwY5KRiDnOSBQU4KxiAneeDX80nBGOQkD5yRk4IxyEkeGOSkYAxykgc+i5wUjEFO8sAZOSkYg5zkgUFOCuZxkJtMJqSnpyMsLAwqlQrHjh3rd3xlZSVUKlWP7fPPPxeNMxqNiI2NhVqtRmxsLEpKSjwtjZSMd62Qgnkc5O3t7YiLi8Oe7m8rd8OVK1dgsVicW1RUlPNn1dXVyMjIQGZmJi5duoTMzEysWbMGH374oaflkVJxRk4K5vHDKNLS0pCWlubxBwUHB2N8Hxegdu7ciWXLliEvLw8AkJeXh6qqKuzcuRNFRUUefxYpEIOcFGzY1sjj4+Oh0+mwZMkSnD17VvSz6upqpKamivqWL1+O8+fP93k8h8MBu90u2kihOjv5UglStCEPcp1Oh3379sFoNKK4uBjR0dFYsmQJTCaTc4zVakVISIhov5CQEFit1j6PazAYoNVqnVtERMSQnQONcG1tXW8I6o5BTgoy5M/5jI6ORnR0tLOdlJSExsZGvPHGG0hJSXH2q1Qq0X6CIPTo6y4vLw+5ubnOtt1uZ5grVW/PIud95KQgktx+mJiYiLq6Omc7NDS0x+y7ubm5xyy9O7VajcDAQNFGCtXb24E0mmEvg0gqkgR5bW0tdDqds52UlISKigrRmPLyciQnJw93aeSLXGfkGg0werQ0tRBJwOOllba2Nly9etXZrq+vh9lsRlBQECZPnoy8vDw0NTWhsLAQQNcdKVOmTMGMGTNw69YtHDx4EEajEUaj0XmMnJwcpKSkYPv27Vi1ahVKS0tx+vRpnDt3bhBOkWSP95CTwnkc5BcvXsTixYud7bvr1FlZWSgoKIDFYkFDQ4Pz57du3cKWLVvQ1NSEgIAAzJgxAydOnMCKFSucY5KTk3H48GG8+uqreO211zBt2jQcOXIE8+bNu59zI6X47jtxOyhImjqIJKISBNfL/b7JbrdDq9XCZrNxvVxp/vQnoNuFbyxeDJw5I109RIPE3Vzjs1bI9337rbg9caI0dRBJhEFOvs91aYVBTgrDICff5zoj5xo5KQyDnHwfl1ZI4Rjk5Pu4tEIKxyAn38cZOSkcg5x8H4OcFI5BTr7N4QDa28V9vNhJCsMgJ9/muj4OcEZOisMgJ9/muqwCABMmDH8dRBJikJNvu35d3B4/Hhgz5I/ZJxpRGOTk277+Wtzu5xn2RHLFICff5hrkwcHS1EEkIQY5+TbOyIkY5OTjGOREDHLycQxyIgY5+TgGORGDnHwcg5yIQU4+TBAY5ETwIshNJhPS09MRFhYGlUqFY8eO9Tu+uLgYy5Ytw6RJkxAYGIikpCScOnVKNKagoAAqlarHdvPmTU/LIyWx27uetdIdg5wUyOMgb29vR1xcHPbs2ePWeJPJhGXLluH9999HTU0NFi9ejPT0dNTW1orGBQYGwmKxiDZ/f39PyyMlcZ2NA7yPnBTJ4+8yp6WlIS0tze3xO3fuFLW3bduG0tJSHD9+HPHx8c5+lUqF0NBQT8shJfvqK3E7MBAYN06aWogkNOxr5J2dnWhtbUWQy6NG29raEBkZifDwcKxcubLHjN2Vw+GA3W4XbaQwjY3idkSENHUQSWzYg3zHjh1ob2/HmjVrnH0xMTEoKChAWVkZioqK4O/vj/nz56Ourq7P4xgMBmi1WucWwT9i5WGQEwEY5iAvKirCb3/7Wxw5cgTB3dYyExMTsXbtWsTFxWHhwoV47733MH36dLz55pt9HisvLw82m825Nbr+UZP8MciJAHixRu6tI0eOYMOGDTh69CiWLl3a79hRo0YhISGh3xm5Wq2GWq0e7DLJlzDIiQAM04y8qKgI69evx6FDh/D0008POF4QBJjNZuh0umGojnyW68VOBjkplMcz8ra2Nly9etXZrq+vh9lsRlBQECZPnoy8vDw0NTWhsLAQQFeIr1u3Drt27UJiYiKsVisAICAgAFqtFgCwdetWJCYmIioqCna7Hbt374bZbMbevXsH4xxJrjgjJwLgxYz84sWLiI+Pd946mJubi/j4ePzmN78BAFgsFjQ0NDjHv/322+jo6IBer4dOp3NuOTk5zjEtLS3YuHEjHnnkEaSmpqKpqQkmkwlz58693/MjuWprA1paxH0MclIolSAIgtRFDAa73Q6tVgubzYbAwECpy6Gh9sknQFycuK+9HXjgAWnqIRoC7uYan7VCvumLL8Tt8HCGOCkWg5x8k+sdTVFR0tRBNAIwyMk3uc7Ip0+Xpg6iEYBBTr7JdUbOICcFY5CTb3KdkXNphRSMQU6+59tvgW++EfcxyEnBGOTke1yfjOnvDzz8sDS1EI0ADHLyPR9/LG4/9hgwZtgeG0Q04jDIyfe4zshnzZKmDqIRgkFOvsd1Rt7tTVNESsQgJ9/yzTc971hhkJPCMcjJt5w9K26PG9fzmStECsMgJ99y5oy4nZIC+PlJUwvRCMEgJ98hCEB5ubjvySelqYVoBGGQk+/45z+B+npx3wCvDSRSAgY5+Y6//U3cfvhhro8TgUFOvsJmA354faDTf/4noFJJUw/RCMIgJ9/w5ps9X+22dq0kpRCNNAxyGvm++AL47/8W9z3zDB+URfQDBjmNbI2NwNNPAzdvivtffVWaeohGII+D3GQyIT09HWFhYVCpVDh27NiA+1RVVWH27Nnw9/fHQw89hLfeeqvHGKPRiNjYWKjVasTGxqKkpMTT0khOmpuBP/0JePxx4OpV8c82b+a3OYm68fiRce3t7YiLi8Nzzz2Hn/zkJwOOr6+vx4oVK/DCCy/g4MGD+Mc//oFf/OIXmDRpknP/6upqZGRk4Pe//z1+/OMfo6SkBGvWrMG5c+cwb948z8/KHc3NQHX1vbYgiH8+UNubfaRuj4Qaemt//33XxcyWFqChAbh8uWvrzWOPAQZD7z8jUiiVIPT21+7mzioVSkpKsHr16j7HvPzyyygrK8Plbn+Y2dnZuHTpEqp/CNKMjAzY7XacPHnSOeapp57ChAkTUFRU5FYtdrsdWq0WNpsNgYGBA+9QXg4sX+7WsWmEmD4dqKwEdDqpKyEaFu7m2pCvkVdXVyM1NVXUt3z5cly8eBG3b9/ud8z58+f7PK7D4YDdbhdtJGNr1gAffsgQJ+rFkAe51WpFSEiIqC8kJAQdHR24fv16v2OsVmufxzUYDNBqtc4tIiJi8IsnaT34IPDss8Df/w4cOQKMHy91RUQj0rC8VkXl8qWNu6s53ft7G+Pa111eXh5yc3Odbbvd7lmYP/AAMG2aa6Ejtz2SahnstloNaLVAYGDXjHvq1K5vbM6ezTf/ELlhyP9KQkNDe8ysm5ubMWbMGEycOLHfMa6z9O7UajXUarX3hS1Y0PNuCCIiHzTkSytJSUmoqKgQ9ZWXl2POnDkYO3Zsv2OSk5OHujwiIp/n8Yy8ra0NV7vNZOvr62E2mxEUFITJkycjLy8PTU1NKPzhuRjZ2dnYs2cPcnNz8cILL6C6uhr79+8X3Y2Sk5ODlJQUbN++HatWrUJpaSlOnz6Nc+fODcIpEhHJnOChs2fPCgB6bFlZWYIgCEJWVpawaNEi0T6VlZVCfHy84OfnJ0yZMkXIz8/vcdyjR48K0dHRwtixY4WYmBjBaDR6VJfNZhMACDabzdNTIiIakdzNtfu6j3wk8fg+ciKiEW7E3EdORERDi0FOROTjZHOT7t0VIn7Dk4jk4m6eDbQCLpsgb21tBQB+w5OIZKe1tRVarbbPn8vmYmdnZyeuXbsGjUbT7zdCXd39RmhjY6PPXSRl7dJg7dJQYu2CIKC1tRVhYWEYNarvlXDZzMhHjRqF8PBwr/cPDAz0uV+Ou1i7NFi7NJRWe38z8bt4sZOIyMcxyImIfJzig1ytVuP111+/vwdwSYS1S4O1S4O19002FzuJiJRK8TNyIiJfxyAnIvJxDHIiIh/HICci8nEMciIiH6foIP/zn/+MqVOnwt/fH7Nnz8bf//53qUtyi8lkQnp6OsLCwqBSqXDs2DGpS3KLwWBAQkICNBoNgoODsXr1aly5ckXqstySn5+Pxx57zPnNvKSkJJw8eVLqsrxiMBigUqnw0ksvSV3KgH77299CpVKJttDQUKnLcltTUxPWrl2LiRMn4oEHHsDjjz+OmpqaQf8cxQb5kSNH8NJLL+HXv/41amtrsXDhQqSlpaGhoUHq0gbU3t6OuLg47NmzR+pSPFJVVQW9Xo8LFy6goqICHR0dSE1NRXt7u9SlDSg8PBx//OMfcfHiRVy8eBFPPvkkVq1ahc8++0zq0jzyz3/+E/v27cNjjz0mdSlumzFjBiwWi3P79NNPpS7JLTdu3MD8+fMxduxYnDx5Ev/617+wY8cOjB8/fvA/bGhfVDRyzZ07V8jOzhb1xcTECL/61a8kqsg7AISSkhKpy/BKc3OzAECoqqqSuhSvTJgwQfjLX/4idRlua21tFaKiooSKigph0aJFQk5OjtQlDej1118X4uLipC7DKy+//LKwYMGCYfksRc7Ib926hZqaGqSmpor6U1NTcf78eYmqUh6bzQYACAoKkrgSz9y5cweHDx9Ge3s7kpKSpC7HbXq9Hk8//TSWLl0qdSkeqaurQ1hYGKZOnYqf/vSn+PLLL6UuyS1lZWWYM2cOnn32WQQHByM+Ph7vvPPOkHyWIoP8+vXruHPnDkJCQkT9ISEhsFqtElWlLIIgIDc3FwsWLMDMmTOlLsctn376KR588EGo1WpkZ2ejpKQEsbGxUpfllsOHD+Pjjz+GwWCQuhSPzJs3D4WFhTh16hTeeecdWK1WJCcn49tvv5W6tAF9+eWXyM/PR1RUFE6dOoXs7Gy8+OKLKCwsHPTPks1jbL3h+txyQRA8epY5eW/Tpk345JNPcO7cOalLcVt0dDTMZjNaWlpgNBqRlZWFqqqqER/mjY2NyMnJQXl5Ofz9/aUuxyNpaWnOf3/00UeRlJSEadOm4a9//Styc3MlrGxgnZ2dmDNnDrZt2wYAiI+Px2effYb8/HysW7duUD9LkTPyH/3oRxg9enSP2Xdzc3OPWToNvs2bN6OsrAxnz569r2fIDzc/Pz88/PDDmDNnDgwGA+Li4rBr1y6pyxpQTU0NmpubMXv2bIwZMwZjxoxBVVUVdu/ejTFjxuDOnTtSl+i2cePG4dFHH0VdXZ3UpQxIp9P1+I/8I488MiQ3VCgyyP38/DB79mxUVFSI+isqKpCcnCxRVfInCAI2bdqE4uJinDlzBlOnTpW6pPsiCAIcDofUZQxoyZIl+PTTT2E2m53bnDlz8LOf/QxmsxmjR4+WukS3ORwOXL58GTqdTupSBjR//vwet9d+8cUXiIyMHPTPUuzSSm5uLjIzMzFnzhwkJSVh3759aGhoQHZ2ttSlDaitrQ1Xr151tuvr62E2mxEUFITJkydLWFn/9Ho9Dh06hNLSUmg0Guf/EWm1WgQEBEhcXf9eeeUVpKWlISIiAq2trTh8+DAqKyvxwQcfSF3agDQaTY/rEOPGjcPEiRNH/PWJLVu2ID09HZMnT0ZzczP+8Ic/wG63IysrS+rSBvTLX/4SycnJ2LZtG9asWYOPPvoI+/btw759+wb/w4bl3pgRau/evUJkZKTg5+cnzJo1y2dugzt79qwAoMeWlZUldWn96q1mAMKBAwekLm1AP//5z52/K5MmTRKWLFkilJeXS12W13zl9sOMjAxBp9MJY8eOFcLCwoRnnnlG+Oyzz6Quy23Hjx8XZs6cKajVaiEmJkbYt2/fkHwOn0dOROTjFLlGTkQkJwxyIiIfxyAnIvJxDHIiIh/HICci8nEMciIiH8cgJyLycQxyIiIfxyAnIvJxDHIiIh/HICci8nH/D0cCYsJvy+ROAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(4, 3))\n",
    "plt.clf()\n",
    "plt.plot(X_plot, odds, label=\"Logistic Regression Model\", color=\"red\", linewidth=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bbabe9e",
   "metadata": {},
   "source": [
    "# Multiple (multi) logistisk regresjon"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35915fba",
   "metadata": {},
   "source": [
    "Selvom modellen vi laget over viste seg å være ganske god til å klassifisere iris, la oss prøve å bruke alle målingene vi har i datasetts til å lage en multi logistisk regresjon. Det er får endringer som trengs for å få til dette. Vi vil altså bruke følgende funksjon\n",
    "\n",
    "$$ p(X) = \\frac{e^{\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\beta_3 X_3 + \\beta_4 X_4}}{1+e^{\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\beta_3 X_3 + \\beta_4 X_4}}$$\n",
    "\n",
    "Vi har nå 4 predikatorer $\\{X_1,X_2,X_3,X_4\\}$ og en parameter per predikator (\\${\\beta_1,\\beta_2,\\beta_3,\\beta_4\\}$) som vi nå skal estimere på samme måte som vi gjorde over for kun en predikator.\n",
    "\n",
    "Først lager vi en 4-dimensjonal numpy-vektor fra kolonnene i data framen. Y-vektoren kan være den samme som over (vi holder oss fortsatt til binær klassifikasjon (setosa eller versicolor)):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "80efc877",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lage en liste med navnene til alle predikatorene\n",
    "predictors = [\"sepal_length\",\"sepal_width\",\"petal_length\",\"petal_width\"]\n",
    "X = df[(df[\"target\"] == 0) | (df[\"target\"] == 1)][predictors].values\n",
    "Y = df[(df[\"target\"] == 0) | (df[\"target\"] == 1)].target.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "7bb9dde5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(C=100000.0)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(C=100000.0)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(C=100000.0)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multilogreg = LogisticRegression(C=1e5)\n",
