{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [], "collapsed_sections": [ "ilL2mEM9TRzv" ] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "source": [ "# Objetivo y código preeliminar" ], "metadata": { "id": "HYOb5gt8LEn8" } }, { "cell_type": "code", "source": [ "#Importamos las librerias necesarias.\n", "import pandas as pd\n", "import numpy as np\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.ensemble import GradientBoostingRegressor\n", "import statsmodels.formula.api as smf\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "from toolz import curry" ], "metadata": { "id": "nN8ompJL0E2N" }, "execution_count": 1, "outputs": [] }, { "cell_type": "code", "execution_count": 2, "metadata": { "id": "m_pAksZczGzP" }, "outputs": [], "source": [ "#Cargamos los datos\n", "\n", "#Direccion del repositorio de github donde se encuentran los datos, en formato csv\n", "url = 'https://raw.githubusercontent.com/matheusfacure/python-causality-handbook/master/causal-inference-for-the-brave-and-true/data/ice_cream_sales_rnd.csv'\n", "prices_rnd = pd.read_csv(url)\n", "\n", "#### En caso ande mal lo del git\n", "# from google.colab import files\n", "# uploaded = files.upload()\n", "# df2 = pd.read_csv(io.BytesIO(uploaded['ice_cream_sales.csv']))\n", "####" ] }, { "cell_type": "code", "source": [ "prices_rnd.head()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 206 }, "id": "BjQ-SjKJ0Oeg", "outputId": "97317cf3-b3d7-4499-e1a9-03e201936fdb" }, "execution_count": 37, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " temp weekday cost price sales\n", "0 25.8 1 0.3 7 230\n", "1 22.7 3 0.5 4 190\n", "2 33.7 7 1.0 5 237\n", "3 23.0 4 0.5 5 193\n", "4 24.4 1 1.0 3 252" ], "text/html": [ "\n", "
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tempweekdaycostpricesales
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\n", " " ] }, "metadata": {}, "execution_count": 37 } ] }, { "cell_type": "markdown", "source": [ "## Objetivo\n", "\n", "Nuestra meta es agrupar a los días en función de cómo reaccionan al tratamiento, es decir cuándo cobrar más y cuándo cobrar menos, en función de las características específicas del día(dia de la semana, costo, temperatura)\n", "\n", "## Problema\n", "\n", "* X → cost, temp, weekday\n", "* Y → Ventas\n", "* T → price\n" ], "metadata": { "id": "xlVvxgGs4OWV" } }, { "cell_type": "code", "source": [ "#Dividimos el conjunto de datos en train y test.\n", "\n", "np.random.seed(123) #Fijamos la semilla.\n", "\n", "train, test = train_test_split(prices_rnd) #Dividimos.\n" ], "metadata": { "id": "zrzDO0TZ4QIE" }, "execution_count": 38, "outputs": [] }, { "cell_type": "markdown", "source": [ "# Estimando ATE" ], "metadata": { "id": "fkIFpROQ7wHc" } }, { "cell_type": "markdown", "source": [ "**Recordar el modelo tenia la siguiente forma:**\n", "\n", "\n", "$sales_i = β_0 + β_1price_i + \\beta_2X_i + e_i$\n" ], "metadata": { "id": "gpA31WRX8emI" } }, { "cell_type": "code", "source": [ "\n", "#C(weekday) lo que hace es crear una columna por cada dia de la semana, y pone 1 si pertenece y 0 si no.\n", "#Quedan 6 columnas porque el septimo se infiere de el valor de los otros (Ya que si son todos 0, es porque es el otro dia)\n", "m1 = smf.ols(\"sales ~ price + temp+C(weekday)+cost\", data=train).fit()\n", "m1.summary().tables[1]" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 254 }, "id": "XchCYjY78iCS", "outputId": "db886bc1-70be-448e-9084-90ab6075b4da" }, "execution_count": 39, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ], "text/html": [ "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 186.7113 1.770 105.499 0.000 183.241 190.181
C(weekday)[T.2] -25.0512 0.924 -27.114 0.000 -26.863 -23.240
C(weekday)[T.3] -24.5834 0.901 -27.282 0.000 -26.350 -22.817
C(weekday)[T.4] -24.3807 0.897 -27.195 0.000 -26.138 -22.623
C(weekday)[T.5] -24.9036 0.894 -27.850 0.000 -26.657 -23.150
C(weekday)[T.6] -24.0921 0.903 -26.693 0.000 -25.862 -22.323
C(weekday)[T.7] -0.8635 0.888 -0.972 0.331 -2.605 0.878
price -2.7515 0.106 -25.970 0.000 -2.959 -2.544
temp 1.9848 0.060 33.117 0.000 1.867 2.102
cost 4.4718 0.528 8.462 0.000 3.436 5.508
