491 lines
192 KiB
Plaintext
491 lines
192 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "1e9456",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"# Generowanie zmiennych losowych o dowolnym rozkładzie w Pythonie. Dyskretne zmienne losowe wielowymiarowe w Pythonie."
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]
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},
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{
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"cell_type": "markdown",
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"id": "382d67",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"## Metoda odwracania dystrybuanty\n",
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"\n",
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"Istnieje wiele różnych metod generowania liczb losowych o zadanym rozkładzie prawdopodobieństwa. Dzisiaj omówimy jedną z nich - będzie to metoda odwracania dystrybuanty."
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]
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},
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{
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"cell_type": "markdown",
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"id": "dcfe80",
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"metadata": {
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"collapsed": false
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},
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"source": [
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"### Dystrybuanta i dystrybuanta empiryczna\n",
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"\n",
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"Przypomnijmy najpierw, że dystrybuanta jest jedną z funkcji, za pomocą której można zdefiniować rozkład prawdopodobieństwa zmiennej losowej. Zgodnie z definicją dystrybuantę zmiennej losowej $X$ liczymy ze wzoru:\n",
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"\n",
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"$$ F_{X}(x)=\\mathbb{P}(X\\le x) = \\mathbb{P}(X^{-1}\\left((-\\infty,x]\\right)),$$\n",
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"\n",
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"dla dowolnego $ x\\in\\mathbb{R}$. Ponadto, jeśli zmienna losowa $X$ jest dyskretna, a jej zbiór atomów to $A=\\{a_1,a_2,\\ldots\\}$, to \n",
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"\n",
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"$$F_{X}(x)=\\sum_{a\\in A, a\\le x}\\mathbb{P}(X=a). $$\n",
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"\n",
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"Chcąc zbadać, jak wygląda rozkład pewnej zmiennej losowej na podstawie próbki, możemy spróbować oszacować właśnie dystrybuantę. W tym celu definiujemy tzw. **dystrbuantę empiryczną**.\n",
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"\n",
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"**Definicja (dystrybuanta empiryczna)**\n",
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"\n",
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"Niech $x_1,x_2,\\ldots, x_n$ będzie próbką wylosowaną z rozkładu o dystrybuancie $F$. Funkcję $\\hat{F}:\\mathbb{R}\\rightarrow [0,1]$ zdefiniowaną wzorem\n",
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"\n",
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"$$\\hat{F}(x)=\\frac{1}{n}\\sum_{i=1}^n\\pmb{1}_{(-\\infty,x]}(x_i)=\\frac{\\#\\{i:x_i\\leq x\\}}{n}$$\n",
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"\n",
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"nazywamy **dystrybuantą empiryczną**.\n",
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"\n",
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"Innymi słowy, chcąc wyznaczyć wartość dystrybuanty empirycznej w punkcie $x$ sprawdzamy, ile wyników z naszej próbki jest mniejszych lub równych od $x$ i porównujemy tę liczbę z całkowitą liczbą otrzymanych wyników.\n",
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"\n",
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"Chcąc wyznaczyć dystrybuantę empiryczną w Pythonie, możemy posłużyć się funkcją `ecdf(x)` z pakietu `stats` z biblioteki `scipy`. Argumentem tej funkcji jest wektor próbek. Załóżmy, że `f` jest dystrybuantą empiryczną wygenerowaną za pomocą polecenia `ecdf(x)`. Wówczas możemy badać jej właściwości za pomocą następujących poleceń:\n",
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"\n",
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"* `f.cdf.quantiles` - zwraca wektor unikalnych wartości w próbce,\n",
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"* `f.cdf.probabilities` - zwraca wektor skumulowanych prawdopodobieństw związanych z wartościami z poprzedniego podpunktu,\n",
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"* `f.cdf.evaluate(t)` - zwraca wartość dystrybuanty empirycznej w punkcie $t$,\n",
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"* `f.cdf.plot(ax)` - rysuje wykres dystrybuanty empirycznej na zadanych osiach.\n",
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"\n",
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"**Przykład 1**\n",
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"\n",
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"Załóżmy, że w $10$ rzutach czworościenną kostką do gry otrzymaliśmy następujące wyniki: $1, 1, 4, 1, 3, 2, 2, 1, 4, 4$. Na podstawie otrzymanych wyników wyznacz dystrybuantę empiryczną zmiennej losowej $X$ oznaczającej liczbę wyrzuconych oczek w rzucie czworościenną kostką. Następnie zbadaj własności tej dystrybuanty i zwizualizuj ją na wykresie."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "9e518c",
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Wartości otzymane w eksperymencie: [1. 2. 3. 4.]\n",
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"Skumulowane prawdopodobieństwa dla otrzymanych wartości: [0.4 0.6 0.7 1. ]\n",
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"Wartości dystrybuany empirycznej w punktach 0, 2, 3.5: 0.0 0.7 1.0\n"
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]
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},
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{
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"data": {
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",
|
|
"text/plain": [
|
|
"<Figure size 864x504 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 3,
|
|
"metadata": {
|
|
"image/png": {
|
|
"height": 440,
|
|
"width": 720
|
|
},
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"from scipy import stats\n",
|
|
"import matplotlib.pyplot as plt\n",
|
|
"\n",
|
|
"# Wprowadzamy dane z zadania i generujemy dystrybuantę empiryczną\n",
|
|
"x = [1, 1, 4, 1, 2, 2, 3, 1, 4, 4]\n",
|
|
"f = stats.ecdf(x)\n",
|
|
"\n",
|
|
"# Badamy własności otrzymanej funkcji\n",
|
|
"x = f.cdf.quantiles\n",
|
|
"print('Wartości otzymane w eksperymencie:', x)\n",
|
|
"p = f.cdf.probabilities\n",
|
|
"print('Skumulowane prawdopodobieństwa dla otrzymanych wartości:', p)\n",
|
|
"print('Wartości dystrybuany empirycznej w punktach 0, 2, 3.5:', f.cdf.evaluate(0),f.cdf.evaluate(3),f.cdf.evaluate(5))\n",
|
|
"\n",
|
|
"# Rysujemy wykres dystrybuanty empirycznej\n",
|
|
"os = plt.subplot()\n",
|
|
"f.cdf.plot(os)\n",
|
|
"plt.title('Dystrybuanta empiryczna')\n",
|
|
"plt.xlabel('x')\n",
|
|
"plt.ylabel('F(x)')\n",
|
|
"plt.xticks(x)\n",
|
|
"plt.yticks(p)\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
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"id": "39c337",
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"### Dystrybuanta pseudoodwrotna\n",
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"\n",
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"Metoda odwracania dystrybuanty opiera się na następującym twierdzeniu:\n",
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"\n",
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"**Twierdzenie (metoda odwracania dystrybuanty)**\n",
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"\n",
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"Niech $F$ będzie dystrybuantą pewnej zmiennej losowej, a $U$ będzie zmienną losową o rozkładzie jednostajnym na odcinku $(0,1)$. Jeśli $F^{-1}$ jest funkcją odwrotną do $F$, to funkcja $X=F^{-1}(U)$ jest zmienną losową o dystrybuancie $F$.\n",
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"\n",
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"Niestety, nie wszystkie zmienne losowe mają dystrybuanty, które są funkcjami odwracalnymi. Dlatego w praktyce będziemy korzystać z tzw. dystrybuanty pseudoodwrotnej, którą możemy zdefiniować dla dowolnej zmiennej losowej.\n",
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"\n",
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"**Definicja (dystrybuanta pseudoodwrotna)**\n",
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"\n",
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"Niech $F:\\mathbb{R}\\rightarrow [0,1]$ będzie dystrybuantą zmiennej losowej $X$. Wtedy funkcję $F^-:(0,1)\\rightarrow \\mathbb{R}$ definiowaną wzorem\n",
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"\n",
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"$$F^-(u)=\\inf\\{x:F(x)\\geq u\\}$$\n",
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"\n",
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"nazywamy **dystrybuantą pseudoodwrotną**.\n",
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"\n",
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"Jeśli $F$ jest dystrybuantą, która posiada funkcję odwrotną $F^{-1}$, to $F^-=F^{-1}$.\n",
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"\n",
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"**Twierdzenie (ogólna metoda odwracania dystrybuanty)**\n",
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"\n",
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"Niech $F$ będzie dystrybuantą pewnej zmiennej losowej, a $U$ będzie zmienną losową o rozkładzie jednostajnym na odcinku $(0,1)$. Jeśli $F^-$ jest dystrybuantą pseudoodwrotną do $F$, to funkcja $X=F^-(U)$ jest zmienną losową o dystrybuancie $F$.\n",
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"\n",
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"Powyższe twierdzenia stanowią podstawę następującego algorytmu, który pozwala generować zmienne losowe o dowolnym rozkładzie.\n",
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"\n",
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"**Algorytm (Generowanie zmiennych losowych przez odwracanie dystrybuanty)**\n",
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"\n",
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"1. Generujemy $n$ liczb pseudolosowych $u_1,u_2,\\ldots,u_n$ z rozkładu jednostajnego na odcinku $(0,1)$.\n",
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"2. Obliczamy $x_i=F^-(u_i)$ dla $i=1,2,\\ldots,n$.\n",
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"\n",
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"Przypomnijmy, że do generowania liczb pseudolosowych o rozkładzie jednostajnym $U(0,1)$ możemy użyć polecenia `uniform.rvs(size=n)` z pakietu `scipy.stats`, gdzie $n$ jest rozmiarem próbki, którą chcemy otrzymać.\n",
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"\n",
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"**Przykład 2**\n",
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"\n",
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" Niech $X$ będzie zmienną losową o dystrybuancie $F:\\mathbb{R}\\rightarrow [0,1]$ danej wzorem:\n",
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" \n",
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" $$F(x)=\\begin{cases} 0, &\\text{ dla }x<0,\\\\\n",
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"x^2, &\\text{ dla } x\\in[0,1],\\\\\n",
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"1, &\\text{ dla } x>1.\\end{cases}$$\n",
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"\n",
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"Wygeneruj $100$ liczb zgodnie z rozkładem zmiennej losowej $X$. Następnie wyznacz dystrybuantę empiryczną na podstawie otrzymanej próbki i porównaj ją z rzeczywistą dystrybuantą zmiennej losowej $X$.\n",
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"\n",
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"Wyznaczmy najpierw dystrybuantę pseudoodwrotną do dystrybuanty $F$. Niech $u\\in (0,1)$. Wówczas:\n",
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"\n",
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"$$F^-(u)=\\inf\\{x:F(x)\\geq u\\}=\\inf\\{x:x>0\\wedge x^2\\geq u\\}=\\sqrt{u}.$$\n",
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"\n",
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"Zobaczmy, jak możemy wykorzystać dystrybuantę pseudoodwrotną do generowania liczb o rozkładzie zgodnym z rozkładem zmiennej losowej $X$."
|
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]
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},