    "multilogreg.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "5ed2f3e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 4)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multilogreg.coef_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "a1cbecbb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta0 = -1.01\n",
      "beta1 (sepal_length) = -1.84\n",
      "beta2 (sepal_width ) = -6.24\n",
      "beta3 (petal_length) = +9.86\n",
      "beta4 (petal_width ) = +5.04\n",
      "Score/R^2 = 1.00\n"
     ]
    }
   ],
   "source": [
    "print(\"beta0 = %.2f\"%multilogreg.intercept_)\n",
    "for i in range(len(multilogreg.coef_[0])):\n",
    "    print(\"beta%i (%-12s) = %+4.2f\"%(i+1,predictors[i],multilogreg.coef_[0][i]))\n",
    "print(\"Score/R^2 = %.2f\"%multilogreg.score(X,Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "759c548e",
   "metadata": {},
   "source": [
    "Husk at dersom $\\beta > 0$ så vil én økning i $X$ øke log(odds) med $\\beta$. Dvs. at dersom $\\beta$ er positiv vil en økning i $X$ gjøre at sannsynligheten blir større for at irisen er av type versicolor. Motsatt; dersom $\\beta < 0$ vil en økning i $X$ minske sansynligheten for versicolor (altså øke sansynligheten for setosa). La oss sjekke om dette gir mening ved å se på variablene i et scatterplot. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "48443006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fd276bdc110>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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N9L+DnoiIiDiPco/eqUt8DNXWQlUVeL2xXc6qVas4/vjjaW1tDSqfN28el19+OQB//OMfmTJlCgMHDuTkk0/mjjvu4MiRIx3TulwuVq5cycUXX0x2djZ33XUXH330EfPnzyc/P5/MzExGjx7NY489BvTcjaS6uprPfe5z5ObmMmjQIM4991z++c9/AtDa2sqdd97JCSecQEZGBpMmTeL555/vc702btzItGnTyMjIYPjw4Xzve98Livn888/n2muvZcmSJQwdOpTPfOYzx7QdRWKjDCgHUoGitnE5sCpOy18IbMDs7oe0jTcAV8Zp+SIiIhJr8co7QLlHvHMPtbDHQEMDlJWBxwN+P+TkQHExlJZCVgwa1L74xS9y/fXX4/F4mD17NgAfffQRL7zwAn/84x954YUXuOyyy3jooYc6/pAXLlwIwO23395Rz+23387y5ct54IEHSE1N5dZbb2Xr1q0899xzDB06lH/84x8cOnSoxxh2797NzJkzOf/889mwYQO5ubm88sorHX/kDz74IPfddx+rVq1i8uTJPProo8ybN4/q6mpGjx7dY31z585lwYIFrFmzhvfee4+rrrqKgQMH8j//8z8d0/3yl7/kW9/6Fq+88gqWZUVrk4pESS2mZb1rN/j2sQeYT2y7x1dhWtZzAHdbWfu4EqhG3eNFREQSV7zzDlDuEffcw+qHfD6fBVg+ny+o/NChQ9bWrVutQ4cOHVP9999vWWefbVmXXGJZl19uxmefbcpjZd68edY3vvGNjverVq2yhg0bZh05csQ699xzrR/+8IdB0//qV7+yhg8f3vEesG644YagaS666CLriiuu6HF5O3futABr8+bNlmVZ1rJly6xRo0ZZTU1NPU4/YsQI6+677w4qO+uss6yrr766x/puvvlma+zYsVZra2vH9D/72c+snJwcq6WlxbIsyzrvvPOsSZMm9bZJOkTrexUJ3zuWZRVblnW5ZVkLuwyXW5Y1q+3zWHrasqw8y7I+ZVnWqV2GT7WVPx3j5UuoejsuSeS0TUXE6aJxjmpH3mFZyj360tf3GsmxSV3io6y21vzCVVBghoyMztceT+y6qcyfP59169YRCAQAeOKJJ/jKV75Camoqb775JnfeeSc5OTkdw1VXXcWePXtobGzsqGPq1KlBdX7rW9/iqaeeYtKkSdx00028+uqrvS5/y5YtnHvuuT1ee1JfX8+HH37IOeecE1R+zjnn8O677/ZY37vvvsuMGTNwuVxB0/v9fv7973/3GrOIs+RjWrd93cp9QDaxv/ncaMw1643dyhvbysfEePkiIiISK3blHaDcI56UsEdZXZ3pjuJ2B5e73abLSqz+cS666CJaW1tZv349NTU1vPzyy1x22WWAuYbjjjvuYMuWLR3DO++8w44dOxg4cGBHHdnZ2UF1XnjhhXzwwQfccMMNfPjhh8yePZsbb7yxx+VnZmZ+Yoxd/wEALMs6qqyvz6y2biddy7vHLOIshZgbzHnbhkCX18XEPmGfiLnBnB/zI0Fz29jfVq7u8CIiIonKrrwDlHvEkxL2KMvPN9eO+Lo1qPl8kJ1tfvGKhczMTC699FKeeOIJfv3rXzNmzBimTJkCwJlnnsm2bds45ZRTjhpSUvr+E8jPz2fBggWsXbuWFStWUFZW1uN0p59+Oi+//DLNzc1HfZabm8uIESP461//GlT+6quvMm7cuB7rGz9+PK+++mrQtSGvvvoqgwYN4vjjj+8zZhFnKQVKgBagpm1c0lYeD6uBWUArsL9tPKutXERERBKVXXkHKPeIJ910LsoKC82NHsrLzXu32/zTeL1QUhLbf5z58+dz0UUXUV1d3fELF8Btt93Gf/3XfzFy5Ei++MUvkpKSwttvv80777zDXXfd1Wt9t912G1OmTGHChAkEAgH+9Kc/9fpHfu211/KTn/yEr3zlKyxbtgy3201lZSXTpk1j7NixfPe73+X222/nU5/6FJMmTeKxxx5jy5YtPPHEEz3Wd/XVV7NixQquu+46rr32WrZt28btt9/OkiVLPvEfXcRZsoDFmBvMeYn/c9iHAr/H3GBuO3oOu4iISHKwM+8A5R7xooQ9BkrbGs48HqipMb9wlZR0lsfKrFmzGDx4MNu2beOrX/1qR/kFF1zAn/70J+68805+/OMfk5aWxqmnnsqVV/b9WKf09HSWLVvG+++/T2ZmJueeey5PPfVUj9MOGTKEDRs28N3vfpfzzjuP1NRUJk2a1HHtyPXXX099fT3f+c538Hq9jB8/nmeffbbHuzQCHH/88fz5z3/mu9/9LmeccQaDBw/mm9/8Jt///vcj3Doidot3ot7dBJSoi4iIJBe78g5Q7hEvLsvqf8/Cqq+vx+124/P5yM3N7Sg/fPgwO3fuZNSoUUHXV0TK6zVD+80fxB7R/l5FRKKtt+OSRE7bVEScLprnqMo7nKOv7zWSY5Na2GNI/zAiIiIiIhJryjuSly4GFhEREREREXEgJewiIiIiIiIiDqSEXURERERERMSBlLCLiIiIiIiIOJASdhEREREREREHUsIuIiIiIiIi4kB6rJuISFzUAnVAQdvwSeWRzhPN2Jwwj5Ml2/qISI9qa6GuTs/NEhFbKGEXEYmpBqAM8AB+IAcoBi4D1vZQXgpYEcyTFcXY+qovXvM4WbKtj4j0qKEBysrA4wG/H3JyoLgYSkshS//rIhIf6hLfD/zP//wPkyZNOuZ6KioqcLlcHDx4MOR5FixYwCWXXHLMyxZJXGVAOZAKFLWNy4GreilfFeE80Yytr/riNY+TJdv6iEiPysqgvBxSU6GoyIzLy2GV/tdF+qLcI7pclmVZdgcRb/X19bjdbnw+H7m5uR3lhw8fZufOnYwaNYqBAwfaGGF0+f1+AoEAQ4YMOaZ6mpqaOHDgAIWFhbhcrpDm8fl8WJZFXl7eMS37WCTr9yqJoBaTZKcS3GV6F7AZmIxJ+Np5gca211lhzNMCrCa8btm9xdZXffGax8lisz69HZckctqmckxqa+Gqq0yS3rUbvNcLLS2werW6x8sxS9ZzVOUevX+vkRyb1MLeD+Tk5PT5D9PU1BRSPenp6QwbNizkfxgAt9tt6z+MiL3qMF2m3d3K04FA27grN3AQ+CjMeRowCWM0YuurvnjN42TJtj4i0qO6OtMN3t3tf93tNl3lvfpfF+mNco/oUsIeU7VAFbE+gVu1ahXHH388ra2tQeXz5s3j8ssvP6pbSntXkeXLlzNixAjGjBkDwKuvvsqkSZMYOHAgU6dO5fe//z0ul4stW7YAR3dLefzxx8nLy+OFF15g3Lhx5OTk8NnPfpY9e/Yctax2ra2t/OhHP+KUU04hIyODoqIi7r777o7Ply5dypgxY8jKyuLkk0/m1ltvpbm5ObobTCRu8jHXN/u6lTcBGW3jrnxAHnBcmPNkE36rbm+x9VVfvOZxsmRbHxHpUX6+uWbd1+1/3eeD7Gy1rosDxSfvAOUe8aaEPSYagAcw3SavB65se9/Y10wR++IXv8i+ffvweDwdZR999BEvvPAC8+fP73Gel156iXfffZcXX3yRP/3pT3z88cdcdNFFnHbaabz11lv84Ac/YOnSpZ+47MbGRu69915+9atfsWnTJnbt2sWNN97Y6/TLli3jRz/6Ebfeeitbt27lySefpLCwsOPzQYMG8fjjj7N161YefPBBHnnkER544IEwtoaIkxRibkbmbRsCbeN6YHrbuGu5F/hs2xDOPMWEnyj2Fltf9cVrHidLtvURkR4VFpobzHm9ZggEOl8XFythFweJb94Byj3iTXeJj4n2GxIVYK419bW9B1gc9aUNHjyYz372szz55JPMnj0bgN/97ncMHjyY2bNn8+qrrx41T3Z2NqtXryY93XSvXblyJS6Xi0ceeYSBAwcyfvx4du/ezVVXXdXnspubm1m5ciWf+tSnALj22mu58847e5z2448/5sEHH+SnP/0pl19+OQCf+tSn+PSnP90xzfe///2O1yeddBLf+c53+M1vfsNNN90UxhYRcZLStrEHqMG0wpYAXwN+1UN5aZd5I5knGrH1VV+85nGyZFsfEelRadv/tMcDNTWmZb2kpLNcxBHim3eAco94U8IedbWYk7iuz+VtH3uA+cSiBWb+/PksXLiQn//852RkZPDEE0/wla98hdTU1B6nP+200zr+YQC2bdvG6aefHnRjhGnTpn3icrOysjr+YQCGDx+Ot5frut59910CgUDHP3ZPysvLWbFiBf/4xz/w+/0cOXJENwuSBJeFOWDOx7TCdt039Fbe12d9zRPN2Oyex8mSbX1EpEdZWbB4Mcyfb1rW9Rx2cRx78g5Q7hFP6hIfdfbckOiiiy6itbWV9evXU1NTw8svv8xll13W6/TZ2dlB7y3LOuqGDqE8QCAtLS3ovcvl6nW+zMzMPuuqrKzkK1/5ChdeeCF/+tOf2Lx5M7fcckvIN6YQcbYCYCJHHzh7K490nmjG5oR5nCzZ1kdEelRQABMnKlkXB7LvRqjKPeJHCXvU2XNDoszMTC699FKeeOIJfv3rXzNmzBimTJkS8vynnnoqb7/9NoFAoKPsjTfeiGqMo0ePJjMzk5deeqnHz1955RVOPPFEbrnlFqZOncro0aP54IMPohqDiIiIiEhysO9GqMo94kcJe9TZd0Oi+fPns379eh599NE+f+HqyVe/+lVaW1tZuHAh7777Li+88AL33nsvQFiPUujLwIEDWbp0KTfddBNr1qzhn//8J5WVlfziF78A4JRTTmHXrl089dRT/POf/+Shhx7imWeeicqyRURERESSi703QlXuER9K2GOiFHMDohbMDYlaiMcNiWbNmsXgwYPZtm0bX/3qV8OaNzc3lz/+8Y9s2bKFSZMmccstt3DbbbcBBF1bcqxuvfVWvvOd73Dbbbcxbtw4vvzlL3dcd3LxxRezePFirr32WiZNmsSrr77KrbfeGrVli4iIiIgkF3vyDlDuES8uK5SLBZJMfX09brcbn88XdFOBw4cPs3PnTkaNGhWlP5T2X7gS84ZETzzxBFdccQU+n+8TrwFxsuh/ryIi0dXbcUkip20qIk4X3XPUxM47oH/kHpEcm3SX+JhKrH+YNWvWcPLJJ3P88cfz97//naVLl/KlL30pof9hRERERESSX2LlHaDcI1RK2KXD3r17ue2229i7dy/Dhw/ni1/8InfffbfdYYmIiIiISJJR7hEaJezS4aabbuKmm26yOwwREREREUlyyj1Co4RdRKRfqMU8rzWcLnORzJOo+tO6iiSY2lqoqzPPQdez0EWkn1HCLiKS1BqAMsAD+DHPay3G3D02K4rzJKr+tK4iCaahAcrKwOMBvx9ycqC4GEpLIUv/nyLSP+ixbj3ohzfOT2r6PqV/KwPKgVSgqG1cDqyK8jyJqj+tq0iCKSuD8nJITYWiIjMuL4dV+v+U5KJz1eQS7e9TCXsXaWlpADQ2NtociURT+/fZ/v2K9B+1mJbj9m7eGV1eezCPf4nGPImqP62rSIKprTUt6+3d4DMyOl97PODV/6ckPuUeySnauYe6xHeRmppKXl4e3raDQFZWFi6Xy+aoJFKWZdHY2IjX6yUvL4/U1FS7QxKJszpMN++ibuVuoIbO57Ue6zyJqj+tq0iCqasz3eCLuv1/ut1QU2MSdl3PLglOuUdyiVXuoYS9m2HDhgF0/ONI4svLy+v4XkX6l3zMNdk+ghNPH5BNz8loJPMkqv60riIJJj/fXLPu8wUn5j4fZGcrWZekodwj+UQ791DC3o3L5WL48OEUFBTQ3NxsdzhyjNLS0tSyLv1YIeYGauVt792YZNQLlNBzQhrJPImqP62rSIIpLDQ3mCtv+/90u02y7vVCSYkSdkkayj2SSyxyDyXsvUhNTVWiJyJJoLRt7MF0887GJKOlvc4R2TyJqj+tq0iCKW37P/R4TDf47GyTrJfq/1OSj3IP6Y3L6oe3Jayvr8ftduPz+cjNzbU7HBGROPDSeU12qC1TkcyTqOxdVx2Xok/bNIl4vZ3XrKtlXUQSWCTHJrWwi4j0C5Ekov0hUW/Xn9ZVJMEoUReRfkyPdRMRERERERFxICXsIiIiIiIiIg6khF1ERERERETEgZSwi4iIiIiIiDiQEnYRERERERERB1LCLiIiIiIiIuJASthFREREREREHEgJu4iIiMTN8uXLcblc3HDDDX1Ot3HjRqZMmcLAgQM5+eSTWblyZXwCFBERcRAl7CIiCacWqAK8YXwWyTyRxuBkiRp3cnj99dcpKyvj9NNP73O6nTt3MnfuXM4991w2b97MzTffzPXXX8+6deviFKmIg9TWQlUVeLXfEumPBtgdgIiIhKoBKAM8gB/IAYqBUsDq5bPLgLVhzlMKZEUQQ2/zOEGixp08/H4/8+fP55FHHuGuu+7qc9qVK1dSVFTEihUrABg3bhxvvPEG9957L1/4whfiEK2IAzQ0QFkZeDzg90NODhQXQ2kpZGm/JdJfqIVdRCRhlAHlQCpQ1DYuB1b18dlVEcyzKsIYnCxR404e11xzDZ/73Of4z//8z0+c9rXXXmPOnDlBZRdccAFvvPEGzc3NsQpRxFnKyqC8HFJToajIjMvLYZX2WyL9iVrYRUQSQi2mdbigbaDL+Pku77t+dhioBCaHMQ9ty5nf5X0oMfQ2jxMkatzJ46mnnuKtt97i9ddfD2n6vXv3UlhYGFRWWFjIkSNH2LdvH8OHDz9qnkAgQCAQ6HhfX19/bEGL2Km21rSsFxSYATrHHg/Mn9/5XkSSmlrYRUQSQh2mK7e7W7kbOAh81MNn6UCgbRzqPG5M9/GerpXsK4be5nGCRI07OdTU1PDtb3+btWvXMnDgwJDnc7lcQe8ty+qxvN3y5ctxu90dw8iRIyMPWsRudXWmG7y7237L7TZd5XU9u0i/oYRdRCQh5GOuu/Z1K/cBecBxPXzWBGS0jUOdxwdk03OLc18x9DaPEyRq3MnhzTffxOv1MmXKFAYMGMCAAQPYuHEjDz30EAMGDKClpeWoeYYNG8bevXuDyrxeLwMGDGDIkCE9LmfZsmX4fL6OoaamJibrIxIX+fnmmnVft/2WzwfZ2WpdF+lH1CVeRCQhFGJuklbe9t6NSTi9QElbWffP6oHpmBZmb4jztH/W08ngJ8Xg1BPIRI07OcyePZt33nknqOyKK67g1FNPZenSpaSmph41z4wZM/jjH/8YVPaXv/yFqVOnkpaW1uNyMjIyyMjIiF7gInYqLDQ3mCtv22+53SZZ93qhpEQJu0g/ooRdRCRhlLaNPUANpnW4pEt5T599DfhVmPN0/SySGJwoUeNOfIMGDWLixIlBZdnZ2QwZMqSjfNmyZezevZs1a9YAsGjRIn7605+yZMkSrrrqKl577TV+8Ytf8Otf/zru8YvYprRt/+TxQE2NaVkvKeksF5F+QQm7iEjCyAIWY26S5iX4Jmr08Vkk80Qag1Mlatz9w549e9i1a1fH+1GjRvHnP/+ZxYsX87Of/YwRI0bw0EMP6ZFu0r9kZcHixeYGc15v8A3oRKTfcFntd3HpR+rr63G73fh8PnJzc+0OR0RE+jkdl6JP21RERJwmkmOTbjonIiIiIiIi4kBK2EVEREREREQcSAm7iIiIiIiIiAMpYRcRERERERFxICXsIiIiIiIiIg6khF1ERERERETEgZSwi4iIiIiIiDiQrQn78uXLOeussxg0aBAFBQVccsklbNu27RPn27hxI1OmTGHgwIGcfPLJrFy5Mg7Rioi0qwWqAG+I5ZHOI72L9nbT9yDSr1RVwTPPQHW13ZGIiPRpgJ0L37hxI9dccw1nnXUWR44c4ZZbbmHOnDls3bqV7OzsHufZuXMnc+fO5aqrrmLt2rW88sorXH311eTn5/OFL3whzmsgIv1LA1AGeAA/kAMUA5cBa3soLwWsCObJitcKJaDevoNIt1u06xMRR/N6YeFCqKyEQAAyMmD6dFi9GoYOtTs6EZGjuCzLsuwOol1dXR0FBQVs3LiRmTNn9jjN0qVLefbZZ3n33Xc7yhYtWsTf//53XnvttZCWU19fj9vtxufzkZubG5XYRaQ/eAAoBwoAN+DDtMjmA3U9lJe0zRfuPIvjsjaJqbfvINLtFu36IqPjUvRpm0qPLrkENmyAnBzIyoLGRvD7YdYs+P3v7Y5ORJJcJMcmR13D7vP5ABg8eHCv07z22mvMmTMnqOyCCy7gjTfeoLm5ucd5AoEA9fX1QYOISHhqMa2wBW1DRts4F6jEJHtdywuA59uG3ubJ7WEeD+qW3ZvevoNIt1u06xMRR6uqMi3rOTngdkNamhnn5JhydY8XEQdyTMJuWRZLlizh05/+NBMnTux1ur1791JYWBhUVlhYyJEjR9i3b1+P8yxfvhy3290xjBw5Mqqxi0h/UIfpMu3uVp4OBIC0buVu4CDwUR/zpPcwTwNKFHvT23cQ6XaLdn0i4mg7dphu8FndLnfJyjLl27fbE5eISB8ck7Bfe+21vP322/z617/+xGldLlfQ+/Ze/d3L2y1btgyfz9cx1NTUHHvAItLP5GOub/Z1K2/CtMx27+HjA/KA4/qYp6mHebIxLbxytN6+g0i3W7TrExFHGz3aXLPe2Bhc3thoyseMsScuEZE+OCJhv+6663j22WfxeDyccMIJfU47bNgw9u7dG1Tm9XoZMGAAQ4YM6XGejIwMcnNzgwYRkfAUYm5G5m0bAm3jemA6ndc+B7pM89m2obd56nuYpxglir3p7TuIdLtFuz4RcbSJE80N5vx+8PmgudmM/X5TPmGC3RGKiBzF1oTdsiyuvfZann76aTZs2MCoUaM+cZ4ZM2bw4osvBpX95S9/YerUqaSlde+SKiISTaWYm5G1ADVt4xJgdS/lpRHOI73rbXtGut2iXZ+IONrq1eYGc62tsH+/Gc+aZcpFRBzI1rvEX3311Tz55JP84Q9/YOzYsR3lbrebzMxMwHRn3717N2vWrAHMY90mTpxIaWkpV111Fa+99hqLFi3i17/+dciPddOdY0Xk2LS3wrbfoOyTyiOdR3oX7e1m7/eg41L0aZtKn6qrzTXrY8aoZV1E4iaSY5OtCXtv15w/9thjLFiwAIAFCxbw/vvvU1FR0fH5xo0bWbx4MdXV1YwYMYKlS5eyaNGikJerg7iIiDiJjkvRp20qIiJOE8mxaUCMY+pTKL8VPP7440eVnXfeebz11lsxiEhERERERETEGRxx0zkRERERERERCaaEXURERERERMSBlLCLiIiIiIiIOJASdhEREREREREHUsIuIiIiIiIi4kBK2EVEREREREQcSAm7iIiIiIiIiAPZ+hx2EZHkUgvUAQVtQ1dVwA5gDDAhCvUlomRbHxGJWEUFbNkCZ54JM2faHU381dZCXR0UFJhBRKIgFucZ9p+7KGEXETlmDUAZ4AH8QA5QDJS2vV8IVAIBIAOYDqwGhkZQX1asViKGkm19RCRiO3fCvHmwfTu0tkJKCowZA+vXQ1GR3dHFXkMDlJWBxwN+P+TkQHExlJZClvaHIpGJxXmGc85d1CVeROSYlQHlQCpQ1DYuB1ZhkvUNmN3tkLbxBuDKCOtLRMm2PiISsXnzYOtWcLkgM9OMt26Fz33O7sjio6wMysshNdX8QJGaat6v0v5QJHKxOM9wzrmLEnYRkWNSi/n1tb2rVEaX188Cr2J+lXUDaW3jHEyLe3WY9XkAb+xWJSaSbX1EJGIVFaZlPS3NJOupqWaclmbKN22yO8LYqq01Levt3eAzMjpfezzg1f5QJHyxOM9w1rmLEnYRkWNSh+kq5e5W7gb2AYc5uutUFqZ7/PYw62sg8RLcZFsfEYnYli2mG3x6enB5eropf+stW8KKm7o60w3e3W1/6HabrvJK2EUiEIvzDGeduyhhFxE5JvmYFnNft3If5hr1gUBjt88aMb/WjgmzvmwS72ZtybY+IhKxSZPMNetNTcHlTU2m/MwzbQkrbvLzzTXrvm77Q58PsrN18zmRiMTiPMNZ5y5K2EVEjkkh5iYk3rYh0OX1POBszK+0PqC5bezH3Hiup7vF91VfMYmX4Cbb+ohIxM4/39xgrrkZDh2ClhYzbm425cl+t/jCQnODOa/XDIFA5+viYiXsIhGJxXmGs85dlLCLiByzUqAEaAFq2sYlbeWrgVlAK7C/bTyrrTyS+hJRsq2PiERs/XoYPx4syyTrlmXer19vd2TxUVoKJSXmx4qaGjMuKTHlIhKhWJxnOOfcxWVZlhX3pdqsvr4et9uNz+cjNzfX7nBEJGm0//ra07M6qzHXrIfzHPa+6ktEybY+0aPjUvRpmzrcpk3mmvX++hz29pZ1PYddJIpicZ4R3TojOTbpOewiIlHT1858AqEn6qHUl4iSbX1EJGIzZ/bPRL2dEnWRGIjFeYb95y7qEi8iIiIiIiLiQErYRURERERERBxICbuIiIiIiIiIAylhFxEREREREXEgJewiIiIiIiIiDqSEXURERERERMSBlLCLiIiIiIiIOJCewy4i0oN9+6poaNhBdvYYhg7t/vz0KmAHMIbQn61eC9QR++d59hZbJMuP1zzxrE9EHKG2Furqov888lDrjdXyRUSiTAm7iEgXDQ1ePvxwIUOHVnLccQFaWjLYsWM6xx+/mqysVmAhUAkEgAxgOrAaGNpbjUAZ4AH8QA5QDJQCWVGM3NtLbA8CT4e5/EhijvZ6xmu7iUhcNTRAWRl4POD3Q04OFBdDaSlkHcP/dqj1xmr5IiIxoi7xIiJdfPjhQkaM2EBrawqNjUNobU1hxIgN7N59JSYh3oDZdQ5pG28AruyjxjKgHEgFitrG5cCqKEfeW2z/FcHyI4k52usZr+0mInFVVgbl5ZCaCkVFZlxeDquO8X871HpjtXwRkRhRwi4i0mbfviqGDq3k8OEcmprcWFYaTU1uDh/OoaDgZVpaXsa09LqBtLZxDqZVu7qHGmsxLcTt3bkzurz2YFrFo6GqLYbusQ0EtreNQ11+JDFHez3jtd1EJK5qa03Ldns39IyMztceD3gj/N8Otd5YLV9EJIaUsIuItGlo2EFqaoDm5uBukc3NWaSlBYDDHN0dOwvTBX17DzXWYbpzu7uVuzFdvqN1crijLYbusWUArW1DqMuPJOZor2e8tpuIxFVdnemG7u72v+12m67qkSbModYbq+WLiMSQEnYRkTbZ2aNpackgLa0xqDwtrZHm5gxMS3Vjt7kaMYnxmB5qzMe0evu6lfuAbKJ3E7XRbTF0jy2A2c1339X3tfxIYo72esZru4lIXOXnm2vGfd3+t30+yM6O/OZvodYbq+WLiMSQEnYRkTZDh05k377pDBzoJz3dh8vVTHq6j4ED/Xi955Kaei6m5dcHNLeN/Zibu/V0t/hCzI3SvG1DoMvrYqKXeE5si6F7bIcxPyQcDmP5kcQc7fWM13YTkbgqLDQ3ePN6zRAIdL4uLo48YQ613lgtX0QkhpSwi4h0cfzxq/nww1mkpLSSlbWflJRWPvxwFscfvxpzN/hZmC7m+9vGs9rKe1MKlAAtQE3buKStPJp6i219BMuPJOZor2e8tpuIxFVpKZSUQEsL1NSYcUmJKY9HvbFavohIjLgsy7LsDiLe6uvrcbvd+Hw+cnNz7Q5HRBxo375qGhq29/Ic9mrMNevhPIe9vYU41s8T7y22SJYfr3niWZ8z6bgUfdqmDtfesh3t56CHWm+sli8i0odIjk1K2HUQFxERm+m4FH3apiIi4jSRHJvUJV5ERERERETEgZSwi4iIiIiIiDiQEnYRERERERERB1LCLiIiIiIiIuJASthFREREREREHEgJu4iIiIiIiIgDKWEXERERERERcSAl7CIiIiIiIiIONMDuAEREoqcWqAMK2oY4L70W6uqgoMAMIiJRYffOJZzl2x2riITI3nMmCZ0SdhFJAg1AGeAB/EAOUAyUAlmxX3oDlJWBxwN+P+TkQHExlJZCVuwXLyLJyu6dSzjLtztWEQmRvedMEj51iReRJFAGlAOpQFHbuBxYFZ+ll0F5OaSmQlGRGZeXw6r4LF5EkpXdO5dwlm93rCISInvPmSR8SthFJMHVYn4lbu/SldHltQfwxnbptaZBqb33Z0ZG52uPB7yxXbyIJCu7dy7hLN/uWEUkRPaeM0lklLCLSIKrw3Tpcncrd2O6fcX24FNXZ3p/urst3u02PUR1nioiEbF75xLO8u2OVURCZO85k0RGCbuIJLh8zPVXvm7lPiCbWN9IJT/fXKrp67Z4nw+ys3XPJRGJkN07l3CWb3esIhIie8+ZJDJK2EUkwRVibpbibRsCXV4XE+uDT2Ghua+S12uGQKDzdXGxzlNFJEJ271zCWb7dsYpIiOw9Z5LI6C7xIpIEStvGHqAG8ytxSZfyGC+9bTEeD9TUmAalkpLOchGRiNi9cwln+XbHKiIhsvecScLnsizLsjuIeKuvr8ftduPz+cjNzbU7HBGJmvZfie15pmh7g5IePyzh0nEp+pJqm9q9cwln+XbHKiIhsvecqb+K5NikFnYRSSL2HnR0fioiMWH3ziWc5dsdq4iESIl6otA17CIiIiIiIiIOpIRdRERERERExIGUsIuIiIiIiIg4kBJ2EREREREREQdSwi4iIiIiIiLiQErYRURERERERBxICbuIiIiIiIiIAylhF5GkUVsLVVXg9cZ2nkjEaznRVQtUAQkVtDjMww8/zOmnn05ubi65ubnMmDGD5557rtfpKyoqcLlcRw3vvfdeHKOWiFVVwTPPQHV1dKYD+3egdi9fRPq1AXYHICJyrBoaoKwMPB7w+yEnB4qLobQUsrKiN0+8YrNfA1AGeAA/kAMUA6WAY4MWhzrhhBO45557OOWUUwD45S9/ycUXX8zmzZuZMGFCr/Nt27aN3Nzcjvf5+fkxj1WOgdcLCxdCZSUEApCRAdOnw+rVMHRo+NOB/TtQu5cvIoJa2EUkCZSVQXk5pKZCUZEZl5fDqlXRnSdesdmvDCgHUoGitnE54OigxaEuuugi5s6dy5gxYxgzZgx33303OTk5VFZW9jlfQUEBw4YN6xhSU1PjFLFEZOFC2LABUlJgyBAz3rABrrwysunA/h2o3csXEUEJu4gkuNpa0/hRUGCGjIzO1x5Pzz0YI5knXrHZrxbTsl7QNmR0ee1B3ePlWLS0tPDUU0/R0NDAjBkz+px28uTJDB8+nNmzZ+PxeD6x7kAgQH19fdAgcVJVZVrMc3LA7Ya0NDPOyTHl7d3eQ50O7N+B2r18EZE2SthFJKHV1Zmeim53cLnbbXoz9nROFck88YrNfnWYbvDdgsaN6SrvyKDF4d555x1ycnLIyMhg0aJFPPPMM4wfP77HaYcPH05ZWRnr1q3j6aefZuzYscyePZtNmzb1uYzly5fjdrs7hpEjR8ZiVaQnO3aY7u3du4lnZZny7dvDmw7s34HavXwRkTa6hl1EElp+vmmc8flMw0c7nw+ys4PLjmWeeMVmv3zMNes+TKt6Ox+Q3a1MJDRjx45ly5YtHDx4kHXr1nH55ZezcePGHpP2sWPHMnbs2I73M2bMoKamhnvvvZeZM2f2uoxly5axZMmSjvf19fVK2uNl9GjTAt3YGJzgNjaa8jFjwpsO7N+B2r18EZE2amEXkYRWWGjuAeT1miEQ6HxdXNzzOVUk88QrNvsVYm4w520bAl1eF6OEXSKRnp7OKaecwtSpU1m+fDlnnHEGDz74YMjzT58+nR07dvQ5TUZGRsed6NsHiZOJE82N4/x+k9A2N5ux32/K228uGOp0YP8O1O7li4i0UcIuIgmvtBRKSqClBWpqzLikxJRHc554xWa/UqAEaAFq2sYlbeUix86yLAKBQMjTb968meHDh8cwIjlmq1fDrFnQ2gr795vxrFmmPJLpwP4dqN3LFxEBXJZlWXYHEW/19fW43W58Pp9+gRdJIu2NH+33BYrVPPGKzX7tLevtN52TWEnm49LNN9/MhRdeyMiRI/n444956qmnuOeee3j++ef5zGc+w7Jly9i9ezdr1qwBYMWKFZx00klMmDCBpqYm1q5dyz333MO6deu49NJLQ15uMm9TR6uuNteijxkT3GIe6XRg/w7U7uWLSNKI5Nika9hFJGlEci4Vr/OvxDzPU6Iux662tpavfe1r7NmzB7fbzemnn96RrAPs2bOHXbt2dUzf1NTEjTfeyO7du8nMzGTChAmsX7+euXPn2rUKEo4JEz45AQ9nOrB/B2r38kWkX1MLu351FxERm+m4FH3apiIi4jSRHJt0DbuIiIiIiIiIAylhFxEREREREXEgJewiIiIiIiIiDqSEXURERERERMSBlLCLiIiIiIiIOJASdhEREREREREHsjVh37RpExdddBEjRozA5XLx+9//vs/pKyoqcLlcRw3vvfdefAIWERERERERiZMBdi68oaGBM844gyuuuIIvfOELIc+3bdu2oOfW5efnxyI8EYmx2lqoq4OCAjMcq0cfhb/+Fc47Dy6/PLTlRBJDVRXs2AFjxsCECUG1AXVAQdsQ6mciztTa2so//vEPvF4vra2tQZ/NnDnTpqj6oWjvLKGvHVl86g1nnRJp/RNILDZreMc6HRdFQmFrwn7hhRdy4YUXhj1fQUEBeXl50Q9IROKioQHKysDjAb8fcnKguBhKSyErK/z6Xn8dZs+Gjz827x97DK67Dp5/Hv7v/3pejmWFH4PXCwsXQmUlBAKQkQHTp8Pq1Q0MHVoGeAA/kAMUA6WABfT2WQQrKxInlZWVfPWrX+WDDz7Asqygz1wuFy0tLTZF1o9Ee2cJfe3IYOjQyGMNtd5w1imR1j+BxGKzQgOhH+vCmVZEIk7YX3rpJV566aUef3V/9NFHjzmwvkyePJnDhw8zfvx4vv/971NcXBzT5YlIdJWVQXm5+UW/qAh8PvMeYPHi8Ovrmqy3+/hjcwIydWrPy4HwY1i4EDZsMCc3Q4ZAY6N5/4c/lPHNb5ZjWgiKAB/QZUH09lkEKysSJ4sWLWLq1KmsX7+e4cOH43K57A6p/4n2zhJ635FdeSV8wqWJUak3nHVKpPVPILHYrCYBD/VYF860IhLRNex33HEHc+bM4aWXXmLfvn189NFHQUOsDB8+nLKyMtatW8fTTz/N2LFjmT17Nps2bepzvkAgQH19fdAgIvaorTW/6rd3wcvI6Hzt8ZjGj3A8+mhnsp6S0jkANDWZc7Huy3n+eTOEE0NVlWmQyckBtxvS0sz4pJNqOeEEDz5fe5e+DDq79z3fNvT0mQcIc2VF4mjHjh388Ic/ZNy4ceTl5eF2u4MGibFo7yyh9x1ZTo4pr66OLNZQ6w1nnRJp/RNILDar6druIbRjXTjTighE2MK+cuVKHn/8cb72ta9FO54+jR07lrFjx3a8nzFjBjU1Ndx77719Xku3fPly7rjjjniEKCKfoK7OdMErKgoud7uhpsacLIRzLd1f/9r3591b3t1u+PBD83r48NBj2LHD9J4cMiS4/Pjj68jM9HPwYBHBOYwbaFsQ3RaEG6jBnJjouj1xpv/4j//gH//4B6eccordofRP0d5ZQu87sqws2L8ftm+P7HruUOsNZ50Saf0TSCw2q7kO3Y9pLQ+qlaOPdeFMKyIQYQt7U1MTZ599drRjicj06dPZsWNHn9MsW7YMn8/XMdTU1MQpOhHpLj/fNGb4fMHlPh9kZ4d/ovDpT/f9+aBBRy8nL88M4cQwerRpiWhsDC7fvTufQ4dyyMvrVhk+IK9t6OmzbHRSIk7z9ttvdwzXXXcd3/nOd3j88cd58803gz57++237Q41+UV7Zwm978gaG035mDGRxRpqveGsUyKtfwKJxWaFfMx16KEc68KZVkQgwoT9yiuv5Mknn4x2LBHZvHkzw7s3k3WTkZFBbm5u0CAi9igsNNeWe71mCAQ6XxcXh3+y8I1vdCblra2dA0B6umk46b6cz37WDOHEMHGiuS+R329ObJqbzfj99wv597+Lcbu9mJaBQNvYC3y2bejps2J0YiJOM2nSJCZPnsykSZP4whe+wLvvvss3vvENzjrrrKDPJk+ebHeoyS/aO0vofUfm95vySFuXQ603nHVKpPVPILHYrFCIOaaFcqwLZ1oRgTC6xC9ZsqTjdWtrK2VlZfzv//4vp59+OmlpaUHT3n///SHV6ff7+cc//tHxfufOnWzZsoXBgwdTVFTEsmXL2L17N2vWrAFgxYoVnHTSSUyYMIGmpibWrl3LunXrWLduXairISIOUFpqxh6P6YKXnQ0lJZ3l4dq0CWbODO7+PmgQvPCCuSyxr+WEE8Pq1ea+RJWVpvdkRgbMmgUXX9w+kwfTpS8bKMHc8ZYQPhNxhp07d9odgnQV7Z0l9L4jW7362GINtd5w1imR1j+BxGKzdh7TQjnWhTOtiLis7s9q6UU4d2L3eDwhTVdRUdFjvZdffjmPP/44CxYs4P3336eiogKAH//4x5SVlbF7924yMzOZMGECy5YtY+7cuSHHBlBfX4/b7cbn86m1XcRG7b/qR+sZsL/8JWzcePRz2PtaTiQxVFebSx2PfnxveytBT8+U7esz6e+ceFzatGkTZ599NgMGBP+2f+TIEV599VXHP4fdids0YtHeWUJfO7L41BvOOiXS+ieQWGzW8I51Oi5K/xPJsSnkhD2ZJNVBXEREEp4Tj0upqans2bOHgm5n8vv376egoMDxz2F34jYVEZH+LZJjU0TXsH/jG9/g4+63XgYaGhr4xje+EUmVIiIi4iCWZfX47PX9+/eTnZ1tQ0QiIiL9T0SPdfvlL3/JPffcw6But18+dOgQa9as4dFHH41KcCIiIhJfl156KQAul4sFCxaQkZHR8VlLSwtvv/22Y54UIyIikuzCStjr6+uxLAvLsvj4448ZOHBgx2ctLS38+c9/PqrrnIiIiCQOt9sNmBb2QYMGkZmZ2fFZeno606dP56qrrrIrPBERkX4lrIQ9Ly8Pl8uFy+ViTA/PqnS5XNxxxx1RC05ERETi67HHHgPgpJNO4sYbb1T3dxERERuFlbB7PB4sy2LWrFmsW7eOwYMHd3yWnp7OiSeeyIgRI6IepIiIiMTX7bffbncIIiIi/V5YCft5550HmOe0FhUV9XgzGhEREUlMkydPDvnY/tZbb8U4GhEREQk5YX/77beD3r/zzju9Tnv66adHHpGIiIjY4pJLLul4ffjwYX7+858zfvx4ZsyYAUBlZSXV1dVcffXVNkUoIiLSv4ScsE+aNAmXy9XrY166cvqzWUUkcrW1UFcHBQVmiLeqKtixA8aMgQkTQpunr5h7q8/u9Yy+WqAOKGgbRI7WtRv8lVdeyfXXX88PfvCDo6apqamJd2iSKELdeSbfTlbCVFdXy8GDdeTlFZCf7+S/gSpgBzAGCPHEQySKQk7Yd+7c2fF68+bN3HjjjXz3u9/t+NX9tdde47777uPHP/5x9KMUEds1NEBZGXg84PdDTg4UF0NpKWRlxX75Xi8sXAiVlRAIQEYGTJ8Oq1fD0KHhx+z391zfgw/C00/bt57R1wCUAR7AD+QAxUApkJArJHHyu9/9jjfeeOOo8ssuu4ypU6fqEa4SLNSDhN0HE7FdQ0MDr79eRmamh7Q0PwcO5FBdXcy0aaVkOepvwAssBCqBAJABTAdWA72ceIjEQMgJ+4knntjx+otf/CIPPfQQc+fO7Sg7/fTTGTlyJLfeemtQlzoRSQ5lZVBebhpCiorA5zPvARYvjv3yFy6EDRvMud2QIdDYaN5feSX8/vfhx7xxY8/1/dd/QW6ufesZfWVAOaZVvQjwtb0HSMgVkjjJzMzkr3/9K6NHjw4q/+tf/xr0WFcRIPSDhN0HE7Hd66+XMXhwOY2NBTQ0FJGW5mPw4HL+9jc4/3wn/Q0sBDZgfugeAjS2vb8S+L19YUm/kxLJTO+88w6jRo06qnzUqFFs3br1mIMSEWeprTWNIe09FzMyOl97PKb1O5aqqkxLeE4OuN2QlmbGOTmmvLo6vJiffRZeffXo+jIzYft2GDjQnvWMvlpMy3p7N/iMLq89mNYDkZ7dcMMNfOtb3+Laa69l7dq1rF27lmuvvZZrrrmGxUqspKtQDxJ2H0zEdnV1tWRmemhsLKCpqQDLyqCpqYDGxgIyMz3U1Tnlb6AK07KeA7iBtLZxTlt5DyceIjESUcI+btw47rrrLg4fPtxRFggEuOuuuxg3blzUghMRZ6irMz0X3e7gcrfb9G6M9TnWjh2m23r3nnJZWaZ8+/aj5+kr5n374PDho+tLT4fWVjN0nyce6xl9dZhu8N02Am5MV/mEWyGJo+9973usWbOGzZs3c/3113P99dezefNmHn/8cb73ve/ZHZ44SagHCbsPJmK7gwfrSEvz09wc/DfQ3OwmLa2Bgwed8jewA9MNvnsX/ay28h5OPERiJKzHurVbuXIlF110ESNHjuSMM84A4O9//zsul4s//elPUQ1QROyXn29ao32+4HsD+XyQnR37+wWNHm0aYhobg8/zGhtN+Zgx4cU8dKhp6OleX1MTpKSYoat4rWf05WNaA3wE32jOB2R3KxM52pe+9CW+9KUv2R2GOF2oBwm7DyZiu7y8fA4cyCEtzUdTU+f3nZbmo7k5m7w8p/wNjMb0Smsk+EfvxrbyHk48RGIkohb2adOmsXPnTu6++25OP/10TjvtNH74wx+yc+dOpk2bFu0YRcRmhYXmnkBerxkCgc7XxcWxP8eaONHcEM7vN+d1zc1m7Peb8p7uFt9XzPPmwdlnH13foUMm+T982J71jL5CzA3mvG1DoMvrYpSwi0hUhHqQsPtgIrbLzy/k0KFisrK8pKd7cbkCpKd7ycrycuhQsYPuFj8Rc4M5P+ZH7ua2sb+tXHeLl/hxWZZl2R1EvNXX1+N2u/H5fOTm5todjkhCaGyEVavMZYYNDaYxJJ439t23z9xgLpy7xPcVc2Njz/U99BCsW2ffekZfI7AKc816A6ZlXXeJdxqnHJcGDx7M9u3bGTp0KMcdd1yfj3E9cOBAHCMLn1O2ab8R6kHC7oOJ2K6xsZG//W1V213iG2huzubQISfeJX4f5gZzuku8RE8kx6aQE/Znn32WCy+8kLS0NJ599tk+p503b15IC7eLDuIikWtvDLHr0bnV1eaa9XCew95XzL3VZ/d6Rl97y7qew+5ETjku/fKXv+QrX/kKGRkZPP74430m7JdffnkcIwufU7ZpvxPqzjP5drISpro6LwcPehPgOezVmGvW9Rx2OXYxTdhTUlLYu3cvBQUFpHS/wLNrhS4XLS0toUVsEx3ERUTESXRcij5tUxERcZpIjk0h33Sutcttk1u730JZREREksr8+fM5//zzOe+88xjT050dRUREJOYiuulcY2NjtOMQERERB8nJyeG+++7j1FNPZcSIEfz3f/83K1eu5L333rM7NBERkX4jooQ9Ly+Ps88+m5tvvpkXXniBhoaGaMclIiIiNlq1ahXvvfceH374Iffffz9ut5sHH3yQCRMmMHz4cLvDExER6RciStg3btzIvHnzeOutt/jiF7/Icccdx/Tp0/ne977Hc889F+0YRURExCaDBg3iuOOO47jjjiMvL48BAwYwbNgwu8MSERHpF475sW4tLS28/vrrrFy5kieeeILW1lbddE5ERCQMTjwuLV26lI0bN/L3v/+diRMnMnPmTM477zxmzpxJXl6e3eF9IiduUxER6d9ietO57t577z0qKirYuHEjFRUVNDc3c9FFF3HeeedFWqWIiIg4xP/7f/+P/Px8br/9di6++GLGjRtnd0giIiL9TkQJ+7Bhw2hubmbWrFmcf/753HzzzZx22mnRjk1ERERssnnz5o4f5e+77z5SU1M577zzOP/88zn//POVwIuIiMRBRNewDxs2DL/fz65du9i1axf//ve/8fv90Y5NREREbHLGGWdw/fXX8/TTT1NXV8cLL7xAVlYW119/PRMnTrQ7PBERkX4hohb2LVu2cPDgQTZt2sTGjRu59dZbqa6u5vTTT6e4uJh77rkn2nGKSIRqa6GuDgoKzBArFRWwZQuceSbMnBn8WVUV7NgBY8bAhAmfXN7XZ32tT2+fxWsbiCSbzZs3U1FRQUVFBS+//DL19fVMmjSJ4uJiu0NzrljscMKps68dazxoh2urZNz8dXW1HDxYR15eAfn5n7RStUAdUNA2xFs4yw9t2th9p3ZvKwnVMd907sCBA1RUVPCHP/yBJ598UjedE3GIhgYoKwOPB/x+yMmB4mIoLYWsrOgtZ+dOmDcPtm+H1lZISTHnievXw8CBsHAhVFZCIAAZGTB9OixfDsuWHV2+erWpo6d5HnwQnn665/WxrJ7X9bLLYO3a2G8DkWPlxOPScccdh9/v54wzzujoBj9z5kzHxPdJ4r5NY7HTDadOr7fnnefq1TB06LGvXzRjlahLxs3f0NDA66+XkZnpIS3NT3NzDocOFTNtWilZR61UA1AGeAA/kAMUA6VAPDZAOMsPbdrYfad2b6v+LZJjU0QJ+zPPPNPxi3t1dTVDhgzh3HPP5fzzz6e4uJgJdvyiGwYnnhiJRNsDD0B5ufk11u0Gn8+cz5WUwOLF0VvOaafB1q2Qlgbp6dDUBM3NMH48fOpTsGGDOchkZUFjoznoZGebA1H38lmzTJ09zXPiiZCb2/P6QM/rmp/f+at0LLeByLFy4nHpT3/6U0gJ+r///W9GjBhBSkpEV9nFTNy3aSx2uuHUecklPe88Z82C3//+WNcuurFK1CXj5q+oeIDBg8tpbCygudlNWpqPrCwvBw6UcP753VfqAaAc01LsBnyAFygB4rEBwll+aNPG7ju1e1v1b3FL2AsKCpg5c2bHL+6Jdi2bE0+MRKKpthauugpSU4O7T3m90NJiGlyi0a2qogIuuABcLsjM7Cw/dMi0lOfkmFZ2t7vzs337YP9+GDzYJNTtfD6T7FuWaRjqOs/+/ebzc86B0aOD16ex0bzOygpep127YPNmmDwZiopitw1EoiGRj0u5ubls2bKFk08+2e5QgsR1m8ZipxtOnVVV8J//abo4dd15+nxmZ/zSS7HtHh+vg470KBk3f11dLf/611VYVipNTZ3Bp6d7cblaOPnk1V26x9cCVwGpBHft9gItwGpi2+U7nOWHNm3svlO7t5VEcmyK6Odwr9dLeXk51157bZ/J+j333MPBgwcjWYSIHIO6OtOw0vW8Dcz7hgazw4+GLVvMuWB6enB5ero5oBw+fHS3rdRUk5QP6HYHjawsk+j3NE9GhllO958X3W44eBA++ujodU1PN71Cu8cW7W0g0t8d45V1ySEWO91w6tyxw+zwuu88s7JM+fbt4S8/VrFK1CXj5j94sK6tG3zwSpmW9gYOHuy6UnWYrt3dNgBuTPfvWG+AcJYf2rSx+07t3lYSiZj2X/vhD3/IgQMHYrkIEelBfr5p3fb5gst9PtMdPVq/tE+aZBp0mpqCy5uaTGI+cGBnC3i7lhbTIn/kSHB5Y6Nppe9pnkDALMflCi73+SAvD4477uh1bWoyiX732KK9DUREYrLTDafO0aPNDq/7zrOx0ZSPGRP+8mMVq0RdMm7+vLx8mptzSEsLXqm0NB/Nzdnk5XVdqXzMddjdNgA+IJvYtxiHs/zQpo3dd2r3tpJIxDRh16/uIvYoLDQ3JvF6zRAIdL4uLo7ewfv88815YHOzaR1vaTHj5mYYO9bcLd7vNweY5mYzDgRMfE1NweV+P3z603DuuUfPc/iwWU77enRdn89+1gzd17W+3txvqb4+tttARCQmO91w6pw40ezwuu88/X5THut7C8XroCM9SsbNn59fyKFDxWRledu6wQdIT/eSleXl0KHibneLL8TcNM3bNgS6vC4m9kloOMsPbdrYfad2byuJhLPuECMiUVNaam5M0tICNTVmXFJiyqNp/XpzgznLMsm6ZZn369eba6xmzTLd2ffvN+NZs8y17z2Vr17d+zzr1/e+Pr2t6+rV8dkGIiIx2emGU2dvO8/VqyNffqxilahLxs0/bVopBw6U4HK1kJ1dg8vVwoEDJUyb1tNKlWJumtYC1LSNS9rK4yGc5Yc2bey+U7u3lYTrmB/r1pdBgwbx97//vX/fiEbEZu2/yMb6maybNsFbb/X8HPbqanMJZffHAvdW3tdnfa1Pb5/FaxuIRCqRj0u66Vw3sdjhhFNnXzvWeNAO11bJuPnr6rwcPOgN8Tns7a3Fdj1bPJzlhzZt7L5Tu7dV/xS3u8SHSgm7iIjIJ0vk45KO9SIiIqGJ5Ng04JMnEREREenZ1q1bGTFihN1hiIiIJKWYJuznnnsumV0fziwiIiKOdemll4Y87dNPPw3AyJEjYxWOiIhIvxdywl5fXx9ype3N+3/+85/Dj0hERERs4e7+0F8RERGxVcgJe15eHq7uD0HuxrIsXC4XLS0txxyYiIiIxNdjjz1mdwgiIiLSRcgJu8fjiWUcIiIiIiIiItJFyAn7eeedF8s4RERExGHKy8v57W9/y65du2hqagr67K233rIpKhERkf4j5Vhmbmxs5L333uPtt98OGkRERCSxPfTQQ1xxxRUUFBSwefNmpk2bxpAhQ/jXv/7FhRdeaHd4IiIi/UJEd4mvq6vjiiuu4Lnnnuvxc13DLpK8