" ] }, "metadata": {}, "execution_count": 39 } ] }, { "cell_type": "markdown", "source": [ "Para el modelo este, la elasticidad es predecida es $\\widehat{\\frac{𝛿sales_i}{𝛿price_i}}$ = $\\hat{β_1}$ que en este va a ser -2.7515. Que esto quiere decir que por cada real que aumentemos se van a vender aproximadamente 3 unidades menos.\n", "Estamos estimando el Avarage Treatment Effect, es decir no es sensible al dia, por lo que si lo queremos es saber en qué días la gente es menos sensible a los precios de los helados, este no es un buen modelo.\n", "\n", "**Recordar**: Nuestro objetivo es particionar a los clientes de forma que podamos personalizar y optimizar nuestro tratamiento (precio) para cada partición individual. Si todas las predicciones son iguales, no podemos hacer ninguna partición" ], "metadata": { "id": "v4HG0nrSNts5" } }, { "cell_type": "markdown", "source": [ "# Estimando CATE" ], "metadata": { "id": "T6wWOPfF0B4l" } }, { "cell_type": "markdown", "source": [ "## Elasticidad en función de la temperatura\n", "\n", "Queremos investigar como varia la elasticidad para distintas temperaturas. Lo que estamos diciendo efectivamente aquí es que la gente es más o menos sensible a las subidas de precios dependiendo de la temperatura.\n", "\n", "**Planteemos el siguiente modelo**\n", "\n", "$sales_i = β_0 + β_1price_i + \\beta_2X_i + \\beta_3temp_iprice_i + e_i$\n" ], "metadata": { "id": "fv-Z-qpz0FGB" } }, { "cell_type": "code", "source": [ "m2 = smf.ols(\"sales ~ price*temp + C(weekday) + cost\", data=train).fit()\n", "m2.summary().tables[1]" ], "metadata": { "id": "0f-2YRedST2w", "colab": { "base_uri": "https://localhost:8080/", "height": 275 }, "outputId": "a75fb1fa-1a5a-42b9-e2d1-5eeb69f02714" }, "execution_count": 40, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "" ], "text/html": [ "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
Intercept 192.4767 4.371 44.037 0.000 183.907 201.046
C(weekday)[T.2] -25.0805 0.924 -27.143 0.000 -26.892 -23.269
C(weekday)[T.3] -24.5871 0.901 -27.290 0.000 -26.354 -22.821
C(weekday)[T.4] -24.4225 0.897 -27.231 0.000 -26.181 -22.664
C(weekday)[T.5] -24.8953 0.894 -27.844 0.000 -26.648 -23.142
C(weekday)[T.6] -24.1269 0.903 -26.726 0.000 -25.897 -22.357
C(weekday)[T.7] -0.8581 0.888 -0.966 0.334 -2.599 0.883
price -3.6299 0.618 -5.873 0.000 -4.842 -2.418
temp 1.7459 0.176 9.912 0.000 1.401 2.091
price:temp 0.0366 0.025 1.443 0.149 -0.013 0.086
cost 4.4558 0.529 8.431 0.000 3.420 5.492
" ] }, "metadata": {}, "execution_count": 40 } ] }, { "cell_type": "markdown", "source": [ " Una vez estimado el modelo, queda que la elasticidad predecidad es $\\widehat{\\frac{𝛿sales_i}{𝛿price_i}}$ = $\\hat{β_1} + \\hat{β_3}temp_i$, por lo que para estos datos nos queda $\\hat{β_3} = 0.0366$ y $\\hat{β_1} = -3.6299$. Esto significa que, en promedio, a medida que aumentamos el precio, las ventas bajan, lo que tiene sentido. También significa que, por cada grado adicional de temperatura, la gente es menos sensible a los aumentos de precio de los helados (aunque no mucho). Por ejemplo para $25°C$ por cada real mas que cobremos, nuestras ventas van a bajar por 2.7 unidades ($-3.6299+ (0.0366*25)$ pero si hay $35°C$, por cada real que agreguemos, las ventas van a bajar 2.3 unidades (-3.6 + (0.03*35). \n", "\n", "Es hasta intuitivo, como los días son cada vez más calurosos, la gente está dispuesta a pagar más por un helado.\n" ], "metadata": { "id": "BjF_gdld4r3E" } }, { "cell_type": "markdown", "source": [ "## Elasticidad en función de todos los párametros\n", "\n", "Queremos investigar como varia la elasticidad en función de todos los párametros.\n", "\n", "**Planteemos el siguiente modelo**\n", "\n", "$sales_i = β_0 + β_1price_i + \\beta_2X_i + \\beta_3X_iprice_i + e_i$\n" ], "metadata": { "id": "ylk_hTrA-Q6P" } }, { "cell_type": "code", "source": [ "m3 = smf.ols(\"sales ~ price*cost + price*C(weekday) + price*temp\", data=train).fit()" ], "metadata": { "id": "VBPkq4pUAmG7" }, "execution_count": 41, "outputs": [] }, { "cell_type": "markdown", "source": [ "Por último, veamos cómo hacer realmente esas predicciones de elasticidad. Una forma es extraer los parámetros de elasticidad del modelo y utilizar la fórmula anterior(Como hicimos antes). Sin embargo, recurriremos a una aproximación más general. Como la elasticidad no es más que la derivada del resultado sobre el tratamiento, podemos utilizar la definición de la derivada. \n", "\n", "$$\\frac{δy}{δt} = \\frac{y(t+ϵ) - y(t)}{(t+ϵ) - ϵ}, ~~ \\epsilon → 0$$\n", "\n", "Podemos aproximar esta definición sustituyendo $\\epsilon$ por 1.