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{
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"execution_count": 4,
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"id": "ad3784",
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"metadata": {
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"outputs": [
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{
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0AcoCy621PwQ59pe4ww2Ran4AH4Hu13/j9EgF5/wM9HtvhfszvTZ5xVobG6D8LZwPYsNwhnjKqgnW2uQg6+bjJKSr4AzllMK9nm50F1PfQ/rifNPkIM4QL9linLkVPgUq4HwTZGQ6m6dpe9c892fqts2r398iIlKAKTEsIiL5qa3P5C7JOP9QPofztdRdQG/3n1xwxnYF7+Q7gaxMtW1q31prE4Osy0r9Z6dKjK5xf7YwxpR2n7fB+b26BmcIjENAG5/EiydJvMFaeyzI8dJMaAdgrT2F04MHnH/A/Rhn4rj/M8Z84U4KlOjTzp+4mwVLVgQ9LrDD53nFdPb3dan7c5A7aU2aB84/7BHudrUyWa/n/doTKIHm+gLn6/FpWGt/wkm+ROB89duXJ5mywlq7PdW6Re7Pt4wz8VQrY0wEuec4zvkSkJuwn+su3pRq9X9whp34w1obMHnoWh2k7sM4Q4hA8GsoW4wxZ7iTR210J5tK8jknX3Q3y8k5meY6yIxcas/c5Gn3Nelsk946zwceA4wxkZ5C94Oq3u7i66n2WYGTHG8GrDbG3JBOMjO7gn345eGJu5sxppqn0DgTuHkSa6nj9rXG/ZAh4Dr353m+bZIbjDPR51zjTD533HcCMLz3yGBt+W06MefovCbn7RmI517eIdi93L2fe+7hge7lJ/AmgFPz/E4L+AECTvIV0m+T1YEK3aTuOncxO/e2oOev+zfFm+5i6nvIlTgfAB/G+8G1Ryv35ypr7fFsxORJPL+H0wv8N5zhHIIlsGOttVuDrAt2vuXV728RESnAlBgWEZH8dArnn709OMMX/IXztfKHcMa6+95n2yruT9/kZGr/uj9PCzLD9r509s1K/Qbna6AAuL2bduL8c+T5R8qT+F3t809pReCCVOvTSzjFp7PuhPvTLylpjDkX2AKMxen1Wgln+IO9OO180N00vR6/AY9rrT3hs5jZZKinB1E5nOE4gj08f4OUTl1BEJ73a2ewDdwepvvTqcOTPEn5Z95NnAx0FwP1En0QJ+FcDngYJ2Fw2Biz0hhzhzGmVObCD+pAOv/Ye3ji7p8q0eVJaKfu5Zxaeue4Z12VdLbJEmNMW5ye8w/hJGUq4Jxjnmvf02M1y+ck3usgPAch5rQ9c1OG5zXpv39LcMYgPw1nTGKP/jhJ7t+stZ/77mCt/QNnrNDjOB9ovQ3sMMbEGGOmpu5JnU3p3Xux1v6Cc12F4/9BTRecxOohnEnvgsnMOV2C7Cda/Rhjwo0xHwMf4kyMWAvn98J+vOe15zoOdl5n+f6eWbnQnoF47uWlSf9eHuGzXWp70kmGJ7k/d2WwPr02yat7W7rnL957SFffRDzee8j7AT4A9mz3dzbi8RgPdMXpnd7TWnsonW2zc77l1e9vEREpwJQYFhGR/PSFtba6+6hhrT3LWtvZWvuctfZgkH1K5uB4SRlvku36Uw8n4fm5JtXPYOtzyxs4/6htwkkClLPWlrfWVrPWVseZPAacJEZ+8PxtMcJaazLxWJ1PcYHT0+oITk/CFm5ZV5x/hg/i7V2dwu1h2hpn8sPJOD1sI4H2wMvAZmPMGTmIKTPn6HKc3vWn4UwKiDHmPJzJ75Lw9l4LObc39Szcr6DjTHRWylpb0XPtA/d5Ng9RmIWmPTPifqjg+UDDt/ei53nAJLe1dgbOxGfDcb5WfgBnjNXbgY3GmEdzGFpmzuvX3J+B4n4vu70q88itOMOMHAPuwRl/taS1torPee1J7ofqvM7t9vTcyydl8l4+MyfBFyTW2nTPX/fDlTU4ifiBAMaYlPsJeTAUjTGmP95JQ6+31v6e28egYP/+FhGRPKLEsIiIFFSeHju109nGk5A7kE6vpNyo35K2J2pK4tcYUx5nDNzfrLW7A6yvA9TB+YfOr/deThhjagMXu/X2tNYuSTWWKHh7KeUXz9d/02vX7PC8X0G/8u72/qwcbL3bNh+4i56EiaeH13upekj77mettcuttfdaa5u5x7gNZ8KlM/EOjZAn3HM7dfLPE/cSd4zS9KQ3TIBnXeoecp7ESLAPTioEKb8E57qJxZkIa12Ads3vc9JPLrRnbsrwvM5gHTivJRnoYoypYYy5AGe81yS8Y8+mYa3dY62dZK3tjdOr8mKcD0cM8F+3nrz0IU7v8cbGmIuMMZXx9nrOKLGWmfZKwvuNCfAOM5Peh4HBzmvPB2z/tda+ZK3913el+82DoPeefJKT9gwkr+7luSk797bckvobKANwPjT82Vr7dYDtPe1ZJ6sHMsY09znewzbAvAi5pDC85yIiksuUGBYRkYJqk/uzfTrbdEi1bXbqbxtkGArf+n+31h5Ntc7TY/hinN6kJfDvDbwJp3fq5TizdQNsstam9/XOrPIkrvdZa4N9pfaKXDxeZnjGZuySy/V63q9qxpizg2xzKRkPMeD55/o/xphaeCcPynTixFp70Fr7KuDpVdk21Saer5TnZs/BN3ASXVe6HzR4vi6embhTxweAMaYc3vE3U19Dce7PYL2hLwpS7tn+93TG0s6rczIr7Z6T9sxNnna/PJ1tAr5/HtaZyGsZzj3oRryJqsXW2mBf009dh7XWbsBJgHom7Wrts0nKcCfp3C+zxD0/3nMXb8abWNvsxpKe9NrEs26z9Y5ZDxmc0+7rCjaBmmef74Ksv4ycfbslmEyf0zlsz0A89/J2uTBkTl4Jdm8zeK+p7Px9kBmzcc6pc40xLcmglz7wlfszS+3pDlUxF2cuhrettROyFW3m5NXvbxERKcCUGBYRkYLKM3FL10BjXhpjGuOddf7DHNTfGGfMyNT1V8P5WnXA+q21W3B6IkXhjD0LPhPhuF9F/Rzn6+p3usW5PYyEZ3zBasaYqqlXGmPOxxlrND+9hdPDupEx5rb0NnQnyMqs7wHPzPUPp17pJgIeyagSa+1XOJMdReMkUSKAH6y1GwPUGWaMSS/R7PlqdlSqcs8YuhUziiez3MT/Ypzk3zs4PTz34cxOn5H7g0zCNRwnmXUYWJpq3U/uz0DXRpS7byCec7KBMSZNoswY05n0P+zJiUy3ew7bMzd95P68xhjTIPVKY8ylpJ809vAMI+BJCEKQycbSm5DNvW+dchd9z+vDPs8rZiKezPLEfT3OcA2QuUnS6hpj/pO60BhTCRjqLn6UarXnnL7IGFODtAYQfDItz3l9foBjhgNPZhhx9njaPVhP5tSy256BfAQcxblXPpHehlm8l+emO4wxFQOU34CTzE8m62MrZ4r7TYhZ7uIEnG8NncIZszuQ2Ti/MzJsTw/3Wp2D81q+wXtu55W8+v0tIiIFmBLDIiJSUH0A/Og+n2uMucLTU80Y0xFYhJPU+xknsZMl1tp1wGfu4gxjTF/368Cer20uxfkHbg8wKUg1nlnPPb0nUyd+12SwPqd+wendZ4APjDFngTPOqzHmGpxehKmHlshTbsLcM7TCy8aYcb5j8BpjyhljOhtjZpE2cZNevRYY7S7ebIx5xpMQcJP4M3B6eAfrperL02v4MvdnsF6i5YE/jTGPGWPO9zk/wtxz8Cl3u9Rf6/3Z/dklSAIqu1LHPctaeyrYxj5qA58YY+oCGGNKG2Pux9uezwTo3ev5MORWY8xNbjLY84HMIoJ/hftznPfgNOAtz+s3xpQyxtyMk+Q4kImYs8PT7tcYYzKTSMtue+amD3Amj4wCFhljWkPKOdYdJ6l1OJ39PT7FmXDybJwk915gQZBtnzbGzDbG9HYTqbjHrGaMmYwz9rDFuX8AYK2NwzuGru8YtjnifiDzPU6yuTGQgDfZlp5DwGvGmAGeD2/coS+W4H39L6fa53Oc1xAJvGeMqefuV9pNgr2G/9ATvjxt8X/GmF4+94KGwHycb46k/lZJbvgDJ9lYwRjTJ6ONc9Cegeo6AIx0Fx8xxrzm+20N95puY4yZijPxXSiUBD5zxwj3/O4bBLzirn/d7VGfV1LfQxZYa/cG2tBaux8Y4y4+YoyZ4g4HBYA7DMx9xhjfpPFkt+6dwNXBhjvKLXn1+1tERAo2JYZFRKRAcr8C3AfYjpPYWgYcMcYcxZk8qjbO7N7XWGtPZvMwN+L8Ex2N80/OEWPMYeBb4AKcJMHV7j/Igfgmev8IMDap7/pkYH024wzInXjqHrfudsAfbvxHcBJwJwneszMvPQRMxfk74xHgH2PMIWNMHE5CZwlO77wSWanUWvsO8D+fY+w3xsTizGo/GHiAzI0n+TZO24CTOEnvg4U6OL0BfwSOG2MOuPssx+nFtRXvZGoen+CMsXs28K8xZpcxZpsxZlsmYkvPQpzX6pHZYQ+GAJ2BGGPMQZz34Hmc92ce8GyAfaYDX+MkLGfgXBuHcHpbNyVIctBNIHqSSf2Ane77fhin5+KfeJMjue1tnPemNc65scNt92DXXXbbM9e4ieh+OOftWcA6Y0w8zjW8AIgHxmayHt/xhN+21iYG2Twc5976CXDAvTYPA7uBu91tHrfWbk61nycJNsEYc8RzThtjhmcUXwam+zyf7ybQMjIV51ychffc/AFnAsFjQD+bakJTtz3uwrlftgW2uvsdwkkkvkvwHuPPA3/hfFg0F+decAjnw7lOON8uyUzcWeIOYeQZHmK2MSbOp937BtktO+0Z7PgvAf+H80HBLcBv7nsfi3OOrsV57XkxjEZmDMPpxf2Te585AswESuMM3ZD63pyrrLU/4Py94JHRPeRZYKL7/E5gu/ueHsJJ/k7AGbfewzOkQ0VgkzFmd5BHsA+vsyNPfn+LiEjBpcSwiIgUWNbaP4EmOIkR3yTFZuC/wAU5mZnbWrsPZ7KsB3D+uTuF05vsD5x/3hpba78MWoF/4jdQb+ANeHuw/ugmzXKVtfYTnJ6yy3CSSBE4yfTngQtxehTnK2ttkrV2GE6CbpYbTxRO8uBvnOTLXXiHAslK3XfhfE34a5zkrsFp+x7W2smZrCMW7/s1L53E/2GcMYgn4nyNdx9QDqdn4AbgMaBp6omo3ERMe5zenvtwejB6JiDMNjexNd9d3BAgcRdsvzluPAtxxtVNxEmi3Y3zwUqaBKKbaOwEPAdsw0mmHcVJujR39w92vMnANXh7D4cDvwKjcMaBzs1xtn2P+6sb82c4CYzqOG0ecEzZ7LZnbnN76TXFSejtwrmGd+P03LsI50OGzPD9ynx6CaoXcT5Qmgf8jnMNRQH/4PRgvtxa+3SA/cbiDOPyo7uP55yumMn4chq3r5M4H4aNxbm/ROJca+8Dzay1awPt5N4vOwOrcM7DEjgfDg6x1g4JdjD3ntEKJ2Hmud6P4ySJ21prZ2Yy7uy4HRiHcw1F4W33skG2z057BmWtfRLn9/CrOL8bw4AyOOfqEpxEYpucHiebvgBa4nzD4SROAvs3nKEa2gWYjDUveNp7F87wNEG5Y3mPwBke5gNgB87YwSdxxkJ+Gu83UXyVxpm0M9gjs0ONZCgvf3+LiEjBZGyWJ3EXERERKbyMMaVx/okvD3S11n6WwS4FhjHmd6ABcIe19pWMtpf0FaX2NMY8htO7/WtrbatQx5NZxpgBOAmoHUAdd5xjyabi0J7GGM8/sPWstdtCHMsynAk1n7HWZjjOfVFljLkC5wPq362154Q6HhERyTz1GBYREZHi5j84SeHtpJ10rcByxzVugNNz990Qh1PoFaX2dMe8vcVdfDWUsWSDZ5LPGUUxiRkCas984o7r3xGnp/L0DDYv6jzjzgccY1lERAouJYZFRESk2HAnYBvtLk52x2ku8IwxlXGGdQAn4ZOZCckkiKLUnsaYMJyvztfFmSzzvXR3KECMMUNwvrJ+Eu+EYZJNas/8Y4wpC7yEM6zKAnfoq2LJGBON94Opb0IZi4iIZF14qAMQERERyWvGmPdxEiY1cD4Y/x14OaRBZYIx5nngWpzxciNwJrh6MqRBFWJFqT2NMa1wxtSNxukBD/CotfZ46KLKmDHmDJyJOMsBldziZwNM3imZoPbMX+5ki8Nx7iFRwAmcSdqKJWPMH0B9nAT5CfSBhIhIoaMewyIiIlIcVAdqAnHAHKCztfZESCPKnMpALZyJrpYCHay1+qpu9hWl9iyJMwlZKZyJyYZaa3M82Vg+CMc7aV0M8CjeXvySdWrP/FURp72TcCa/6+xOIFlcVcaZZHQ1cIW19o/QhiMiIlmlyedEREREREREREREihn1GBYREREREREREREpZpQYFhERERERERERESlmlBgWERERERERERERKWaUGBYREREREREREREpZpQYFhERERERERERESlmwkMdQH4yxsQA5YFtIQ5FREREREREREREJKfqAoettfWyumOxSgwD5UuVKlWpUaNGlUIdSH6Jj48HoFy5ciGORERyStezSNGga1mk6ND1LFI06FoWKTqK4/X8yy+/cPz48WztW9wSw9saNWpUaePGjaGOI9+sXr0agHbt2oU0DhHJOV3PIkWDrmWRokPXs0jRoGtZpOgojtdz8+bN2bRp07bs7KsxhkVERERERERERESKGSWGRURERERERERERIoZJYZFREREREREREREihklhkVERERERERERESKGSWGRURERERERERERIoZJYZFREREREREREREihklhkVERERERERERESKmfBQB1BQJScnExsbS3x8PCdPnsRaG+qQsqV06dIA/PLLLyGORERyStezSNGQV9eyMYaoqCjKlStHpUqVCAvT5/8iIiIiIhKcEsMBJCcn888//3Ds2LFQh5Jjnn8+RaTw0/UsUjTk1bVsreXEiROcOHGCo0ePUqtWLSWHRUREREQkKCWGA4iNjeXYsWOEh4dTvXp1ypQpU2j/sYqPjwegXLlyIY5ERHJK17NI0ZBX13JycjJHjx5l9+7dHDt2jNjYWCpXrpyrxxARERERkaKjcGY785jnH7bq1atTrly5QpsUFhERkeIjLCyMcuXKUb16dcD794yIiIiIiEggyngGcPLkSQDKlCkT4khEREREssbz94vn7xkREREREZFAlBgOwDPRnHoKi4iISGFjjAEotBPnioiIiIhI/lDmU0RERKQI8SSGRURERERE0qPEsIiIiIiIiIiIiEgxo8SwiIiIiIiIiIiISDGjxLBkW926dalbt26ow8gzxhjatWsX6jAkEwYPHowxhm3btoU6lDyR1WtN525aRf1+JSIiIiIiIpJVSgxLobBt2zaMMQwePDjUoRQ6M2fOxBjDzJkzQx2KSKGwfPlywsLCaNKkCQkJCQG3GTZsGMYYHnrooXyOTkRERERERCR3KDEsIoXeuHHj+OWXX6hZs2aoQ8kTK1asYMWKFaEOo1DLShteccUV3HXXXfz444889thjadYvWrSIqVOncsEFF/Dkk0/mdqgiIiIiIiIi+UKJYREp9GrUqEHDhg2JiIgIdSh5on79+tSvXz/UYRRqWW3DZ555hoYNG/LCCy+wZs2alPL9+/czZMgQoqKieOedd4iMjMyLcEVERERERETynBLDki5rLVOmTKFx48aULFmSmjVrctddd3Ho0KE0206bNg1jDGPGjAlY1+7du4mIiOD8889PKYuPj+e///0v5513HuXLl6dcuXLUr1+f6667jo0bNwIwevRo6tWrB8Cbb76JMSbl4RkeYfXq1RhjGD16NN988w3du3enUqVKGGP466+/qFWrFuXLl+fIkSMBY7v77rsxxjB79uw063bu3MnAgQOpWrUqpUqVonnz5rz77rtptstoyIZA477u3LmTsWPHctlll1G9enUiIyM5/fTT6d+/P1u2bElTh++QGtu2beP666+ncuXKlCxZkhYtWrBgwQK/7du1a8dNN90EwE033eTXdp7xeLMaQzCjR4/2qz/Qw8P3/fr222/p0qULFSpUIDo6mj59+vDPP/8AsHXrVq6//nqqVKlCqVKlaN++PT/88EOaY6c3xvDXX39N3759U15brVq1uO2229i5c2eabdu1a4cxhsTERJ5++mkaNGhAVFQUtWrV4uGHHw44rIDnfd2/fz9Dhw6lRo0aREVF0bhxY954442g7bVkyRK6detG5cqViYqKon79+jz44IPExcWl2Ta3xsc9dOgQI0eO5JxzzqFkyZJER0dz5ZVXsnz58jTbWmt58803ufTSS6lSpQolS5akVq1aXHnllXzwwQdptt+4cSN9+vShatWqREVFUadOHYYNG8auXbv8ths5ciTGGJYtW+ZXPmrUKIwxAZO31atXp3bt2mnK87INS5Uqxdtvv01YWBiDBg3i8OHDAAwdOpTdu3fz9NNPc95552W6PhEREREREZGCJjzUAUjBNnz4cCZPnkyNGjUYOnQoERERzJs3j6+//pqEhAS/3nIDBgzgoYce4vXXX+fxxx+nRIkSfnXNmDGDxMREbrvtNsBJPHXp0oUvvviCSy65hFtuuYXw8HD+/fdfVq1aRZs2bWjevDnt2rUjLi6OSZMm0aRJE3r37p1SZ9OmTf2O8eWXXzJu3Dhat27NzTffzP79+ylVqhS33noro0aN4r333uPWW2/12+f48ePMmjWL6tWr06tXL791Bw8e5NJLL6VixYrcdNNNxMXF8eGHHzJgwAB27NjBgw8+mKP2Xbt2LePHj6d9+/b06dOHsmXL8scffzB79mw+/fRTPv/8c5o0aZJmv+3bt3PxxRdz5plnMnDgQGJjY/nggw/o1asXy5cvp3379oCTMK1YsSLz5s2jV69efu1VsWLFHMWQWrDJzv755x9mzJhBqVKl0qzbsGEDzzzzDG3btuXWW2/lp59+4uOPP2bz5s3MmzeP1q1b07BhQ2688Ua2b9/Oxx9/TKdOndi6dStly5bNMKYZM2YwdOhQoqKi6NmzJ7Vq1eKPP/5g+vTpzJ8/n6+++ipgwrF///6sW7eOrl27Ur58eRYtWsSzzz7L3r17AyZ74+LiuOyyy4iMjKRv376cPHmSjz76iJtvvjklsehrzJgxjB49mkqVKtGjRw+qVq3Kjz/+yPPPP8+iRYv48ssvKV++fIavLys8MW7ZsoWLLrqI4cOHs3//fj788EM6d+7M1KlTU65NgMcee4xx48ZRr149rr32WipUqMCuXbvYsGEDH330Edddd13KtgsWLKBPnz5Ya+nbty916tRh48aNTJ06lXnz5rF+/fqUD3c6duzI+PHjWbFiBZ06dUqpwzPMw9atW9m2bVtKEnfz5s3s2bMnzfji+dGGLVq04IknnuCJJ57grrvuol27dnzyySd06NCBESNG5KhuERERERERkZCz1habB7CxWbNmNiNbtmyxW7ZsyXC7wuDw4cP28OHD2dr3888/t4CtX7++PXDgQEr58ePHbatWrSxg69Sp47fPnXfeaQE7f/58v/Lk5GRbr149W7p0aRsXF2ettfbHH3+0gO3du3eaYyclJdnY2NiU5ZiYGAvYQYMGBYx11apVFrCAfeWVV9Ks37lzpw0PD7fNmzdPs+6NN96wgH300Uf9yj319evXzyYlJaWUb9261UZHR9uIiAj7119/pannjTfeCBgjYNu2betXtmfPnoDvz/fff2/LlClju3Tp4lfuaQfAjh492m/dZ599ZgHbtWvXgK8vWFxZjSErDh06ZM8//3wbFhZm58yZk1Lu+37NmjXLb5+bb77ZAjY6Oto++eSTfuvGjh1rATtx4kS/8kGDBlnAxsTEpJT99ttvNiIiwtavX9/++++/ftsvX77choWFpTn32rZtawHbrFkzv3P+yJEjtn79+jYsLMzu2rXLbx/P6xgyZIhNTExMKf/5559tiRIlbKNGjfy2X7lypQXsJZdcYg8ePOi3zvNeDR8+3K+8Tp06tk6dOpm+ngOda0OHDrWAHTp0qE1OTk4p//3332358uVtZGSkX/tVqlTJ1qxZ0x49ejRN/fv27Ut5Hh8fbytVqmTDwsLs2rVr/bYbP368BWynTp1Syo4dO2ajoqJsixYt/OqIiIiwnTp1soCdPn16yrqJEydawL711lspZTlpw6xKTEy0LVu2tICNioqyFStWtH///XeW6xHxlZPfzZlVlP6WESnIVq1aZVetWhXqMEQkh3QtixQdxfF6btasmQU22mzkSjWURHYYU3geOeDpGfnYY49RqVKllPKSJUsybty4gPvccccdgDOshK+lS5cSExPDddddR4UKFfzWBepJGhYWRnR0dJZjbtq0qV+vR48aNWrQu3dvNm7cmDJEhce0adMICwtL05MYoESJEjzzzDOEhXkvlXr16nHPPfdw6tQp3n777SzH6Ktq1aqUK1cuTXmTJk3o0KEDq1at4tSpU2nW16lTh8cff9yv7Morr6R27dp88803+RJDRhITE+nXrx8//fQTzz33HNdcc02abVq3bs2AAQP8yjy9aytUqMAjjzzit+7GG28E4Pvvv8/w+FOnTuXUqVNMmjQpzaR0HTt2pGfPnsyfP5/4+Pg0+z7zzDN+53yZMmUYMGAAycnJfPvtt2m2L126NC+88IJfL/lzzz2Xyy67jF9++cVvCJPJkycD8Nprr6X02vYYPHgwTZs25Z133snw9WVFQkICs2bNomzZsowbN85vWI8GDRpwzz33kJCQwFtvveW3X0RERJqe/wCVK1dOeT5v3jxiY2O57rrraNOmjd92999/P3Xr1mXZsmX8/fffgHO9X3LJJWzatImDBw8CTq/1U6dOMXz4cKpUqeI3SZzneceOHVPK8rMNS5Qowfjx4wE4efIk48aNo1atWrlSt4iIiIiIiEgoaSgJCWrTpk0AtG3bNs261q1bB0wYNW7cmMsvv5zFixfzzz//pCRQXn31VQBuv/32lG3PPfdcmjZtynvvvcf27dvp1asXrVu3pkWLFtme0Oniiy8Oum7YsGHMnj2badOmpcTz008/8dVXX9G1a9eA44/Wrl075Svwvtq1a8eYMWP47rvvshWnr4ULF/LKK6/w7bffsn//fhITE/3W79+/nxo1aviVNW3aNGD716pViy+//DJfYsjIHXfcwdKlSxk2bBj33XdfwG1atGiRpuz0008HAr9GT4L333//zfD4nnZYs2YNGzZsSLN+7969JCUl8fvvv9O8efMM4/Kcy55kpq8GDRoEHLbAdx/P0BdffvklERERfPTRR3z00Udp9klISGDfvn0cOHCA0047LaOXmSm//fYbx44d47LLLvNLeHt06NCBJ5980u98HjBgAC+99BLnnnsu1157LW3btuWSSy5J88GO5z7RoUOHNPWGh4dz+eWXs23bNr777ruUYTs6dOjA6tWrWb16NVdffTUrV64kIiKCtm3b0r59e1auXAlAUlISa9eu5Zxzzkk5LyB/29Bay9ixY1OW58yZw2233eaXXBcREREREREpjJQYlqA8E8xVq1Ytzbrw8HC/XoO+hg0bxtq1a5k+fTpjxoxh9+7dfPrppzRt2tQvcVuiRAlWrlzJ2LFjmT17Ng8//DAA5cqVY9CgQYwbNy5T48j6ql69etB17du3p1GjRrz33ntMmDCBcuXKpSSIA/UyhsCv3fc4gSbhy4pJkyYxfPhwoqOj6dSpE7Vr16Z06dIYY5g7dy4//PADJ0+eTLNf6l6SHuHh4SQnJ+dLDOkZN24c06dPp3v37im9OwNJnWT0vIaM1mWmB/OBAwcAeO6559LdLtCEhIHa13PspKSkTG0fbJ8DBw6QmJgYdJJG37hyKzHsOU+DJfc95b6Ttr344ouceeaZvPHGG4wfP57x48cTHh5Ot27dmDBhAmeddVa26+7YsSNPPPEEK1as4Oqrr2bFihW0bNmSMmXK0LFjRz788EM2b97M0aNHOXToUJpe5fnZhi+88AKrVq2ib9++HD9+nIULFzJlyhTuvvvuHNUrIiIiIiIiEmq5khg2xvQF2gJNgSZAOeAda+0N2ajrDGAs0AU4DdgFzAXGWGvTdtULBWe84sIhwNfkM8uTmNuzZw9nnnmm37rExET279/PGWeckWa/a665hmrVqvH666/zxBNPpJl0zld0dDQvvvgiL774In/++Sdr1qxh2rRpTJkyhbi4uCwP1ZBRL77bb7+de++9l3feeYdBgwYxa9YsatasSY8ePQJuv2fPnoDlu3fvBvyTl57hJlL3tgX/pJhHYmIio0ePpnr16mzatClNYi07PX+zKi9i+OCDD3jssce48MILef/99wP2bM4Pnvfm0KFDuT6RW05UqFCB5ORkYmNj8/WY4D1vU9u1a5ffduB8cDN8+HCGDx/O3r17Wb9+Pe+//z4fffQRP//8Mz///DNRUVHZqvviiy+mbNmyLF++nAMHDvDDDz/wxBNPAN6ex8uXL+fYsWN+Zb6vJz/a8KeffuKxxx6jRo0aTJs2jYSEBM477zweeeQRrrzySs4+++w8Pb6IiIiIiIhIXsqtMYYfB+7CSQzvyG4lxpj6wEbgJuAb4EVgK3Av8KUxJne6z0mmNGvWDHC+ip/a+vXrA/acBGdc0ltuuYUdO3Ywf/58pk+fTtmyZdP0+kvtrLPOYsiQIaxZs4ayZcsyb968lHWe5GKwY2bWoEGDKF26NK+++ioffPABcXFxDBkyJGjy8u+//2bbtm1pylevXg3AhRdemFLmGRP5n3/+SbN9oHFp9+/fT1xcHJdeemmahOyRI0dSvqKfU+m1XW7H8PnnnzNo0CBq1qzJggULstzjOze1atUKgHXr1oUshkBatWrFwYMH+fnnn/PtmOeccw6lS5fmhx9+CPghxapVqwDvNZ9a1apVueaaa/jwww/p0KEDf/31F5s3bwa814DnmvCVmJiY0v6+dXuGmPjtt994++23sdamjCF81llnUbt2bVasWMHKlSsJCwujffv2fvXmRxsmJCRwww03cPLkSWbMmEGlSpWoXr06U6dO5dixY9x44405vh+JiIiIiIiIhFJuJYZHAGcD5YE7clDPy0BV4B5rbW9r7SPW2g44CeJzgKdyHKlk2uDBgwF46qmn/HrmnThxgpEjR6a779ChQylRogR33XUXMTEx9O/fP80EZzExMWzdujXNvgcPHuTkyZN+k9JFR0djjEmZwCq7KlSoQP/+/fnuu+94/PHHKVGiRMBJ5zySkpJ4+OGH/YZniImJYfLkyYSHh3PDDd5O8S1atCAsLIx33303pacjQGxsLA899FCauqtWrUrp0qXZuHGj33AGp06d4t5772X//v05eq0enq/SB2q73Izhzz//pHfv3kRGRrJw4UK/MWFD4a677iIiIoIRI0bw+++/p1mfkJAQkqTxiBEjALj11lvZuXNnmvVHjx7lq6++ytVjRkZGMmDAAOLj4/m///s/v3V//fUXkydPJiIigoEDBwLOJGuff/55mnpOnTqVci8oXbo0AL1796ZSpUq89957aeKeOHEiMTExXHHFFSnjC3t4egGPGzeOMmXKpCTyPevWrFnD559/TpMmTdKMi5wfbfj444/z448/MmzYMLp06ZJS3q9fP/r378/XX38ddBJOERERERERkcIgV4aSsNau8jzP7oQ8bm/hzsA24H+pVo8ChgIDjTH3W2uPZi9SyYrLLruMu+++m5deeonzzjuPvn37EhERwbx584iOjk53MrLatWvTvXt3Pv30UyDwGL4//PAD11xzDRdddBGNGjXi9NNPZ9++fcybN49Tp06ljDkMULZsWVq2bMm6desYMGAAZ599NiVKlKBnz55ccMEFWXpdw4YNY/r06ezYsYOrrroq4HAYHhdccAFff/01zZs3p3PnzsTFxfHhhx8SFxfHs88+S/369VO2rVGjBgMGDODtt9+madOmdO/encOHD7No0SIuv/zyNBPVhYWFcc899zB+/HjOP/98evXqRUJCAqtWrSI2Npb27dun9OTMiUsuuYTSpUszceJEDhw4kDI+8t13302FChVyLYZ77rmH/fv306FDBz7++GM+/vjjNNuMHj06x68nsxo2bMiMGTO4+eabady4MV26dOHss8/m1KlT/P3336xbt44qVarw66+/5ltM4IyvO378eEaOHEmDBg3o1q0b9erV48iRI2zfvp01a9bQunVrPvvss1w97vjx41m3bh1Tpkxhw4YNtG/fnv379/Phhx8SHx/PlClTUiZaPH78OK1bt+ass86iefPm1KlThxMnTrBs2TJ++eUXevbsSaNGjQDn2pwxYwb9+vWjbdu29OvXj9q1a7Nx40aWLl1K9erVmTZtWsB2AGcSwC5duhAREeG3bubMmX7b5Wcbrl27lgkTJnD22WcHHKP6f//7H2vWrGHs2LF0797d75sDIiIiIiIiIoWGtTZXH0A7wAKzsrjfLe5+04KsX+Ku75iD2DY2a9bMZmTLli12y5YtGW5XGBw+fNgePnw42/snJyfbl156yTZs2NBGRkbaGjVq2GHDhtm4uDhbp04dW6dOnaD7zp071wK2RYsWAdf/888/duTIkfbSSy+11apVs5GRkbZmzZq2S5cudtGiRWm2/+OPP2yPHj1spUqVrDHGAvaNN96w1lq7atUqC9hRo0Zl6nU1bdrUAnbBggVBtwFs27Zt7Y4dO+yAAQNslSpVbFRUlL3wwgvtO++8E3CfEydO2AceeMDWrFnTRkRE2Pr169unn37anjp1KqU+X6dOnbITJkywjRo1siVLlrTVqlWzN9xwg922bZsdNGiQBWxMTEzK9jExMRawgwYNCnj8tm3bWuey9rd48WLbqlUrW6ZMGeteRyn1ZjWGYDzHTu/hkd77ldFrDNSO6cX5448/2kGDBtnatWvbyMhIGx0dbRs3bmyHDh1qV6xYEfA1BPLGG2/4nXPpxZOZuNatW2f79etna9SoYSMiImzlypVtkyZN7IgRI+yGDRv8tvVca5m9noPFdPDgQfvQQw/Zs846y0ZGRtoKFSrYK664wi5ZssRvu4SEBPvMM8/YLl262Fq1atmoqChbuXJl27JlSzt16lR78uTJNHV/8803tnfv3rZy5co2IiLC1qpVy95+++12x44dAWNMTk62lStXtoB99tln/dbt2LEj5ZwJdC/wyE4bZuTQoUO2Tp06Njw83H7zzTdBt1u6dKk1xtjGjRvbEydOZFiviK+c/m7OjKL0t4xIQbZq1Sq7atWqUIchIjmka1mkaDi676i9MnqdnfnQ7FCHkq+aNWtmgY02G7lSY3N5IjVjTDtgFVmcfM4Y8xzwAPCAtXZCgPVTgDuBYdbaqRnUtTHIqoYNGjQo/eqrr6YbS+nSpSldujR16tTJXPAFmGcMzFBMAPb0008zfvx4pkyZwo033pjvxw8mPj6ec845h+joaH766aeUSeNECqqzzjqL8uXLs2HDBiA013Nh52nD3Bq7WyQn8uN38/bt2zl27Jjf0EYikvvi3YmeUw+ZJiKFi65lkcIvKSGJ56+P5LODbSjFMZ4duIDzbq4a6rDyxdChQ/njjz82WWubZ3XfgpQR80xZfyjIek95xbwPRXIqPj6eGTNmEB0dTd++fUMdjp/XX3+dI0eOcMsttygpLAVebGwsBw4coGbNmqEOpdBSG4qIiIiIiBRdNtny1m0n+exgGwCOU5q9fyvfkxm5MsZwQRMsQ26M2ViuXLlm7dq1S3f/X375BSganxbm9yefCxcuZNOmTcyfP5+9e/fy/PPPU61atXw5dnoOHTrE1KlT2bFjB6+99ho1atRgxIgRReI9lqLp0KFDPP/88yxZsoSkpCSuu+66lN6FOm8zJ1Abqu2kIMiP380lSpSgXLlyXHzxxXl2DBGB1atXA5DR/xciUrDpWhYp3MZ3Xc1b27qlLN/e8FPGri5YnRTzUk7+ryhIiWFPj+AKQdZ7yuPyPhTJro8++og333yTatWqMXLkSEaMGBHqkAA4ePAgI0eOJCoqiubNm/PSSy8pQSQF2sGDBxk3bhz16tVj3Lhx3HbbbRw9qnk3syJQG4qIiIiIiEjR8fYdXzDys3Ypy1dXW0G/l8qGLqBCpiAlhn9zf54dZH0D9+fv+RCLZNPMmTOZOXNmqMNIo27duuT2eNoiealu3bokJiaGOoxCTW0oIiIiIiJSdC1//ntufuWilOX2FTdxx/RkwsIjQhhV4VKQBtxY5f7sbIzxi8sYUw64DDgGfJXfgYmIiIiIiIiIiEjB8MPsP7jmwTNJxEkCnxf1Ox9/X5+IskoKZ0W+J4aNMRHGmIbGmPq+5dbav4ClQF3gzlS7jQHKAG9ba/VdahERERERERERkWLo76930e26csRTHoCaYbtYtLoMFesEG51WgsmVoSSMMb2B3u5idffnJcaYme7z/dbaB9znNYFfgO04SWBfw4AvgMnGmI7udi2B9jhDSDyWG/GKiIiIiIiIiIhIIXPoEDd33M7O5FYAlOcQiz84TK1W54Q4sMIpt8YYbgoMSlV2pvsAJwn8ABmw1v5ljGkBjAW6AN2AXcAkYIy19mAuxSsiIiIiIiIiIiKFxcmT7Ol+MyuOzgEgjCQ+efZPzu/bPMSBFV65khi21o4GRmdy222ASWf9P8BNuRGXiIiIiIiIiIiIFHLJyTB4MIs/L5dS1KbhPjo8qKRwThSkyedERERERERERERE/D34ILz/PgvokVLU/ebq6ewgmaHEsIiIiIiIiIiIiBRML7wAL7xAAhEspXNKcY8e6ewjmaLEsIiIiIiIiIiIiBQ8778P998PwDraEE95AOrVg4YNQxlY0aDEsIiIiIiIiIiIiBQsq1bBoEEpiwtPH5ryvEcPMEFnMJPMUmJYREREJBN27NhB9erVad68OfHx8aEOR0RERESk6PrpJ+jdGxISnOVGjVhQqm/K6u7dQxNWUaPEsGRb3bp1qVu3bqjDyDPGGNq1axfqMCSP6X0WKZjatWuHKUBdAE6dOkW/fv0oV64cixcvply5cmm2yer9ZPXq1RhjGD16dKa2Hzx4MMYYtm3bluljiIiIiIgUOn//DV26wOHDzvLpp/P7y8v5468SAJQpA23bhjC+IkSJYSkUtm3bhjGGwYMHhzqUQmfmzJkYY5g5c2aoQxERKbRGjBhBTEwMS5cupWrVqqEOR0RERESkaDp4ELp2hZ07neXy5WHxYhZ+d3rKJldcASVLhii+IiY81AGIiITSL7/8QunSpUMdhoik8tZbb3Hs2LFQhwHAvn37qFKlCkuXLqVevXohi2PcuHE88sgj1KxZM2QxiIiIiIjkmRMnoFcv2LLFWY6IgLlz4YILWHifd7MePUISXZGkxLCIFGsNNY2pSIFUu3btUIeQokqVKowaNSrUYVCjRg1q1KgR6jBERERERHJfUhLccAOsW+cte+staN+ew4dhzRpvcbdu+R9eUaWhJCRd1lqmTJlC48aNKVmyJDVr1uSuu+7i0KFDabadNm0axhjGjBkTsK7du3cTERHB+eefn1IWHx/Pf//7X8477zzKly9PuXLlqF+/Ptdddx0bN24EYPTo0Sk9tN58802MMSkPz/AIvuM0fvPNN3Tv3p1KlSphjOGvv/6iVq1alC9fniNHjgSM7e6778YYw+zZs9Os27lzJwMHDqRq1aqUKlWK5s2b8+6776bZLqMhGwKNPblz507Gjh3LZZddRvXq1YmMjOT000+nf//+bPF8QubDd0iNbdu2cf3111O5cmVKlixJixYtWLBggd/27dq146abbgLgpptu8ms7zxiVWY0hI7GxsYwcOZJGjRpRqlQpKlSoQMeOHVm6dGm6bbZs2TLatGlD2bJlqVKlCjfddBNxcXEAfPfdd/To0YPo6GjKli1Lz549A46x6RmT9OTJkzz++OPUq1ePqKgo6tevz5gxY0jwDFrvI9D7Mnr0aIwxrF69mnfffZeWLVtStmxZ6taty6+//ooxhvbt2wdtg/PPP5+IiAh27drlV7506VKuuuoqqlatSlRUFLVq1aJXr14sX77cL55gj/Lly/P000+neb2JiYk8/fTTNGjQIKXehx9+OODrnTt3LjfccANnn302ZcqUoUyZMjRv3pzJkyeTnJwc9DX5+u233zDGMGDAAL/ymJiYlFjX+f4yBx5++GGMMaxcuZKkpKRsX5PvvPMOzZo1o1SpUlStWpWBAweyc+fOdMejXbJkCd26daNy5cop58ODDz6Ycn758oydfvToUR588EFq165NVFQUZ511Fs888wzW2oDH+Prrr+nbt2/KNVSrVi1uu+02dnq+/uTDE2tCQgJjx47lnHPOISoqym+onI0bN9KnT5+Uc6VOnToMGzYszTk1cuRIjDEsW7bMr3zUqFEYY6hfv36a41evXt0v6ZqQkMCUKVPo1q0bderUISoqikqVKnHFFVewePHigK83P9spszwxHTp0iLvuuouaNWtSsmRJzj33XCZPnpwmJt/76e+//851111H1apVCQsLY/Xq1QAkJyfzyiuvcNFFF1G2bFnKlCnDRRddxNSpU9O9XjL7eyOYEydO0LdvX4wx3HnnnSnH0hjDIiIiIlIkWQvDh8OcOd6yCRPg+usBWLYMEhOd4gsvhNNPT1uFZI96DEu6hg8fzuTJk6lRowZDhw4lIiKCefPm8fXXX5OQkEBkZGTKtgMGDOChhx7i9ddf5/HHH6dEiRJ+dc2YMYPExERuu+02wEk6d+nShS+++IJLLrmEW265hfDwcP79919WrVpFmzZtaN68Oe3atSMuLo5JkybRpEkTevfunVJn06ZN/Y7x5ZdfMm7cOFq3bs3NN9/M/v37KVWqFLfeeiujRo3ivffe49Zbb/Xb5/jx48yaNYvq1avTq1cvv3UHDx7k0ksvpWLFiimJyg8//JABAwawY8cOHnzwwRy179q1axk/fjzt27enT58+lC1blj/++IPZs2fz6aef8vnnn9OkSZM0+23fvp2LL76YM888k4EDBxIbG8sHH3yQkmT0JC0HDx5MxYoVmTdvHr169fJrr4oVK+YohkC2b99Ou3bt2LZtG23atKFLly4cPXqUBQsW0KVLF6ZNm5am/QE+/fRTFixYQI8ePbj99tv54osvmDlzJtu2bWPcuHF07NiRNm3aMGTIEH766Sfmz5/P1q1b+fHHHwkLS/v51rXXXsuGDRvo27dvyjk7evRovv32Wz799NNMJ5smTJjAsmXLuOqqq2jfvj2HDh2iYcOGtG/fnlWrVvH7779z9tln++3zxRdfsHnzZvr06ePXs2/UqFGMHTuWsmXL0rt3b2rVqsXOnTv54osvmDVrFldccUXKdoG8/fbbbN26NeCwF/3792fdunV07dqV8uXLs2jRIp599ln27t3LG2+84bftI488QlhYGC1btqRmzZocOnSIlStXcu+997JhwwbefvvtDNvlnHPOoWbNmqxcudKvfMWKFX7P27Rp47dcsmRJLr30UkqUKJGta/LZZ5/l4YcfJjo6mkGDBlGhQgWWLVvGZZddRoUKFQLGOmbMGEaPHk2lSpXo0aMHVatW5ccff+T5559n0aJFfPnll5QvX95vn1OnTnHllVeyc+dOunbtSnh4OHPnzuWRRx7hxIkTad6jGTNmMHToUKKioujZsye1atXijz/+YPr06cyfP5+vvvoqYO/XPn36sGHDBrp27Urv3r1Txq1dsGABffr0wVpL3759qVOnDhs3bmTq1KnMmzeP9evXp3xY1rFjR8aPH8+KFSvo1KlTmvdi69atbNu2LWWi0M2bN7Nnzx6/JHRsbCz33nsvl156KZ06daJKlSrs2rWL+fPn061bN1577TVuueWWNPHnVztlRUJCAldccQVxcXFcf/31JCQkMGfOHO69915+++03/ve//6XZ56+//qJly5acffbZDBgwgOPHj6ecEwMHDuTdd9+lVq1a3HLLLRhj+OSTTxg2bBjr16/nnXfeSVNfTn9vHDx4kJ49e/L555+nDB0hIiIiIlKkPfccTJniXR4xAu7zjh3h2wdOw0jkMmttsXkAG5s1a2YzsmXLFrtly5YMtysMDh8+bA8fPpytfT///HML2Pr169sDBw6klB8/fty2atXKArZOnTp++9x5550WsPPnz/crT05OtvXq1bOlS5e2cXFx1lprf/zxRwvY3r17pzl2UlKSjY2NTVmOiYmxgB00aFDAWFetWmUBC9hXXnklzfqdO3fa8PBw27x58zTr3njjDQvYRx991K/cU1+/fv1sUlJSSvnWrVttdHS0jYiIsH/99Veaet54442AMQK2bdu2fmV79uwJ+P58//33tkyZMrZLly5+5Z52AOzo0aP91n322WcWsF27dg34+oLFldUY0tO2bVtrjLHvvfeeX/nBgwdtkyZNbMmSJe3u3bvTxFaiRAm7evXqlPKkpCR7xRVXWMBGR0fbWbNm+dV38803W8DOnTs3zfEB26BBA7/zx/ecfeutt/z2CfS+jBo1ygK2dOnSdtOmTWle50cffWQBe//996dZN2jQIAvYpUuXppQtWbLEArZevXr233//TbPPP//8k6bM14wZMyxgL774Yrt37940r7dZs2Z+1+iRI0ds/fr1bVhYmN21a5dfXX/++Wea+pOSkuyNN95oAfvVV1+lG4vHwIEDLWA3b96cUnb99dfbypUr26ZNm9rWrVunlMfGxtqwsDDboUOHlLKsXpN//fWXDQ8Pt5UrV7Z///13SnlycrK9/vrrU64LXytXrrSAveSSS+zBgwcDHmP48OF+5XXq1Em5jo4dO5ZSvmfPHluhQgVboUIFm5CQkFL+22+/2YiICFu/fv007+3y5cttWFhYmnuc5307//zz7b59+/zWxcfH20qVKtmwsDC7du1av3Xjx4+3gO3UqVNK2bFjx2xUVJRt0aKFXx0RERG2U6dOFrDTp09PWTdx4sQ018GJEycCnoNxcXG2cePGNjo62q8t8rudMssT02WXXWZPnDiRUn7gwAF75plnWsCuWbMmpdz3fjpy5Mg09b377rsWsBdeeKGNj49PKT9y5Iht3ry5Bew777zjt09mf294fjd7fneNGjXKWmvttm3bbKNGjWxERESa+5613vtLTExMhu1RlP6WESnIVq1aZVetWhXqMEQkh3Qti4TQ229b6/QZdh7XXmutz9/SSUnWVq3qXZ3Rv6zF8Xpu1qyZBTba7ORKs7NTYX3kVmLY93wt6I+cJIZvueUWC9gZM2akWef5ZzZ1Ynjz5s0WsD169PAr9yQtb7rpppQyT2L4P//5T4axZDYx3LRp06B19O3b1wL222+/9Stv1aqVDQsLS/OPtidhuXXr1jR1eRKHvsnZ7CSG03PVVVfZqKgov+SKpx3q1KljExMT0+xTu3Zte9ppp/mVZRRXVmMI5vvvv7eA7du3b8D1c+fOtYD93//+lya2G264Ic32b775pgVsmzZt0qxbvXp1wOS4J5GUOvlrrfccadeunV95eonh1ElDj1OnTtkaNWrY0047zS8BdfDgQVuqVClbv359m5ycnFLeo0cPC9iPP/44YH3pWb58uY2IiLBnnnmm3bp1q9/17Hm9y5YtS7PfE088EfBDmmA2btxoATtmzJhMbT9z5kwL2EmTJqWUVa1a1V577bX2gQcesBEREfbIkSPWWmvnzJljAfvUU0/51ZGVa/K///1v0Pi2bdtmS5QokSaJ2Lt37zTJa19Nmza1VapU8SvzJBf/+OOPNNt7kuc//fRTStnw4cMtYBcsWBDwGL1797YlSpQI+L6l/mDDWmtnzZoV9L546tQpW7duXQvY7du3p5S3a9fOhoWFpXwYsnDhQgvYhQsX2ipVqvjVddVVV1nA7tixI2C8qU2YMCFNQtXa/G2nzPLElDqhbq33XjN48OCUMs/9tFq1an7XsYfnw6klS5akWbd8+XIL2Pbt2/uVZ/b3RqDE8HfffWdr1Khhy5cvb5cvXx7wNSoxLFLwFMd/PkWKIl3LIiGydKm14eHeJFa7dtam+tv8m2+8q6tU8csZB1Qcr+ecJIY1lIQEtWnTJgDatm2bZl3r1q3TDBUB0LhxYy6//HIWL17MP//8Q61atQB49dVXAbj99ttTtj333HNp2rQp7733Htu3b6dXr160bt2aFi1a+A1RkRUXX3xx0HXDhg1j9uzZTJs2LSWen376ia+++oquXbumfNXaV+3atQPOQN+uXTvGjBnDd999l604fS1cuJBXXnmFb7/9lv3795PoGTjHtX///jSTDTVt2jRg+9eqVYsvv/wyX2JIzXPcQ4cOMXr06DTr9+3bB8Avv/ySZl2LFi3SlJ3uDhrUvHnzNOtq1qwJwL///hswlvTO2ay8Z8HOp/DwcG699VbGjh3LnDlz6N+/P+AM93D8+HGGDh3qN1zFV199hTGGLl26ZPrYAFu2bEkZ3mPRokVUrlw54HaB2s9z7R08eNCv/MCBAzz33HMsWrSIrVu3cvToUb/1O3bsyFRsHTp0AJwhC+655x42b97M3r176dixI7Vq1eL5559n7dq1dO3aNWXICc8+Hlm5Jj3vW+vWrdPEUqdOHWrVqpVm3NUvv/ySiIgIPvroIz766KM0+yUkJLBv3z4OHDjAaaedllJeoUIFzjrrrDTbB2pTz3m/Zs0aNmzYkGafvXv3kpSUxO+//57mXA50fnnuu6nbCpzz7vLLL2fbtm189913KcMudOjQgdWrV7N69WquvvpqVq5cSUREBG3btqV9+/Yp7Z+UlMTatWs555xzUq4vj59//pnnnnuOtWvXsmvXLk6cOOG3PtB5kV/tlBXh4eFceumlaco944gHuv6bNGlCVFRUmvJNmzYRFhaWZgxycO4xwe4n2fm9sX79el544QXKlSvH2rVrMz18j4iIiIhIofXdd3DNNd7Bg887Dz75BFL9be47jES3bhBgNEnJASWGJSjPBHPVqlVLsy48PDxokmrYsGGsXbuW6dOnM2bMGHbv3s2nn35K06ZN/RIhJUqUYOXKlYwdO5bZs2fz8MMPA1CuXDkGDRrEuHHjKFu2bJZirl69etB17du3p1GjRrz33ntMmDCBcuXKpSSjPOMepxbotfseJ9AkfFkxadIkhg8fTnR0NJ06daJ27dqULl0aYwxz587lhx9+4OTJk2n284wPnFp4eHimJxDLaQypHThwAIBly5almQjLV6DJxgKNDxseHp7hulOnTgU8Rnrn7N69e4PGllp659PQoUN56qmnmDZtWkpi+NVXXyUyMjJlwj+PuLg4oqOjKVWqVKaPvXv3brp168bx48dZtmwZ55xzDvHx8QG3DXQ+eNooKSnJL46LLrqImJgYLr74Ym688UYqVapEeHh4yjjemXmvwUn+NWjQgDVr1pCUlJQypm3Hjh2pXr06ERERrFixgq5du7JixQrKly/PRRdd5FdHVq7J9O5HnvLUieEDBw6QmJgYdEJMjyNHjvglhtO7vsC/TT3n/XPPPZfhMVILdH55XmewD2I85b4T53Xs2JEnnniCFStWcPXVV7NixQpatmxJmTJl6NixIx9++CGbN2/m6NGjHDp0KM2kgV999RUdOnQgMTGRjh070rNnT8qXL09YWBjff/898+bNy/J9CHKvnbKicuXKAT80S++eHew6P3ToEJUqVQr4QWV695Ps/N747rvviI+P59JLL6Vhw4YB9xcRERERKTK2bXOyvJ6//884AxYvhgD/Yyxc6H2u8YVznxLD2eCMSlE4BMkjZYonIbdnzx7OPPNMv3WJiYns37+fM844I81+11xzDdWqVeP111/niSeeSDPpnK/o6GhefPFFXnzxRf7880/WrFnDtGnTmDJlCnFxcZmaCMtXRpOK3X777dx777288847DBo0iFmzZlGzZk16BLm77NmzJ2D57t27Af+kpWcStNS9bcE/ieORmJjI6NGjqV69Ops2bUqTCMpOz9+sys0YPG0xadIk7rnnnlyNM6v27NmTZhIrzzmbeqKx9KR3PtWsWZOePXvyySef8OuvvxIbG8vmzZu57rrrqFKlit+2FStW5MCBAxw/fjxTyeFjx45x1VVXsX37dmbNmsXll1+e6ZjTM336dGJiYhg1alSaXt1ffvklkyZNylJ9HTp0YNq0aWzYsIEVK1ZQp04d6tevDzi9YZcvX87OnTv59ddf6dGjR8CEXWavSc/7tmfPHho3bpymnkDXaoUKFUhOTiY2NjZLrysrPOf9oUOHsnRuQeDzy1Of5x6T2q5du/y2A6ety5Yty/Llyzlw4AA//PADTzzxBODtebx8+XKOHTvmV+bx5JNPcvz4cVatWpWmd+y4ceOYN29ell5XIDlpp6zYv38/SUlJac61QPdsj2DXeYUKFYiNjeXUqVNERET4rUvvfpKV3xsed911F3v37uWVV16hZ8+ezJ07N0sfJImIiIiIFBoHDkCXLuD5n6diRfjsMyc5nMquXbBxo/M8PBx85tuWXKIO2BJUs2bNAOerv6mtX7/erzeYr4iICG655RZ27NjB/PnzmT59OmXLlk3TSy21s846iyFDhrBmzRrKli3rl4zw/JMf7JiZNWjQIEqXLs2rr77KBx98QFxcHEOGDAmYsAL4+++/0/RCBFi9ejUAF154YUpZdHQ0AP/880+a7b/99ts0Zfv37ycuLo5LL700TUL2yJEjKV8pz6n02i43Y2jVqhUA69aty0G0uSO9c9b3PcupYcOGAfgNhRDoA5BWrVphreWzzz7LsM7k5GT69+/Pt99+y9ixYzO8brLizz//BKBPnz5p1gVqs4x07NgRgCVLlrB27dqUZc+6H3/8kQ8++MBv29Qye0163rf169enqWP79u0Br7tWrVpx8OBBfv755yy/tszK7fPe8zo99xhfiYmJKcfx3J/BO8TEb7/9xttvv421NqW9zzrrLGrXrs2KFStYuXIlYWFhtG/f3q/eP//8k0qVKgUcMiE750Ug+XV/SExM5IsvvkhTHuienZELL7yQ5ORk1q5dm2bd2rVrSUpK8nsfPLLye8PDGMPUqVMZPnw4S5cupXv37mmGeRERERERKfSOHYOrroLffnOWIyNh3jwI0PkHYNEi7/PLL4cAfSwkh5QYlqAGDx4MwFNPPeXX4+7EiROMHDky3X2HDh1KiRIluOuuu4iJiaF///6UK1fOb5uYmBi2bt2aZt+DBw9y8uRJv95S0dHRGGP4+++/c/CKnJ5a/fv357vvvuPxxx+nRIkS3HrrrUG3T0pK4uGHH/YbniEmJobJkycTHh7ODTfckFLeokULwsLCePfdd1N65gHExsby0EMPpam7atWqlC5dmo0bN/p9ffrUqVPce++97N+/P0ev1cPzFflAbZebMbRo0YI2bdrw8ccfM2PGjIDb/PTTT1kayiG7/vvf//qNb+p7zqYe5iEnOnbsyNlnn82bb77Jhx9+yDnnnJMm6QZw9913A3D//fcHHKvVt+y+++5j3rx5DBo0iP/7v//LtViBlDF7Uycdv/vuO8aNG5fl+tq3b48xhpdffplDhw75JX87dOiAtZbx48enLAeS2Wuyf//+hIeH89JLL/klga21jBw5MuAHHyNGjADg1ltvZefOnWnWHz16lK+++iprLzqVu+66i4iICEaMGMHvv/+eZn1CQkKWkqG9e/emUqVKvPfee2limzhxIjExMVxxxRVpesR72nfcuHGUKVMmJRHrWbdmzRo+//xzmjRpQqVKlfz2rVu3LrGxsfz4449+5a+//jpLlizJdOzpye12Ss/IkSP9hr6IjY3lySefBLJ2/d98880p9fne048dO8YjjzwCwJAhQ9Lsl5XfG6m9+OKLjBw5klWrVnHllVdy+PDhTMcrIiIiIlKgJSZC//7g+WayMfDOO07GNwjf8YW7d8/j+IopDSUhQV122WXcfffdvPTSS5x33nn07duXiIgI5s2bR3R0dLqTkdWuXZvu3bvz6aefAoF7Uf7www9cc801XHTRRTRq1IjTTz+dffv2MW/ePE6dOpUy5jBA2bJladmyJevWrWPAgAGcffbZlChRgp49e3LBBRdk6XUNGzaM6dOns2PHDq666qqAw2F4XHDBBXz99dc0b96czp07ExcXx4cffkhcXBzPPvtsytfmwRn7c8CAAbz99ts0bdqU7t27c/jwYRYtWsTll1+eZsKhsLAw7rnnHsaPH8/5559Pr169SEhIYNWqVcTGxtK+fXtWrVqVpdcWyCWXXELp0qWZOHEiBw4cSBnn8u6776ZChQq5GsO7775Lhw4dGDJkCJMnT6Zly5ZUrFiRf//9lx9//JHNmzfz5ZdfUrVq1Ry/rvQ0atSIxo0b+52zf/31F927d2fgwIG5dhxjDLfffjv33Xcf4HwgEkjnzp15/PHHefLJJ2nUqBG9e/emVq1a7Nmzh/Xr19OqVStmzpzJN998w6RJkyhZsiQ1a9ZMM9zDyZMnadOmDd26dctWvDfeeCPPPfccw4cPZ9WqVTRo0IA//viDBQsWcM0116T07s2sypUrc8EFF/DDDz8A/slfz3m3d+9eqlSpwvnnnx+0nsxck/Xr12fs2LE8+uijNGnShOuuu44KFSqwbNkyYmNjadKkSZrEZseOHRk/fjwjR46kQYMGdOvWjXr16nHkyBG2b9/OmjVraN26daZ6cgfTsGFDZsyYwc0330zjxo3p0qULZ599NqdOneLvv/9m3bp1VKlShV9//TVT9ZUtW5YZM2bQr18/2rZtS79+/ahduzYbN25k6dKlVK9enWnTpqXZz5OU37t3L126dPEb+qBjx47MnDnTbztfw4cPZ8mSJbRu3Zprr72WChUq8O2337J+/Xr69u3L7Nmzs9Ey/nK7nYKpUaMGJ0+e5LzzzqNnz56cOnWK2bNns2vXLoYNG5alYVn69+/PvHnz+PDDD2ncuDG9e/dOGXs9JiaG6667LmCP/sz83gg2XjjA008/TcmSJRk1ahSdOnXis88+S/lGioiIiIhIoWQtDBvm9A72mDQJ+vYNusuhQ7B0qXdZ4wvnEWttsXkAG5s1a2YzsmXLFrtly5YMtysMDh8+bA8fPpzt/ZOTk+1LL71kGzZsaCMjI22NGjXssGHDbFxcnK1Tp46tU6dO0H3nzp1rAduiRYuA6//55x87cuRIe+mll9pq1arZyMhIW7NmTdulSxe7aNGiNNv/8ccftkePHrZSpUrWGGMB+8Ybb1hrrV21apUF7KhRozL1upo2bWoBu2DBgqDbALZt27Z2x44ddsCAAbZKlSo2KirKXnjhhfadd94JuM+JEyfsAw88YGvWrGkjIiJs/fr17dNPP21PnTqVUp+vU6dO2QkTJthGjRrZkiVL2mrVqtkbbrjBbtu2zQ4aNMgCNiYmJmX7mJgYC9hBgwYFPH7btm2tc1n7W7x4sW3VqpUtU6aMBfzqzWoMGTl8+LB96qmnbLNmzWyZMmVsyZIlbd26dW23bt3stGnT7JEjR1K2feONN/zeR1/pvafB2sHz+k+cOGEfe+wxW7duXRsZGWnr1atnR48ebU+cOJGmrkDvy6hRoyxgV61aleHrjY2NtWFhYbZkyZJ2//796W67cOFCe+WVV9ro6GgbGRlpzzjjDNu7d2+7YsUKv9ec3uORRx5J83oDCda2P//8s73qqqtslSpVbOnSpW2zZs3sa6+9luG5Fcx9991nAXvuueemWde5c2cL2GuvvTbDejJzTVpr7VtvvWWbNm1qo6KibOXKle2AAQPsjh07bOPGjW2FChUC7rNu3Trbr18/W6NGDRsREWErV65smzRpYkeMGGE3bNjgt21697X0zosff/zRDho0yNauXdtGRkba6Oho27hxYzt06NCU99cjvffN45tvvrG9e/e2lStXthEREbZWrVr29ttvtzt27Ai4fXJysq1cubIF7LPPPuu3bseOHSnnT6B7q7XWzp8/37Zs2dKWLVvWVqhQwXbq1MmuWbMm6HlUUNopUExxcXF22LBh9vTTT7eRkZG2YcOGdtKkSTY5Odlv+8yc80lJSfZ///ufbd68uS1VqpQtVaqUbdasmZ0yZYpNSkpKs31mf294fjend5979tlnLWAvvPBCu2/fPmutzdI9uSj9LSNSkK1atSpTfy+ISMGma1kkjz3xhLVOeth5PPhghrs8/7x38/POy/yhiuP13KxZMwtstNnIlRpbmGZSyyFjzMZmzZo12+gZuTqIX375BXB6HRZ2nl5JqYdxyA+jR49mzJgxTJ8+PeDXbUMlPj6e008/nUqVKhETE5MyaZwUfu3atWPNmjXk531t9erVtG/fnhtuuCHLkyVmVSiv57yU02vy8OHDVKtWjaZNm+bLpI2SP1q1asV3333nNyxEejxDpQQa37egyY9ruSj9LSNSkHmGZwo0TruIFB66lkXy0Msvw513epcHDoSZMyGd//sSE6F+ffCMiPnaa3DLLZk7XHG8nps3b86mTZs2WWubZ3VfZcQkT8THx/PKK69QqVIl/vOf/4Q6HD9Tp07lyJEjDBs2TElhybFnn30WcMZQlezJ7DW5b98+Tp065VeWmJjI/fffz4kTJ7j66qvzOlTJJ0lJSWzdujXdoX5ERERERKSAmz0bfP9X7toVXn893aQwwCefeJPClStDLs7JLqlojGHJVQsXLmTTpk3Mnz+fPXv28Pzzz1O6dOlQh8WhQ4eYOnUqO3bs4LXXXqNGjRoMGzYs1GFJIfXTTz+xYMECNm7cyOLFi+nRowctW7YMdViFSnauyTlz5vDEE09wxRVXUKtWLWJjY1m7di2///47TZs2TZnkTwq30aNHs379evbt25erk0WKiIiIiEg+Wr3ayeh6vtF78cXw0UfgMx9KMC++6H1+xx1QqlTehChKDEsu++ijj3jzzTepVq0aI0eOZMSIEaEOCYCDBw8ycuRIoqKiaN68OS+99FKR+zq+5J+NGzfy6KOPUr58efr168fLL78c6pAKnexcky1btqR169asXbuWAwcOAFCvXj0ee+wxHn74YUrpr4UiYezYsdSuXZsHHniAMWPGhDocERERERHJqu+/h169ICHBWT7nHFi4EMqUyXDXr74CzwiBkZHOnHWSd5QYllw1c+ZMZs6cGeow0qhbt26+jjsroeEZSyivDR48mMGDB+fLsYqq7FyTF154IR9//HEeRSQFRXJycrb2KwxjC4uIiIiIFHkxMc6QEYcPO8unnw5LljhjQmSCb2/h/v2hevU8iFFSaIBVERERERERERERyZm9e6FzZ9i921muUAE++wzq1MnU7n//DXPmeJeHD8/9EMWfEsMiIiIiIiIiIiKSffHx0L07/PmnsxwVBZ9+Cuefn+kqXnoJkpKc5x06QJMmeRCn+FFiWERERKQI0dBJIiIiIpKvEhKgTx/49ltnOSwM3n8fLr8801UcOQKvveZdLiBTVhV5SgwHYIwBsj/OoYiIiEioeBLDnr9nRERERETyTHIy3HQTLFvmLZs6FXr3zlI1b7wBhw45z88+G7p1y70QJTglhgOIiooC4OjRoyGORERERCRrPH+/eP6eERERERHJE9bCAw/Au+96y8aMgaFDs1RNUhJMnOhdvvdep9Ox5D01cwDlypUDYPfu3cTHx5OcnKyvZYqIiEiBZa0lOTmZ+Ph4druTfXj+nhERERERyRPPPw8vvuhdvuMO+L//y3I18+fD1q3O8+hoGDQol+KTDIWHOoCCqFKlShw9epRjx47x77//hjqcHElyR+0uUaJEiCMRkZzS9SxSNOTHtVy6dGkqVaqUZ/WLiIiISDH35pvw0EPe5T594KWXOHLUcOedsGFD5qty+zUAcNttUKZM7oUp6VNiOICwsDBq1apFbGws8fHxnDx5stD2GD527BigXkMiRYGuZ5GiIa+uZWMMUVFRlCtXjkqVKhGm79+JiIiISF5YtAiGDPEut20Ls2aRaEtw3XXO6uwID4e77sqdECVzlBgOIiwsjMqVK1O5cuVQh5Ijq1evBuDiiy8ObSAikmO6nkWKBl3LIiIiIlJoffUV9OvnDAwMcMEFMG8eNqokdwzNflIY4P77oWbN3AlTMkeJYREREREREREREUnfL79A9+7gfgOOunVh8WKoUIEn/wvTp3s3feihrI0VXL48nHFGrkYrmaDEsIiIiIiIiIiIiAS3YwdceSXExjrLlSvDkiVw+um88QY88YR30xtvhPHjwZjQhCqZp8HnREREREREREREJLCDB6FLF/jnH2e5TBlnzIizz2bJErj1Vu+mnTrBa68pKVxYKDEsIiIiIiIiIiIiaR0/Dj17wubNznJ4OMyZAxddxKZN0Levd7jhpk1h9myIjAxZtJJFSgyLiIiIiIiIiIiIv8REuP56WL/eWzZzJlx5Jdu2OcMNHzniFNeuDQsXOmMFS+GhxLCIiIiIiIiIiIh4WeuMEfHpp96y55+HAQOIjXVGlti92ymuWNGZg+7000MSqeSAEsMiIiIiIiIiIiLisBYefNDpHezx0ENw//0pI0v89ptTHBnp5I7PPTckkUoOKTEsIiIiIiIiIiIijmefhQkTvMtDhsD48SQlwQ03wOefe1fNmgVt2uR/iJI7lBgWEREREREREREReP11eOQR73Lv3vDKK1gM990HH3/sXfXCC9CvX75HKLlIiWEREREREREREZHi7pNPYOhQ73K7dvDeexAezgsvwOTJ3lUjRjgPKdyUGBYRERERERERESnOVq2C66+H5GRnuVkzmDcPSpbk/ffhgQe8m/br58xDJ4WfEsMiIiIiIiIiIiLF1aZN0KsXJCQ4yw0awOLFUL48X38NgwZ5N23TBt56C8KUUSwS9DaKiIiIiIiIiIgUR7//Dl26QHy8s3z66bB0KVStCsCjj3rzxY0awdy5ULJkaEKV3KfEsIiIiIiIiIiISHGzYwd07gz79jnL0dGwZAnUrQvA99/DypXOqhIl4NNPoVKlkEQqeUSJYRERERERERERkeIkNtZJCm/f7iyXLg0LF8J556VsMnGid/O+feGss/I3RMl7SgyLiIiIiIiIiIgUF0ePQvfusGWLsxweDnPmwCWXpGyyeze89553lxEj8jlGyRdKDIuIiIiIiIiIiBQHCQlO99+vvnKWjXFmk+vSxW+zl1/2ji18ySXQsmU+xyn5QolhERERERERERGRoi45GQYPhs8+85ZNngz/+Y/fZsePw9Sp3mX1Fi66lBgWEREREREREREpyqyFe+/1Hx/iiSfgrrvSbDprFuzf7zyvUweuvjqfYpR8p8SwiIiIiIiIiIhIUfbf/8KUKd7lYcNg9Og0m1nrP+ncPfc4QxBL0aTEsIiIiIiIiIiISFH18sswapR3+brr4KWXnPGFU1m61DsnXdmyMGRIPsUoIaHEsIiIiIiIiIiISFH0/vv+w0V07uxMNhcWOCX44ove50OGQIUKeRyfhJQSwyIiIiIiIiIiIkXN0qVw443O+BAALVvCnDkQGRlw8y1bYMkS57kxzjASUrQpMSwiIiIiIiIiIlKUfP21M2vcqVPOcqNGsHChMz5EEL5jC/fuDWeemacRSgGgxLCIiIiIiIiIiEhRsXkzdO0Kx445y7VrO72HTzst6C779jkjTHiMGJHHMUqBoMSwiIiIiIiIiIhIUbB1qzOO8MGDznLlyk5S+Iwz0t1t2jQ4edJ53qIFtG6dx3FKgaDEsIiIiIiIiIiISGG3cydccQXs2uUslysHn30G55yT4a7vved9Pny4M8awFH1KDIuIiIiIiIiIiBRmBw44PYVjYpzlkiVhwQJo3jzDXWNinInnPLtdfXUexikFihLDIiIiIiIiIiIihVV8PHTrBj//7CyHh8Ps2XD55ZnafeFC7/P27aF06TyIUQokJYZFREREREREREQKoxMnoHdv+OYbZ9kYZxa57t0zXYVvYrhHj9wNTwo2JYZFREREREREREQKm8RE+M9/YOVKb9nLLztlmXT0KKxa5V3OQj5ZigAlhkVERERERERERAqT5GQYMgTmzvWWPf003H57lqpZsQJOnnSen3ce1KmTeyFKwafEsIiIiIiIiIiISGFhLQwf7gwZ4fHgg/DII1muasEC73P1Fi5+lBgWEREREREREREpLEaPhpde8i7feis884wzvnAWWKvxhYs7JYZFREREREREREQKg4kTYexY7/K118LUqVlOCgN8/z3s3Ok8j46GVq1yJUIpRJQYFhERERERERERKejeeANGjPAud+kCb78NJUpkqzrf3sJdukB4eA7jk0JHiWEREREREREREZGC7OOP4ZZbvMuXXQZz5kBkZLar9B1fWMNIFE9KDIuIiIiIiIiIiBRUy5fDf/4DycnOctOmTla3dOlsV7lvH3zzjfM8LMzpMSzFjxLDIiIiIiIiIiIiBdFXX0Hv3pCQ4Cw3aACffQYVK+ao2sWLncnnAC69FCpVylF1UkgpMSwiIiIiIiIiIlLQ/PQTdO0KR486y2ec4fQerlYtx1X7DiPRvXuOq5NCSolhERERERERERGRguTPP6FzZ4iLc5YrV4Zly6B27RxXfeoULFniXdb4wsWXEsMiIiIiIiIiIiIFxY4d0KkT7N7tLJcv72RyGzbMlerXr4fDh53ntWtD48a5Uq0UQkoMi4iIiIiIiIiIFAQHDjg9hbdtc5ZLloT586FZs1w7xMKF3uc9eoAxuVa1FDJKDIuIiIiIiIiIiITa4cPOmMJbtjjL4eEwZw5cfnmuHkbjC4uHEsMiIiIiIiIiIiKhdOwYXHUVbNjgLBsDb78N3brl6mH+/BN++815XqoUtG+fq9VLIaPEsIiIiIiIiIiISKicPAl9+sDatd6yl1+G66/P9UP5DiPRsaOTHJbiS4lhERERERERERGRUEhMhP794bPPvGXPPQe3354nh/NNDGsYCVFiWEREREREREREJL8lJ8PNN8PHH3vLnngCHnggTw4XHw9r1niXlRgWJYZFRERERERERETyk7Vw113OOMIeI0bA6NF5dsjlyyEhwXl+wQVQq1aeHUoKCSWGRURERERERERE8ou18MgjMHWqt+yWW2DCBGfSuTziO4xEjx55dhgpRJQYFhERERERERERyS9PPQXPPutd/s9/4JVX8jQpnJys8YUlLSWGRURERERERERE8sPEifB//+dd7tkT3nwTSpTI08N+9x3s3u08P+00aNkyTw8nhYQSwyIiIiIiIiIiInnt9dedcYQ9OnaEDz6AiIg8P/SCBd7nXbvmeR5aCgklhkVERERERERERPLSBx/Arbd6ly+9FObNg5Il8+XwGl9YAlFiWEREREREREREJK/Mnw833OBMOgdw4YVOprZMmXw5/O7dsGGD87xECbjyynw5rBQCSgyLiIiIiIiIiIjkhRUroF8/SEx0lhs1giVLoGLFfAth8WLv88suy9dDSwGnxLCIiIiIiIiIiEhu+/JL6NULTp50ls88E5YvhypV8jUM3/GFNYyE+FJiWEREREREREREJDd9950zy9vRo85yzZpO7+HTT8/XMBISYNky73L37vl6eCnglBgWERERERERERHJLb/8Ap07w6FDznKVKk5P4bp18z2UdesgPt55Xq+eM5KFiIcSwyIiIiIiIiIiIrlh61a44grYv99ZrljR6bLbsGFIwvEdRqJ7dzAmJGFIAaXEsIiIiIiIiIiISE7t2OEkhXfudJbLlHFmfmvSJGQhLVzofa7xhSU1JYZFRERERERERERyYu9eJykcE+MslywJ8+dDq1YhC+n33+GPP5znpUtD27YhC0UKKCWGRUREREREREREsisuDq68En791VkOD4fZs6F9+5CG5dtbuFMnJ1ct4kuJYRERERERERERkeyIj4cuXeD7753lsDB4911nQN8QSz2+sEhqSgyLiIiIiIiIiIhk1bFjzsC9X3/tLXv9dejXL3QxuQ4fhrVrvcvduoUuFim4lBgWERERERERERHJihMnoFcv/+zrlCkweHDIQvK1dCkkJjrPL7wQatYMbTxSMCkxLCIiIiIiIiIiklkJCdC3Lyxf7i17/nm4887QxZSK7/jCGkZCglFiWEREREREREREJDMSE6F/f//M63//C/ffH7qYUtm4ET780Lvco0foYpGCTYlhERERERERERGRjCQlwaBBMGeOt+zRR+Hxx0MXUyoxMU4P4WPHnOVzzoGLLgptTFJwKTEsIiIiIiIiIiKSnuRkGDoU3n3XWzZiBDz5ZOhiSuXAAejaFfbscZYrVoRPPoEwZf8kCJ0aIiIiIiIiIiIiwVgLd98NM2Z4y+64AyZMAGNCF5eP48ehZ0/47TdnOSoKPv0UGjUKbVxSsCkxLCIiIiIiIiIiEoi18OCD8PLL3rKbboIpUwpMUjgpCQYMgC++cJaNgVmzoE2b0MYlBZ8SwyIiIiIiIiIiIoE88YTTM9jjP/+B114rMOMzWOuMaPHJJ96yF16Avn1DF5MUHuGhDkBERERERERERKTAefppvzGEf7viTkYlTuZAl4KRFAZnCInPP/cujxgBw4eHLBwpZJQYFhERERERERER8TVxIjz2WMqi7dqNAXsms3F5wUkKp3bttfD886GOQgqTgns2i4iIiIiIiIiI5LdXXnG63np07MjaER+zcVPBTaO1awdvvllgRriQQkI9hkVERERERERERABmzoQ77vAut2kD8+bx4oColKJ+/eDWW/M/tGBKlYKWLSEiItSRSGGjxLCIiIiIiIiIiMj778OQId7lli1hwQL+3FWGTz/1Fo8ZA40a5X94IrlNHcxFRERERERERKR4++QTuOEGSE52lps2hcWLoXx5Jk8Ga53irl2VFJaiQ4lhEREREREREREpvhYtguuug6QkZ7lxY1i2DKKjiYuDGTO8m/oOPSxS2CkxLCIiIiIiIiIixdOKFXDNNXDqlLN89tmwfDlUrgzA9Olw9Kiz6rzz4IorQhSnSB5QYlhERERERERERIqf9euhZ084edJZrlfPSRRXrw5AYiJMnuzdfPhwMCb/wxTJK0oMi4iIiIiIiIhI8fLVV86AwceOOctnnAErVzo/XXPmwD//OM+rVIEBA0IQp0geUmJYRERERERERESKjw0b4Mor4cgRZ7l6dScpXLeu32Yvvuh9fscdULJk/oUokh+UGBYRERERERERkeJh0ybo3BkOH3aWq1Rxho9o0MBvsy+/hK+/dp5HRsKwYfkcp0g+UGJYRERERERERESKvh9+cGaPi4tzlk87zekpfO65aTb17S08YABUq5Y/IYrkJyWGRURERERERESkaNu82UkKHzzoLEdHw/LlcN55aTbdts0ZX9hjxIj8CVEkvykxLCIiIiIiIiIiRdcvv0DHjrB/v7NcoQIsWwZNmwbc/KWXIDnZed6xI5x/fv6EKZLflBgWEREREREREZGi6bffoEMH2LvXWS5fHpYuhebNA24eHw/Tp3uX1VtYirJcSwwbY84wxswwxuw0xpw0xmwzxkw0xkRnsZ7Wxph57v4njDF/G2MWGWO65FasIiIiIiIiIiJSxP35p5MU3r3bWS5bFj77DC6+OOguM2Z456U75xzo2jUf4hQJkVxJDBtj6gMbgZuAb4AXga3AvcCXxpjTMlnPHcA6oKP780VgDdAWWGyMeSw34hURERERERERkSJs61Zo3x527nSWS5eGRYvgkkuC7pKUBJMmeZeHD4cwfddeirDwXKrnZaAqcI+19iVPoTHmBWAE8BRwe3oVGGMigHHACaC5tfY3n3VPA98BjxljnrfWnsyluEVEREREREREpCjZvt1JCv/7r7NcqhQsXAht2qS726efQkyM87xSJbjxxjyOUyTEcvy5h9tbuDOwDfhfqtWjgKPAQGNMmQyqqgRUAH73TQoDWGt/AX4HSgFlcxqziIiIiIiIiIgUQf/84ySF//7bWS5Z0sn4tmuX4a4vvuh9ftttTidjkaIsNzrEt3d/LrXWJvuusNbGA58DpYFWGdSzF9gHnG2MaeC7whhzNtAA+N5aeyAXYhYRERERERERkaJkxw5nTGFPt9/ISJg7F664IsNdv/0W1q1znoeHw5135l2YIgVFbiSGz3F//h5k/R/uz7PTq8Raa4E73Zg2GmPeNMaMM8a8hTN+8c9Av1yIV0REREREREREipJdu5yk8J9/OssREfDxx3DllZna3be38HXXQc2aeRCjSAGTG2MMV3B/Hgqy3lNeMaOKrLUfGWN2Au8BviO57AHewJnQLkPGmI1BVjWMj49n9erVmammSIiPjwcoVq9ZpKjS9SxSNOhaFik6dD2LFA26lgu/iNhYmt53H2W2bwcguUQJfn7iCQ6UKQOZeF/37Yvkgw9a4ek/2abNt6xefSQPI5a8UhyvZ89rzo4CNbeiMeYGYDmwDmiEMwRFI2AFMAV4P3TRiYiIiIiIiIhIQRJx6BBNHnggJSlsw8LY8n//x4HWrTNdx9y5NUlKclJkF1wQxznnKCksxUNu9Bj29AiuEGS9pzwuvUrccYRnAD8CA33GK/7VGDMQZ8iKfsaYdtba1enVZa1tHuQYG8uVK9esXSYGHC8qPJ+QFKfXLFJU6XoWKRp0LYsUHbqeRYoGXcuFWGys/5jCYWGYd9/lvOuuy3QVR4/CNdd4l8eMqahzoRArjtdzuXLlsr1vbvQY/s39GWwMYc9EcsHGIPboDEQAawJMYpcMrHUXAyZ9RURERERERESkmDh4EDp1gh9+cJaNgbfecgYIzoK33nKqAjjzTLjqqlyOU6QAy43E8Cr3Z2djjF99xphywGXAMeCrDOqJcn9WCbLeU56QnSBFRERERERERKQIOHTImVRu0yZn2Rh44w0YMCBL1SQn+086d++9UKJELsYpUsDlODFsrf0LWArUBe5MtXoMUAZ421p71FNojGlojGmYatt17s++xpgLfFcYY5oCfQELrMxpzCIiIiIiIiIiUggdPgxdu8KGDd6y116DQYOyXNWiRfDHH87z8uXhpptyKUaRQiI3xhgGGAZ8AUw2xnQEfgFaAu1xhpB4LNX2v7g/jafAWvuNMeYN4CZggzHmE2A7TsK5NxAJTLTW/pxLMYuIiIiIiIiISGHhSQp/+aW3bOpUGDIkW9X59hYeOhRyMFSrSKGUK4lha+1fxpgWwFigC9AN2AVMAsZYaw9msqohOGMJDwauBMoBh4H1wGvW2vdzI14RERERERERESlE4uOdpPAXX3jLJk+G22/PVnU//AAr3e+klygBd9+dCzGKFDK51WMYa+0/OL19M7OtCVJugZnuQ0REREREREREirv4eOjSxT8pPGlSjrK5Eyd6n/fpA7VrZz88kcIqNyafExERERERERERyX2BegpPmgT33JPtKnfvhnff9S6PGJGD+EQKMSWGRURERERERESk4PEkhT//3Fs2cWKOksIAL78MCQnO81atnIdIcaTEsIiIiIiIiIiIFCzx8dCtW9qk8L335qja48ed+eo87rsvR9WJFGpKDIuIiIiIiIiISMFx5IiTFF6/3lv24os5TgoDvPMO7N/vPK9TB66+OsdVihRaSgyLiIiIiIiIiEjBcOSIM3yEb1L4hRdg+PAcV22t/6Rzd98N4eE5rlak0FJiWEREREREREREQi9QT+EXXsi12eGWLYOff3aely0Lt9ySK9WKFFpKDIuIiIiIiIiISGgdOQLdu8O6dd6yCRNyLSkMzmgUHjffDBUq5FrVIoWSEsMiIiIiIiIiIhI6nqTw2rXesgkTcnVmuC1b4LPPnOfGwD335FrVIoWWEsMiIiIiIiIiIhIaR4+mTQo//3yuJoXBf2zh3r2hfv1crV6kUFJiWERERERERERE8l+gpPBzz8H99+fqYfbvh7ff9i7n4ugUIoWaEsMiIiIiIiIiIpK/PEnhNWu8Zc89Bw88kOuHeuUVOHHCed68ObRuneuHECmUlBgWEREREREREZH8c/Qo9OjhnxR+9tk8SQrv3QtTpniXR4xwxhgWESWGRUREREREREQkvxw9ClddBatXe8uefRYefDBPDtWjB+zZ4yyffjr065frhxEptJQYFhERERERERGRvHfsmJMUXrXKW/bMM3mSFE5MhOuvhw0bnOWwMJg2DSIjc/1QIoWWEsMiIiIiIiIiIpK3jh1zuu/6JoXHj4eHHsr1Q1kLd94JCxZ4y/73P+fwIuKlxLCIiIiIiIiIiOQdz5gOqZPCDz+cJ4d7+ml49VXv8siRcPvteXIokUItPNQBiIiIiIiIiIhIEXXkCHTvDmvXesvGjcuzpPCbb8Ljj3uXBw6Ep57Kk0OJFHpKDIuIiIiIiIiISO6Lj4euXeHzz71lWegpvGUL/PVX5g+3cyfcdZd3uWNHmD4djMl8HSLFiRLDIiIiIiIiIiKSuw4dcpLCX37pLXv+ebj//kzt/uabcNNNznjB2XHBBTBnjiabE0mPEsMiIiIiIiIiIpJ74uLgyivhm2+8ZS++CMOHZ2r3JUvglluynxSuVQsWLYIKFbK3v0hxocSwiIiIiIiIiIjkjthY6NwZNm70lr30kv8YD+nYtAn69oXERGe5Xj1o3Djzh69YEUaNgpo1M7+PSHGlxLCIiIiIiIiIiOTcgQPQqRN895237OWX4Y47MrX7tm3OPHVHjjjLtWrB+vVw+um5H6qIKDEsIiIiIiIiIiI5tX8/XHEF/PCDt+zVV+HWWzO1e2ysMyTx7t3OcsWKsHixksIieUmJYRERERERERERyb69e52k8E8/OcvGwPTpcPPNmdr9xAno1Qt+/dVZjoyEuXOzNoSEiGSdEsMiIiIiIiIiIpI9e/ZAhw6wZYuzbAzMnAk33pip3ZOT4YYbnCEjPN5+G9q2zf1QRcSfEsMiIiIiIiIiIpJ1u3Y5SWFPV9+wMHjrLRgwINNV3H8/zJnjXZ4wAa69NpfjFJGAlBgWEREREREREZGs2bHDSQr//ruzXKIEzJoF11+f6SpeeAEmTvQu33svjBiRu2GKSHBKDIuIiIiIiIiISOb98w+0bw9//eUslygB770H/fpluooPPnB6C3v07eskio3J5VhFJCglhkVEREREREREJHO2b3eSwjExznJ4uJPlveaaTFexZo3/EMStWzvjCoeF5XKsIpIuJYZFRERERERERCRjMTFOUnj7dmc5IgI++gh69cp0FT//DL17Q0KCs9ywIcybByVL5n64IpI+JYZFRERERERERCR9W7c6SeG//3aWIyOdWeN69Mh0FTt3QteuEBfnLFevDosXQ6VKuR+uiGRMiWEREREREREREQnojz/g0xn7SXz5fTjsTixXIhz6D4SfG8LPma/rnXec4YkBypaFRYugbt1cD1lEMkmJYRERERERERERSePnn6H1pUnEHa4MPOpdkQTMzH694eFOZ+MLL8xhgCKSIxrWW0RERERERERE/OzYAV2uOEXc4RK5Xvdrr0HnzrlerYhkkXoMi4iIiIiIiIhIikOHoFuH4/y7uxQA5TjMbeEzCOt7NdSuk+16jYHLL4du3XIrUhHJCSWGRUREREREREQEgIQE6NPpMD/+Xh6AcE4xp+QNdFryAFye/aSwiBQ8SgyLiIiIiIiIiAjWwpCee1mxoWpK2eul7qbTykehVasQRiYieUGJYRERERERERER4bGBfzNrSe2U5SdLPcWN626F5s1DGJWI5BVNPiciIiIiIiIiUsxNvXsL497xJoVvK/kmj355lZLCIkWYEsMiIiIiIiIiIsXYn6+u5J4pDVKWe0QtY8o3F2OaXBDCqEQkrykxLCIiIiIiIiJSXH38MZPu+IVEIgBoFvET739zJuHnNwpxYCKS1zTGsIiIiIiIiIhIcfTeexy84W5mJG9PKXpmRhXKXFA9hEGJSH5Rj2ERERERERERkeJm5kwYMIDXkm/mGGUAOL9hAh0HKCksUlwoMSwiIiIiIiIiUpxMmwY33cQpW4KXuDuleMRDkRgTwrhEJF8pMSwiIiIiIiIiUlxMmgS33w7AHPrwL7UAqFoV/vOfUAYmIvlNiWERERERERERkeLgmWdg+HAALPBC6f9LWTVsGJQsGZqwRCQ0lBgWERERERERESnKrIUxY+CRR1KKvjjvNjYcawxAVBTccUeoghORUFFiWERERERERESkqLIWHn0URo/2lrVrx4v1p6QsDhjgDCUhIsVLeKgDEBERERERERGRPGAt3HcfTJzoLevcmZgX5/LJ+d6U0IgR+R+aiISeegyLiIiIiIiIiBQ1yclw553+SeEePWDePF6aXorkZKeoUyc477yQRCgiIabEsIiIiIiIiIhIUZKUBLfeClOnesv69IE5czicUJLp073F6i0sUnwpMSwiIiIiIiIiUlScOuUMGjxjhresf394/32IjOT11yE+3ilu2BCuvDI0YYpI6GmMYRERERERERGRouDECbj2Wk7MX8ooxvMT50PNMyD2fOhpAPjmG+/mw4dDmLoMihRbSgyLiIiIiIiIiBR2R49Cr14kr1jJQD5gNv2c8h3uI5VKlWDgwHyNUEQKGCWGRUREREREREQKs0OHoHt3+Pxz7ucFb1I4HY89BqVL50NsIlJgKTEsIiIiIiIiIlJY7d/vDBS8aRMvMIKJeGeTu/VW6N077S41akDTpvkWoYgUUEoMi4iIiIiIiIgURjt3QqdOsGULH3At9/NCyqo+fWDqVChRIoTxiUiBpsSwiIiIiIiIiEhhs307dOwIf/3FWtpwI2+lrGrdGmbNUlJYRNKnuSdFRERERERERAqT3393sr9//cXPnEsv5pFAFAANG8K8eVCyZIhjFJECT4lhEREREREREZHC4qef4PLL4d9/2U01urKYOKIBqF4dFi+GSpVCHKOIFApKDIuIiIiIiIiIFAbffANt28KePQCMCn+Kf6gNQNmysGgR1K0bwvhEpFBRYlhEREREREREpKBbu9YZU/jgQQD2l63LW2GDU1bPmgUXXhii2ESkUFJiWERERERERESkIFuyBLp0gSNHnOXTTmPawPWcSHBml7vwQujZM4TxiUihpMSwiIiIiIiIiEhB9ckncNVVcPy4s1y9OieXrWXKJzVTNhkxAowJUXwiUmgpMSwiIiIiIiIiUhDNmgX9+sGpU85y7dqwbh0f/HQuu3c7RTVqwHXXhS5EESm8wkMdgIiIiIiIiIiIpPLqq3D77WCts9ygASxfjq1Vmxf7eTe76y6IjAxNiCJSuKnHsIiIiIiIiIhIQTJhAtx2mzcpfN55zuRztWuzZg18/71TXKqUs5mISHYoMSwiIiIiIiIiUhBYC2PGwAMPeMtatIDVq6F6dQBefNG76sYb4bTT8jdEESk6/p+9+46Oqlr7OP49Cb1IE+yCDcGCBTt6BStFUETsir0iinrV13K91nvtoGIXe68oCvaKvV3sYkGxAFLEUAPkvH/shEkgQEimZGa+n7Vmzex9zpx54vKQ8GPn2baSkCRJkiRJyrQ4hn/+M6wWLrPTTjByJKy0EgDjxsGzzyYOn3ZaekuUlFsMhiVJkiRJkjJp4UI47jgYPjwxt8ce8NRT0KjRoqmhQxPdJXr0gA4d0lynpJxiMCxJkiRJkpQp8+bBIYfAE08k5vr2hYcegvr1F01Nnw533ZU45fTT01ijpJxkj2FJkiRJkqRMmDUL+vSpGAoPGACPPlohFAa4/XaYPTu83nRT2HXXNNYpKScZDEuSJEmSJKXb9OmhXcSLLybmTj01tJOoU/EXvOfPhxtuSIxPOw2iKD1lSspdBsOSJEmSJEnpNGkSdO0K77yTmLvoIrjuOihYMqp55BH49dfwuk0bOPjg9JQpKbfZY1iSJEmSJCldxo+H3XeH779PzA0dCoMGVXr6Z5/BSSclxieeCA0apLRCSXnCYFiSJEmSJCkdvv46hMK//RbGhYWhdcThh1d6+i+/QM+eUFQUxmuuCaeckqZaJeU8g2FJkiRJkqRU++gj6N4dpk4N43r1Qo+Iffap9PTp06FHD/jjjzBu1gxGjYJWrdJTrqTcZzAsSZIkSZKUSm+8Ab17J5b+Nm4MI0bArrtWevrcuSEv/uqrMK5XD556CjbZJD3lSsoPbj4nSZIkSZKUKiNHhpXCZaFwixbwyitLDYVLSmDAAHjzzcTc3XdDt26pL1VSfjEYliRJkiRJSoUHH4S+fcMSYIDVVguJ77bbLvUt//wnPPpoYnzllXDQQSmuU1JeMhiWJEmSJElKtptvhkMPhQULwniddeDtt5fZD2LIELj22sR44EA488zUlikpfxkMS5IkSZIkJUscw+WXw0knhdcAG28cQuF1113q2x5/HE4/PTHu2zcExVGU2nIl5S83n5MkSZIkSUqGOIazzoKrr07MbbMNPP88tGq11Le99VZYXFyWI2+/PTzwABQWprheSXnNYFiSJEmSJKmmFi6EE06AO+5IzO2yCzz9NDRtutS3ff017L03zJsXxu3bw7PPQsOGqS1XkgyGJUmSJEmSaqK4OCz5feyxxNzee8PDD0ODBkt92x9/QI8eMH16GLdpA6NHL3NxsSQljT2GJUmSJEmSqmvWLOjTp2IofPjhoWnwMkLhoiLo1Qt+/jmMGzcOHSfWWSfF9UpSKVcMS5IkSZIkVcfUqSHdff/9xNwpp4Rd4wrCWrzJk2Hu3Ipvi2M47jj49NMwLiwMuXLnzukpW5LAYFiSJEmSJGnF/for7LFHaBJc5l//gn//G6IIgCOOgHvuWf6lbr01tJSQpHQyGJYkSZIkSVoR334bQuFffgnjKILrr4eBAxed8sEHVQuFL7wQjj46RXVK0jIYDEuSJEmSJFXVRx+F5b1TpoRxnTpw771w0EEVTrvuusTrZs1gpZUqXqZOHTj44BAMS1ImGAxLkiRJkiRVxcsvQ9++MHNmGDdqBE8+CXvuWeG0CRMq7kX3+uuw+eZpq1KSqqQg0wVIkiRJkiTVeo89Bj17JkLhli3h1VeXCIUBbrwRFi4Mr7t2NRSWVDsZDEuSJEmSJC3LLbfAAQfA/PlhvOaa8NZbsO22S5w6c2bYTK7M4MFpqlGSVpDBsCRJkiRJUmXiGC65BE48MbwG2HBDGDMGNtqo0rfcfTfMmBFer78+7LVXekqVpBVlj2FJkiRJkqTFlZTAaafBDTck5rbeGp5/HlZeealvGTo0MT7tNChwSZ6kWspgWJIkSZIkqbziYjjiCHjoocTcbruFjeaaNl3q20aOhO+/D6+bN4cBA1JapSTViMGwJEmSJElSmVmzoF8/eOGFxNz++8O990L9+st863XXJV4fdxw0aZKiGiUpCfyFBkmSJEmSJIBp08LK4PKh8IknwoMPLjcU/vRTeP318LqwEAYOTF2ZkpQMBsOSJEmSJEm//go77QTvvZeYu/BCGDYsJL3LUX61cP/+sNZaKahRkpLIYFiSJEmSJOW1hr/8Al26wFdfhYkoCpvO/fvf4fVy/PEHPPxwYjx4cGrqlKRkssewJEmSJEnKSz/9BJ8/OZt2d45g9OyOQEcorANnngnrd4XRVbvO44/D/PnhdZcusM02qapYkpLHYFiSJEmSJOWd11+H3XYtYWFJT6Bn4sBC4IrSRzW4WlhStrCVhCRJkiRJyjsXnjSZhSXJjUXWWQf22Sepl5SklHHFsCRJkiRJyisf//Mh3vz6IADqMJ9udd+iYNttoHGTal+zWTM455wq7VMnSbWCwbAkSZIkScoPcQznnst1V2+8aGrfRs9x2vB5bH9A9UNhScpGBsOSJEmSJCn3zZ8PxxzDb/e+zCOMXzS9+8UtmLdKnLm6JClDDIYlSZIkSVJumzkT+veH0aMZxmUsoC4AO3VZyPqdDYUl5SeDYUmSJEmSlLv+/BN69YIPP2Q2DbmV4xcdGnyGDYEl5a/kbr8pSZIkSZJUW/z0E3TpAh9+CMC9HM40WgGw7rrQp08mi5OkzDIYliRJkiRJuefTT2GHHWDcOABKKGDIKv9ZdHjQICh0wbCkPGYwLEmSJEmScssrr8DOO8PEiWFcvz6jzn2Lbye1AGClleCoozJYnyTVAgbDkiRJkiQpdzz8MPToAUVFYdy8Obz0Ete9v8OiU449Fpo2zUx5klRbGAxLkiRJkqTcMHQoHHQQzJ8fxmusAW+9xdhmO/HKK2GqoABOOSVzJUpSbVEn0wVIkiRJkiTVSBzDOefAlVcm5jp2hBdegLXWYki5thH9+kHbtukvUZJqG4NhSZIkSZKUvebPh2OOgXvvTcztsAM8+yy0bMmkSfDAA4lDgwenv0RJqo0MhiVJkiRJUnaaORP22y+sDC7Tp0/oM9ywIXEMZ50FxcXh0LbbwvbbZ6ZUSapt7DEsSZIkSZKyz+TJ0K1bxVD42GPhiSegYUMA/v3viguJzzwzvSVKUm1mMCxJkiRJkrLLjz9Cly7w0UeJuQsvhFtvhTrhl6PvuAMuvjhx+IgjQn9hSVJgKwlJkiRJkpQ9Pv0UevSASZPCuKAAhg2DE05YdMrzz1cYsueecNttEEVprlWSajGDYUmSJEmSlB1eeCH0FJ45M4zr14eHHoK+fRed8tFH0L8/LFwYxltsAY89BnXrZqBeSarFbCUhSZIkSZJqv7vugl69EqFw8+bw8ssVQuEffwynzJ4dxm3bwnPPQdOm6S9Xkmo7g2FJkiRJklR7xXFoFnzUUYllwGuvDWPGwI47LjptyhTo3j3sSQfQogWMGgWrrZaBmiUpC9hKQpIkSZIk1U7z58OJJ8KddybmNtssNBFeffUKp552GowbF17Xrw/PPAMdO6avVEnKNgbDkiRJkiSp9pk5MzQLHj06Mbf77vD447DSShVO/eUXePjhxPj++yssJpYkVSJprSSiKFoziqLhURT9HkXRvCiKxkdRNCSKohbVuNaWURQ9GEXRr6XXmhRF0RtRFB2erHolSZIkSVItNXEi7LxzxVB4wIDQMHixUBjgxhsTXSa6dQv700mSli0pwXAUResBHwNHAh8A1wE/AqcC70ZR1GoFrjUQ+BDYA3gFuAZ4CigEeiajXkmSJEmSVEt98w1svz188kli7oILwuZzdesucfrMmXDbbYnx4MFpqFGSckCyWkncBLQBBsVxfEPZZBRF1wKDgcuAE5Z3kSiK9gCuB14C9ovjuGix40t+B5AkSZIkSbnh7behTx+YPj2MCwvh5pvh2GOX+pa774YZM8LrDTaAXr1SX6Yk5YIarxguXS28BzAeGLbY4QuBWcBhURQ1rsLlrgLmAAcvHgoDxHE8v2bVSpIkSZKkWumJJ2C33RKhcKNGMGLEMkPhhQthyJDE+NRToSBpTTMlKbcl44/LbqXPL8ZxXFL+QGm4OwZoBGy3rItEUbQJ0Al4EZgWRVG3KIrOjKLojCiKdo2iyD/aJUmSJEnKRUOHho3m5s0L4zZt4I03lrv8d+RI+OGH8LpFCzjiiNSWKUm5JBmtJDYsff5uKcfHEVYUtyf0DF6arUufJwOvA/9Y7PjnURTtG8fx98srKIqij5dyqENRURGvv/768i6RM4qKwsLrfPqapVzl/SzlBu9lKXd4P0tJUFLCerfcwlqPPbZoavaaazL2iiuYO3MmLOf+uvDCzYHmAHTv/gsffvjjCpfgvSzljny8n8u+5upIxircZqXPM5ZyvGy++XKu06b0+WigHdCr9NrtgfuBTYHnoiiqV91CJUmSJElS7VBQXMxGl1xSIRSesfHGfHrjjcxdffXlvn/cuCb873/NASgsLKFv399SVaok5aRkbT6XDGUhdSFwYBzH75aO/46i6HCgA7AV0A94aFkXiuO4c2XzURR93LRp0y27du2anIqzQNm/kOTT1yzlKu9nKTd4L0u5w/tZqoFp02CffeCttxJzffvS7IEH6NKwYZUuMXx44vX++xfQv//21SrFe1nKHfl4Pzdt2rTa703GiuGyFcHNlnK8bP6v5Vyn7PjEcqEwAHEcx8CI0uE2K1ifJEmSJEmqLX7+GXbcsWIofMop8NhjUMVQ+Pff4aFyS8YGD05yjZKUB5IRDH9b+tx+Kcc3KH1eWg/ixa/z11KOl25LStW+S0iSJEmSpNrl009hu+3g668Tc1dfHTafKyys8mWGDYMFC8LrHXeErbde9vmSpCUlo5XEa6XPe0RRVBDHcUnZgSiKmgJdgNnAe8u5znvALKBdFEWN4zietdjxTUqff0pCzZIkSZIkKZ1eeAH22w9mzgzjevXgnnvgwANX6DKzZ8MttyTGrhaWpOqpcTAcx/EPURS9COwBnAzcUO7wRUBj4NbyQW8URR1K3/tNuevMjqLoTmAQcGkURaeXtpAgiqJNgSOABcDjNa1ZkiRJkiSl0R13wAknwMKFYdy8OTz9NOy8M08/Dfffn1gBvDxTpoQWxQDrrAN7752CeiUpDyRr87mTgHeA66Mo2hX4GtgW6EZoIXHeYueX/c5ItNj8BcA/gNOA7aMoGgOsAuwLNABOi+P4hyTVLEmSJEmSUqmkBM4/H/7zn8TcWmvBqFGw8cY89RT06wdhWdiKGzRohTpQSJLKSUaPYUrD2q2AuwmB8BnAesBQYLs4jqdW8Tp/AzsBlwMtgYHAXsDbwJ5xHA9NRr2SJEmSJCnF5s6Fgw+uGApvsQW8+y5svDHvvBMOVzcUbtsWjjoqOaVKUj5K1oph4jieABxZxXMXXylc/thMwgrjxVcZS5IkSZKkbDBlCuyzD4wZk5jr2RMeeQSaNOHbb6F375AdA6y/PlxxBRRUcflanTqwww6w0kpJr1yS8kbSgmFJkiRJkiTGjQsh8PffJ+ZOPBGuvx7q1GHiROjePdEnuHVrGD0a1lsvM+VKUr5KSisJSZIkSZIkxoyB7bdPhMJRBFdfDcOGQZ06zJwJe+0F48eHw40awXPPGQpLUia4YliSJEmSJNXcI4/AgAEwb14YN2gA998fdpcD5s+H/feHjz8OhwsK4NFHYeutM1SvJOU5VwxLkiRJkqTqi+PQIPjAAxOhcOvW8Npri0LhOA7dJEaNSrzt5puhV68M1CtJAlwxLEmSJEmSqmv+fDj5ZLj99sTchhvC88/Duusumrr4YrjzzsQp558Pxx2XxjolSUswGJYkSZIkSSvu779Db4gXXkjM7bwzPPkktGy5aGr4cPj3vxOnDBgQgmJJUmbZSkKSJEmSJK2YCRNgxx0rhsKHHBLG5ULhUaMqrgzeffewuDiK0lirJKlSBsOSJEmSJKnqPv0UttsOPv88MXfBBXDffVC//qKpjz+G/v1h4cIw3nxzePxxqFs3veVKkipnKwlJkiRJklQ1zz8f2kfMmhXGdeqEJcBHHFHhtJ9+ChvLlZ229trw3HOw0krpLVeStHSuGJYkSZIkSct3003Qu3ci7W3WDEaPXiIUnjoVevSASZPCuHnzcNrqq6e1WknScrhiWJIkSZIkLV1JCZx9Nlx99aKpWWt14OhN3uOTE5stcfr06TBlSnhdrx488wx07JiuYiVJVWUwLEmSJEmSKjdnDhx2GDzxRGJuq6248h+v8ci1TZb51iiC+++HnXZKcY2SpGoxGJYkSZIkSUuaOBH69IEPP0zM9enDnDsf5KaOjZf51iiC668Pm89Jkmong2FJkiRJklTR2LGw114wYUJi7tRT4ZpreOCuwkWtItZeG158MQTB5bVoAa1bp69cSdKKMxiWJEmSJEkJzz8PBxwAM2eGcUEBDB0KAwcSxzBkSOLUQYNgww0zUqUkqYYKMl2AJEmSJEmqBeI49H/o3TsRCjdtCiNHwsCBALz0Enz5ZTjUpAkcc0yGapUk1ZgrhiVJkiRJyncLFoRWETfdlJhr2zaEwptssmjquusSh486Cpo1S2ONkqSkMhiWJEmSJCmfzZgRWke88EJibtttYcQIWGWVRVNffQWjR4fXURRyZElS9rKVhCRJkiRJ+Wr8eNhhh4qh8P77w2uvVQiFoWJv4X32gXXXTUeBkqRUMRiWJEmSJCkfvftuWBn81VeJufPPh4cegoYNK5w6ZQrcd19iPHhwmmqUJKWMrSQkSZIkSco3Dz8MRxwB8+aFcb16cMcdcNhhlZ5+yy0wd2543bkz7LhjesqUJKWOK4YlSZIkScoXcQwXXwwHHZQIhVu1gldeWWooPG8eDBuWGA8eHHoMS5KymyuGJUmSJEnKB3PnwjHHwAMPJOY6dICRI2G99Zb6tkcegYkTw+vVV4f+/VNcpyQpLQyGJUmSJEnKdX/+GXaMe+edxNyuu8Ljj0Pz5kBYTFxSUvFtcQzXXZcYn3JK6DohScp+tpKQJEmSJCmXffVV2GSufCh83HEwatSiUPi552DllaFOnYqPunXhs8/CWxo1Cm+TJOUGg2FJkiRJknLVSy/BDjvATz+FcRTBNdeE3eTq1gXg3Xdhv/1g2rRlX2rAAGjZMsX1SpLSxlYSkiRJkiTloltugYEDYeHCMG7cGB58EPr0WXTKd99B796h/XCZgkqWkG22GfzrXymuV5KUVgbDkiRJkiTlkgUL4J//hCFDEnNrrBE2mdt880VTkyZB9+4wdWoYr7xyWD28/vpprVaSlCEGw5IkSZIk5YoZM+DAA2H06MRc587wzDOw+uqLpmbOhF69Eh0mGjYMubGhsCTlD3sMS5IkSZKUC77/HrbbrmIo3LcvvPFGhVB4wQI44AD4+OMwLiiARx4J+9NJkvKHK4YlSZIkScpi06fDvFfHwDHHwF/TgVXCgdMGh5YSRQVQlDj/ggvg+ecT45tuCn2GJUn5xWBYkiRJkqQsdeyxcMcdAF2AryseHFL6WIZzz4Xjj09FZZKk2s5WEpIkSZIkZaGP3ltQGgpXz+GHw6WXJq8eSVJ2ccWwJEmSJEnZZvp0ruv7KbALAE0oonGdedCiBRQULvOtBQXQvTvccgtEURpqlSTVSgbDkiRJkiRlk+++49fux/DoxFcWTb2x26VsOeJCaLTsUFiSpDK2kpAkSZIkKVu8/DJsuy03/tSTBdQFYOe249nyhf9Ao0YZLk6SlE0MhiVJkiRJygY33QTduzPrr2Ju47hF04OHtgv9ISRJWgF+55AkSZIkqTabPx9OOglOPhkWLuQeBjCdlgCstx7stVeG65MkZSV7DEuSJEmSVFtNmwb77w+vhH7CJUQMqX8OzAuHTz0VCm0rLEmqBlcMS5IkSZJUG33zDWy77aJQGOC5na5g3Ly1AWjWDI48MlPFSZKyncGwJEmSJEm1zYsvwnbbwfffJ+Yuvpjr6py5aHjccdCkSQZqkyTlBINhSZIkSZJqiziG66+HHj1gxoww16gRPP44n/W+gNdei4DQPuKUUzJYpyQp69ljWJIkSZKk2qC4OKS9t92WmFtzTXjmGdhiC4YckZjebz9Ya620VyhJyiEGw5IkSZIkZdrkydCvH7z9dmJu223hqadgtdX44w948MHEocGD01+iJCm32EpCkiRJkqRM+vRT2GqriqHwwQfD66/DaqsBcNNNMH9+OLT99iEzliSpJgyGJUmSJEnKlIcfhi5dYMKEMI4iuOIKuP9+aNAAgN9+g5tvTrzl9NMzUKckKefYSkKSJEmSpHRbuBDOPx/++9/EXLNmoV9Ez56LpmbMCMOpU8O4bVvYZ5/0lipJyk0Gw5IkSZIkpdOMGXDIIfDcc4m59u3DJnMbbrhoqrg4tB0eOzaM69SB228Pz5Ik1ZStJCRJkiRJSpfvvgsNgsuHwj17wvvvVwiF4xiOPhpeeSVx2u23w+67p7FWSVJOMxiWJEmSJCkdRo2CbbaBb79NzJ19dlgp3Lx5hVPPOy+0GS5zySVwxBFpqVKSlCcMhiVJkiRJSqU4hquugl69QhsJCBvLPfhg6DFcWFjh9Jtvhv/8JzE+9tgQFEuSlEx2JpIkSZIkKVXmzIFjjgkhcJk11+THG5/nw7mbwiMVT//tN/jnPxPjXr3gppsgitJTriQpfxgMS5IkSZKUCr/+CvvsAx9/nJjr0oWvLn+aLXZfmeLiZb99663hkUfcbE6SlBq2kpAkSZIkKdnGjIGttqoYCh97LLz6KnePXH4ovO66MHIkNG6c2jIlSfnLf3eUJEmSJCmZ7rgDTjoJ5s8P4zp1YOhQOPFEiCJGjkycuttu0LJlxbe3aAHnngtt2qSvZElS/jEYliRJkiQpGebPh8GDYdiwxNzKK8Njj0HXrgD8+CN8/XU41KABjBgBjRqlv1RJkgyGJUmSJEmqqSlToH9/eP31xFynTiH5bddu0dRzzyUO77KLobAkKXPsMSxJkiRJUk38739hp7jyofB++8E771QIhaFiMLzXXmmpTpKkShkMS5IkSZJUXQ89BNtvD+PHJ+YuuQQefXSJneNmzoTXXkuMe/VKT4mSJFXGVhKSJEmSJK2oBQvgnHPgmmsSc02awP33w957V/qWV16B4uLwepNNYO2101CnJElLYTAsSZIkSdKKmDIFDjgAXn01Mde+PTz9NHTsuNS32UZCklSb2EpCkiRJkqSq+uQT6Ny5Yijcuzd88MEyQ+E4rhgM20ZCkpRpBsOSJEmSJFXFffdBly7wyy+JuX//O6wUbtZsmW/97DP4/ffwumVL2G67VBUpSVLV2EpCkiRJkqRlmT8fzjwTrr8+MbfSSqGfcO/eVbrEyJGJ1927Qx3/Ni5JyjC/FUmSJEmStDSTJ0P//vDmm4m5Dh3CKuENN6zyZewvLEmqbWwlIUmSJElSZT78MPQTLh8K9+0L77+/QqHw5MmhBTFAQQHsuWeS65QkqRoMhiVJkiRJWtzdd8NOO8Gvv4ZxFMFll8Hjj4c2Eitg1Kiw+RyEFsUtWya3VEmSqsNWEpIkSZIklSkuhsGD4aabEnPNmsGDD0LPntW6ZPn+wr161bA+SZKSxGBYkiRJkiSAiRNhv/1gzJjE3CabwFNPwfrrV+uSxcXw4ouJsf2FJUm1ha0kJEmSJEl6773QT7h8KNy/P7z7brVDYYC334a//w6v27aFjTaqYZ2SJCWJwbAkSZIkKb/dfjvsvDP8/nsYFxTAFVfAI49AkyY1uvRzzyVe9+oVWhVLklQb2EpCkiRJkpSf5s2DQYPgttsScy1awMMPwx57JOUjyvcXto2EJKk2MRiWJEmSJOWfX38NrSLeey8x16lT6Ce87rqVvmXKFBg6FKZNq9pHFBfDd9+F1w0bQteuNStZkqRkMhiWJEmSJOWXV1+FAw+EP/9MzB10UGgp0bhxpW/5+2/YbTf43/+q95G77RbCYUmSagt7DEuSJEmS8kMcw5VXwu67J0LhwkK45hp44IGlhsLFxdCvX/VDYYCjjqr+eyVJSgVXDEuSJEmSct/ff8MRR4RWEWVWWSVsMLfzzkt9WxzDMcfAyy8n5s4+G9Zaq+ofvfHGtpGQJNU+BsOSJEmSpNz25Zew776Jhr8AO+wAjz0Gq6++zLdecAHcd19ifNFF8K9/pahOSZLSyFYSkiRJkqTc9dBDsM02FUPhQYPgtdeWGwrfeitcdllifMwxISiWJCkXuGJYkiRJkpR75s+Hf/4Thg5NzDVqBHfcETaaW45nn4WTTkqMe/aEm2+GKEpBrZIkZYDBsCRJkiQpt/zxB/TvD2PGJOY22ACefBI22WS5b//gAzjgACgpCeOttgqtiOv4N2hJUg6xlYQkSZIkKXe8+SZssUXFULhvX/jwwyqFwt9/D716wZw5YbzOOjByJDRpkqJ6JUnKEINhSZIkSVL2i2O49lrYZReYNCnMFRTAFVfAE09As2bLvcSff0L37jBlShi3agWjR8Mqq6SwbkmSMsRfhJEkSZIkZbeiIjj6aHjsscRc69bw8MMhKK6C2bNhr73ghx/CuEGD0Ge4ffsU1CtJUi1gMCxJkiRJyl5ffw39+oXnMttuC48/DmuuWaVLLFgABx4YegtDWGj80EOw/fYpqFeSpFrCVhKSJEmSpOz0+OOwzTYVQ+GTToI33qhyKBzHcMopYXVwmeuvh332SW6pkiTVNgbDkiRJkqTssmABnHkm9O8PM2eGuYYN4d57YdgwqF+/ypf673/hllsS47PPhpNPTnK9kiTVQraSkCRJkiRlzJ9/wllnwfjxVXxD8Tz48iuY0QvoFeYaNISNN4HhTWB41T974UJ4663E+JBD4PLLq/5+SZKymcGwJEmSJCkjZs2CXr3gww9X5F31gS0qTs0FPqpZLbvsAsOHh/7CkiTlA7/lSZIkSZLSbsECOOCAFQ2FU2OLLeDJJ6FevUxXIklS+rhiWJIkSZKUVnEc9oh77rnE3GWXwfbbV3LyjBmhEfD77yXmmreA88+HLbescS1168JWW0GDBjW+lCRJWcVgWJIkSZKUVpddBrffnhj/3//BuedWcuIHH8AR/eGXXxJzO+0ED98Iq6+e8jolScpltpKQJEmSJKXN3XfDBRckxocdFoLiCuIYbrgBdtyxYih81lnw6quGwpIkJYErhiVJkiRJafHCC3DssYnxbrvBHXdAFJU76e+/4Zhj4LHHEnPNm8M990CfPukqVZKknGcwLEmSJElKuU8+gf32C5vOAXTqBE88sdiGb2PHhpPGjUvMde4cQuJ11klrvZIk5TpbSUiSJEmSUmr8eOjVC2bODOO11oLnn4eVVip30t13w7bbVgyFTzwR3n7bUFiSpBRwxbAkSZIkKWWmTYMePWDixDBu3hxGjYI11ig9Yc4cGDgQhg9PvKlxY7jtNjj44HSXK0lS3jAYliRJkiSlxNy5sPfe8M03YVyvHjz9NGy8cekJ48aF1hFjxybetNFG8Pjj0LFjusuVJCmv2EpCkiRJkpR0JSVw6KGhE0SZe++FnXcuHTz+eOgfXD4UPvRQ+OADQ2FJktLAYFiSJEmSlFRxDKefHjaXK3P11XDAAUBxMZx6KvTvD0VF4WD9+nDrrSE5btw4IzVLkpRvbCUhSZIkSUqq666DoUMT41NPDUExv/wC++8P77+fOLjOOmH18JZbpr1OSZLymcGwJEmSJKlScQyXXRYW8xYXV/19kycnXvfrB9dcA9Go5+Gww8JudGX22QfuuivsSCdJktLKYFiSJEmSVKlrr4ULLqj++7t0gfuGz6fw/86Dq65KHCgshCuuCMuIo6jmhUqSpBVmMCxJkiRJWsLDD8OZZ1b//Z07wzPDJtBwz/3hvfcSB1ZfHR55BHbcseZFSpKkajMYliRJkiRV8MYbMGBAYrzTTvDQQ1Cnin+DLCiAlceMIOp2JEyfnjjQowfccw+0bp3cgiVJ0gozGJYkSZIkLfLll6H1b1lP4Y4d4emnoWXLKl6guBjOPhuGDEnMFRbC5ZeHJcgFBcktWJIkVYvBsCRJkiQJgN9+C4t6//orjFddFUaNWoFQ+Kef4IAD4MMPE3NrrRX6UuywQ7LLlSRJNeA/1UqSJEmS+Ptv6NkTJkwI4yZNQijctm0VL/DEE7DFFhVD4d694bPPDIUlSaqFDIYlSZIkKc8VF8O++8LYsWFcp07IeTffvApvnjsXBg6E/faDGTPCXN26cO21MGLECiw3liRJ6WQrCUmSJEnKY3EMRx8Nr7ySmLvjDthjjyq8+fvvYf/94dNPE3Pt2sEjj8A22yS7VEmSlESuGJYkSZKkPHb++XD//YnxJZfAgAFVeOPDD8OWW1YMhffdN4wNhSVJqvUMhiVJkiQpT91yC1x+eWJ83HFw3nnLedOcOXD88XDQQVBUFObq1YMbboDHH4fmzVNVriRJSiJbSUiSJElSHnrmGTj55MR4r71g2DCIomW86dtvQ+uIsmbEAOutF1pHdO6cslolSVLyuWJYkiRJkvLM++/DgQdCSUkYb7116AxRZ1lLh+6/P4S/5UPhAw6ATz4xFJYkKQu5YliSJEmSssCCBfD33zW/zq+/htXBc+aE8brrwsiR0LjxUt4wezYMHAh33ZWYq18fhg4NvSeWucRYkiTVVgbDkiRJklTLvfce9OoF06Yl97orrwyjR0ObNks54fPPw9Lir75KzLVvD48+CpttltxiJElSWtlKQpIkSZJqucsuS34o3LBhWCm8wQaVHIxjuOmm0GOifCh86KHw8ceGwpIk5QBXDEuSJElSLTZnDrzySmLcvHnNuze0aBE2mtt220oOTpsGRx8NTz+dmGvUCG64AY480tYRkiTlCINhSZIkSarFXnst0Q+4Qwf4+usUftibb8Ihh4RGxGU6dQo703XsmMIPliRJ6WYrCUmSJEmqxUaOTLzea68UfciCBfDvf0O3bhVD4VNOgfffNxSWJCkHuWJYkiRJkmqpOIbnnkuMe/VKwYf88kvoHfzWW4m5Vq3grrugd+8UfKAkSaoNXDEsSZIkSbXUl1+G3BagWTPo0iXJH/Dkk7D55hVD4a5d4X//MxSWJCnHGQxLkiRJUi1Vvo3EnntC3bpJuvCcOXDiidCvH0yfHuYKC+HSS+Hll2GNNZL0QZIkqbaylYQkSZIk1VLl20gkrb/wF1/AgQeG5chl1l4bHnoIdtghSR8iSZJqu6StGI6iaM0oioZHUfR7FEXzoigaH0XRkCiKWtTgmv+IomhhFEVxFEWXJqtWSZIkSartpk6Fd94Jr6MIunev4QXjGG65BbbeumIovN9+8NlnhsKSJOWZpKwYjqJoPeAdoA0wAvgG2AY4FegeRVGXOI6nruA1mwL3ALOBJsmoU5IkSZKyxQsvQElJeL3tttC6dQ0uNm0aHHts6ClcpmFDGDoUjjkmJM+SJCmvJGvF8E2EUHhQHMf7xHF8ThzHuwDXARsCl1XjmkOBZsB/klSjJEmSJGWN8v2Fa9RG4u23wwZz5UPhTTeFjz4KYbGhsCRJeanGwXDpauE9gPHAsMUOXwjMAg6LoqjxClxzb+BIYBDwe01rlCRJkqRssmABjB6dGPfqVY2LLFwIF18MO+8MEyYk5k86Cd5/HzbaqMZ1SpKk7JWMFcPdSp9fjOO4pPyBOI6LgDFAI2C7qlwsiqI2wO3A03Ec35+E+iRJkiQpq7z7LkyfHl6vsQZsttkKXmDCBNhlF7jwwkQ/ihYt4KmnYNiw0EZCkiTltWT0GN6w9Pm7pRwfR1hR3B54pQrXu50QWJ9Q3YKiKPp4KYc6FBUV8frrr1f30lmnqKgIIK++ZilXeT9LucF7Wcodqbyfb7ttXWBtALbY4nfeeGNpf91aUuvXXqP9tddSd+bMRXN/derE1+edx7zmzcE/f6QK/N4s5Y58vJ/LvubqSEYw3Kz0ecZSjpfNN1/ehaIoOgroAxwQx/GkmpcmSZIkSdnn3XdbLXq9/fZV28e7cPZsNrj+elZ94YVFc3FBAeMPP5yfDz0UCguTXqckScpeyQiGkyKKonbAEOCxOI4frcm14jjuvJTP+Lhp06Zbdu3atSaXzypl/0KST1+zlKu8n6Xc4L0s5Y5U3c/jx4cHQP36cOqpm9J4eTu2vPceHH00/PhjYq5dO6L772edLl1YJ6kVSrnF781S7sjH+7lp06bVfm8yegyXrQhutpTjZfN/Lec6w4E5wElJqEmSJEmSstJzzyVe77ILyw6FFywIG8ztuGPFUPiww+Czz6BLl1SVKUmSslwyVgx/W/rcfinHNyh9Xl5TrC0JIfKfURRVdvy8KIrOA0bEcbzPihYpSZIkSdmgfDDcq9cyTvzpJzj0UHjnncRcs2Zw881w0EEpq0+SJOWGZATDr5U+7xFFUUEcxyVlB6Ioagp0AWYD7y3nOvcCjSqZ3wD4B/AZ8DHwaU0LliRJkqTaaNYsePXVxLjSYDiO4YEH4KSToPyGMzvtBPfdB23bprxOSZKU/WocDMdx/EMURS8CewAnAzeUO3wR0Bi4NY7jWWWTURR1KH3vN+WuM6iy60dRdAQhGH4ujuPza1qvJEmSJGXa/Pnw1lswY7EtvD//HObNC6833hjatVvsjX/9FQLhhx5KzBUWwkUXwTnnuMGcJEmqsmRtPncS8A5wfRRFuwJfA9sC3QgtJM5b7PyvS58r7RkhSZIkSbnsuOPg7ruXfc5eey028dZboXXEL78k5tZbDx58ELbZJtklSpKkHJeMzeeI4/gHYCvgbkIgfAawHjAU2C6O46nJ+BxJkiRJynbffw/33LP88/bdt/TF/Plw/vnQtWvFUPioo8IGc4bCkiSpGpK1Ypg4jicAR1bx3CqvFI7j+G5C4CxJkiRJWe/660ObYIB114VOnSoeLygIvYW32QYYNw4OOQQ+/DBxQosWcNttsN9+aatZkiTlnqQFw5IkSZKkZfvrLxg+PDG+5RbYffdKToxjGH4XDBoUdqQr060b3HsvrLlmqkuVJEk5LimtJCRJkiRJy3f77Ymcd5NNYLfdKjlp2jTo3x+OPjpxct26cOWV8PLLhsKSJCkpXDEsSZIkSWmwYAHccENiPHgwRIs32XvlFRgwAH77LTG34YZhg7ktt0xLnZIkKT+4YliSJEmS0uCJJ2DChPC6TRs4+OByB+fMgdNOC0uIy4fCJ5wAn3xiKCxJkpLOFcOSJEmSlAbXXZd4feKJ0KBB6eDjj+Gww+DrrxMntGoVmhH36ZPWGiVJUv5wxbAkSZIkpdi778L774fX9eqFYJgFC+Cyy2C77SqGwj17whdfGApLkqSUcsWwJEmSJKXYtdcmXh9yCKxS9D3scxi8917iQKNGYVnxscdW0nxYkiQpuQyGJUmSJCmFxo+HJ59MjAev9RhsdgTMnp2Y3G47uO8+WH/9dJcnSZLylK0kJEmSJCmFbrgBSkrC691W/pRNL94/EQrXqQOXXgpvvWUoLEmS0soVw5IkSZKUIkVFcMcdifHgKeclBh07hlXCnTunvzBJkpT3XDEsSZIkSSkyfNgc/v47vN6Qb+jO6DA49VT4+GNDYUmSlDGuGJYkSZKkFPjl0ff47/nrAg0BOI0hFKy5Btx1F+y2W2aLkyRJec8Vw5IkSZKUTPPmMf2Uf9HjgKZMXNgGgNZM5vD958HYsYbCkiSpVjAYliRJkqRkGTuWeZ13oO+Nu/AVGwNQl2IeOf8LGj1yF7RokeECJUmSAoNhSZIkSaqphQvhyisp6bw1A778J2/QddGhe26cSbdLdslcbZIkSZWwx7AkSZIk1cQPP8CRR8Jbb3E2V/IIBy46dOUVJRx0cssMFidJklQ5VwxLkiRJUnWUlLD6009Dp07w1ltczylczT8XHR44EM78p3/lkiRJtZMrhiVJkiTlhKIiuOEG+PPPdHzY38x9diINJrcFLmU2jbidYxcd7tsXhgyBKEpDLZIkSdVgMCxJkiQp682dCz17wttvp+sTVwIOrvTI9tvDAw9AYWG6apEkSVpx/l6TJEmSpKxWUgKHHZbOUHjp2reHZ56Bhg0zXYkkSdKyuWJYkiRJUlY74wx4/PHE+MQTYYMNkvgBcQyffgJPPAlzZi+aLm7WjMm77MqaO+0EhDC4f39o1SqJny1JkpQiBsOSJEmSstZ114VevmUGDUpyb9/Jk0PS/OSTFecHDeLNHttR0mAhXbsm6bMkSZLSyFYSkiRJkrLSo4/C6acnxv36wbXXJjEUfvJJ2GSTiqFwu3bw2mswdCglDRok6YMkSZLSz2BYkiRJUtZ5883QV7hMly5w331J2vBt2jQ45JCQNP/5Z2L+uONg7FhcIixJknKBrSQkSZIk1UqffQbDhsGcOUsee+45KC4Orzt0SOKGb88/D8ccA3/8kZhbYw24807Yc88kfIAkSVLtYDAsSZIkqdb58kvo1g3++mvZ5626KowaBS1b1vAD//4bBg+G4cMrzg8YEJoWN29eww+QJEmqXQyGJUmSJNUqv/8OPXosPxRu2jSsHG7XroYf+MorcNRR8MsviblVVoHbboM+fWp4cUmSpNrJYFiSJElSrfH33yEUnjAhjJs0gauvhsaNK55XUBD6CrdtW4MPmzkTzj4bbrqp4vwBB8CNN8LKK9fg4pIkSbWbwbAkSZKkWqG4OOz3NnZsGNepA088AXvskYIPe+WV0Et4/PjEXKtWISTef/8UfKAkSVLtUpDpAiRJkiQpjkNO+/LLibnbb09BKPz333D88bDbbhVD4b33Do2NDYUlSVKecMWwJEmSpIw7/3y4777E+OKL4Ygjkvwho0fDscfCr78m5lq2hKFD4ZBDIIqS/IGSJEm1l8GwJEmSpKSJY7jySnjttfC6KubNgzfeSIyPPTYExUkzfTqcfjrcfXfF+X33hWHDYNVVk/hhkiRJ2cFgWJIkSVLSnHce/Oc/1X9/z56hzW/SFu8++2xoHfHHH4m5lVcOgXD//q4SliRJecsew5IkSZKS4uabaxYKb7stPPJI2HSuxqZOhUMPhT59KobCBxwAX30VegkbCkuSpDzmimFJkiRJNTZiBAwcmBj37AmDBlX9/fXrw3bbQYMGSSjmySfhpJNg0qTE3CqrhOS6b98kfIAkSVL2MxiWJEmSVCPvvQcHHQQlJWG89dbw6KPQuHGaC/nzz5BOP/poxfnDDoMhQ8JGc5IkSQIMhiVJkiTVwLhx0Ls3zJkTxuuuCyNHpjkUjuMQBg8cCFOmJOZXXx1uvRX22iuNxUiSJGUHewxLkiRJqpbJk6FHj0QWu/LKMHo0tGmTxiImToR+/eDAAyuGwkcdBV9+aSgsSZK0FK4YliRJkrLYyJFw5ZUwc2b6P3vixMS+bg0bhlo22CBNHx7HcP/9cOqpMH16Yn6tteD222HPPdNUiCRJUnYyGJYkSZKy1IIFMGAATJuW2ToKCuDhh2HbbdP0gb/+CiecAM89V3H++ONDSr7SSmkqRJIkKXsZDEuSJElZ6osvakcofPPN0KdPGj6spARuuw3OOguKihLz7drBnXfCLrukoQhJkqTcYDAsSZIkZan33ku87t4dLrss/TWssgqssUYaPujbb+HYY+GttyrOn3IKXH45NGmShiIkSZJyh8GwJEmSlKXefTfxevfdYcstM1dLysyfH9pDXHwxFBcn5tu3hzvugJ12ylxtkiRJWcxgWJIkScpS5YPh7bfPXB0p8+GHcPTR8Pnnibk6deDss+H886FBg8zVJkmSlOUMhiVJkqQsNHUqjBsXXtetC1tskdl6kmrWLLjgAhg6NPQVLrP11mGVcKdOmatNkiQpRxgMS5IkSVmofH/hLbfMocWzL74Ixx8P48cn5ho2hEsvhVNPhcLCjJUmSZKUSwyGJUmSpCxUPhjebrvM1ZE0U6fCGWfAPfdUnN99d7jlFlh33czUJUmSlKMKMl2AJEmSpBWXM/2F4xgeeQQ22qhiKNyiBdx9N7zwgqGwJElSCrhiWJIkScoyCxfC++8nxlm7YvjXX+HEE2HkyIrzBxwQ+guvskpm6pIkScoDrhiWJEmSssxXX8HMmeH1aqvB2mtntp4VVlICN90UVgmXD4XXWANGjICHHzYUliRJSjFXDEuSJElZZvE2ElGUuVpW2DffwDHHwJgxFedPPBH+8x9o1iwzdUmSJOUZg2FJkiQpy2TlxnPz5sGVV8Kll0JxcWJ+ww3hjjtgxx0zV5skSVIeMhiWJEmSskzWbTz35ptw/PFhtXCZOnXg7LPh/POhQYPM1SZJkpSnDIYlSZKkLDJtWiJfrVMHOnfObD3LNG0anHUW3Hlnxfmttw6rhDt1ykxdkiRJcvM5SZIkKZt88EHi9eabQ8OGGStl6eIY7r8fOnSoGAo3aQJDh4Ylz4bCkiRJGeWKYUmSJCmLlG8jUSv7C48bFzaSe+WVivN9+8L118Oaa2amLkmSJFXgimFJkiQpi5TfeK5W9RcuLg4by226acVQeM014emn4cknDYUlSZJqEVcMS5IkSVmipATefz8xrjXB8Ftvhc3lvv46MVdQAKeeChddBE2bZq42SZIkVcpgWJIkScoSX38NM2aE123aQLt2GS0nbC539tlhI7nyttwSbrutlu+MJ0mSlN9sJSFJkiRlicXbSERRhgqJY3jggbC5XPlQuEkTGDIkLGs2FJYkSarVXDEsSZIkZYlasfHc99+HzeVefrni/D77hM3l1lorI2VJkiRpxbhiWJIkScoSGd14rrgYLrsMNtmkYii85prw1FPhYSgsSZKUNVwxLEmSJGWBGTPgq6/C68JC2GqrNH7422+HzeXKCoCwudygQXDxxW4uJ0mSlIUMhiVJkqQs8P77obUvQKdO0LhxGj70zz/D5nJ33VVx3s3lJEmSsp6tJCRJkqQskNY2EiUlIfjdcMOKobCby0mSJOUMVwxLkiQpb8UxTJoEc+ZkupLle+ONxOuUbjz3ySdhc7kPPqg47+ZykiRJOcVgWJIkSXmppASOOw7uvDPTlay4lKwY/usvuOACuOmm8B+nzDrrwA03QK9eKfhQSZIkZYrBsCRJkvLSuedmZyi86qqw3npJvGAcwwMPwJlnhuXTZerVg3POCY+GDZP4gZIkSaoNDIYlSZKUd4YNgyuuSIxXWw3q189cPVXVrBlccglEUZIu+NVXcNJJFftUAOyxB9x4I2ywQZI+SJIkSbWNwbAkSZLyylNPwSmnJMZ9+sCTT0JhYeZqSruZM0PCfO21sGBBYn6NNcLmcv36JTF9liRJUm1kMCxJkqS88e67cPDBoXsCwLbbwkMP5VEoHMchGT/tNJgwITFfWBjmLrwQmjbNVHWSJElKI4NhSZIk5YXvvoPevWHu3DBef3149llo1CizdaXNDz+EpdKjRlWc33HHsOHcpptmpi5JkiRlhMGwJEmSMm7iRPjll9Rdf948GDAApk4N49atYfTo8Jzz5s4NDZX/85/wH6JM69Zw1VVw+OG2jZAkScpDBsOSJEnKqCefhAMPhPnz0/N5DRvCyJGw3nrp+byMGj0aBg4Mq4XLRBGccAJcdhm0aJG52iRJkpRRBsOSJEnKmDFjQs/fdIXCBQXw6KOwzTbp+byMGT8ezjgjpO7lde4MN98MW2+dkbIkSZJUexgMS5IkKSO++Qb69El0N2jdGtq1S93n1a8PgwbBXnul7jMybs4cuPJK+O9/E82UAZo1C60kjjsuj3bakyRJ0rIYDEuSJCntJk6EHj1g2rQwbtMG3nknT9o7pEIcw4gRMHhwWC1c3uGHh7B4lVUyUpokSZJqJ4NhSZIkpVVREfTqlcgvGzXKo56/qfDtt2Ep9IsvVpzfYgu48UbYYYfM1CVJkqRarSDTBUiSJCl/zJ8P++8Pn3wSxoWFoeevLW+roagIzjoLNt20YijcsiXccgt8+KGhsCRJkpbKFcOSJElKiziGE06A0aMTczffHFYPawXEMTz4IPzzn/DHH4n5ggI4/ni45BJo1Spz9UmSJCkrGAxLkiQpLS66CIYPT4wvuACOPTZz9WSlzz6DU06Bt9+uON+lC9xwQ2gfIUmSJFWBrSQkSZKUcnfeGYLhMkccUXGs5Zg2DU4+GTp3rhgKr7oq3HcfvPWWobAkSZJWiCuGJUmSlFKjRoUOB2X22ANuuw2iKHM1ZY2FC+GOO+C882Dq1MR8nTpw2mlh2fVKK2WsPEmSJGUvg2FJkiSlzEcfQf/+Id+EsKj18cehbt3M1pUV3n0XBg5M7NRXZvfd4frroUOHzNQlSZKknGArCUmSJKXEjz+GjeVmzQrjtm3hueegadPM1lXrTZwYem3ssEPFULhtW3jySXjhBUNhSZIk1ZgrhiVJkpR0U6dCjx4weXIYt2gRWkqstlpm66rV5s2DIUPgssugqCgx36ABnH12eDRsmLHyJEmSlFsMhiVJkpRUc+ZAnz7w3XdhXL8+PPMMdOyY2bpqrTiGp5+GM88My6zL69sXrr0W2rXLRGWSJEnKYQbDkiRJSqqzzoJ33gmvowgeeAB23DGzNdVaY8eGTeRee63ifIcOMHRo2KlPkiRJSgF7DEuSJClp/vwTbr89Mb7uOujXL3P11Fp//gknnBB24ysfCrdoEQLhsWMNhSVJkpRSrhiWJElS0txyS2iVC7DVVjBoUGbrqXWKi2HYMLjoIpgxIzFfWAgnngj//je0apWx8iRJkpQ/DIYlSZKUFPPmhcyzzODBoZWECH2En3sOzjgj0Xy5zB57hD7CG2+cmdokSZKUlwyGJUmSlBQPPwyTJoXXa6wB/ftntp5a46uvQkr+4osV5zfYIATCvXqZoEuSJCnt7DEsSZKkGovjkHGWGTgQ6tbNXD21wrRpcMop0KlTxVC4WTO45hr44gvYay9DYUmSJGWEK4YlSZJUY6+9FvZLA2jUCI47LrP1ZNT8+aHZ8oUXwvTpifmCAjj2WLjkEmjdOnP1SZIkSRgMS5IkKQmuuy7x+ogjoGXLjJWSWS+8ENpGfP11xflddgn/kTp1ykxdkiRJ0mJsJSFJkqQa+e47GDkyMT711MzVkjHffBPaQnTvXjEUXnddeOopePllQ2FJkiTVKgbDkiRJqpGhQxOv99oL2rfPXC1pN3kynHwybLIJPPdcYr5pU7jiirDx3D772EdYkiRJtY6tJCRJklRt06bB3XcnxoMHZ6yU9JozJyTil18ORUWJ+SiCo46CSy+FVVfNXH2SJEnSchgMS5Ikqdpuuw1mzw6vO3WCbt0yW0/KlZTAQw/BuefCL79UPLbLLnD11bDFFpmpTZIkSVoBBsOSJEmqlvnz4cYbE+PTT8/xjglvvglnnAEffVRxvmNHuOoq6Nkzx/8DSJIkKZfYY1iSJEnV8thj8Ntv4fUqq8CBB2a2npT57jvo2xd23rliKNy6Ndx8M4wdC716GQpLkiQpq7hiWJIkSSts0iQ4//zE+OSToX79zNWTElOmwMUXh/B3wYLEfIMGYXn02WfDSitlrj5JkiSpBgyGJUmStEJmzoS99oKffgrjJk3ghBMyW1NSzZ0LN9wAl10GM2ZUPHbooWF+7bUzU5skSZKUJAbDkiRJqrIFC+CAAxIdFQoK4MEHQ1eFrBfH8Mgj8H//B+PHVzy2885wzTXQuXNGSpMkSZKSzWBYkiRJVRLHcOKJ8PzzibmbboLevTNXU9KMGRPaQ3zwQcX59u3DxnK9e9tDWJIkSTnFzeckSZJUJZdeCnfckRifey4cf3zm6kmK77+H/faDHXesGAq3ahXaSXzxBfTpYygsSZKknOOKYUmSJC3XXXfBv/6VGB92WAiKs9akSWFjudtuq7ixXP36cOqpIfVu1ixz9UmSJEkpZjAsSZIkAF5+ObTYLZ+TQhg/9FBivNtuYeVwVi6iLSqCq68O/YJnzap47KCD4PLLoV27jJQmSZIkpZPBsCRJkhg9GvbaCxYuXPZ5nTrBE09AvXrpqStpiovD6uCLL4Y//6x4bOed4corYZttMlObJEmSlAEGw5IkSXnuk09Cm93lhcJrrx02nltppfTUlRQlJfDoo3DeefDjjxWPbbopXHEFdO+epcufJUmSpOozGJYkScpj48dDz56Jrgprrx16CRcstkVxvXqwxx7QunXaS6y+l1+Gs88OyXd5a68Nl1wChxwChYWZqU2SJEnKMINhSZKkPDV1algsO2lSGDdvDqNGwUYbZbSsmvvkEzjnHHjppYrzLVuGlcMnnQQNGmSmNkmSJKmWMBiWJEnKQ3PmQJ8+8O23YVyvHowYkeWh8I8/wgUXwIMPVpxv0ABOOy2sHm7ePBOVSZIkSbWOwbAkSVKeWbgQDj0U3nknMXf//fCPf2Suphr580+49FK4+WaYPz8xX1AARx0F//43rLFGxsqTJEmSaiODYUmSpDwSx3D66fDkk4m5a6+F/v0zV1O1zZwJ110HV10FRUUVj+2zD1x+OXTsmJHSJEmSpNrOYFiSJCmPXHstXH99Yjx4cHhkleJiuPNOuOiiRIPkMl26wJVXwg47ZKY2SZIkKUsYDEuSJOWJhx+GM89MjPv3h6uvzlw9K2zhwtA/+MIL4aefKh7r2BH++1/o3RuiKDP1SZIkSVnEYFiSJCkPvP46DBiQGO+0E9x7b2jDW+vFMTz1VNhY7quvKh5bYw24+GI4/HCo44+2kiRJUlX507MkSVKO+/LL0HK3uDiMO3aEp5+GBg0yWVUVxDG89BKcdx589FHFYy1bwtlnw8CB0KhRZuqTJEmSspjBsCRJUg777Tfo3h1mzAjjVVeFUaNCrlqrjRkTAuE33qg436QJnHFGaIzcrFlmapMkSZJygMGwJElSjpoxA3r2hF9/DeMmTUIo3LZtZutapk8/hfPPh+efrzjfoAGcfDKccw6svHJmapMkSZJyiMGwJElSDiouhn79YOzYMK5TB554AjbfPKNlLd2338K//gWPPlpxvk4dOOaYEBavsUZmapMkSZJykMGwJElSjoljOPpoeOWVxNwdd8Aee2SupqX6+eewedzdd0NJSWI+iuCQQ+Df/4b11stUdZIkSVLOSto+1FEUrRlF0fAoin6PomheFEXjoygaEkVRiyq+v3EURYdEUfRgFEXfRFE0K4qioiiKPoqi6Iwoiuolq1ZJkqRcdt55cP/9ifGll8KAAZmrp1ITJ8KgQdC+PQwfXjEU7ts3LHW+7z5DYUmSJClFkrJiOIqi9YB3gDbACOAbYBvgVKB7FEVd4jieupzL7ATcD0wDXgOeBloAfYCrgX2jKNo1juO5yahZkiQpF918M/znP4nxccfBuedmrp4lTJ8OV10FQ4fC7NkVj+2+O1x2GWy9dWZqkyRJkvJIslpJ3EQIhQfFcXxD2WQURdcCg4HLgBOWc42JwKHAY3EcF5e7xpnA68AOwMnANUmqWZIkKaeMGAEDBybGe+0Fw4aFrgwZN2NGCIOvvTa8Lm+HHUIg3LVrRkqTJEmS8lGNW0mUrhbeAxgPDFvs8IXALOCwKIoaL+s6cRx/FsfxA+VD4dL5IhJhcNea1itJkpSL3nsPDjoo0ZFh663h4YfD3m0ZVVQUQt911oELL6wYCm+2GYwcCW+/bSgsSZIkpVkyegx3K31+MY7jkvIHSkPdMUAjYLsafMb80ucFNbiGJElSTho3Dnr3hjlzwnjddUPe2niZ/yyfYjNnhp4W7drB+eeHFhJl2reHRx6BTz6BXr1qyZJmSZIkKb8kIxjesPT5u6UcH1f63L4Gn3FU6fPoGlxDkiQp50yeDN27w5QpYbzyyjB6NLRpk6GCZs2CK68MK4TPPRemTUscW289uPde+PJL2H9/KEjaPsiSJEmSVlAyfrmwWenzjKUcL5tvXp2LR1E0EOgOfAYMr+J7Pl7KoQ5FRUW8/vrr1SklKxUVFQHk1dcs5SrvZyk3JPNenjOngNNP35wff1wJgPr1F3LRRZ/x229F/PZbjS+/QgrmzmX1Z55h7Ycfpl751cHAnNVW4+fDD2fS7rsTFxaG1hFSDvB7s5QbvJel3JGP93PZ11wdme46t0xRFO0LDCFsTNcvjuP5y36HJElSfli4MOLiizfmm29CKFxQEHPBBV+x0UbV/8GwOgrmzWP1Z59l7QcfXCIQnrvKKow/7DAm7bknccabHUuSJEkqLxk/oZetCG62lONl83+tyEWjKNoHeBiYDHSL4/jHqr43juPOS7nmx02bNt2yax5tblL2LyT59DVLucr7WcoNybiX4xiOPz5sOFfmxhsjTjxx05oVtyLmzoXbbw99hP/4o+KxtdaC88+nwRFH0KFePTqkryoprfzeLOUG72Upd+Tj/dy0adNqvzcZwfC3pc9L6yG8Qenz0noQLyGKov7Ag4SVwrvEcTxuOW+RJEnKG5dfHjLZMv/3f3DiiWn68Hnz4M47QxGL96tYYw047zw46iioXz9NBUmSJEmqjmQEw6+VPu8RRVFBHMclZQeiKGoKdAFmA+9V9ubFRVF0CHAP8BsruFJYkiQp191zD5x/fmJ86KFw2WVp+ODiYrjrrvBhEyZUPLbaamGjuWOOgQYN0lCMJEmSpJqq8VbQcRz/ALwItANOXuzwRUBj4L44jmeVTUZR1CGKoiV+qzCKogHAvcAvwD8MhSVJkhJefDFkr2V23TUs3o2iFH7ovHlw223Qvj2ccELFUHjVVWHIEPjhBxg40FBYkiRJyiLJ2gXkJOAd4PooinYFvga2BboRWkict9j5X5c+L/prTBRF3YDhhLD6NeDIaMm/5fwVx/GQJNUsSZJU67z2Wgh///xzyWOzZkFJ6e9mdeoETzwB9eqlqJA5c0LqfMUV8OuvFY+1aQNnnx2C4kaNUlSAJEmSpFRKSjAcx/EPURRtBVwMdAd6An8AQ4GL4jievqz3l2pLYgXzUUs552dgSM2qlSRJqp0+/RT69IGZM5d93lprwfPPQ7Olbf1bE7Nmwa23wlVXwcSJFY+tvDKcdRacdBI0bpyCD5ckSZKULslaMUwcxxOAI6t47hJLgeM4vhu4O1n1SJIkZZOff4aePZcfCq+9dgiF11gjyQUUFcGwYXDNNTBlSsVjbdrAmWeGHe6aNEnyB0uSJEnKhKQFw5IkSaqeadOge/fEAt1mzeDVV2H99Zc8t2nTJPcU/usvuP760Ct4+mK/5LX66qFlxLHHQsOGSfxQSZIkSZlmMCxJkpRBc+fC3nvDN9+Ecb16MGIEbLllij94ypQQBt9wA/z9d8Vja68N55wDRx7phnKSJElSjjIYliRJypCSEjjsMHj77cTcvffCzjun8EMnTQrtIm66KfQTLm+99eDcc+HQQ1O4q50kSZKk2sBgWJIkKcUWLICFC8Pr4uLQB2LevLAo9/HHE+ddfTUccECKivjtt7Ch3G23wZw5FY916ADnnQcHHgh1/PFQkiRJygf+5C9JkpRC//oX/Oc/IRwOKl8OfOqpcPrpKSjg55/hiivgzjuhuLjisU03hfPPh379oLAwBR8uSZIkqbYyGJYkSUqR666DSy5Z/nn9+oXuDkndVO677+DKK+Gee8qn0sGWW8IFF0CfPlBQkMQPlSRJkpQtDIYlSZJS4NFHK64ArlMnZLBxXAJAFBVQUAA9e8J99yVxwe7HH8N//wtPPAFxXPHYdtuFQLhHjySn0JIkSZKyjcGwJElSkr35ZthUrsyOO8JLL0GDBvD6628C0LVr1+R9YBzD66+HnhUvvbTk8X/8IwTCu+5qICxJkiQJMBiWJElKqi+/hL33TrTz7dABRowIoXDSlZTAM8+EQPiDD5Y83rNn2OFup51S8OGSJEmSspnBsCRJUpL8/nvo0vDXX2G86qowahS0bJnkD5o/Hx58MGwq9/XXFY8VFMABB8DZZ8NmmyX5gyVJkiTlCoNhSZKkJPj777BAd8KEMG7SBJ5/Htq1S+KHzJ4Nd94JV18Nv/xS8Vj9+nDkkXDmmbDeekn8UEmSJEm5yGBYkiQpCY48Ev73v/C6sBAefxy22CJJF58+HYYNg6FDYcqUiseaNoUTT4TTToPVVkvSB0qSJEnKdQbDkiRJNfTnn/Dkk4nxHXfAnnsm4cK//w7XXQe33AIzZ1Y81rp1CINPOgmaN0/Ch0mSJEnKJwbDkiRJNfT554nXnTvDEUfU8ILffw9XXgn33JPYxa5M27bwz3+GJcqNGtXwgyRJkiTlK4NhSZKkGiofDHfqVIMLvf9+6B/85JNQUlLx2MYbwznnhI3l6tatwYdIkiRJksGwJElSjZUPhjfddAXfXFICzz4bAuG3317y+Hbbwf/9H+y1FxQU1KhOSZIkSSpjMCxJklRDY8cmXlc5GJ4zB+67D665Br77bsnje+4ZAuF//AOiKCl1SpIkSVIZg2FJkqQaKCmBL79MjJfXSqLujBmsPmIE7L9/2LWuwsG6cPDBcMYZ1Vh6LEmSJElVZzAsSZJUAz/+CLNnh9dt2oRHpb7/Hq67ju3uvJPCefMqHltpJTjhBBg0CNZYI6X1SpIkSRIYDEuSJNXIcttIvPceXHUVPPUUxDGF5Y+ttRYMHgxHHx3CYUmSJElKE4NhSZKkGii/8dyiNhIlJfDMM2FDuTFjlnhP0frr0/Sii6B//9A+QpIkSZLSzGBYkiSpBsoHw5tuWAy33hU2lBs3bsmTu3fns913568ttqBrt27pK1KSJEmSFmMwLEmSVAMVguFzesFfL1c8oW5dOOSQsKHcJpvw1+uvp7U+SZIkSaqMwbAkSVI1zX7nM8Z91wkooICFbPRXubYRzZolNpRbffWM1ShJkiRJlTEYliRJWhELF4b+wUOG8NWbs4j5CID1+Z5GzIG1105sKNe0aYaLlSRJkqTKGQxLkiRVxYwZMHw4XH89jB8PwOccsejwpi1/h5sfgb593VBOkiRJUq1nMCxJkrQs338fwuC77oKZMysc+jzaDOLwetNB3WD/DNQnSZIkSdVgMCxJkrS4OIbXXoMhQ2DkyDAur2VLOOEExr55Arwdpjp1SnuVkiRJklRtBsOSJEll5s6FBx8MgfDnny95fKON4LTT4JBDoFEjPl8lcWjTTdNVpCRJkiTVnMGwJEnSH3/ATTfBLbfAlClLHu/VC049FXbbDaIIgEmTYPLkcLhRI1h33TTWK0mSJEk1ZDAsSZLyUxzD++/DjTfCo4/C/PkVjzdqBEceCaecAhtuuMTbyy8o3mQTKChIcb2SJEmSlEQGw5IkKb/MmQMPPxwC4U8+WfL42muHMPjoo6FFi6VepnwwbBsJSZIkSdnGYFiSJOWHn36Cm2+GO++EadOWPL7jjqF/8N57Q53l/4hkMCxJkiQpmxkMS5Kk3FVSAi++GFYHP/98aB9RXoMGcNBBcPLJ0LnzCl26fDDcqVMSapUkSZKkNDIYliRJuWf6dLj77rCh3PffL3l8nXXgxBPhqKOgVasVvvzChfDFF4mxK4YlSZIkZRuDYUmSlDv+9z8YNgzuvz/0El5c9+5hdXCPHlBYWO2P+eEHmDs3vF51VVh55WpfSpIkSZIywmBYkiRlt+JiePLJ0C5izJgljzdrFlYGn3gibLBBUj7S/sKSJEmSsp3BsCRJyk6//Qa33RYeEycuebxTJxg4EA4+GBo3TupH219YkiRJUrYzGJYkSdmjpARefhluvRVGjAjNfsurUwf69QuBcJcuEEUpKWPs2MRrVwxLkiRJykYGw5IkqfabNAnuugtuvx1+/HHJ46utBscfD8cdF16nmK0kJEmSJGU7g2FJklQ7lZTAa6+F1cFPPw3z5y95zj/+EVYH77MP1K2blrJmzQqbzwEUFMBGG6XlYyVJkiQpqQyGJUlS7TJlCtx9dwiEv/9+yePNm8OAAWF1cAZS2a++gjgOr9u3hwYN0l6CJEmSJNWYwbAkScq8OIY33wxh8BNPQHHxkudsv31oF7H//tCwYfprLGV/YUmSJEm5wGBYkiRlzrRpcM89cNtt8M03Sx5faSU47LAQCNeSFNb+wpIkSZJygcGwJElKrziGMWPC6uDHHoN585Y8Z5ttQhh8wAHQuHH6a1yG8sFwp06Zq0OSJEmSasJgWJIkpcfUqXD//XD77fDll0seb9IEDj00BMKbb57Ujy4pgXvvrbxl8Yr6+OPEa1cMS5IkScpWBsOSJCl1Fi6El1+GO++EESMq7x3cuXMIgw86KITDSRbHcMopcNNNyb1u48bQrl1yrylJkiRJ6WIwLEmSku+nn+Cuu+Duu2HChCWPN24cguDjj4ettkppKVdemfxQGKBHDygoSP51JUmSJCkdDIYlSVJyzJ0LTz4Jw4fDK69Ufs4228BRR4VQeKWVUl7SAw/AOeckxt27Q5cuNb9uq1Zw4IE1v44kSZIkZYrBsCRJqplPPw2tIh54AP76a8njrVrBYYeFQDiNTXlfeQWOPDIx7toVnn4a6tdPWwmSJEmSVGsZDEuSpBU3fXoIgu+8Ez77bMnjUQR77glHHw29e6c9jR07FvbdF+bPD+ONN4annjIUliRJkqQyBsOSJKlqSkrg1VdDGPzUUzBv3pLnrLNOWBk8YACstVb6ayS0NO7RA/7+O4xXXx1GjYLmzTNSjiRJkiTVSgbDkiRp2X78Ee67L2wm9/PPSx5v0AD69Qurg3feOS07sk2aBNddFxYuL+611+D338PrlVYKoXCGMmpJkiRJqrUMhiVJ0pJmzIDHHoN774W33qr8nM6dQxh80EFpXY7711+w667w5ZfLPq9u3bCwuVOntJQlSZIkSVnFYFiSJAULFsBLL4Uw+OmnYe7cJc9p2RIOPTS0i9hss7SXOG8e7LPP8kNhgOHDYZddUl6SJEmSJGUlg2FJkvLd2LEhDH7gAZg4ccnjhYVhI7kBA6BPn9A6IgNKSuCII+CNNxJzF1wAa6yx5LlbbAHbbJO20iRJkiQp6xgMS5KUjyZNggcfDIHwZ59Vfs7mm8Phh4dWEauums7qKnXOOfDww4nxFVfAWWdlrh5JkiRJymYGw5Ik5Yu5c+GZZ0IYPHo0LFy45DmrrgqHHBIC4VrUnPeGG+CqqxLjk0+Gf/4zc/VIkiRJUrYzGJYkKZfFMbzzDtxzDzz6aNhUbnENGoTGvYcfDrvvDnVq148HTz4Jp56aGO+zDwwdClGUsZIkSZIkKevVrr/5SZKk5PjmG3joodA3+IcfKj9np51CGNy/PzRrlt76qmjMmLCAOY7DePvtQweMwsLM1iVJkiRJ2c5gWJKkXPHrr6EJ74MPwqefVn7OuuuGMPiww8LrWuzbb8Ned3PnhvEGG4ROGA0bZrYuSZIkScoFBsOSJGWzadPg8cdDGPzmm4mlteU1awb77w8DBsAOO2RFD4aJE6F79/DlAbRpE9oir7xyZuuSJEmSpFxhMCxJUraZNQuefTaEwaNHw/z5S55Trx7stRccfDD07JlVy2yLiqBXLxg/PowbNYLnnqv1C5wlSZIkKasYDEuSlA3mz4eXXgph8NNPh3B4cQUFsMsuIQzu2xeaN093lTU2f35Y3PzJJ2FcWAiPPQZbbZXZuiRJkiQp1xgMS5JUW5WUwDvvhDD40Udh6tTKz9t2WzjooJCorrZaemtMojiGE04Ii6DL3HxzWPAsSZIkSUoug2FJkmqTOIb//S9sIvfQQ/DLL5Wf16EDHHIIHHggrL9+emtMkYsuguHDE+MLLoBjj81cPZIkSZKUywyGJUnKtLIw+LHHwsrg77+v/Lw11wwrgw8+GDbbLCs2kVvcHXeEBdALFlScX7AA3n03MT7iiBAUS5IkSZJSw2BYkqRMiGMYOzYRBo8bV/l5LVtC//4hDN5xx9BHOEvdcUfVVgDvsQfcdltW5t6SJEmSlDUMhiVJSpfyYfBjj8F331V+XtOm0Lt3CIN33x3q1UtvnSnw/POhf/DybL01PP441K2b+pokSZIkKZ8ZDEuSlEpxDJ9/nlgZvLQwuEkT2HvvsDp4zz2hQYP01plCH30UvqyFC8N4iy3guuuWXBFcr144Vr9++muUJEmSpHxjMCxJUrLFMXzxRQiCH3sMvv228vOaNIE+fRJhcMOG6a0zDX78EXr1gtmzw7htW3juOVhttczWJUmSJEn5zmBYkqRkKAuDy1YGLysM7t0b9t8/Z8PgMlOmQPfuMHlyGLdoAaNHGwpLkiRJUm1gMCxJUnWVlMB778FTT4XHDz9Ufl7jxomVwd2753QYXGb27JB/l+2pV78+PPMMdOiQ2bokSZIkSYHBsCRJK6K4GF5/PQTBTz8NEydWfl7jxiEZ7d8fevTIizC4zMKFcMghITOH0Ev4gQdgxx0zW5ckSZIkKcFgWJKk5Zk1K/RAeOopGDkSZsyo/LwmTUJD3f33DyuDGzVKb521QBzDoEEhMy8zZAj065epiiRJkiRJlTEYliSpMtOmwbPPhjD4hRdg7tzKz2vdOrSJ2Hdf2HXX0DMhj111Fdx0U2J8xhkhKJYkSZIk1S4Gw5Iklfn117DU9amn4I03Qk+EyrRtC337hkeXLlBYmNYya6sHH4Szz06MDzgArrwyc/VIkiRJkpbOYFiSlL/iGL76KuyK9tRT8OGHSz93443DquC+fWHzzUPjXC3y6qtwxBGJ8c47wz33QEFBxkqSJEmSJC2DwbAkKb8UF8Obb4Y2Ec8+Cz/9tPRzt9susTJ4gw3SV2OW+fzz8J9o/vww3njjsPA6z7tqSJIkSVKtZjAsScp9U6bA88+HIPiFF6CoqPLz6tSBbt1Cyrn33rD66umtMwtNmAA9esDff4fx6quH/9TNm2e0LEmSJEnSchgMS5JyT1mLiLJVwe++G+Yq07Qp7Lln2EBur72gRYv01lqLfPEFHH44/PJL1d8zezbMmRNeN20aQuG1105NfZIkSZKk5DEYliTlhuLisGHcs8/CyJHLbhGxzjrQu3cIgnfeGerVS1+dtdSECSEf//336r2/Tp3QpnmzzZJblyRJkiQpNQyGJUnZ688/wxLVkSOX3SIiimD77UMY3Ls3bLSRm8eV89dfoR1EdUPhBg3grrtg112TWpYkSZIkKYUMhiVJ2aOkBD76CEaPDo/33lt+i4jevUPq2bp1emvNEvPmwT77wJdfhnHdumHjuG22qfo1mjZ1ozlJkiRJyjYGw5Kk2m3y5LAaePRoePHFsJHc0tgiYoWUlMCAAaEDR5m77oKePTNXkyRJkiQpPQyGJUm1y4IF8P77IQgeNQo+/njp59oiokbOPhseeSQx/u9/4ZBDMlePJEmSJCl9DIYlSZn3+++J9hAvvRSa3i5NmzbQvXt47L47rLxy2srMJddfD1dfnRifdBKcdVbm6pEkSZIkpZfBsCQp/YqL4Z13EquCx45d+rmFhWFVcI8eIQzefHMoKEhbqbnoiSfgtNMS4733DkGxi60lSZIkKX8YDEuSUi+O4bvv4OWXw4rgV1+FoqKln7/GGiEE7tEDdt0VmjdPW6m5bsyY0C6ibM++7baDBx8M+bskSZIkKX8YDEuSUmPiRHjllRAGv/wy/Prr0s+tWxd22ikRBm+8sctXU+Cbb6BPH5g3L4w32ACefRYaNcpsXZIkSZKk9DMYliQlR1ERvPFGCIFfeQW++GLZ57drl2gP0a0bNG2aljLz1cSJ4T/3tGlh3KZN6OJhi2ZJkiRJyk8Gw5Kk6pk/H95/P7Ei+P33YcGCpZ+/0kohAN5tt/DYcENXBadJURH06gXjx4dxo0YwciSst15Gy5IkSZIkZZDBsCSpauIYvvwyEQS/8QbMnLn08+vWhR12SATBW20Fdfy2k27z50P//vDJJ2FcWAiPPgpbb53ZuiRJkiRJmeXf0CVJlYtj+PbbEAC//np4TJy47PdsvnkiCN5xR2jcOA2FamniGI4/Hl54ITF3881h9bAkSZIkKb8ZDEuSgjgOu5OVhcBvvAGTJi37PW3bwu67hyB4l12gdet0VKoquugiuOuuxPiCC+DYYzNXjyRJkiSp9jAYlqR8Fcfw1VeJEPiNN2Dy5GW/p0UL2HXXxKrgdde1T3AtdccdIRguc8QRFceSJEmSpPxmMCxJ+aKkJBEEv/46vPkm/Pnnst/TvDnsvHPisdlmoUmtarXnn4cTTkiM99gDbrvNDF+SJEmSlGAwLEm5auFC+PxzeOutxKrgqVOX/Z4WLUIA3LVreN50U4PgLPPRR2GzuYULw3jzzeHxx8NegJIkSZIklTEYlqRcMXMmvP8+jBkTHu++C0VFy35Pq1aJ1cBdu8Imm0BBQVrKVfL9+GPYWG727DBu2zasHm7aNLN1SZIkSZJqH4NhScpWv/0WAuC33w7P//tfYpno0qy8csUVwRtvbBCcI6ZMge7dE22iW7SAUaNgtdUyW5ckSZIkqXYyGJakbLBwIY1/+IFmn38Ot98eguCff17++1ZfHbp0SYTBG21ko9kV8Ntv8Ndfma5i+UpK4PjjYdy4MK5fH555Bjp2zGxdkiRJkqTay2BYkmqjWbOWaAux9d9/L/s9URRaQXTpkni0a2cQXE2XXAL/+lemq1hxUQT33w877pjpSiRJkiRJtZnBsCRl2sKF8M03IQgue3zxxfLbQjRsCNtumwiBt98emjdPS8m57tZbszMUBrjuOthvv0xXIUmSJEmq7QyGJSnd/vijYgj80UfL3yQOmNeyJX9vsgmt99knLAfdfHOoWzfl5eabkSPhpJMS49VXz468vW5dOOwwOPXUTFciSZIkScoGBsOSlEqzZsHHH4cA+IMPwvOECct/XxSFfsBduoQQuEsX3v35Z4giunbtmvKy89UHH8ABB4SevQCdO8Prr0OTJhktS5IkSZKkpDMYlqRkWbgQvv46EQBXtSUEwKqrhrYQ22wTnrfaCpo1q3jOL7+kpm4B8P33sNdeMHt2GK+zDjz3nKGwJEmSJCk3GQxLUnUsWABffQWffBJWBH/yCXz2WSJVXJaGDcNS1G23TTzWWstN4jLozz+hR4/wDNCqFYweDausktm6JEmSJElKFYNhSVqe4uKw8rd8CDx2LMydu/z3RhF07FgxBN5kE6iTv3/8fv89/PprpqtIiGM455xQF0CDBvDMM9C+fWbrkiRJkiQplfI3mZCkysydC59/ngiAP/44jOfPr9r7V1sttIMoawmx9daw0kqprTmL3HJL2NgtjjNdSeWiCB58EHbYIdOVSJIkSZKUWgbDkvLXtGkh9B07Fj79NATBX34Z2kRUxVprhZYQW24ZnrfYIgTDqtSIEXDyybU3FAa44Qbo2zfTVUiSJEmSlHoGw5Jy3/z58N13IQAu/1iRfgbrrJMIgLfcMjxat05dzTnm3XfhwAOhpCSM27aFdu0yWlIFhYXQr19YzSxJkiRJUj4wGJaUWyZPrhj+/u9/YZO44uKqX2ODDSqGwFtsAS1bpq7mHPfdd9C7d6Il83rrwTvvQJs2ma1LkiRJkqR8ZjAsKTvNmQPffJNoBVH2mDSp6teoVw823hg6dQqPzp1h882hWbOUlZ1vJk+GHj1g6tQwXnllGD3aUFiSJEmSpEwzGJZUu/39dwiAv/oqPL7+Ojz/9NOKNatda61EAFz2aN8e6vjHYKrMmgV77QU//hjGDRvCyJGw/vqZrUuSJEmSJBkMS6otpk5NhL7lA+AV6QMM0KgR769zIBNW3To0sm3bFtZeG5o0qXjeV6WPLPLll6Gn8ZQpGS6kioYPhw8/DK8LCuDhh2HbbTNbkyRJkiRJCgyGJaVPSQn8/ntoOls+/P3qq9BzYEUUFIRmtRtvDJtttmgV8OWPrMt55xfAl6n5EjJr40wXUG3DhkGfPpmuQpIkSZIklTEYlpRccRxC3nHjQgA8blzFx5w5K3a9unVDy4eNNoKOHcPzRhuFDeIaNKhw6t13w3nnJ+9LUXL83//BCSdkugpJkiRJklSewbCk6pk2rfLw97vvoKhoxa/XoEEi+C0fAK+7bgiHl+PFF+HYYxPjTTaBDTdc8TJqsz///BOA1q1bZ7iSqoki6NIFTj0105VIkiRJkqTFGQxLqlxZ24effko8fvghEQRPm1a967ZsGVb7lg9/O3YMvYALC6t1yU8/hX79YMGCMO7UCd56C1ZaqXol1lavvx76Y3Tt2jWzhUiSJEmSpKxnMCzlqzgOu5iVD35/+gnGjw/PP/8MxcXVu3bTpqH9wwYbJB5l45Ytk/pljB8PPXvCzJlhvNZa8PzzuRcKS5IkSZIkJZPBsJSr4himT4cJEyoGvuUfs2ZV//oNG1YMfsuHv23ahD4CKTZtGvToARMnhnHz5jBqFKyxRso/WpIkSZIkKasZDEvZKI7hr79C6DthAvz665LPv/4Ks2fX7HNWXhnWWafioyz8XX11KChY4Uv+/ntY0Tt/fs1KA7j/fvjmm/C6Xj14+mnYeOOaX1eSJEmSJCnXGQxLtU1JSVgK+8cfSw99J0yoeegL0KTJksFv2aNdu9ASIol++gl22CGxwjeZ7r0Xdt45+deVJEmSJEnKRQbDUrrMmhUS0eU9Jk1KznJagMaNQ9Pdtm0rD39btkxLyweAqVMrtn1IpmuugQMOSP51JUmSJEmSclXSguEoitYELga6A62AP4CngYviOJ6+AtdpCfwL2AdYDZgKjAb+Fcfxr8mqV6qxhQtDD98pUxKPqVNDsFtZ4FtUlNzPLwt911xz6c/NmqUt+F2WOXOgTx/49tswrlcPBgyAwsKaXTeKoEsXOPjgmtcoSZIkSZKUT5ISDEdRtB7wDtAGGAF8A2wDnAp0j6KoSxzHU6twnVal12kPvAo8DHQAjgR6RVG0fRzHPyajZqmCspB36tQlg96ljadPD71+U6FZM1h11aWHvmutVWtC3+VZuBAOPRTeeScxd999sP/+matJkiRJkiQp3yVrxfBNhFB4UBzHN5RNRlF0LTAYuAw4oQrXuZwQCl8bx/EZ5a4zCBha+jndk1SzckUch367f/0FM2aEx4q+/vvv1NdZr14Ie8seq61WcVz2WGUVaNgw9fWkQRzD4MHw5JOJuWuvNRSWJEmSJEnKtBoHw6WrhfcAxgPDFjt8IXAccFgURWfEcTxrGddpAhwGzAL+vdjhG4HTgT2jKFrXVcNZZuFCKC6GefMSz3PmhJ67NX3MnBmC3YULM/O1tWgBK68cHq1ahefWrSsPfZs3z4oVvsl0zTVwww2J8WmnhaBYkiRJkiRJmZWMFcPdSp9fjOO4pPyBOI6LoigaQwiOtwNeWcZ1tgMall6nQjPWOI5Loih6gRAydwMMhqtgwnu/MeL06RDDm81eDcs3F3+UlFQ+H1cyXxKHAHbhQliwYDmvS58XLAzXqpb6pY+WSfyvsgwNGkCjxtCoUemj4bLHDRtAwVKa5BaVPsalp/TaaPp0GDIkMe7fPwTFkiRJkiRJyrxkBMMblj5/t5Tj4wjBcHuWHQxX5TqUXmeZoij6eCmHOhQVFfH6668v7xI5YfyIPxnyaf9Ml5E95pY+pmW6kNzTqdNfHHPMWN58s7r/SCCAotINDPPlzzApV3kvS7nD+1nKDd7LUu7Ix/u57GuujoIkfH6z0ucZSzleNt88TddRqTjP2haodmrbdhaXXPIF9eoZCkuSJEmSJNUWydp8rlaJ47hzZfNRFH3ctGnTLbt27ZrmijJj3Qa/c8rLT0MEzZu3CP1tCwrCc4UHEFU2H0HB4uNCKCyEOnXCc2Eh1Cl9Liw/V+512Wcq7zRpAkce2ZjWrXfMdCk5oexfPPPlzzApV3kvS7nD+1nKDd7LUu7Ix/u5adOm1X5vMoLhspW8zZZyvGz+rzRdR6XW3m519r2+OQBdu+6c2WIkSZIkSZIk1RrJaCXxbenz0nr/blD6vLTewcm+jiRJkiRJkiRpGZIRDL9W+rxHFEUVrhdFUVOgCzAbeG8513kPmAN0KX1f+esUEDawK/95kiRJkiRJkqRqqHEwHMfxD8CLQDvg5MUOXwQ0Bu6L43hW2WQURR2iKOqw2HVmAveVnv/vxa4zsPT6L8Rx/GNNa5YkSZIkSZKkfJaszedOAt4Bro+iaFfga2BboBuh9cN5i53/denz4juSnQt0BU6Pomhz4AOgI7A3MJklg2dJkiRJkiRJ0gpKRiuJslXDWwF3EwLhM4D1gKHAdnEcT63idaYC2wPXA+uXXmdb4C6gc+nnSJIkSZIkSZJqIFkrhonjeAJwZBXPXXylcPlj04BTSx+SJEmSJEmSpCRLyophSZIkSZIkSVL2MBiWJEmSJEmSpDxjMCxJkiRJkiRJecZgWJIkSZIkSZLyjMGwJEmSJEmSJOUZg2FJkiRJkiRJyjMGw5IkSZIkSZKUZwyGJUmSJEmSJCnPGAxLkiRJkiRJUp4xGJYkSZIkSZKkPGMwLEmSJEmSJEl5xmBYkiRJkiRJkvKMwbAkSZIkSZIk5RmDYUmSJEmSJEnKMwbDkiRJkiRJkpRnDIYlSZIkSZIkKc8YDEuSJEmSJElSnjEYliRJkiRJkqQ8YzAsSZIkSZIkSXnGYFiSJEmSJEmS8ozBsCRJkiRJkiTlGYNhSZIkSZIkScozBsOSJEmSJEmSlGcMhiVJkiRJkiQpzxgMS5IkSZIkSVKeieI4znQNaRNF0dSGDRu27NixY6ZLSZuioiIAmjZtmuFKJNWU97OUG7yXpdzh/SzlBu9lKXfk4/389ddfM2fOnGlxHLda0ffmWzD8E7ASMD7DpaRTh9LnbzJahaRk8H6WcoP3spQ7vJ+l3OC9LOWOfLyf2wF/x3G8zoq+Ma+C4XwURdHHAHEcd850LZJqxvtZyg3ey1Lu8H6WcoP3spQ7vJ9XjD2GJUmSJEmSJCnPGAxLkiRJkiRJUp4xGJYkSZIkSZKkPGMwLEmSJEmSJEl5xmBYkiRJkiRJkvJMFMdxpmuQJEmSJEmSJKWRK4YlSZIkSZIkKc8YDEuSJEmSJElSnjEYliRJkiRJkqQ8YzAsSZIkSZIkSXnGYFiSJEmSJEmS8ozBsCRJkiRJkiTlGYNhSZIkSZIkScozBsNZKIqiNaMoGh5F0e9RFM2Lomh8FEVDoihqsYLXaVn6vvGl1/m99Lprpqp2SQk1vZejKGocRdEhURQ9GEXRN1EUzYqiqCiKoo+iKDojiqJ6qf4aJAXJ+t682DX/EUXRwiiK4iiKLk1mvZIql8x7OYqiLUu/R/9aeq1JURS9EUXR4amoXVJFSfx7845RFI0off/cKIp+iaLo+SiKuqeqdklBFEX7RVF0QxRFb0VR9Hfpz8X3V/NaSf95PRdEcRxnugatgCiK1gPeAdoAI4BvgG2AbsC3QJc4jqdW4TqtSq/THngV+BDoAOwNTAa2j+P4x1R8DZKScy+X/jA6CpgGvAZ8D7QA+gCrll5/1ziO56boy5BE8r43L3bNpsBYYGWgCXBZHMfnJ7NuSRUl816OomggMBSYDjwH/Aa0BDYBfo3j+MCkfwGSFkni35tPBG4CZgFPAb8CawL7Ao2A8+M4viwVX4MkiKLoM2AzYCbh/usAPBDH8aEreJ2k/7yeKwyGs0wURS8AewCD4ji+odz8tcBg4NY4jk+ownVuBY4Dro3j+Ixy84MIP8S+EMex/wIqpUgy7uUoijYHNgYei+O4uNx8U+B1YEvgzDiOr0n6FyBpkWR9b17smsOBfYCrgcswGJZSLok/Z+8BjAZeAvaL47hoseN14zien9TiJVWQpJ+16wJ/AvWBzeM4/rbcsY7Ap0AJ0CKO43nJ/yokRVHUjRAIfw/sTFgQVZ1gOOk/r+cKg+EsUvovHN8D44H14jguKXesKfAHEAFt4