amuhrg4KCszwSeWR1BXteeJZn0iy+PnPf05ZWRn//d//zS9/+UtuuukmTj75ZG677TYOHDhgd3j9Syx2VOHUWVUFO3bAmDEwYUJ0li8SslqgDihoG+Lr3Xdr2b27jhNOKODUU6O3/H37qmho2EF29hiGDtX/lfQuooT9hhtu4KOPPqKyspLi4mKeeeYZamtrueuuu7jvvvuiHaOIOEBDA5SVgccDfj/k5EBxMVx2Gaxde3R5aSlkZYVXV7TniWR9Iq1PJNns2rWLs88+G4DMzEw+/vhjAL72ta8xffp0fvrTn9oZXv8Qix1VOHV6vbBwIVRWQiAAGRkwfTqsXg1Dhx77+on0qQEoAzyAH8gBioFSIPYHaq+3gT/+sYwTTvCQmenngw9yeOWVYi6+uJShQyNffkODlw8/XMjQoZUcd1yAlpYMduyYzvHHryYrS/9XcrSIusRv2LCBBx54gLPOOouUlBROPPFELrvsMn784x+zfPnyaMcoIg5QVgbl5ZCaCkVFZlxeDldd1XP5qlXh1xXteSJZn0jrE0k2w4YNY//+/QCceOKJVFZWArBz504sy7IztP4jFjuqcOpcuBA2bICUFBgyxIw3bIArr4x8+SIhKwPKgVSgqG1cDsTnQP3HP5YxYUI5ra2peL1FtLamMmFCOX/4w7Et/8MPFzJixAZaW1NobBxCa2sKI0ZsYPdu/V9JzyJK2BsaGiho6z41ePBg6urqADjttNN0ExqRJFRbaxpj2ntOZmSYcW6uaXjJzQ0uLygw03u9odcV7XkiWZ9I6xNJRrNmzeKPf/wjAN/85jdZvHgxn/nMZ/jyl7/M5z//eZuj6wdisaMKp86qKrODz8kBtxvS0sw4J8eUV1dHb11FjlKLaVlv7waf0eW1B4jtgfrdd2s54QQPH31UQH19AS0tGdTXF/DRRwUcf7yH996LbPn79lUxdGglhw/n0NTkxrLSaGpyc/hwDkOHVrJvn/6v5GgRJexjx45l27ZtAEyaNIlVq1axe/duVq5cyfDhw6MaoIjYr67O9Jx0u4PL09NNL8n09OByt9v0uuzpfLK3uqI9TyTrE2l9IsmorKyMW265BYBFixbx+OOPM27cOO644w4efvhhm6PrB2Kxowqnzh07zA6+ezf5rCxTvn17+MsXCVkdpht8t79V3Jiu8rE9UO/eXUdmpp+GhuDlNzS4ycxs4N//jmz5DQ07SE0N0Nwc/H/V3JxFamqAhgb9X8nRIr6Gfc+ePQDcfvvtXHDBBTzxxBOkp6fz+OOPRzM+EXGA/HzTqOLzBd+bqKnJNNB0e9oTPh9kZ/d8H6Pe6or2PJGsT6T1iSSjlJQUUlI6f9f/0pe+xJe+9CUbI+pnYrGjCqfO0aPNDr6xMTjBb2w05WPGhL98kZDlY65Z9xF8ozkfkN2tLPqOPz6fXbtyyM72UV/fuazsbB+HDmVz0kmRLT87ezQtLRmkpTXS1NT5f5WW1khLSwbZ2fq/kqNF1MI+f/58FixYAMDkyZN5//33ef3116mpqeHLX/5yNOMTEQcoLDT3JPJ6zRAImHF9vbn/UH19cLnXa6bv6Xyyt7qiPU8k6xNpfSLJ6qOPPuLee+/lm9/8JldeeSX33Xef7hAfL7HYUYVT58SJZgfv95uEvrnZjP1+U667xUtMFWJuMOdtGwJdXhcT64R93LhC/v3vYo47zkturpfU1AC5uV6OO87L7t3FEd8tfujQiezbN52BA/2kp/twuZpJT/cxcKCfffum627x0qOIEvY777yTxsbGjvdZWVmceeaZZGdnc+edd0YtOBFxjtJSKCmBlhaoqTHjkhJzs+CeyktLw68r2vNEsj6R1ieSbDZu3MioUaN46KGH+Oijjzhw4AAPPfQQo0aNYuPGjXaH1z/EYkcVTp2rV8OsWdDaCvv3m/GsWaZcJOZKgRKgBahpG5e0lcfexReXUl1dgsvVQn5+DS5XC9XVJVx88bEt//jjV/Phh7NISWklK2s/KSmtfPjhLI4/Xv9X0jOXFcGtXlNTU9mzZ0/Hjefa7d+/n4KCAsc/h72+vh63243P5yM3N9fucEQSSntjTPdH9/ZWHkld0Z4nnvWJRMKJx6WJEydy9tln8/DDD5OamgpAS0sLV199Na+88gpVVVU2R9g3J27TiMViRxVOndXV5pp1PYddbNHesm7Pc9jfe8/Lv//tjcFz2KtpaNiu57D3M5EcmyJK2FNSUqitrSU/Pz+ofMOGDXz5y1/uuGu8UyXVQVxERBKeE49LmZmZbNmyhbFjxwaVb9u2jUmTJnHo0CGbIguNE7epiIj0b5Ecm8K66dxxxx2Hy+XC5XIxZswYXC5Xx2ctLS34/X4WLVoUXtQiIiLiOGeeeSbvvvvuUQn7u+++y6RJk+wJSkREpJ8JK2FfsWIFlmXxjW98gzvuuAN3l7uGpqenc9JJJzFjxoyoBykiIiLxdf311/Ptb3+bf/zjH0yfPh2AyspKfvazn3HPPffw9ttvd0x7+umn2xWmiIhIUouoS/zGjRs555xzGDAgoqfC2U7d5ERExEmceFzq+ki3nrhcLizLwuVyOfLeNU7cpiIi0r/FvEt8u/POO49//vOfPPbYY/zzn//kwQcfpKCggOeff56RI0cyQTckERERSWg7d+60OwQREZF+L6KEfePGjVx44YWcc845bNq0ibvvvpuCggLefvttVq9eTXl5ebTjFBERkTg68cQT7Q5BRESk34voOezf+973uOuuu3jxxRdJT0/vKC8uLua1116LWnAiIiJin1/96lecc845jBgxgg8++AAw97P5wx/+YHNkIiIi/UNECfs777zD5z//+aPK8/Pz2b9//zEHJSIiIvZ6+OGHWbJkCXPnzuXgwYMd16nn5eWxYsUKe4MTERHpJyJK2PPy8tizZ89R5Zs3b+b4448/5qBERETEXj/5yU945JFHuOWWW0hNTe0onzp1Ku+8807I9Tz88MOcfvrp5Obmkpuby4wZM3juuef6nGfjxo1MmTKFgQMHcvLJJ7Ny5cqI10NERCSRRZSwf/WrX2Xp0qXs3bsXl8tFa2srr7zyCjfeeCNf//rXox2jiOPV1kJVFXi9dkcSHX2tT7Ktq4j0bOfOnUyePPmo8oyMDBoaGkKu54QTTuCee+7hjTfe4I033mDWrFlcfPHFVFdX97rcuXPncu6557J582Zuvvlmrr/+etatWxfxuhyzcHZ8ibKTrKqCZ56BXr6HIEm4/rEKM9TNGqvl19XVsmNHFXV1oVRcC1QBfU8bXp12qwBWAJs+ccpQv4NYbNPYCWf5dscaqmRcp/BEdNO5u+++mwULFnD88cdjWRbjx4/nyJEjzJ8/n+9///vRjlHEsRoaoKwMPB7w+yEnB4qLobQUsrLsji58fa2PZSXXuopI30aNGsWWLVuOuvncc889x/jx40Ou56KLLgp6f/fdd/Pwww9TWVnZ41NlVq5cSVFRUUe3+3HjxvHGG29w77338oUvfCH8FTkW4ezkE+WA4PXCwoVQWQmBAGRkwPTpsHo1DB0aPG0Srn+swgx1s8Zq+Q0NDbz+ehmZmR7S0vwcOJBDdXUx06aVknVUxQ1AGeAB/EAOUAyUAlkR1mm3ncA8YDvQimmTHAOsB4qCpgz1O4jFNo2dcJZvd6yhSsZ1ikxELexpaWk88cQT7Nixg6eeeoonnniC7du386tf/Sqo25xIsisrg/JySE2FoiIzLi+HVavsjiwyfa1Psq2riPTtu9/9Ltdccw2/+c1vsCyLv/3tb9x9993cfPPNfPe7342ozpaWFp566ikaGhqYMWNGj9O89tprzJkzJ6jsggsu4I033qC5uTmi5UYsnB1fouwkFy6EDRsgJQWGDDHjDRvgyiuPnjYJ1z9WYYa6WWO1/NdfL2Pw4HIsK5WGhiIsK5XBg8v52996qrgMKAdSMclsatv74GnDq9Nu84CtgAvIbBtvBT531JShfgex2KaxE87y7Y41VMm4TpGJKGEH+MUvfsG8efP42te+xmWXXcYll1zC6tWroxmbiKPV1ppfZwsKzJCR0fna43F8b8Cj9LU+zz9vhmRZVxH5ZFdccQW33347N910E42NjXz1q19l1apVPPjgg3zlK18Jq6533nmHnJwcMjIyWLRoEc8880yvrfR79+6lsLAwqKywsJAjR46wb9++XpcRCASor68PGo5JODv5RDkgVFWZJuCcHHC7IS3NjHNyTHnXftxJuP6xCjPUzRqr5dfV1ZKZ6aGxsYCmpgIsK4OmpgIaGwvIzPR068pdi2mFLGgbMrq89tDelTi8Ou1WgWlZT8Mk66lt47S28s7u8aF+B7HYprETzvLtjjVUybhOkYsoYb/11lv59re/zUUXXcTvfvc7fve733HRRRexePFidYmXfqOuznSlcruDy91u093KIecnIetrfQ4ehI8+Sp51FZFPdujQIebPn88HH3yA1+ulsrKSxYsXc8IJJ4Rd19ixY9myZQuVlZV861vf4vLLL2fr1q29Tu9yuYLeW5bVY3lXy5cvx+12dwwjR44MO84g4ezkE+WAsGOH6a/dvTtvVpYp3769sywJ1z9WYYa6WWO1/IMH60hL89PcHFxxc7ObtLQGDh7sWnEdpstwtyBwY7oVeyOo025bMN3g07uVp7eVv9VREup3EIttGjvhLN/uWEOVjOsUuYgS9ocffphHHnmE5cuXM2/ePObNm8fy5cspKyvTnVyl38jPN7+e+3zB5T4fZGebX2sTSV/rk5cHxx2XPOsqIp/s4osvZs2aNQAMGDCAefPmcf/993PJJZfw8MMPh1VXeno6p5xyClOnTmX58uWcccYZPPjggz1OO2zYMPbu3RtU5vV6GTBgAEOGDOl1GcuWLcPn83UMNTU1YcV4lHB28olyQBg92jQpNjYGlzc2mvIxYzrLknD9YxVmqJs1VsvPy8unuTmHtLTgitPSfDQ3Z5OX17XifMz1vd2CwAdkY1olw63TbpMwKU1Tt/KmtvIzO0pC/Q5isU1jJ5zl2x1rqJJxnSIXUcLe0tLC1KlTjyqfMmUKR44cOeagRBJBYaG5SYnXa4ZAoPN1cbFjzk9C1tf6fPazZkiWdRWRT/bWW29x7rnnAlBeXk5hYSEffPABa9as4aGHHjqmui3LIhAI9PjZjBkzePHFF4PK/vKXvzB16lTS0tJ6rTMjI6Pj0XHtwzEJZyefKAeEiRPNndD8fpOhNDebsd9vyrveBDAJ1z9WYYa6WWO1/Pz8Qg4dKiYry0t6uheXK0B6upesLC+HDhWTn9+14kLMzbi8bUOgy+ti2pOb8Oq02/mYG8w1A4eAlrZxc1v5zI4pQ/0OYrFNYyec5dsda6iScZ0iF1HCftlll/X463pZWRnz588/5qBEEkVpKZSUQEsL1NSYcUmJKU9Efa1Psq2riPStsbGRQYMGASZhvvTSS0lJSWH69Ol88MEHIddz88038/LLL/P+++/zzjvvcMstt1BRUdFxvrBs2bKgR8IuWrSIDz74gCVLlvDuu+/y6KOP8otf/IIbb7wxuisYinB2fImyk1y9GmbNgtZW2L/fjGfNMuXdJeH6xyrMUDdrrJY/bVopBw6U4HK1kJ1dg8vVwoEDJUyb1lPFpUAJJrGtaRuXtJVHWqfd1gPjAQuTrFtt79cfNWWo30EstmnshLN8u2MNVTKuU2RcVvuFYWG47rrrWLNmDSNHjmT69OkAVFZWUlNTw9e//vWgX8Dvv//+6EUbJfX19bjdbnw+37H/Ai9C56+z7TcuSXR9rU+yrauIEzjxuHT66adz5ZVX8vnPf56JEyfy/PPPM2PGDN58800+97nPHdVtvTff/OY3eemll9izZw9ut5vTTz+dpUuX8pnPfAaABQsW8P7771NRUdExz8aNG1m8eDHV1dWMGDGCpUuXsmjRorDij+o2DWfHlyg7yepqc3H1mDHBLes9ScL1j1WYoW7WWC2/rs7LwYNe8vIKQmgFb2+FbL9BVzTqtNsmzDXrZ9K1Zb0noX4HsdimsRPO8u2ONVTJtU6RHJsiStiLi4tDq9zlYsOGDeFWH3NOPDESEZH+y4nHpfLycr761a/S0tLC7Nmz+ctf/gKYm7tt2rSJ5557zuYI++bEbSoiIv1bJMemAZEsyOPxRDKbiIiIJIiSkhI+/elPs2fPHs4444yO8tmzZ/P5z3/exshERET6j4gSdhEREUl+w4YNY9iwYUFl06ZNsykaERGR/ieim86JiIiIiIiISGwpYRcRERERERFxICXsIiIiIiIiIg6khF1ERERERETEgZSwi4iIiIiIiDiQrQn7pk2buOiiixgxYgQul4vf//73nzjPxo0bmTJlCgMHDuTkk09m5cqVsQ9UJM6qquCZZ6C6Orbz1Naa+bze8GMMp65oLkdExNG0w+vXQv36nfBnEotYw1uvWqAK6HviWG0rJ3wHiSG070lix9bHujU0NHDGGWdwxRVX8IUvfOETp9+5cydz587lqquuYu3atbzyyitcffXV5OfnhzS/iNN5vbBwIVRWQiAAGRkwfTqsXg1Dh0ZvnoYGKCsDjwf8fsjJgeJiKC2FrKzwYu6rLsuK3nJERBwtmjtWSTihfv1O+DOJRazhrVcDUAZ4AD+QAxQDpUBWhHVGf/0ltO9JYs/WFvYLL7yQu+66i0svvTSk6VeuXElRURErVqxg3LhxXHnllXzjG9/g3nvvjXGkIvGxcCFs2AApKTBkiBlv2ABXXhndecrKoLwcUlOhqMiMy8th1arwY+6rrmguR0TE0bTD69dC/fqd8GcSi1jDW68yoBxIBYraxuVA8MSx2lZO+A4SQ2jfk8ReQl3D/tprrzFnzpygsgsuuIA33niD5ubmXucLBALU19cHDSJOU1VlWslzcsDthrQ0M87JMeU9dXWPZJ7aWvOrckGBGTIyOl97POF1DeurruefN0M0liMi4mjR3LFKwgn163fCn0ksYg1vvWoxLbYFbUNGl9ce2rtdx2pbOeE7SAyhfU8SHwmVsO/du5fCwsKgssLCQo4cOcK+fft6nW/58uW43e6OYeTIkbEOVSRsO3aYLu3du2NlZZny7dujM09dnekC5nYHl7vdpptYOAervuo6eNAM0ViOiIijRXPHKgkn1K/fCX8msYg1vPWqw3Sv7jYxbkwXbG8EdYbOCd9BYgjte5L4SKiEHcDlcgW9tyyrx/Kuli1bhs/n6xhqampiGqNIJEaPNr/0NjYGlzc2mvIxY6IzT36+aYH3+YLLfT7Izja/Moeqr7ry8swQjeWIiDhaNHesknBC/fqd8GcSi1jDW698zLXQ3SbGB2RjWnBjt62c8B0khtC+J4mPhErYhw0bxt69e4PKvF4vAwYMYMiQIb3Ol5GRQW5ubtAg4jQTJ5qbxfn95sDR3GzGfr8pnzAhOvMUFpqbq3i9ZggEOl8XF4d3sOqrrs9+1gzRWI6IiKNFc8cqCSfUr98JfyaxiDW89SrE3LjM2zYEurwupj0RjNW2csJ3kBhC+54kPmy9S3y4ZsyYwR//+Megsr/85S9MnTqVtLQ0m6ISiZ7Vq83N4iorYf9+00o+a5Ypj+Y8paVm7PFATY35VbmkpLM8HKHUFY3liIg4WjR3rJJwQv36nfBnEotYw1uv9kIPUINpsS3pUh5JnaFzwneQGEL7niT2XFZ7n3Ib+P1+/vGPfwAwefJk7r//foqLixk8eDBFRUUsW7aM3bt3s2bNGsA81m3ixImUlpZy1VVX8dprr7Fo0SJ+/etfh/VYt/r6etxuNz6fT63t4kjV1eb68zFjem4lj9Y87b8qt99w5Vj0VVc0lyOSjHRcij7btql2eP1aqF+/E/5MYhFreOvV3mLbfjOzaNQZOid8B4khtO9JQhPJscnWhL2iooLi4uKjyi+//HIef/xxFixYwPvvv09FRUXHZxs3bmTx4sVUV1czYsQIli5dyqJFi8Jark6MRETESXRcij5tUxERcZqES9jtooO4iIg4iY5L0adtKiIiThPJsSmhbjonIiIiIiIi0l8