\n", "\n", "$$\\frac{δy}{δt} ≈ \\hat{y}(t+1) - \\hat{y}(t)$$\n", "\n", "donde $\\hat{y}$ viene dada por las predicciones de nuestro modelo. Es decir, hacemos dos predicciones con el modelo: una pasando los datos originales y otra pasando los datos originales pero con el tratamiento incrementado en una unidad. La diferencia entre esas predicciones es la predicción del CATE.\n", "\n", "*Nota: Esto lo hacemos ya que llegamos al CATE y queremos trabajar con el resultado*\n" ], "metadata": { "id": "iGmvtbxPDvSU" } }, { "cell_type": "code", "source": [ "#Funcion para predecir el CATE de cada individuo de un dataset(Utilizando el 3 modelo)\n", "def pred_elasticity(m, df, t=\"price\"):\n", " return df.assign(**{\n", " \"pred_elast\": m.predict(df.assign(**{t:df[t]+1})) - m.predict(df)\n", " })\n", "\n", "pred_elast = pred_elasticity(m3, test)\n", "\n", "np.random.seed(1)\n", "pred_elast.sample(5)" ], "metadata": { "id": "swOCHwyfA1kV", "colab": { "base_uri": "https://localhost:8080/", "height": 206 }, "outputId": "951d2339-f418-41af-f698-a01a836c8f09" }, "execution_count": 42, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " temp weekday cost price sales pred_elast\n", "4764 31.1 6 1.0 3 212 1.144309\n", "4324 24.8 7 0.5 10 182 -9.994303\n", "4536 25.0 2 1.5 6 205 0.279273\n", "3466 26.0 3 1.5 3 205 0.308320\n", "115 19.3 3 0.3 9 177 -0.349745" ], "text/html": [ "\n", "
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tempweekdaycostpricesalespred_elast
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\n", " " ] }, "metadata": {}, "execution_count": 42 } ] }, { "cell_type": "markdown", "source": [ "Observar en que las predicciones son números que van desde -10 hasta 1 (aprox). Estas **NO** son predicciones de la columna de ventas, que es del orden de las centenas. Más bien, es una predicción de cuánto cambiarían las ventas si aumentáramos el precio en una unidad.\n", "\n", "¿Hay resultados raros no? Por ejemplo el dia 4764 nos dice que si aumentamos el precio vamos a vender más, esto no tiene mucho sentido. Esto se trata de un error del modelo, que obvio puede pasar, el modelo es bastante sencillo. De todas formas recordar que nuestra meta es agrupar a los días en función de cómo reaccionan al cambio de precio. Por lo que para nuestro objetivo principal, basta con que las predicciones de elasticidad ordenen las unidades en función de su sensibilidad. En otras palabras, aunque las predicciones de elasticidad positiva como 1.1, o 0.5 no tengan mucho sentido, lo único que necesitamos es que el ordenamiento sea correcto. " ], "metadata": { "id": "XXpLGq-7JnhO" } }, { "cell_type": "code", "source": [ "pred_elast = pred_elast[pred_elast[\"pred_elast\"] < 0]\n", "pred_elast" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 424 }, "id": "kJ8uctCqbnMj", "outputId": "7e039c94-b7dc-49ee-bafc-219f10a46017" }, "execution_count": 43, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " temp weekday cost price sales pred_elast\n", "2648 18.6 7 0.5 10 185 -10.301045\n", "4557 23.7 3 0.3 8 192 -0.132057\n", "92 23.7 1 0.5 8 207 -9.953698\n", "31 21.5 1 1.0 6 243 -9.926465\n", "1880 25.5 5 0.5 5 190 -0.063437\n", "... ... ... ... ... ... ...\n", "3602 21.6 1 1.0 10 170 -9.921517\n", "1576 17.0 2 0.5 7 169 -0.388679\n", "1949 18.7 1 0.3 4 247 -10.255502\n", "4548 23.5 7 0.5 7 236 -10.058620\n", "2502 19.7 3 1.0 7 180 -0.139448\n", "\n", "[629 rows x 6 columns]" ], "text/html": [ "\n", "
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tempweekdaycostpricesalespred_elast
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}, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "source": [ "# Evaluando los Modelos Causales\n" ], "metadata": { "id": "fwxfvajulYC6" } }, { "cell_type": "markdown", "source": [ "**Warning!!**\n", "\n", "El autor del libro utilizo los datos random de los precios para todo lo anterior. Por lo tal vez es medio confuso, pero ahora vamos a utilizar los no random para entrenar y los random para validar." ], "metadata": { "id": "_rb8M-aUoFvs" } }, { "cell_type": "code", "source": [ "url = 'https://raw.githubusercontent.com/matheusfacure/python-causality-handbook/master/causal-inference-for-the-brave-and-true/data/ice_cream_sales.csv' #Cargo los datos normales\n", "prices = pd.read_csv(url) " ], "metadata": { "id": "7uz6qu5VnDI9" }, "execution_count": 12, "outputs": [] }, { "cell_type": "markdown", "source": [ "Para tener algo que comparar, vamos a entrenar dos modelos. El primero es con el que ya trabajamos:\n", "\n", "$$sales_i = β_0 + β_1price_i + \\beta_2X_i + \\beta_3X_iprice_i + e_i$$\n", "\n", "El segundo modelo será