jietYzrNCGsCi4BViv/w2oURQXAj0Db0s9w1bCUZMm6l5fzGQcDDwAj4zjuXeOiJVUqFfdzFEV7A08DhwF1gLswGJZSKpn3chRF/wPWB9bO19VHUiYl8e/NqwATgbFxHG9WyfGxwKbAyt7rUupFUdSVagTD6fj7dzazx3B26Vb6/GL5/5EBSsPdMYRfZ9luOdfZDmgIjFl8BUPpdV9Y7PMkJVey7uVlKVuJtKAG15C0fEm9n6MoagPcDjwdx3G1+qdJqpak3MtRFG0CdAJeBKZFUdQtiqIzS3v/71q6CENSaiXre/Nkworh9lEUbVD+QBRF7YENgM8MhaVaLx1//85a/mCSXTYsff5uKcfHlT63T9N1JFVPOu7Bo0qfR9fgGpKWL9n38+2En8/y8lfZpAxK1r28denzZEJbp1eBqwhtYV4GPouiaP3qlympCpJyP8fh16tPJnxf/jiKonuiKPpPFEX3Ah8DXwL9k1CvpNQyA1uGOpkuQCukWenzjKUcL5tvnqbrSKqelN6DpRvedAc+A4ZX5xqSqixp93MURUcRNo88II7jSTUvTdIKSNa93Kb0+WjChnO9gLeBVYB/AYcCz0VRtGn5/QEkJVXSvjfHcfxYFEW/Aw8Bh5c7NInQ6snWi1LtZwa2DK4YlqQcEkXRvsAQQj+0fm5uI2WHKIraEe7dx+I4fjSz1UiqgbK/XxUCB8Zx/Hwcx3/HcTyOECp9RFiR1C9TBUqquiiKDiWs9n8L6Ej4dfOOwCvAjcDDmatOkmrOYDi7lP0rRrOlHC+b/ytN15FUPSm5B6Mo2ofww+lkoKubR0ppkaz7eTgwBzgpCTVJWnHJupfLjk+M4/jd8gdKfy19ROlwmxWsT1LVJeV+Lu0jPJzQMuKwOI6/ieN4ThzH3xA2iP0Y6F+6IZak2ssMbBkMhrPLt6XPS+t7UtYQf2l9U5J9HUnVk/R7MIqi/sBjhF9r2zmO42+X8xZJyZGs+3lLwq+g/xlFUVz2IPyaKsB5pXNP16haSUuT7J+z/1rK8emlzw2rVpakakjW/bwHUBd4o5INq0qAN0uHnatTpKS0MQNbBnsMZ5fXSp/3iKKooPw3pyiKmgJdgNnAe8u5znuEVUldoihqWroLY9l1CgjfAMt/nqTkSta9XPaeQ4B7CL0Mu7lSWEqrZN3P9xJ+PXVxGwD/IPQM/xj4tKYFS6pUMn/OngW0i6KocRzHsxY7vknp809JqFlS5ZJ1P9cvfW69lONl8/YLl2q3pP79O9e4YjiLxHH8A/Ai0I6wO2p5FwGNgfvK/wAaRVGHKIo6LHadmcB9pef/e7HrDCy9/guGS1JqJOteLp0fQAiUfgH+4X0rpVcSvzcPiuP4mMUfJFYMP1c6NyxlX4yUx5J4L88G7gQaAJdGURSVO39T4AhgAfB48r8KSZDUn7XfKn3eL4qiTuUPRFG0ObAfEAOvJq14SdUWRVHd0nt5vfLz1fkzIZ9EodWVskXp/+DvEH7ddATwNbAt0I2w7H2HOI6nljs/BojjOFrsOq1Kr9Oe8I3sA0IT/b0J/Ul3KL15JKVAMu7lKIq6ETbDKCD0P5tQyUf9FcfxkNR8FZIged+bl3LtIwjh8GVxHJ+f9OIlLZLEn7NXAt4ANgfeB8YAqwD7ElpInBbH8dAUfzlSXkvi/TwcOJKwKvgp4GdCuLQPUA8YEsfx4NR+NVL+Kt1HZ5/S4arAnsCPJP7hZkocx2eWntuO8Bs5P8dx3G6x66zQnwn5xGA4C0VRtBZwMdAdaAX8QfgmdVEcx9MXO3epf/mMoqglcCHhJlsNmAqMAv4Vx/GvKfwSJFHze7lcYLQsS3xTlJR8yfreXMl1j8BgWEqbJP6c3QT+v707dr2yjuI4/jkRNEQILbVUk2OoQUHRJrhKgwgujW7uDmLgIIRDa0RTg7mIY9jkUFCBughO2t/gIFLBcXgu9VMzhB57jPN6jd9nOc9wL9w3X87N6STHkryTZY3bz0kudPfV5/kOwGKNz/Pu1v+nWW77H0jyWpJ7WVY7fdXd3z7ft4DZquqzLN3qaf78vftPYXj3/Jm/EyYRhgEAAAAAhrFjGAAAAABgGGEYAAAAAGAYYRgAAAAAYBhhGAAAAABgGGEYAAAAAGAYYRgAAAAAYBhhGAAAAABgGGEYAAAAAGAYYRgAAAAAYBhhGAAAAABgGGEYAAAAAGAYYRgAAAAAYBhhGAAAAABgGGEYAAAAAGAYYRgAAAAAYBhhGAAAVlBVV6qqq+rU3zw7t3v29RazAQDA46q7t54BAAD+96rq9SQ3kryR5MPuvrE7P5zkapLbSd7v7vvbTQkAAAthGAAAVlJVHyW5luRukveSvJrkZpJ9WaLwre2mAwCAv1glAQAAK+nuH5OcSbI/yZdJvknyZpJTojAAAC8SN4YBAGBFVVVJvktyZHd0sbtPbDgSAAA8wY1hAABYUS83Ly7vOfpio1EAAOCp3BgGAIAVVdX+JNeT/J5lt/CtJB9094NNBwMAgD3cGAYAgJVU1StJLmX507njSc4neTduDQMA8IIRhgEAYD0XkhxK8nl3f5/kbJIfkpysqmObTgYAAHtYJQEAACuoqk+y7Bb+KcnH3f3H7vytJDeTvJzkUHff2WxIAADYEYYBAOBfqqq3s8Tfl5Ic7O5fH3t+NMmVJL9kica//ccjAgDAI4RhAAAAAIBh7BgGAAAAABhGGAYAAAAAGEYYBgAAAAAYRhgGAAAAABhGGAYAAAAAGEYYBgAAAAAYRhgGAAAAABhGGAYAAAAAGEYYBgAAAAAYRhgGAAAAABhGGAYAAAAAGEYYBgAAAAAYRhgGAAAAABhGGAYAAAAAGEYYBgAAAAAYRhgGAAAAABhGGAYAAAAAGOYh8w/561iIuIkAAAAASUVORK5CYII=",
|
|
"text/plain": [
|
|
"<Figure size 864x504 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 4,
|
|
"metadata": {
|
|
"image/png": {
|
|
"height": 441,
|
|
"width": 707
|
|
},
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"import numpy as np\n",
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"\n",
|
|
"# Definiujemy dystrybuantę pseudoodwrotną\n",
|
|
"def F_pseudoinverse(u):\n",
|
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" x = [i**(1/2) for i in u]\n",
|
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" return x\n",
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"\n",
|
|
"# Generujemy 100 liczb o rozkładzie zgodnym z rozkładem zmiennej losowej X, używając dystrybuanty pseudoodwrotnej\n",
|
|
"u = stats.uniform.rvs(size=100)\n",
|
|
"probki = F_pseudoinverse(u)\n",
|
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"\n",
|
|
"# Wyznaczamy dystrybuantę empiryczną na podstawie wygenerowanej próbki\n",
|
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"F_empirical = stats.ecdf(probki)\n",
|
|
"\n",
|
|
"# Narysujemy wykresy dystrybuanty zmiennej losowej i dystrybuanty empirycznej\n",
|
|
"x = np.linspace(0, 1, 200)\n",
|
|
"y1 = [i**2 for i in x]\n",
|
|
"y2 = F_empirical.cdf.evaluate(x)\n",
|
|
"\n",
|
|
"plt.plot(x, y1, label='dystrybuanta zmiennej losowej X', color='red')\n",
|
|
"plt.plot(x, y2, label='dystrybuanta empiryczna wygenerowanej próbki', color='blue')\n",
|
|
"plt.title('Porównanie dystrybuanty i dystrybuanty empirycznej')\n",
|
|
"plt.xlabel('x')\n",
|
|
"plt.legend()\n",
|
|
"plt.grid()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "ba7094",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"**Przykład 3**\n",
|
|
"\n",
|
|
"Załóżmy, że $X$ jest zmienną losową o następującym rozkładzie:\n",
|
|
"\n",
|
|
"\n",
|
|
"| $k$ | $0$ | $1$ |\n",
|
|
"| --- | --- | --- |\n",
|
|
"| $\\mathbb{P}(X=k)$ | $0{,}8$ | $0{,}2$ | \n",
|
|
"\n",
|
|
"Znajdź dystrybuantę i dystrybuantę pseudoodwrotną dla tej zmiennej losowej. Następnie wygeneruj próbkę $100$ liczb zgodnie z rozkładem zmiennej losowej $X$, używając metody odwracania dystrybuanty i porównaj rozkład otrzymanych liczb z rozkładem tej zmiennej losowej.\n",
|
|
"\n",
|
|
"Zacznijmy od wyznaczenia wzoru dystrybuanty:\n",
|
|
"\n",
|
|
"$$F(x)=\\begin{cases}\n",
|
|
"0, &\\text{ dla } x<0,\\\\\n",
|
|
"0{,}8, &\\text{ dla } 0\\leq x<1,\\\\\n",
|
|
"1, &\\text{ dla } 1\\leq x.\n",
|
|
"\\end{cases}$$\n",
|
|
"\n",
|
|
"Przejdziemy teraz do dystrybuanty pseudoodwrotnej. Spróbujemy najpierw wyznaczyć jej wartość w przykładowym punkcie $u=0{,}1$. Zgodnie z definicją dystrybuanty pseudoodwrotnej musimy znaleźć możliwie najmniejszą liczbę rzeczywistą $x$, dla której zachodzi nierówność $F(x)\\geq u$. Patrząc na wzór dystrybuanty, możemy łatwo zauważyć, że taką liczbą będzie $x=0$. Możemy też łatwo stwierdzić, że dystrybuanta pseudoodwrotna będzie przyjmować wartość $0$ dla wszystkich argumentów $0< u\\leq 0{,}8$. W podobny sposób możemy wyznaczyć pozostałą część wzoru na dystrybuantę pseudoodwrotną:\n",
|
|
"\n",
|
|
"$$F^-(u)=\\begin{cases}\n",
|
|
"0, &\\text{ dla } 0<u\\leq 0{,}8,\\\\\n",
|
|
"1, &\\text{ dla } 0{,}8<u\\leq 1.\n",
|
|
"\\end{cases}$$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 5,
|
|
"id": "63f4ab",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 864x504 with 1 Axes>"
|
|
]
|
|
},
|
|
"execution_count": 5,
|
|
"metadata": {
|
|
"image/png": {
|
|
"height": 441,
|
|
"width": 721
|
|
},
|
|
"needs_background": "light"
|
|
},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Definiujemy dystrybuantę zmiennej losowej X\n",
|
|
"def F(x):\n",
|
|
" n = len(x)\n",
|
|
" y = [0]*n\n",
|
|
" for i in range(n):\n",
|
|
" if x[i] < 0:\n",
|
|
" y[i] = 0\n",
|
|
" elif x[i] < 1:\n",
|
|
" y[i] = 0.8\n",
|
|
" else:\n",
|
|
" y[i] = 1\n",
|
|
" return y\n",
|
|
"\n",
|
|
"# Definiujemy dystrybuantę pseudoodwrotną zmiennej losowej X\n",
|
|
"def F_inv(u):\n",
|
|
" n = len(u)\n",
|
|
" y = [0]*n\n",
|
|
" for i in range(n):\n",
|
|
" if u[i] < 0.8:\n",
|
|
" y[i] = 0\n",
|
|
" else:\n",
|
|
" y[i] = 1\n",
|
|
" return y\n",
|
|
"\n",
|
|
"# Generujemy próbkę 100 liczb używając metody odwracania dystrybuanty\n",
|
|
"u = stats.uniform.rvs(size=100)\n",
|
|
"probki = F_inv(u)\n",
|
|
"\n",
|
|
"# Aby porównać rozkład zmiennej losowej X z rozkładem wylosowanych liczb możemy porównać funkcję masy prawdopodobieństwa zmiennej losowej X z częstotliwością wylosowanych liczb\n",
|
|
"atomy = [0, 1]\n",
|
|
"pr = [0.8, 0.2]\n",
|
|
"\n",
|
|
"jedynki = np.count_nonzero(probki)\n",
|
|
"zera = 100 - jedynki\n",
|
|
"czestotliwosc = [zera/100, jedynki/100]\n",
|
|
"\n",
|
|
"plt.bar(atomy, pr,label='Funkcja masy prawdopodobieństwa zmiennej losowej X', width=0.3, color='blue', align='center')\n",
|
|
"plt.bar(atomy, czestotliwosc, label='Częstotliwość liczb w próbce', width=0.3, color='red', align='edge')\n",
|
|
"plt.legend()\n",
|
|
"plt.xlabel('Atomy')\n",
|
|
"plt.ylabel('Prawdopodobieństwa / częstotliwości')\n",
|
|
"plt.title('Porównanie funkcji masy prawdopodobieństwa X i częstotliwości liczb w próbce')\n",
|
|
"plt.grid()\n",
|
|
"plt.show()"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "90ade4",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"Ogólnie, w przypadku zmiennej losowej dyskretnej o rozkładzie $\\mathbb{P}(X=x_i)=p_i$ dla $i=1,2,\\ldots,n$ dystrybuantę pseudoodwrotną możemy przedstawić graficznie w następujący sposób:\n",
|
|
"\n",
|
|
"\n",
|
|
"\n",
|
|
"Zatem jeśli chcemy znaleźć wartość $F^-(u)$, możemy podzielić przedział $(0,1)$ na mniejsze przedziały, których długości są równe kolejnym wartościom $p_i$ i które odpowiadają kolejnym atomom $x_i$. Następnie wystarczy sprawdzić, do którego z przedziałów należy $u$."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "3f5655",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"source": [
|
|
"## Dyskretne zmienne losowe wielowymiarowe\n",
|
|
"\n",
|
|
"W celu badania dyskretnych zmiennych losowych wielowymiarowych w Pythonie, będziemy posługiwać się macierzami, czyli obiektami klasy `ndarray`. Sposób ich generowania został już omówiony na początku poprzedniego przewodnika *03LRAP*. Warto jednak znać klika innych przydatnych funkcji z biblioteki NumPy. \n",
|
|
"\n",
|
|
"* `A.sum(axis=k)` - jeśli *A* jest obiektem klasy `ndarray`, to ta funkcja zwróci sumy elementów tej macierzy. Opcjonalny argument `axis` pozwala sumować elementy z poszczególnych kolumn (jeśli $k=0$) lub wierszy (jeśli $k=1$);\n",
|
|
"* `numpy(A, weights=None)` - oblicza średnią wartość elementów z macierzy *A*. W opcjonalnym argumencie `weights` możemy podać wagi, aby wyznaczyć średnią ważoną. Wagi powinny być podane jako macierz liczb o tych samych wymiarach, co macierz *A*.\n",
|
|
"\n",
|
|
"**Przykład 4**\n",
|
|
"\n",
|
|
"Dany jest dyskretny wektor losowy $(X,Y)$ o rozkładzie podanym w poniższej tabeli:\n",
|
|
"\n",
|
|
"| $X$ \\ $Y$ | $1$ | $2$ | $3$ | $4$ |\n",
|
|
"| --- | --- | --- | --- | --- |\n",
|
|
"| $-2$ | $0{,}1$ | $0{,}2$ | $0$ | $0{,}1$ |\n",
|
|
"| $2$ | $0{,}3$ | $0$ | $0{,}2$ | $0{,}1$ |\n",
|
|
"\n",
|
|
"* Znajdź rozkład brzegowy zmiennej losowej $Y$.\n",
|
|
"* Oblicz $\\mathbb{E}Y$ oraz $Var(Y)$.\n",
|
|
"* Oblicz $\\mathbb{E}(\\sqrt{|XY|})$.\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 10,
|
|
"id": "4f9d77",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"Rozkład brzegowy zmiennej losowej Y:\n",
|
|
"P(Y=1)=0.4\n",
|
|
"P(Y=2)=0.2\n",
|
|
"P(Y=3)=0.2\n",
|
|
"P(Y=4)=0.2\n",
|
|
"EY=2.2\n",
|
|
"Var(Y)=1.3599999999999994\n",
|
|
"E(sqrt(|XY|))=2.021268798455112\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"# Definiujemy wektory atomów zmiennych losowych X i Y oraz tabelkę z prawdopodobieństwem łącznym\n",
|
|
"atomy_X = np.array([[-2], [2]])\n",
|
|
"atomy_Y = np.array([[1, 2, 3, 4]])\n",
|
|
"pr_laczne = np.array([[0.1, 0.2, 0, 0.1], [0.3, 0, 0.2, 0.1]]) # Zakładamy, że wiersze tej tabeli odpowiadają atomom zmiennej losowej X, a kolumny atomom zmiennej losowej Y\n",
|
|
"\n",
|
|
"# Szukamy rozkładu brzegowego zmiennej losowej Y\n",
|
|
"pr_Y = np.array([pr_laczne.sum(axis=0)])\n",
|
|
"print('Rozkład brzegowy zmiennej losowej Y:')\n",
|
|
"for k in range(4):\n",
|
|
" print('P(Y=', atomy_Y[0, k], ')=', pr_Y[0, k], sep=\"\")\n",
|
|
" \n",
|
|
"# Szukamy EY oraz Var(Y)\n",
|
|
"EY = np.average(atomy_Y, weights=pr_Y)\n",
|
|
"print('EY=', EY, sep=\"\")\n",
|
|
"EY2 = np.average(atomy_Y**2, weights=pr_Y)\n",
|
|
"VarY = EY2 - EY**2\n",
|
|
"print('Var(Y)=', VarY, sep=\"\")\n",
|
|
"\n",
|
|
"# Szukamy E(sqrt(|XY|)). Skorzystamy z ,,prawa leniwego statystyka''\n",
|
|
"XY = np.dot(abs(atomy_X)**(1/2), atomy_Y**(1/2)) # pomocnicza tabelka, która zawiera wszystkie iloczyny postaci (pierwiastek z |x_i|)*(pierwiastek z y_j), gdzie x_i, y_j to odpowiednio atomy zmiennych losowych X i Y\n",
|
|
"E = np.average(XY, weights=pr_laczne)\n",
|
|
"print('E(sqrt(|XY|))=', E, sep=\"\")"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 0,
|
|
"id": "a1029e",
|
|
"metadata": {
|
|
"collapsed": false
|
|
},
|
|
"outputs": [
|
|
],
|
|
"source": [
|
|
]
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"argv": [
|
|
"/usr/bin/python3",
|
|
"-m",
|
|
"ipykernel",
|
|
"--HistoryManager.enabled=False",
|
|
"--matplotlib=inline",
|
|
"-c",
|
|
"%config InlineBackend.figure_formats = set(['retina'])\nimport matplotlib; matplotlib.rcParams['figure.figsize'] = (12, 7)",
|
|
"-f",
|
|
"{connection_file}"
|
|
],
|
|
"display_name": "Python 3 (system-wide)",
|
|
"env": {
|
|
},
|
|
"language": "python",
|
|
"metadata": {
|
|
"cocalc": {
|
|
"description": "Python 3 programming language",
|
|
"priority": 100,
|
|
"url": "https://www.python.org/"
|
|
}
|
|
},
|
|
"name": "python3",
|
|
"resource_dir": "/ext/jupyter/kernels/python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 3
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython3",
|
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"version": "3.10.12"
|
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|
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|
|
"nbformat": 4,
|
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"nbformat_minor": 4
|
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} |