oYRcRERERERFxICXsIiIiIiIiIg6khF1ERERERETEgZSwi4iIiIiIiDiQEnYRERERERERB1LCLiIiIiIiIuJAA+wOQEREREQkOdQCdUBB29CzqirYsQPGjIEJE6JTZ6zELtZQp60CdgBjgL4DqK2FujooKDBDvNm9fPvZ+7dq//JjQwm7iIiIiMgxaQDKAA/gB3KAYqAUyOqYyuuFhQuhshICAcjIgOnTYfVqGDo0sjpjJXaxhjqtF1gIVAIBIAOYDqwGggNoaICyMvB4wO+HnBwoLobSUsiK/aayffn2s/dv1f7lx5a6xIuIiIiIHJMyoBxIBYraxuXAqqCpFi6EDRsgJQWGDDHjDRvgyisjrzNWYhdrqNMuBDZg0pUhbeMNwNEBlJVBeTmkpkJRkRmXl8Oq+Gwq25dvP3v/Vu1ffmwpYRcRERERiVgtpmWvvRtuRpfXHkxLselaXllpWl/dbkhLM+OcHFNeXR1+nbESu1hDnbYK07KeA7iBtLZxTlt5ZwC1taZlu70bekZG52uPx/QUiCW7l28/e/9W7V9+7ClhFxERERGJWB2mG667W7kb01XXJAw7dpiu5d27SGdlmfLt28OvM1ZiF2uo0+7AdIPv3p05q628M4C6OtMN3d2tSrfbdFWPdcJs9/LtZ+/fqv3Ljz0l7CIiIiIiEcvHtPz6upX7gGzab341erRpfW1sDJ6qsdGUjxkTfp2xErtYQ512NKaltFsANLaVdwaQn29a/n3dqvT5IDs79jd/s3v59rP3b9X+5ceeEnYRERERkYgVYm5w5W0bAl1eF9OeMEycaG7a5vebZK652Yz9flMefAf20OqMldjFGuq0EzE3mPNjEq/mtrG/rbwzgMJCc4M3r9cMgUDn6+Li2CfMdi/ffvb+rdq//NhTwi4iIiIickxKgRKgBahpG5e0lXdavRpmzYLWVti/34xnzTLlkdYZK7GLNdRpVwOzgFZgf9t4Vlt5txpLoaQEWlqgpsaMS0pMeTzYvXz72fu3av/yY8tlWZZldxDxVl9fj9vtxufzkZuba3c4IiLSz+m4FH3apmKP9pa9vp8DXV1trgMP7dnmodUZK7GLNdRpqzHXrH/yc9jbW7bteg663cu3n71/q/Yv/5NFcmxSwq6DuIiI2EzHpejTNhUREaeJ5NikLvEiIiIiIiIiDqSEXURERERERMSBlLCLiIiIiIiIOJASdhEREREREREHUsIuIiIiIiIi4kBK2EVEREREREQcSAm7iIiIiIiIiAMNsDsAEREREZHe1NZCXR0UFJjByWIR6/btVezfv4OhQ8cwevSE6FSKE7ZrLVAHFLQNxzqdSHJSwi4iIiIijtPQAGVl4PGA3w85OVBcDKWlkJVld3TBYhGr1+vlX/9ayMknV5KfH6C5OYPKyumccspqhg4d6qhYw4wAKAM8gB/IAYqBUiArgulEkpu6xIuIiIiI45SVQXk5pKZCUZEZl5fDqlV2R3a0WMT6r38tZPz4DbS2puDzDaG1NYXx4zfwj39c6bhYw4wAKAdSgaK2cTnQPYBQpxNJbkrYRURERMRRamtNC3B7d+2MjM7XHg94vXZH2CkWsW7fXsXJJ1fS2JhDQ4OblpY0GhrcNDbmMGpUJTt2VDsm1jAjwLSYt3dvz+jy2gN4w5xOJPkpYRcRERERR6mrM9213e7gcrfbdOl2UsIei1j3799BWlqAw4eDu34fPpxFenqAffu2OybWMCPAdG/vFgBuTBd4b5jTiSQ/JewiIiIi4ij5+ebaap8vuNzng+xsZ918LhaxDhkymubmDAYObAwqHziwkaamDIYOHeOYWMOMAHMtercA8AHZdN5ULtTpRJKfEnYRERERcZTCQnMjNK/XDIFA5+viYmcl7LGIdcyYifzrX9PJyvKTne0jNbWZ7GwfWVl+du6cHvHd4u3froWYG8d524ZAl9fFdCbioU4nkvyUsIuIiIiI45SWQkkJtLRATY0Zl5SYcqeJRaynnLKarVtn4XK14nbvx+VqZevWWZxyymrHxRpmBEAJ0ALUtI1L2sojmU4kubksy7LsDiLe6uvrcbvd+Hw+cnNz7Q5HRET6OR2Xok/bNHm0twAnwnPYYxHrjh3V7Nu3PerPYbd/u7a3mH/S89VDnU7E+SI5Nuk57CIiIiLiWImQqLeLRayjR0+IaqLezv7tGmoCrkRd+jd1iRcRERERERFxICXsIiIiIiIiIg6khF1ERERERETEgZSwi4iIiIiIiDiQEnYRERERERERB1LCLiIiIiIiIuJASthFREREREREHEgJu4iIiIiIiIgDDbA7ABERERERp6qthbo6KCgwQ7zrjMXyw1ML1AEFbYOIUyXn36oSdhERERGRbhoaoKwMPB7w+yEnB4qLobQUsrJiX2cslh9mtEAZ4AH8QA5QDJQCcQlAJETJ/beqLvEiIiIiIt2UlUF5OaSmQlGRGZeXw6pV8akzFssPM1qgHEgFitrG5UDcAhAJUXL/rSphFxERERHporbWtGy3d0PPyOh87fGA1xvbOmOx/DCjxbRWtnctzujy2gPEPACRECX/36oSdhERERGRLurqTDd0tzu43O02XdUjSZjDqTMWyw8zWkzX4m4B4MZ0P078JEiSRfL/rSphFxERERHpIj/fXDPu8wWX+3yQnR3Zzd/CqTMWyw8zWsx1wN0CwAdkk0w39JJEl/x/q0rYRURERES6KCw0N3jzes0QCHS+Li6OLGEOp85YLD/MaDE37fK2DYEur4tJhiRIkkXy/63qLvEiIiIiIt2UlpqxxwM1NaZlu6SkszzWdcZi+WFG2zb2ADWY1sqSLuUiTpHcf6suy7Isu4OIt/r6etxuNz6fj9zcXLvDERGRfk7HpejTNpVoaW/ZjuZz0MOpMxbLD097a2VyPdtakpHz/1YjOTaphV1EREREpBexSJTDqdO+RL0jApya/IgES86/VV3DLiIiIiIiIuJASthFREREREREHEgJu4iIiIiIiIgDKWEXERERERERcSAl7CIiIiIiIiIOpIRdRERERERExIGUsIuIiIiIiIg4kBL2ZFZbC1VV4PXaHYmIiPRTy5cv56yzzmLQoEEUFBRwySWXsG3btj7nqaiowOVyHTW89957cYpagtUCVUD0zicS6RQlnFhDnzb62zTR1NXVsmNHFXV1Tt8G+q7EXgPsDkBioKEBysrA4wG/H3JyoLgYSkshK8vu6EREpB/ZuHEj11xzDWeddRZHjhzhlltuYc6cOWzdupXs7Ow+5922bRu5ubkd7/Pz82MdrgRpAMoAD+AHcoBioBSI7HwikU5Rwok19Gmjv00TTUNDA6+/XkZmpoe0ND8HDuRQXV3MtGmlZDnqj0DflTiDWtiTUVkZlJdDaioUFZlxeTmsWmV3ZCIi0s88//zzLFiwgAkTJnDGGWfw2GOPsWvXLt58881PnLegoIBhw4Z1DKmpqXGIWDqVAeVAKlDUNi4HIj+fSKRTlHBiDX3a6G/TRPP662UMHlyOZaXS0FCEZaUyeHA5f/ub07aBvitxBiXsyaa21vy8W1BghoyMztceT2L0PRMRkaTl8/kAGDx48CdOO3nyZIYPH87s2bPxeDx9ThsIBKivrw8a5FjUYloWC9qGjC6vPUTSPTiRTlHCiTX0aaO/TRNNXV0tmZkeGhsLaGoqwLIyaGoqoLGxgMxMj4O6x+u7EudQwp5s6upMXyy3O7jc7Tb9tZx0NBQRkX7FsiyWLFnCpz/9aSZOnNjrdMOHD6esrIx169bx9NNPM3bsWGbPns2mTZt6nWf58uW43e6OYeTIkbFYhX6kDtMNuNv5BG5MV+HwzycS6RQlnFhDnzb62zTRHDxYR1qan+bm4G3Q3OwmLa2Bgwedsg30XYlz6Br2ZJOfby6c8vnMT7vtfD7Izg4uExERiaNrr72Wt99+m7/+9a99Tjd27FjGjh3b8X7GjBnU1NRw7733MnPmzB7nWbZsGUuWLOl4X19fr6T9mORjrtn1YVoV2/mA7G5lIdaYQKco4cQa+rTR36aJJi8vnwMHckhL89HU1Lm+aWk+mpuzyctzyjbQdyXOoRb2ZFNYaO5y4vWaIRDofF1c7KyjoYiI9BvXXXcdzz77LB6PhxNOOCHs+adPn86OHTt6/TwjI4Pc3NygQY5FIeYGW962IdDldTGRJCyJdIoSTqyhTxv9bZpo8vMLOXSomKwsL+npXlyuAOnpXrKyvBw6VEx+vlO2gb4rcQ61sCej0lIz9nigpsb8vFtS0lkuIiISJ5Zlcd111/HMM89QUVHBqFGjIqpn8+bNDB8+PMrRSd/azxs8QA2mZbGkS3kENSbQKUo4sYY+bfS3aaKZNq2Uv/0NMjM9ZGfX0NyczYEDJUyb5rRtoO9KnMFlWZZldxDxVl9fj9vtxufzJfcv8O0/77bf+URERBwpmY9LV199NU8++SR/+MMfgrq5u91uMjMzAdOdfffu3axZswaAFStWcNJJJzFhwgSamppYu3Yt99xzD+vWrePSSy8NabnJvE3jr71lsf2mW1GoMYFOUcKJNfRpo79NE01dnZeDB73k5RU4qGW9J/quJHoiOTaphT2ZJcJRUEREktrDDz8MwPnnnx9U/thjj7FgwQIA9uzZw65duzo+a2pq4sYbb2T37t1kZmYyYcIE1q9fz9y5c+MVtgSJfqKSSKco4cQa+rRK/vLznZ6ot9N3JfZSC7t+dRcREZvpuBR92qYiIuI0kRybdNM5EREREREREQdSwi4iIiIiIiLiQErYRURERERERBxICbuIiIiIiIiIAylhFxEREREREXEgJewiIiIiIiIiDuSIhP3nP/85o0aNYuDAgUyZMoWXX36512krKipwuVxHDe+9914cIxYRERERERGJrQF2B/Cb3/yGG264gZ///Oecc845rFq1igsvvJCtW7dSVFTU63zbtm0LenZdfn5+PMJNDrW1UFcHBQVmEBEREelFfz9tqKqCHTtgzBiYMMHuaESkv7E9Yb///vv55je/yZVXXgnAihUreOGFF3j44YdZvnx5r/MVFBSQl5cXpyiTREMDlJWBxwN+P+TkQHExlJZCVpbd0YmIiIiD9PfTBq8XFi6EykoIBCAjA6ZPh9WrYehQu6MTkf7C1i7xTU1NvPnmm8yZMyeofM6cObz66qt9zjt58mSGDx/O7Nmz8Xg8sQwzeZSVQXk5pKZCUZEZl5fDqlV2RyYiIiIO099PGxYuhA0bICUFhgwx4w0boK2NSUQkLmxN2Pft20dLSwuFhYVB5YWFhezdu7fHeYYPH05ZWRnr1q3j6aefZuzYscyePZtNmzb1upxAIEB9fX3Q0O/U1pqfyNv7s2VkdL72eMzPyCIiIiLotKGqyrSs5+SA2w1paWack2PKq6vtjlBE+gvbu8QDuFyuoPeWZR1V1m7s2LGMHTu24/2MGTOoqanh3nvvZebMmT3Os3z5cu64447oBZyI6upMf7bu9wVwu6Gmxhx5++OFaSIiInKU/n7asGOH6QY/ZEhweVYW7N8P27frenYRiQ9bW9iHDh1KamrqUa3pXq/3qFb3vkyfPp0dO3b0+vmyZcvw+XwdQ01NTcQxJ6z8fPOzsM8XXO7zQXZ2ch91RUREJCz9/bRh9GjTq6CxMbi8sdGUjxljT1wi0v/YmrCnp6czZcoUXnzxxaDyF198kbPPPjvkejZv3szw4cN7/TwjI4Pc3Nygod8pLDR3ivF6zRAIdL4uLk7+I6+IiIiErL+fNkycaG4w5/ebHymam83Y7zflal0XkXixvUv8kiVL+NrXvsbUqVOZMWMGZWVl7Nq1i0WLFgGmdXz37t2sWbMGMHeRP+mkk5gwYQJNTU2sXbuWdevWsW7dOjtXIzGUlpqxx2P6s2VnQ0lJZ7mIiIhIm/5+2rB6tbnBXGWl6QafkQGzZplyEZF4sT1h//KXv8z+/fu588472bNnDxMnTuTPf/4zJ554IgB79uxh165dHdM3NTVx4403snv3bjIzM5kwYQLr169n7ty5dq1C4sjKgsWLYf78zovPkv0nchEREYlIfz9tGDoUfv97c4O57dv1HHYRsYfLsizL7iDirb6+Hrfbjc/n65/d40VExFF0XIo+bVMREXGaSI5Ntl7DLiIiIiIiIiI9U8IuIiIiIiIi4kBK2EVEREREREQcSAm7iIiIiIiIiAMpYRcRERERERFxICXsIiIiIiIiIg6khF1ERERERETEgQbYHYB0UVsLdXVQUGCGUFRUwJYtcOaZMHNmaPVFspxI5hEREZGeJelxNRlXKxnXyQm0XUVCo4TdCRoaoKwMPB7w+yEnB4qLobQUsrJ6nmfnTpg3D7Zvh9ZWSEmBMWNg/XoYMqTn+i67DNauDW85kcQmIiIiPUvS42oyrlYyrpMTaLuKhEdd4p2grAzKyyE1FYqKzLi8HFat6n2eefNg61ZwuSAz04y3boXPfa73+q66KvzlRBKbiIiI9CxJj6vJuFrJuE5OoO0qEh4l7HarrTU/Mbb3B8rI6Hzt8YDXe/Q8FRWmZT0tzSTrqalmnJZmysvLj64vNxcqK8HtDn05kcQmIiIiPUvS42oyrlYyrpMTaLuKhE8Ju93q6kx/ILc7uNztNn2GetpzbdliusGnpweXp6dDS4uZp3t96ekQCJikPtTlRBKbiIiI9CxJj6vJuFrJuE5OoO0qEj4l7HbLzzcX7/h8weU+H2Rn93wXjkmTzDXrTU3B5U1NprW9oODo+pqazM+Yzc2hLyeS2ERERKRnSXpcTcbVSsZ1cgJtV5HwKWG3W2GhudOG12uGQKDzdXFxz3uu8883N5hrboZDh0yr+qFD5v2YMVBScnR99fUwfbrZI4a6nEhiExERkZ4l6XE1GVcrGdfJCbRdRcKnu8Q7QWmpGXs8UFNjfmIsKeks78n69eYGc9u3m2Q9JQXGjzflQ4f2XN/Xvga/+lV4y4kkNhEREelZkh5Xk3G1knGdnEDbVSQ8LsuyLLuDiLf6+nrcbjc+n4/c3Fy7w+nU/hNjOA+k3LQJ3nqr5+ew91ZfJMuJZB4REQmJY49LCczx2zRJj6vJuFrJuE5OoO0q/VEkxyYl7E48iIuISL+i41L0aZuKiIjTRHJs0jXsIiIiIiIiIg6khF1ERERERETEgZSwi4iIiIiIiDiQEnYRERERERERB1LCLiIiIiIiIuJASthFREREREREHEgJu4iIiIiIiIgDKWEXERERERERcaABdgcgXVRVwY4dMGYMTJgQ/FlFBWzZAmeeCTNndpbX1kJdHRQUmCEUkcwjIiIiIkmjrq6WgwfryMsrID8/OueDOsUUiT4l7E7g9cLChVBZCYEAZGTA9OmwejV8/DHMmwfbt0NrK6SkmIT+d7+D554Djwf8fsjJgeJiKC2FrKyel9PQAGVl4c0jIiIiIkmjoaGB118vIzPTQ1qanwMHcqiuLmbatFKyIjwf1CmmSOyoS7wTLFwIGzaYZHzIEDPesAGuvNIk61u3gssFmZlmvHWr2QuWl0NqKhQVmXF5Oaxa1ftyysrCn0dEREREksbrr5cxeHA5lpVKQ0MRlpXK4MHl/O1vkZ8P6hRTJHaUsNutqsq0rOfkgNsNaWlmnJMDmzbBtm2mLDPT7P0yM2HAANPnKCXF9DfKyOjse+TxmBb77mprzWft04Uyj4iIiIgkjbq6WjIzPTQ2FtDUVIBlZdDUVEBjYwGZmR7q6sI/H9QppkhsKWG3244dpht89/5CWVlw+DC0tEB6evBnAwaAZZnPu3K7TZ+knvaMdXWmj5LbHfo8IiIiIpI0Dh6sIy3NT3Nz8Plgc7ObtLQGDh4M/3xQp5gisaWE3W6jR5ufIhsbg8sbG2HgQNOq3tQU/NmRI6Zr/MCBweU+H2Rn93yXj/x802rv84U+j4iIiIgkjby8fJqbc0hLCz4fTEvz0dycTV5e+OeDOsUUiS0l7HabONHcYM7vN3u25mYz9vvN3eDHjjVlhw6Z1vZDh0zCXlhobkLn9ZoWeq/XDMXFPe8ZCwvNZ+3ThTKPiIiIiCSN/PxCDh0qJivLS3q6F5crQHq6l6wsL4cOFUd0t3idYorElhJ2J1i9GmbNMgn4/v1mPGuWKV+/HsaPN13gDx0y4/HjzWPeSkpMEl9TY8YlJeZ2nL0pLQ1/HhERERFJGtOmlXLgQAkuVwvZ2TW4XC0cOFDCtGmRnw/qFFMkdlyWZVl2BxFv9fX1uN1ufD4fubm5dofTqbraPL6tp+ewb9oEb7119HPY23/CDOeBl5HMIyIiMePY41IC0zYV6VtdnZeDB71RfQ67TjFF+hbJsUkJuw7iIiJiMx2Xok/bVEREnCaSY5O6xIuIiIiIiIg4kBJ2EREREREREQdSwi4iIiIiIiLiQErYRURERERERBxICbuIiIiIiIiIAylhFxEREREREXEgJewiIiIiIiIiDqSE/VjV1kJVFXi9oc9TVQXPPAPV1cHlTz8NS5fCH/5w9Dw33QT/8R9w883B5XfeCbNnww9/ePQ8jz4K3/gG/PKXxx5zJPOIiIiIiIhIxFyWZVl2BxFvkTyw/igNDVBWBh4P+P2QkwPFxVBaCllZPc/j9cLChVBZCYEAZGTA9Olw443wxS+apNiywOWCwkKoqID33oNLLjm6rjvvhP/5H2ht7SxLSYH//V8Ty+zZ8PHHnZ8NGgTPPw//93/hxRzJeoqISFiiclySINqmIiLiNJEcm5SwR3oQf+ABKC+HggJwu8HnMwl5SQksXtzzPJdcAhs2mKQ3KwsaG00SHAhAU5NJ1FNToaXFJO7DhsHeveHFlZIC2dnByXq79HSYOjW8mCNZTxERCYuSy+jTNhUREaeJ5NikLvGRqK01Lc4FBWbIyOh87fH03G28qsq0rOfkmMQ3Lc2MU1I6k/W0NPM+Lc28DzdZB9Pi3p6sp6R0DmCW09gYesyRrKeIiIiIiIhEhRL2SNTVmZZxtzu43O02Xch7SmR37DAt6b11I3e5gt+npkYn1u66t7z3FXMk6ykiIiIiIiJRoYQ9Evn5pqXc5wsu9/lMd/SCgqPnGT3atFA3NvZcZ/crE1paohNrd4MGBb/vK+ZI1lNERERERESiQgl7JAoLzY3XvF4zBAKdr4uLe05kJ040N5jz+03C29xsxq2t5tpyyzJlra1m3H4Ne7hSUjqT8tbWzgHMcrKyQo85kvUUERERERGRqFDCHqnSUnPjtZYWqKkx45ISU96b1ath1iyTQO/fb8azZpm7wbcn50eOmPGwYab8z3/uua7lyzuvTW/Xfpf4TZuObkkfNMjUF27MkayniIiIiIiIHDPdJf5Y7xzb3uLcfjO2UFRXw/btMGYMTJjQWf6HP8Crr8LZZ8PFFwfPc/PN8NJLRz9z/Yc/7Czv/oz2X/4SNm6E886Dyy8/tpgjmUdEREKiO5pHn7apiIg4jR7rFiIdxEVExEl0XIo+bVMREXEaPdZNREREREREJEkoYRcRERERERFxICXsIiIiIiIiIg6khF1ERERERETEgZSwi4iIiIiIiDiQEnYRERERERERB1LCLiIiIiIiIuJASthFREQkZpYvX85ZZ53FoEGDKCgo4JJLLmHbtm2fON/GjRuZMmUKAwcO5OSTT2blypVxiFZERMRZlLDHSm0tVFWB1xud+qqq4JlnoLo6tHIREREH2LhxI9dccw2VlZW8+OKLHDlyhDlz5tDQ0NDrPDt37mTu3Lmce+65bN68mZtvvpnrr7+edevWxTFyiUS0T39ERPq7AXYHkHQaGqCsDDwe8PshJweKi6G0FLKywq/P64WFC6GyEgIByMiA6dNh+XJYtuzo8tWrYejQ6K+XiIhIBJ5//vmg94899hgFBQW8+eabzJw5s8d5Vq5cSVFREStWrABg3LhxvPHGG9x777184QtfiHXIEoFon/6IiIihFvZoKyuD8nJITYWiIjMuL4dVqyKrb+FC2LABUlJgyBAz3rABZs3qufzKK6O7PiIiIlHk8/kAGDx4cK/TvPbaa8yZMyeo7IILLuCNN96gubk5pvFJZKJ9+iMiIoYS9miqrTU/LRcUmCEjo/O1xxN+/7CqKtOCnpMDbjekpZlxRoZZVkZGcHlOjple3eNFRMSBLMtiyZIlfPrTn2bixIm9Trd3714KCwuDygoLCzly5Aj79u3rcZ5AIEB9fX3QIPER7dMfERHppIQ9murqTD8wtzu43O02fcXCPWLt2GG6u3fvS5aaCpZlxl1lZZnpt28PP3YREZEYu/baa3n77bf59a9//YnTulyuoPeWZfVY3m758uW43e6OYeTIkccesIQk2qc/IiLSSQl7NOXnm1butu5+HXw+yM42PzWHY/Ro8zN1Y2NweUsLuFxm3FVjo5l+zJjwYxcREYmh6667jmeffRaPx8MJJ5zQ57TDhg1j7969QWVer5cBAwYwZMiQHudZtmwZPp+vY6ipqYla7NK3aJ/+iIhIJyXs0VRYaO6w4vWaIRDofF1cHP4Ra+JEcyM5v98c9ZqbzTgQMMsKBILL/X4z/YQJsVk/ERGRMFmWxbXXXsvTTz/Nhg0bGDVq1CfOM2PGDF588cWgsr/85S9MnTqVtLS0HufJyMggNzc3aJD4iPbpj4iIdFLCHm2lpVBSYlq/a2rMuKTElEdi9Wpzg7nWVti/34xnzYKKip7LV6+O6uqIiIgci2uuuYa1a9fy5JNPMmjQIPbu3cvevXs5dOhQxzTLli3j61//esf7RYsW8cEHH7BkyRLeffddHn30UX7xi19w44032rEKEoJon/6IiIjhstovCutH6uvrcbvd+Hy+2P0C3/7TcvtdV45VdbW5Nn3MmOAW9N7KRUQkYcTluGST3q45f+yxx1iwYAEACxYs4P3336eioqLj840bN7J48WKqq6sZMWIES5cuZdGiRSEvN5m3qZNF+/RHRCSZRHJsUsKug7iIiNhMx6Xo0zYVERGnieTYpC7xIiIiIiIiIg6khF1ERERERETEgZSwi4iIiIiIiDiQEnYRERERERERB1LCLiIiIiIiIuJASthFREREREREHEgJu4iIiIiIiIgDOSJh//nPf86oUaMYOHAgU6ZM4eWXX+5z+o0bNzJlyhQGDhzIySefzMqVK+MUqYiIiIiIiEh82J6w/+Y3v+GGG27glltuYfPmzZx77rlceOGF7Nq1q8fpd+7cydy5czn33HPZvHkzN998M9dffz3r1q2Lc+QiIiIiIiIiseOyLMuyM4D/+I//4Mwzz+Thhx/uKBs3bhyXXHIJy5cvP2r6pUuX8uyzz/Luu+92lC1atIi///3vvPbaayEts76+Hrfbjc/nIzc399hXQkRE5BjouBR92qYiIuI0kRybbG1hb2pq4s0332TOnDlB5XPmzOHVV1/tcZ7XXnvtqOkvuOAC3njjDZqbm3ucJxAIUF9fHzSIiIiIiIiIOJmtCfu+fftoaWmhsLAwqLywsJC9e/f2OM/evXt7nP7IkSPs27evx3mWL1+O2+3uGEaOHBmdFRARERERERGJEduvYQdwuVxB7y3LOqrsk6bvqbzdsv/f3r1HRXHebwB/VlhABDQgIKhcVBRURCpEF/SHOVisl9REa43G+6VSb3hJRavHkBhFazEaa/SgHtHQaFsvqSZaUSua2KiIWDUqooByLJZq0XgrBvj+/shhkvXGsiw7s/B8zplznNmd2eedL77vvOywO38+7t27pyxFRUW1TExERERERERUt+zVfPHmzZvDzs7umXfTS0pKnnkXvUqLFi2e+3x7e3t4eHg8dx9HR0c4OjpaJjQRERERERGRFag6YXdwcEC3bt1w8OBBvPnmm8r2gwcPYtCgQc/dx2AwYO/evUbbMjIyEBERAb1eb9LrVr0jz79lJyIiLagaj1T+HNh6hWM9ERFpjVnjvahs+/btotfrZdOmTXLx4kWZOXOmNGnSRAoLC0VEZN68eTJq1Cjl+fn5+eLs7CyzZs2SixcvyqZNm0Sv18uOHTtMfs2ioiIBwIULFy5cuGhqKSoqsvg421BxrOfChQsXLlpdajLeq/oOOwAMGzYMd+7cwfvvv4/i4mJ07twZ+/btg7+/PwCguLjY6DvZAwMDsW/fPsyaNQtr166Fr68vPvroIwwZMsTk1/T19UVRURFcXV1f+rfypvj222/RunVrFBUVNdivjeE54DkAeA4AngOA56BKTc+DiOD+/fvw9fW1QrqGwZJjfV2or/9X6mO76mObgPrZLrbJdtTHdpnSJnPGe9W/h93W8XteeQ4AngOA5wDgOQB4DqrwPFB16uvPSH1sV31sE1A/28U22Y762K66apMmPiWeiIiIiIiIiIxxwk5ERERERESkQZyw15KjoyPefffdBv21cTwHPAcAzwHAcwDwHFTheaDq1NefkfrYrvrYJqB+tottsh31sV111Sb+DTsRERERERGRBvEddiIiIiIiIiIN4oSdiIiIiIiISIM4YSciIiIiIiLSIE7YiYiIiIiIiDSIE3YzHTt2DK+//jp8fX2h0+nw2WefqR3JqpKTkxEZGQlXV1d4eXnhjTfeQG5urtqxrG7dunXo0qUL3Nzc4ObmBoPBgP3796sdSzXJycnQ6XSYOXOm2lGsKikpCTqdzmhp0aKF2rGs7ubNmxg5ciQ8PDzg7OyMrl27Ijs7W+1YVhMQEPDMz4FOp8PUqVPVjkYqM6VvzMzMfO7Pz+XLl60XtBrm9HVHjx5Ft27d4OTkhDZt2mD9+vVWSmuamrbJFuoEmNcfa71WQM3bpfV6mTNu2EKdatourdcJAMrLy7Fw4UIEBgaicePGaNOmDd5//31UVla+dD9L1Mve3NAN3cOHDxEWFoZx48ZhyJAhasexuqNHj2Lq1KmIjIxEeXk5FixYgLi4OFy8eBFNmjRRO57VtGrVCsuWLUO7du0AAFu2bMGgQYOQk5ODTp06qZzOurKyspCamoouXbqoHUUVnTp1wqFDh5R1Ozs7FdNYX2lpKaKjo/Haa69h//798PLywrVr19CsWTO1o1lNVlYWKioqlPULFy7gpz/9KYYOHapiKlJbTfvG3NxcuLm5Keuenp51Fc0sNenrCgoK0L9/f0yaNAnp6ek4fvw4pkyZAk9PT01dO5nTf2u5Tub0x7ZQq9qMM1qtV03HDVuoE2D+eKjVOgHA8uXLsX79emzZsgWdOnXC6dOnMW7cODRt2hQJCQnP3cdi9RKqNQCye/dutWOoqqSkRADI0aNH1Y6iuldeeUU2btyodgyrun//vgQFBcnBgwclJiZGEhIS1I5kVe+++66EhYWpHUNViYmJ0rNnT7VjaEpCQoK0bdtWKisr1Y5CKqlJ33jkyBEBIKWlpVbLV1M17evmzp0rwcHBRtsmT54sPXr0sHAy89W0TbZQJ3P6Y1uolTntsoV6/Vh144Yt1Ol5qmuXLdRpwIABMn78eKNtgwcPlpEjR75wH0vVi7fEk0Xcu3cPAODu7q5yEvVUVFRg+/btePjwIQwGg9pxrGrq1KkYMGAA+vTpo3YU1eTl5cHX1xeBgYF46623kJ+fr3Ykq9qzZw8iIiIwdOhQeHl5ITw8HBs2bFA7lmqePHmC9PR0jB8/HjqdTu04pBJz+sbw8HD4+PggNjYWR44cqcN05qlJX/f1118jLi7OaFvfvn1x+vRpfPfdd3Ud1WTm9N9arpM5/bEt1Ko244yW61XFlHHDFur0tJqMh1quU8+ePXH48GFcuXIFAPDPf/4TX331Ffr37//CfSxVL07YqdZEBLNnz0bPnj3RuXNnteNY3fnz5+Hi4gJHR0fEx8dj9+7d6Nixo9qxrGb79u04c+YMkpOT1Y6imu7du2Pr1q04cOAANmzYgFu3biEqKgp37txRO5rV5OfnY926dQgKCsKBAwcQHx+PGTNmYOvWrWpHU8Vnn32Gu3fvYuzYsWpHIZXUtG/08fFBamoqdu7ciV27dqFDhw6IjY3FsWPH6jip6Wra1926dQve3t5G27y9vVFeXo7bt29bI3K1atomW6iTOf2xLdTKnHbZQr2qmDJu2EKdnmZKu2yhTomJiRg+fDiCg4Oh1+sRHh6OmTNnYvjw4S/cx2L1qtH78fRcaOC3xE+ZMkX8/f2lqKhI7SiqKCsrk7y8PMnKypJ58+ZJ8+bN5ZtvvlE7llXcuHFDvLy85OzZs8q2hnhL/NMePHgg3t7ekpKSonYUq9Hr9WIwGIy2TZ8+XfO36dWVuLg4GThwoNoxSCWW6hsHDhwor7/+uoXTWU51fV1QUJAsXbrUaNtXX30lAKS4uNgaEWvMnP5ba3Uypz+2hVpZapzRWr2qmDJu2EKdnmbueKi1Om3btk1atWol27Ztk3PnzsnWrVvF3d1d0tLSXriPperFd9ipVqZPn449e/bgyJEjaNWqldpxVOHg4IB27dohIiICycnJCAsLw+rVq9WOZRXZ2dkoKSlBt27dYG9vD3t7exw9ehQfffQR7O3tjT5wpCFp0qQJQkNDkZeXp3YUq/Hx8XnmzpKQkBDcuHFDpUTquX79Og4dOoSJEyeqHYVUYqm+sUePHpruR6rr61q0aIFbt24ZbSspKYG9vT08PDysEbHGzOm/tVYnc/pjW6iVpcYZrdULMH3csIU6/VhtxkOt1ek3v/kN5s2bh7feeguhoaEYNWoUZs2a9dK7qCxVL35KPJlFRDB9+nTs3r0bmZmZCAwMVDuSZogIysrK1I5hFbGxsTh//rzRtnHjxiE4OBiJiYkN7pPSq5SVleHSpUvo1auX2lGsJjo6+pmvdrxy5Qr8/f1VSqSezZs3w8vLCwMGDFA7CqnEUn1jTk4OfHx86iKiRVTX1xkMBuzdu9doW0ZGBiIiIqDX660RscbM6b+1Vidz+mNbqJWlxhmt1QswfdywhTr9WG3GQ63V6dGjR2jUyPi9bjs7u5d+rZvF6mXmXQEN3v379yUnJ0dycnIEgKxcuVJycnLk+vXrakezil//+tfStGlTyczMlOLiYmV59OiR2tGsav78+XLs2DEpKCiQc+fOyW9/+1tp1KiRZGRkqB1NNQ3xlvg5c+ZIZmam5Ofny4kTJ2TgwIHi6uoqhYWFakezmlOnTom9vb0sWbJE8vLy5I9//KM4OztLenq62tGsqqKiQvz8/CQxMVHtKKQxT/eN8+bNk1GjRinrH374oezevVuuXLkiFy5ckHnz5gkA2blzpwppn6+6vu7pNuXn54uzs7PMmjVLLl68KJs2bRK9Xi87duxQqwnPqGmbbKFOpvTHtlgrc9plC/V62bhhi3WqUpN22UKdxowZIy1btpTPP/9cCgoKZNeuXdK8eXOZO3eu8py6qhcn7Gaq+vqBp5cxY8aoHc0qntd2ALJ582a1o1nV+PHjxd/fXxwcHMTT01NiY2Mb9GRdpGFO2IcNGyY+Pj6i1+vF19dXBg8e3GA+x+DH9u7dK507dxZHR0cJDg6W1NRUtSNZ3YEDBwSA5Obmqh2FNObpvnHMmDESExOjrC9fvlzatm0rTk5O8sorr0jPnj3liy++sH7Ql6iur3u6TSIimZmZEh4eLg4ODhIQECDr1q2zcuqXq2mbbKFOItX3x7ZYK5Gat8sW6vWyccNW6yRSs3bZQp2+/fZbSUhIED8/P3FycpI2bdrIggULpKysTHlOXdVLJyJi+vvxRERERERERGQN/NA5IiIiIiIiIg3ihJ2IiIiIiIhIgzhhJyIiIiIiItIgTtiJiIiIiIiINIgTdiIiIiIiIiIN4oSdiIiIiIiISIM4YSciIiIiIiLSIE7YichIZmYmdDod7t69W+1z09LS0KxZszrPZKqAgACsWrVK7RhEREQ2YezYsXjjjTdMem7v3r0xc+bMOs1jqppcqxDZOk7YieoprU2mLak+t42IiIh+oKVfFBCpgRN2IiIiIiIiIg3ihJ1Io3r37o1p06Zh2rRpaNasGTw8PLBw4UKICADgyZMnmDt3Llq2bIkmTZqge/fuyMzMBPD9rWLjxo3DvXv3oNPpoNPpkJSUBABIT09HREQEXF1d0aJFC4wYMQIlJSUWy713715069YNTk5OaNOmDd577z2Ul5crj+t0OmzcuBFvvvkmnJ2dERQUhD179hgdY8+ePQgKCkLjxo3x2muvYcuWLcqtby9rGwA8evQI48ePh6urK/z8/JCammqxthEREVnSjh07EBoaisaNG8PDwwN9+vTBw4cPAQCbN29GSEgInJycEBwcjI8//ljZr7CwEDqdDtu3b0dUVBScnJzQqVMn5ToAACoqKjBhwgQEBgaicePG6NChA1avXm2x7C+7DgF+uBvuwIEDCAkJgYuLC372s5+huLhYeU55eTlmzJihXOckJiZizJgxym36Y8eOxdGjR7F69WplzC8sLFT2z87ORkREBJydnREVFYXc3FyLtY9IM4SINCkmJkZcXFwkISFBLl++LOnp6eLs7CypqakiIjJixAiJioqSY8eOydWrV2XFihXi6OgoV65ckbKyMlm1apW4ublJcXGxFBcXy/3790VEZNOmTbJv3z65du2afP3119KjRw/p16+f8rpHjhwRAFJaWlptxs2bN0vTpk2V9b/97W/i5uYmaWlpcu3aNcnIyJCAgABJSkpSngNAWrVqJZ9++qnk5eXJjBkzxMXFRe7cuSMiIgUFBaLX6+Wdd96Ry5cvy7Zt26Rly5ZKppe1zd/fX9zd3WXt2rWSl5cnycnJ0qhRI7l06VJty0FERGRR//rXv8Te3l5WrlwpBQUFcu7cOVm7dq3cv39fUlNTxcfHR3bu3Cn5+fmyc+dOcXd3l7S0NBH5fqysGk937NghFy9elIkTJ4qrq6vcvn1bRESePHkiixYtklOnTkl+fr5yHfGnP/1JyTBmzBgZNGiQSXljYmIkISFBWX/ZdYjI99cIer1e+vTpI1lZWZKdnS0hISEyYsQI5RgffPCBuLu7y65du+TSpUsSHx8vbm5uSqa7d++KwWCQSZMmKWN+eXm5cq3SvXt3yczMlG+++UZ69eolUVFRtagIkTZxwk6kUTExMRISEiKVlZXKtsTERAkJCZGrV6+KTqeTmzdvGu0TGxsr8+fPF5FnJ9MvcurUKQGgTHprM2Hv1auXLF261Og5n3zyifj4+CjrAGThwoXK+oMHD0Sn08n+/fuVNnbu3NnoGAsWLDDK9KK2+fv7y8iRI5X1yspK8fLyknXr1lXbFiIiImvKzs4WAFJYWPjMY61bt5ZPP/3UaNvixYvFYDCIyA8T9mXLlimPf/fdd9KqVStZvnz5C19zypQpMmTIEGXd3Am7qdchAOTq1avK42vXrhVvb29l3dvbW1asWKGsl5eXi5+fn1Gmp39RIPLDtcqhQ4eUbV988YUAkMePH5vUHiJbYa/Gu/pEZJoePXpAp9Mp6waDASkpKTh9+jREBO3btzd6fllZGTw8PF56zJycHCQlJeHs2bP473//i8rKSgDAjRs30LFjx1rlzc7ORlZWFpYsWaJsq6iowP/+9z88evQIzs7OAIAuXboojzdp0gSurq7Kbfm5ubmIjIw0Ou6rr75qcoYfH1un06FFixYWveWfiIjIEsLCwhAbG4vQ0FD07dsXcXFx+MUvfoHy8nIUFRVhwoQJmDRpkvL88vJyNG3a1OgYBoNB+be9vT0iIiJw6dIlZdv69euxceNGXL9+HY8fP8aTJ0/QtWvXWmc/c+aMSdchzs7OaNu2rbLu4+OjjMn37t3Dv//9b6Mx3s7ODt26dVOuTarz4zHfx8cHAFBSUgI/P7+aN4pIozhhJ7JRdnZ2yM7Ohp2dndF2FxeXF+7z8OFDxMXFIS4uDunp6fD09MSNGzfQt29fPHnypNaZKisr8d5772Hw4MHPPObk5KT8W6/XGz2m0+mUwVlEjH5JUbXNVC87NhERkVbY2dnh4MGD+Mc//oGMjAysWbMGCxYswN69ewEAGzZsQPfu3Z/ZpzpVY+if//xnzJo1CykpKTAYDHB1dcWKFStw8uTJWmevrKw06TrkeWPy02O6pcb8quNwzKf6hhN2Ig07ceLEM+tBQUEIDw9HRUUFSkpK0KtXr+fu6+DggIqKCqNtly9fxu3bt7Fs2TK0bt0aAHD69GmL5f3JT36C3NxctGvXzuxjBAcHY9++fUbbns74vLYRERHZGp1Oh+joaERHR2PRokXw9/fH8ePH0bJlS+Tn5+Ptt99+6f4nTpzA//3f/wH4/h347OxsTJs2DQDw5ZdfIioqClOmTFGef+3aNYvkNuU6pDpNmzaFt7c3Tp06pRyjoqICOTk5RncBcMynho4TdiINKyoqwuzZszF58mScOXMGa9asQUpKCtq3b4+3334bo0ePRkpKCsLDw3H79m38/e9/R2hoKPr374+AgAA8ePAAhw8fRlhYGJydneHn5wcHBwesWbMG8fHxuHDhAhYvXmyxvIsWLcLAgQPRunVrDB06FI0aNcK5c+dw/vx5fPDBByYdY/LkyVi5ciUSExMxYcIEnD17FmlpaQB++O3589pWdbs9ERGRLTh58iQOHz6MuLg4eHl54eTJk/jPf/6DkJAQJCUlYcaMGXBzc0O/fv1QVlaG06dPo7S0FLNnz1aOsXbtWgQFBSEkJAQffvghSktLMX78eABAu3btsHXrVhw4cACBgYH45JNPkJWVhcDAwFpnN+U6xBTTp09HcnIy2rVrh+DgYKxZswalpaVG77oHBATg5MmTKCwshIuLC9zd3Wudn8iW8GvdiDRs9OjRePz4MV599VVMnToV06dPx69+9SsA33/dy+jRozFnzhx06NABP//5z3Hy5EnlnfOoqCjEx8dj2LBh8PT0xO9+9zt4enoiLS0Nf/nLX9CxY0csW7YMv//97y2Wt2/fvvj8889x8OBBREZGokePHli5ciX8/f1NPkZgYCB27NiBXbt2oUuXLli3bh0WLFgAAHB0dHxh24iIiGyJm5sbjh07hv79+6N9+/ZYuHAhUlJS0K9fP0ycOBEbN25EWloaQkNDERMTg7S0tGcm28uWLcPy5csRFhaGL7/8En/961/RvHlzAEB8fDwGDx6MYcOGoXv37rhz547Ru+21Vd11iCkSExMxfPhwjB49GgaDAS4uLujbt6/Rn9G98847sLOzQ8eOHZU/5SNqSHRSkz8UISKr6d27N7p27YpVq1apHUV1S5Yswfr161FUVKR2FCIiItUVFhYiMDDwmdvHbV1lZSVCQkLwy1/+0qJ3ABLZMt4ST0Sa8/HHHyMyMhIeHh44fvw4VqxYofxNHhEREdUP169fR0ZGBmJiYlBWVoY//OEPKCgowIgRI9SORqQZvCWeiF6oX79+cHFxee6ydOnSOnvdvLw8DBo0CB07dsTixYsxZ84cJCUl1dnrERERNWQ3btx44Xjv4uJSZ7ehN2rUCGlpaYiMjER0dDTOnz+PQ4cOISQkpE5ej8gW8ZZ4Inqhmzdv4vHjx899zN3dnR/8QkREVA+Ul5ejsLDwhY8HBATA3p435hKpgRN2IiIiIiIiIg3iLfFEREREREREGsQJOxEREREREZEGccJOREREREREpEGcsBMRERERERFpECfsRERERERERBrECTsRERERERGRBnHCTkRERERERKRBnLATERERERERadD/A9eSaYDewvQkAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Putt plottene ved siden av hverandre\n",
    "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(12, 6))\n",
    "colors = {'setosa': 'red', 'versicolor': 'blue', 'virginica': 'yellow' }\n",
    "for t in df['species'].unique():\n",
    "    # Argumentet ax = ax[0] eller ax[1] definerer hvilke ramme vi vil plotte i.\n",
    "    df[df[\"species\"] == t].plot.scatter(x=\"petal_length\",y=\"petal_width\",c=colors[t],ax=ax[0],label=t,alpha=0.6)\n",
    "    df[df[\"species\"] == t].plot.scatter(x=\"sepal_length\",y=\"sepal_width\",c=colors[t],ax=ax[1],label=t,alpha=0.6)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "839ca77d",
   "metadata": {},
   "source": [
    "# Multinomial (multinomisk) logistisk regresjon\n",
    "\n",
    "La oss prøve å legge til en tredje kategori for å lage den ultimate *iris-type* modellen. Vi kan velge om vi vil bruke *one-vs-rest* implementeringen (hvor vi velger en baseline-kategori) eller om vi bruker *softmax*. Vi ser først på det siste tilfellet. Den logistiske funksjonen vår for k = 1,2,3 ser nå slik ut\n",
    "\n",
    "$$ p(Y=k|X=x) = \\frac{e^{\\beta_{k0} + \\beta_{k1} x_1 + \\beta_{k2} x_2 + \\beta_{k3} x_3 + \\beta_{k4} x_4}}{\\sum_{l=1}^{3}\\left(e^{\\beta_{l0} + \\beta_{l1} x_1 + \\beta_{l2} x_2 + \\beta_{l3} x_3 + \\beta_{l4} x_4}\\right)}$$\n",
    "\n",
    "\n",
    "I følge dokumentasjonen til *LogisticRgeression()* i scikit learn oppnår vi dette ved å sette argumentet ```multi_class = \"multinomial\"```. Men først må vi utvide X- og Y-vektorene vår med den siste typen iris."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "19372a02",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[predictors].values\n",
    "Y = df.target.to_numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "7796663e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(C=100000.0, multi_class=&#x27;multinomial&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(C=100000.0, multi_class=&#x27;multinomial&#x27;)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(C=100000.0, multi_class='multinomial')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multinomreg = LogisticRegression(C=1e5,multi_class = \"multinomial\")\n",
    "multinomreg.fit(X, Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f873ae1",
   "metadata": {},
   "source": [
    "Koeffisientene til modellen vår har nå 3 koeffisenter for hver av de 4 predikatorene:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "112d11ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 4)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multinomreg.coef_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "a7e59b50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  2.15237727,  20.21907037, -22.37144764])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "multinomreg.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4d4aec96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7.3, 2.9, 6.3, 1.8])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = df[df[\"target\"]==2].sample()[predictors].values[0]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "4a56dfb5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta0 = 2.15, 20.22, -22.37\n",
      "beta1 (sepal_length) = +3.93\n",
      "beta2 (sepal_width ) = +9.18\n",
      "beta3 (petal_length) = -12.37\n",
      "beta4 (petal_width ) = -5.93\n",
      "Score/R^2 = 0.99\n"
     ]
    }
   ],
   "source": [
    "print(\"beta0 = %.2f, %.2f, %.2f\"%(multinomreg.intercept_[0],multinomreg.intercept_[1],multinomreg.intercept_[2]))\n",
    "for i in range(len(multinomreg.coef_[0])):\n",
    "    print(\"beta%i (%-12s) = %+4.2f\"%(i+1,predictors[i],multinomreg.coef_[0][i]))\n",
    "print(\"Score/R^2 = %.2f\"%multinomreg.score(X,Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "c92c71ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25.06723552870938"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# La oss velge en tilfeldig måling av setosa, for å sjekke om odd-ratioen blir veldig stor\n",
    "\n",
    "# catogory 1: versicolor\n",
    "k = 1\n",
    "# catogory 0: setosa\n",
    "kp = 0\n",
    "logpred = multinomreg.intercept_[k]-multinomreg.intercept_[kp]\n",
    "for i in range(multinomreg.coef_.shape[1]-1):\n",
    "    logpred += (multinomreg.coef_[i][k]-multinomreg.coef_[i][kp])*x[i]\n",
    "logpred"
   ]
  }
 ],
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