totalmente no paramétrico. Sera un algoritmo de aprendizaje automático de predicción:\n", "\n", "$$sales_i = G(X_i, price_i) + e_i$$\n", "\n", "\n", "El autor decidio utilizar Graadient Boost Regression. \n", "Recomiendo serie de videos de Youtube del canal StatQuest ([link](https://www.youtube.com/watch?v=3CC4N4z3GJc&t=1s))" ], "metadata": { "id": "NnB4n0yjo8gE" } }, { "cell_type": "code", "source": [ "#Modelo 1\n", "m1 = smf.ols(\"sales ~ price*cost + price*C(weekday) + price*temp\", data=prices).fit()\n", "\n", "#Modelo 2\n", "X = [\"temp\", \"weekday\", \"cost\", \"price\"] #Aca X va a ser las variables de antes y el precio\n", "y = \"sales\" \n", "m2 = GradientBoostingRegressor()\n", "m2.fit(prices[X], prices[y]);" ], "metadata": { "id": "xbfDKOBFpQB6" }, "execution_count": 13, "outputs": [] }, { "cell_type": "markdown", "source": [ "Para asegurarnos de que el modelo no está sobreajustado, podemos comprobarlo con los datos que hemos utilizado para entrenarlo y con los nuevos datos no vistos. Obvio que va a haber una baja en la performance porque la \"naturaleza\" de los datos es distinta, la del train son datos reales mientras que los otros son aleatorios.\n", "\n", "Recordar que para obtener la prediccion de la elasticidad usabamos la aproximacion numerica de la derivada:\n", "\n", "$$\\frac{δy(t)}{δt} ≈ \\frac{y(t+h) - y(t)}{h}$$" ], "metadata": { "id": "bMZ50ScRs0Pj" } }, { "cell_type": "code", "source": [ "print(\"Train Score:\", m2.score(prices[X], prices[y]))\n", "print(\"Test Score:\", m2.score(prices_rnd[X], prices_rnd[y]))" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "tbaQcVJKra7q", "outputId": "112d666c-e9ad-4c11-af21-5fc8ac3a43b0" }, "execution_count": 14, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Train Score: 0.9251704824568053\n", "Test Score: 0.7711031039505963\n" ] } ] }, { "cell_type": "markdown", "source": [ "Por ultimo creemos un tercer modelo, que en realid es para usar de referencia, este tercer modelo es un modelo \"random\" que la idea de este modelo es que devuelva numeros random como predicciones. Este modelo va a ser:\n", "$$ y_i \\sim Unif(0, 1) $$\n", "Evidentemente, no es muy útil, pero servirá de referencia. Pero si el modelo random tiene una buena performance es que probablemente el metodo de evaluacion este mal." ], "metadata": { "id": "D53dnFURwTHc" } }, { "cell_type": "code", "source": [ "def predict_elast(model, price_df, h=0.01):\n", " return (model.predict(price_df.assign(price=price_df[\"price\"]+h))\n", " - model.predict(price_df)) / h\n", "\n", "np.random.seed(123)\n", "prices_rnd_pred = prices_rnd.assign(**{\n", " \"elast_m_pred\": predict_elast(m1, prices_rnd), ## elasticity model\n", " \"pred_m_pred\": m2.predict(prices_rnd[X]), ## predictive model\n", " \"rand_m_pred\": np.random.uniform(size=prices_rnd.shape[0]), ## random model\n", "})\n", "\n", "prices_rnd_pred.head()" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 206 }, "id": "fhGvcFA7wp9H", "outputId": "6267d198-2319-4e36-ffa4-a73b9bf12c00" }, "execution_count": 15, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ " temp weekday cost price sales elast_m_pred pred_m_pred rand_m_pred\n", "0 25.8 1 0.3 7 230 -13.096964 224.067406 0.696469\n", "1 22.7 3 0.5 4 190 1.054695 189.889147 0.286139\n", "2 33.7 7 1.0 5 237 -17.362642 237.255157 0.226851\n", "3 23.0 4 0.5 5 193 0.564985 186.688619 0.551315\n", "4 24.4 1 1.0 3 252 -13.717946 250.342203 0.719469" ], "text/html": [ "\n", "
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\n", " " ] }, "metadata": {}, "execution_count": 15 } ] }, { "cell_type": "markdown", "source": [ "## La elasticidad por bandas\n", "\n", "Nuestro objetivo siempre fue segmentar en bandas la poblacion respecto a su sensibilidad al tratamiento. Dado que lo que predejimos fue la elasticidad podemos ordenar las unidades por esa predicción y esperar que también las ordene por la elasticidad real. Lamentablemente, no podemos evaluar esa ordenación a nivel de unidad. \n", "\n", "Lo que si podemos es estimar el ATE para un grupo de unidades. Recordar que el ATE para un tratamiento continuo es $E[y'(t)]$ y que podiamos estimarlo con el modelo lineal\n", "$$y_i = \\beta_0 + \\beta_1t_i + e_i$$ donde nos va aquedar que $y'(t) = \\beta_1$. Utilizando la teoria detras de los modelos lineales(No lo vamos a demostrar), tenemos que:\n", " $$\\hat{\\beta_1} = \\frac{∑(t_i - \\bar{t})(y_i - \\bar{y})}{\\sum(t_i - \\bar{t})^2}$$\n", " Utilizamos este resultado para calcular los ATE para cada banda que formemos." ], "metadata": { "id": "8MqN6rjqEZ9m" } }, { "cell_type": "code", "source": [ "#Funciones para hacer los calculos ...\n", "@curry\n", "def elast(data, y, t):\n", " # line coeficient for the one variable linear regression \n", " return (np.sum((data[t] - data[t].mean())*(data[y] - data[y].mean())) /\n", " np.sum((data[t] - data[t].mean())**2))\n", " \n", "def elast_by_band(df, pred, y, t, bands=10):\n", " return (df\n", " .assign(**{f\"{pred}_band\":pd.qcut(df[pred], q=bands)}) # makes quantile partitions\n", " .groupby(f\"{pred}_band\")\n", " .apply(elast(y=y, t=t))) # estimate the elasticity on each partition" ], "metadata": { "id": "YydrgiJG2OVZ" }, "execution_count": 16, "outputs": [] }, { "cell_type": "code", "source": [ "fig, axs = plt.subplots(1, 3, sharey=True, figsize=(10, 4))\n", "for m, ax in zip([\"elast_m_pred\", \"pred_m_pred\", \"rand_m_pred\"], axs):\n", " #No logre graficarlo pero el eje Y es el ATE dentro de cada grupo\n", " elast_by_band(prices_rnd_pred, m, \"sales\", \"price\").plot.bar(ax=ax) \n", " " ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 437 }, "id": "jOO9MUoh2guf", "outputId": "6475c00f-9153-4629-9164-d4b16340461e" }, "execution_count": 17, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "source": [ "\n", "\n", "\n", "1. Modelo Aleatorio: Tiene aproximadamente la misma elasticidad estimada en cada una de sus particiones. Con el grafico vemos que no nos ayudará mucho con la personalización, ya que no puede distinguir entre los días de alta y baja elasticidad del precio.\n", "2. Modelo predictivo. Consigue construir grupos donde la elasticidad es alta y otros donde la elasticidad es baja. Eso es exactamente lo que necesitamos.\n", "3. El modelo causal parece un poco raro. Identifica grupos de elasticidad realmente negativa, donde negativa significa en realidad alta sensibilidad al precio (las ventas disminuirán mucho cuando aumentemos los precios). Detectar esos días de alta sensibilidad al precio es muy útil para nosotros. Si sabemos cuándo son, tendremos cuidado de no seguir aumentando los precios en ese tipo de días. El modelo causal también identifica algunas regiones menos sensibles, por lo que puede distinguir con éxito las elasticidades positivas de las negativas. Pero el orden en el que aparece no es muy bueno, primero estan los de elasticidad negativa, despues aparecen los de elasticidad positiva y por ultimo los inelasticos.\n", "\n", "*RECAP: Lo que hicimos fue primero estimar la elasticidad de cada dia, ordenamos los dias segun su elasticida y creamos 10 grupos con la misma cantidad de dias. Luego para cada grupo calculamos su correspondiente ATE*\n", "\n", "Entonces, ¿qué debemos decidir? ¿Cuál es más útil? ¿El modelo predictivo o el causal? El modelo predictivo está mejor ordenado, pero el modelo causal puede identificar mejor los extremos\n" ], "metadata": { "id": "tSd69X4fAhpp" } }, { "cell_type": "markdown", "source": [ "# Curva de elasticidad acumulada\n", "\n", "El primer paso consiste en ordenar los grupos en función de que tan sensibles son (Que tanto afecta las ventas en el cambio del precio). Es decir, tomamos el grupo más sensible y lo colocamos en primer lugar, el segundo grupo más sensible en segundo lugar y así sucesivamente\n", "\n", "Una vez que tenemos los grupos ordenados, podemos construir lo que llamaremos la Curva de Elasticidad Acumulada. \n", "\n", "*Nota: La elasticidad de cada grupo en realidad es el ATE*\n", "\n", "Calculamos a la estalicidad acumulada como el ATE estimado hasta la unidad k (Recordar que previamente ordenamos a las unidades en funcion de su elasticidad)\n", "\n", "$$\\widehat{y'(t)_k} = \\hat{\\beta}_{1k} = \\frac{\\sum_{k}^{i}(t_i - \\bar{t})(y_i - \\bar{y})}{\\sum_{k}^{i}(t_i - \\bar{t})^2}$$" ], "metadata": { "id": "mZhzNrTxD-bc" } }, { "cell_type": "code", "source": [ "'''\n", "min_periods: Hasta donde va el primer grupo\n", "steps: tamanio de todos los grupos salvo el primero y el ultimo. El ultimo es de tamanio size - size // step(// es la division natural)\n", "prediction: nombre de la columna de donde la estan las predicciones de la elasticidad\n", "'''\n", "def cumulative_elast_curve(dataset, prediction, y, t, min_periods, steps):\n", " size = dataset.shape[0]\n", " # orders the dataset by the `prediction` column\n", " ordered_df = dataset.sort_values(prediction, ascending=False).reset_index(drop=True)\n", " \n", " # Define hasta que individuo va cada grupo,\n", " n_rows = list(range(min_periods, size, size // steps)) + [size]\n", "\n", " # cumulative computes the elasticity. First for the top min_periods units.\n", " # then for the top (min_periods + step*1), then (min_periods + step*2) and so on\n", " return np.array([elast(ordered_df.head(rows), y, t) for rows in n_rows])\n" ], "metadata": { "id": "hso2bVz_DcBn" }, "execution_count": 18, "outputs": [] }, { "cell_type": "markdown", "source": [ "En general tomamos al primer conjunto mas grande ya que si no el ATE podría tener bastante ruido(Por trabajar con menos individuos)" ], "metadata": { "id": "cqRA4JkVR8q9" } }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10,6))\n", "\n", "for m in [\"elast_m_pred\", \"pred_m_pred\", \"rand_m_pred\"]:\n", " cumu_elast = cumulative_elast_curve(prices_rnd_pred, m, \"sales\", \"price\", min_periods=100, steps=100)\n", " x = np.array(range(len(cumu_elast)))\n", " plt.plot(x/x.max(), cumu_elast, label=m)\n", "\n", "plt.hlines(elast(prices_rnd_pred, \"sales\", \"price\"), 0, 1, linestyles=\"--\", color=\"black\", label=\"Avg. Elast.\")\n", "plt.xlabel(\"% of Top Elast. Days\")\n", "plt.ylabel(\"Cumulative Elasticity\")\n", "plt.title(\"Cumulative Elasticity Curve\")\n", "plt.legend();\n" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 404 }, "id": "8GhCuJOeFvZx", "outputId": "0cc4ee05-e660-4022-e4e2-020b3d8a133e" }, "execution_count": 20, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "code", "source": [ "prices_rnd_pred[\"abs\"] = -abs(prices_rnd_pred[\"elast_m_pred\"])\n" ], "metadata": { "id": "s259vrvYY9dR" }, "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "source": [ "## ¿Cómo interpretar la gráfica?\n", "\n", "El eje X representa el porcentaje de los días que fueron tomados, es decir, cuando X = 0.4 vemos el ATE para el 40% de los dias con más elasticidad, en el grafico vemos que el 40% de los dias con mas sensibilidad tienen un ATE cercano a -1.\n", "\n", "Una curva ideal comenzaría entonces muy arriba en el eje Y y descendería muy lentamente hasta la elasticidad media, lo que representa que podemos tratar un alto porcentaje de unidades manteniendo una elasticidad superior a la media. (Esto a mi me genera duda ya que seria en un mundo donde queremos elasticidad positiva, aumentar el tratamiento aumenta el resultado).\n", "\n", "El modelo aleatorio, se comporta como esperaría del aleatorio, oscila cerca del ATE total nunca despegandose mucho. Recordar como para el aleatorio lo que hacemos es practicamente ir agarrando dias al azar y calcularle el ATE, por lo que tiene todo el sentido que se parezca al ATE total.\n", "\n", "El modelo causal, si bien no tiene un comportamiento ideal, nos puede llegar a servir ya que arranca ascendiendo rapido y luego desciende subitamene para convergir en el ATE estimado, podemos identificar que para X = 75% de la población tenemos una elasticidad de 0. Si dejamos fuera el restante 25% dias(Que probablemente sean el grupo de dias que detectamos que tenian una elasticidad muy negativa) tenemos una gran cantidad de dias que en promedio no son muy sensible al cambio de precio.\n", "\n", "El modelo predictivo no nos sirve mucho porque si bien arranca arriba se va rapidisimo abajo, y ademas converge relativamente rapido al ATE( X = 50%)\n" ], "metadata": { "id": "ilL2mEM9TRzv" } }, { "cell_type": "markdown", "source": [], "metadata": { "id": "oOrHfeHwp4hl" } }, { "cell_type": "markdown", "source": [ "## Curva de ganancia acumulada " ], "metadata": { "id": "s_-WJ1zaqIhN" } }, { "cell_type": "markdown", "source": [ "Defininamos a la curva de gananancia acumulada como la elasticidad acumulada multiplicada por el tamaño proporcional del grupo. Por ejemplo, si la elasticidad acumulada es, digamos, de -0,5 al 40%, terminaremos con que la curva es -0,2 (-0,5 * 0,4) en ese punto. \n", "\n", "Tomemos como referencia una curva teorica donde cada grupo tiene que la elasticidad dentro del grupo es igual a la elasticidad total, esta va a ser una recta de 0 a ATE\n", "\n", "Todas las curvas empezarán y terminarán en el mismo punto. Sin embargo, cuanto mejor sea el modelo a la hora de ordenar la elasticidad, más se apartará la curva de la línea aleatoria en los puntos comprendidos entre el cero y el uno. \n", "\n", "Calculamos la curva con:\n", "\n", "$$\\widehat{F(t)}_k = \\hat{\\beta}_{1k}*\\frac{k}{N} = \\frac{\\sum_{k}^{i}(t_i - \\bar{t})(y_i - \\bar{y})}{\\sum_{k}^{i}(t_i - \\bar{t})^2}*\\frac{k}{N}$$" ], "metadata": { "id": "NpoRuDDqqNMF" } }, { "cell_type": "code", "source": [ "def cumulative_gain(dataset, prediction, y, t, min_periods=30, steps=100):\n", " size = dataset.shape[0]\n", " ordered_df = dataset.sort_values(prediction, ascending=False).reset_index(drop=True)\n", " n_rows = list(range(min_periods, size, size // steps)) + [size]\n", " \n", " ## add (rows/size) as a normalizer. \n", " return np.array([elast(ordered_df.head(rows), y, t) * (rows/size) for rows in n_rows])" ], "metadata": { "id": "OotsKgABvcX8" }, "execution_count": 22, "outputs": [] }, { "cell_type": "code", "source": [ "for m in [\"elast_m_pred\", \"pred_m_pred\", \"rand_m_pred\"]:\n", " cumu_gain = cumulative_gain(prices_rnd_pred, m, \"sales\", \"price\", min_periods=50, steps=100)\n", " x = np.array(range(len(cumu_gain)))\n", " plt.plot(x/x.max(), cumu_gain, label=m)\n", " \n", "plt.plot([0, 1], [0, elast(prices_rnd_pred, \"sales\", \"price\")], linestyle=\"--\", label=\"Random Model\", color=\"black\")\n", "\n", "plt.xlabel(\"% of Top Elast. Days\")\n", "plt.ylabel(\"Cumulative Gain\")\n", "plt.title(\"Cumulative Gain\")\n", "plt.legend();" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 295 }, "id": "lwMZNU7Bvacz", "outputId": "8852707b-309e-49dc-82c6-4348351ac14a" }, "execution_count": 23, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
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\n" }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "source": [ "Ahora está muy claro que el modelo causal (elast_m) es mucho mejor que los otros dos. Se desvía mucho más de la línea aleatoria que tanto rand_m como pred_m. Además, se puede observar cómo el modelo aleatorio real sigue muy de cerca el modelo aleatorio teórico." ], "metadata": { "id": "FXJoUNW8wb8t" } }, { "cell_type": "markdown", "source": [ "# ¿Que pasa con la varianza?" ], "metadata": { "id": "MVG4rgAH0VSI" } }, { "cell_type": "markdown", "source": [ "No es correcto no tener en cuenta la varianza cuando se trata de las curvas de elasticidad. Especialmente porque todas ellas utilizan la teoría de la regresión lineal, por lo que añadir un intervalo de confianza en torno a ellas debería ser bastante fácil. Para ello, primero crearemos una función que devuelva el Intervalo de Confianza de un parámetro de regresión lineal. Mediante teoria de modelo lineal que no vamos a explicar....\n", "\n", "$$s_{\\hat{\\beta}_1} = \\sqrt{\\frac{\\sum_i\\hat{\\epsilon}_i^2}{(n-2)\\sum_i(t_i - \\bar{t})^2}}$$\n", "\n", "El intervalo de confianza del 95% queda:\n", "\n", "$$[\\hat{\\beta_1} - 1.96*s_{\\hat{\\beta}_1}, \\hat{\\beta_1} + 1.96*s_{\\hat{\\beta}_1}]$$" ], "metadata": { "id": "asZWO8np0lR3" } }, { "cell_type": "code", "source": [ "def elast_ci(df, y, t, z=1.96):\n", " n = df.shape[0] #Tamanio de muestra\n", " t_bar = df[t].mean() #precio promedio\n", " beta1 = elast(df, y, t) #ATE estimado (beta1)\n", " beta0 = df[y].mean() - beta1 * t_bar #Nunca la vimos pero esta es la forma de estimar beta0\n", " e = df[y] - (beta0 + beta1*df[t]) #El epsilon se consigue despejando en el modelo lineal con el beta1 estimado\n", " se = np.sqrt(((1/(n-2))*np.sum(e**2))/np.sum((df[t]-t_bar)**2))\n", " return np.array([beta1 - z*se, beta1 + z*se])\n", "\n", "def cumulative_elast_curve_ci(dataset, prediction, y, t, min_periods=30, steps=100):\n", " size = dataset.shape[0]\n", " ordered_df = dataset.sort_values(prediction, ascending=False).reset_index(drop=True)\n", " n_rows = list(range(min_periods, size, size // steps)) + [size]\n", " \n", " # just replacing a call to `elast` by a call to `elast_ci`\n", " return np.array([elast_ci(ordered_df.head(rows), y, t) for rows in n_rows])" ], "metadata": { "id": "rZAc6F2H254J" }, "execution_count": 31, "outputs": [] }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10,6))\n", "\n", "cumu_gain_ci = cumulative_elast_curve_ci(prices_rnd_pred, \"elast_m_pred\", \"sales\", \"price\", min_periods=50, steps=200)\n", "x = np.array(range(len(cumu_gain_ci)))\n", "plt.plot(x/x.max(), cumu_gain_ci, color=\"C0\")\n", "\n", "plt.hlines(elast(prices_rnd_pred, \"sales\", \"price\"), 0, 1, linestyles=\"--\", color=\"black\", label=\"Avg. Elast.\")\n", "\n", "plt.xlabel(\"% of Top Elast. Days\")\n", "plt.ylabel(\"Cumulative Elasticity\")\n", "plt.title(\"Cumulative Elasticity for elast_m_pred with 95% CI\")\n", "plt.legend();" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 404 }, "id": "-YtZIQsz3C7W", "outputId": "eb28c8da-0f4e-43fc-cba7-73a124b62ddf" }, "execution_count": 33, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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Lq+7jyJEjtGrV6uLrTz/9lFtuueWSbWbMmIGPjw95eXlER0czePBgEhISSE5OZu/evQCcO3cOLy8vpk2bxpQpU4iKirrqvq+F1KQJIYSo8rTWxJ3MpNiorR2KuEFz585l6NChAAwdOpS5c+diZ2dHnz59WLZsGQaDgV9//ZWBAweybds2unXrho+PD/b29pfUtl3JhebOC4/LEzSAqVOn0rJlSzp06EBiYiKHDh0iLCyMo0eP8sQTT7BixQo8PDwseuyXk5o0IYQQVVpGTgGv/LSHlXGpjO4UyqQ7m1s7pGrjSjVfLi4uV1zv5+dXrpqzks6cOcOff/7Jnj17UEpRXFyMUor333+foUOHMm3aNHx8fIiKisLd3f2ayr4Wa9asYfXq1WzevBkXFxe6d+9Ofn4+3t7e7Nq1i5UrV/LFF1+wYMECZsyYUWFxSJImhBCiSskrLGZRbCLncovINxQz/+9EsvIMRId6M3NTAt0a+9OjaYC1wxTXYdGiRdx///18+eWXF5d169aN9evX061bN8aMGcPXX399saYtOjqap556irNnz+Lu7s7ixYuJjIy84TgyMzPx9vbGxcWFAwcOsGXLFgDS09NxcHBg8ODBNGnShJEjRwLg7u5Odnb2De/3ctLcKYQQosooNBh5ZE4sr/8cxwe/H+Szv44Q6OnM0ic6893Y9jSt7c7zi3ZxOrvA2qGK6zB37lwGDRp0ybLBgwczd+5cbG1tGTBgAMuXL79400BQUBCvvPIK7dq1o3PnzoSGhuLp6QnA0qVL+de//lXqfi70SbvwmDp16iXr+/Tpg8FgIDw8nJdeeokOHToAkJycTPfu3WnVqhUjR47k7bffBkz98B555JGLNw7861//YunSpTd8PpTW1a/9PioqSsfExFg7DCGEEBZkKDYycd4OftuTwtt3RzKkbV3sbNQlA4QeTM3mjk830D7Ml29HR2NrIwOzXov9+/cTHh5u7TCuSU5ODm5ubhgMBgYNGsSYMWP+kehVJqWdY6VUrNb6H3cdWLUmTSnVRykVr5Q6rJR6qZT1o5VSp5VSO82PcdaIUwghhPUUGoz8eSCVcbNj+G1PCq/1D2dYu2DsbW3+MYJ741ruvHFHc9YdPM2bv+yzUsTiZpo0aRKtWrUiIiKC+vXrc9ddd1k7JIuxWp80pZQt8BnQG0gC/lZKLdVaX/5XNV9rbZlBT4QQQlQJhmIjW46eYdmuk6yISyEzrwgPJzte6deUcbeEXfG9w9sHc+R0DtM3HCPYx4UxXco3mbWomqZMmWLtECqMNW8caAcc1lofBVBKzQMGAvLVRwghaqDY42f5duMxjqWfJyH9POcLi3F1sOW25rW5o2UgXRr642BXvgagV/qFk3Q2lzd/3UdtTyf6RQZWcPRCWJ41k7QgILHE6ySgfSnbDVZKdQUOAk9rrRNL2Qal1HhgPEBwcLCFQxVCCFGRVuxNYeK8Hbg72hER5El0qA/t6/vQo2kATva211yerY3i4/taM+KbLUycuwMHWxt6NatVAZFXP1prmWS9glzrfQCV/e7OZUCo1roF8Dswq6wNtdZfaa2jtNZR/v7+Ny1AIYQQ5Xf5RSotK59v1h9lwvexNAv04PdnujFrTDsm3dmcvpGB15WgXeDsYMvMMe1oXseDCd9v56/4tBsNv9pzcnIiIyPjmpMJcXVaazIyMnBycir3e6xZk5YM1Cvxuq552UVa64wSL78B3rsJcQkhhKgAv+4+xYuLd6O1xtvVgfwiI+k5pqEybm0awLThrXFxsOxlycPJntlj2jNi+hYe+S6W3568hQb+bhbdR3VSt25dkpKSOH36tLVDqZacnJyoW7duube3ZpL2N9BIKVUfU3I2FBhecgOlVKDW+pT55Z3A/psbohBCCEv4bnMC/1oaR8u6XrQN8ebs+UJsbBTNAj1oXseDqFCfChsuw9PFnhmjo+n94TpeWryb+eM7YiNDc5TK3t6e+vXlRovKwmpJmtbaoJR6HFgJ2AIztNZxSqn/A2K01kuBiUqpOwEDcAYYba14hRBCXJ/P/jrM+yvj6RUewLThbW6oCfN6Bbg78fqAZjy3cBdzth5nVMfQmx6DENdKBrMVQghRYZbsSOap+Tu5q1UdptzTEjtb63WF1lozasY2th8/y8qnu1LX28VqsQhRUqUczFYIIUT1FXv8LC8s3k37+j68N8S6CRqAUoq3BkWigVd/2iud40WlJ0maEEIIi0s+l8fD38VQx9OJL0a2Lff4ZhWtno8LL9zehLUHT/PTjuSrv0EIK6ocfzVCCCGqjfyiYh75LpaCIiPfPBCNt6uDtUO6xP0dQ2kb4s3//bJPJmIXlZokaUIIISzqjZ/j2JOcyYf3taJhQOUb7sLWRvHu4EhyC4qZtDTO2uEIUSZJ0oQQQlhEgaGYr9cdZX5MIo/3aEjvSjzCf8MAdyb2bMive06x9qCMCSYqJ2uOkyaEEKIaSDyTywer4vljfxrZBQa6Nfbn6d6NrR3WVT3UNYwFMUm89et+ujT0q7Bx2oS4XlKTJoQQ4rrlFxXz0OwYft+XSt/I2nw7OppvHoiqEgmPo50tL/ZpSnxqNotjk6wdjhD/IDVpQgghrtukpXEcSMnm2wej6dEkwNrhXLN+kbVpHezFlFXxDGgZaPFpqYS4EVKTJoQQ4rr8tCOJeX8nMqF7gyqZoIFp7LRX+4WTll3A1+uOWTscIS4hSZoQQohrtiY+jZd/3EO7UB+eqQL9z64kKtSH25vX4pv1R8nMK7J2OEJcJEmaEEKIa7Js10kemh1DmJ8bn49sY/WZBCzhiVsbkV1g4LvNCdYORYiLqv5flhBCiJsiv6iYj1cfZOK8HbSu5828hzvg5+Zo7bAsIiLIk1ubBjB9wzHOFxisHY4QgCRpQgghrkJrzc87k7l1yho+Xn2IAS3qMGtMOzyc7K0dmkU91qMhZ3OLmLvthLVDEQKQJE0IIcQVFBs1k5bG8eS8nfi6OTJ/fAc+HdYaZwdba4dmcW1DvOnUwJcv1x0lv6jY2uEIIUmaEEKI0uUVFvPwd7HM2nyc8V3D+PmxzrQP87V2WBXqiVsbcTq7gE/+OGTtUISQJE0IIcQ/HUzNZtDnG/nzQCr/N7A5r/QLx6YKDFB7ozo28GVYu3p8sfYIGw+nWzscUcNJkiaEEOIirTWzNiVwx6cbSM8pYProaEZ1DLV2WDfVvwY0p4G/G0/P30lGToG1wxE1mCRpQgghLpq5KYE3lsbRqYEvy5/sWmUHqb0Rzg62TB3amnN5RTwyJ5bEM7nWDknUUJKkCSGEAGBvciZv/3aAXuEBzBgdjb979Rhe43o0q+PBe4NbsDc5i94frWXan4coNBitHZaoYSRJE0IIwfkCAxPn7sDb1Z73hrREqerf/+xq7modxB/PduPWpgFMWXWQ91YcsHZIooaRJE0IIWq4omIjLy7ezbGM83x8X2t8XB2sHVKlUcfLmc9HtGVYu2C+3ZTA/lNZ1g5J1CCSpAkhRA2WmVvE6G+38cvuU7xwe1M6Nqi6Q2xorSus7Bdub4Knsz2vLdmL0Vhx+xGiJEnShBCihtqTlMmg/25k27EzTLmnJY92b2DtkK5Lek4B//5lHy0mreLnnckVsg9vVwde6tuU2ONnWbQ9qUL2IcTl7KwdgBBCiIoXn5LNzzuTCfZxIcTXlQUxify0IxlfVwfmjG1fpQapXb7nFG8sjcPR3gZ/N0cOpGSTX1SMv7sjry/ZS4cwX2p5OFl8v0Pa1GVhTCJv/7afnk0D8K0m85aKyktVZPWwtURFRemYmBhrhyGEEJVC4plcBn2+kfScwovLHOxsGNulPo92b1Cl5uBcFJvEC4t20ayOBw393UjNKiDQy4nHejTERin6frKOTg38mP5AVIXc/HAwNZv+U9fTNyKQqcNaW7x8UTMppWK11lGXL5eaNCGEqMbO5RbywLfbMBg1q5/pir2tDYfTcggP9KCOl7O1wysXQ7GRfaeyWLE3hc/XHKFLQz++GtUWF4d/XsKev70pb/6yjx+3JzO4bV2Lx9K4ljuP92jER6sPcmfLOvRqVsvi+xDiAknShBCimsrMK2L87FiSzuQxZ1x7Gga4AxDi62rlyMqWlV9ERk4h6TkF7Dxxji1HM9h27AzZBQYA+kcG8sG9LXGyL32C99GdQlm+5xSTlsbRJsSb+n6WP9ZHuzfgtz2neG3JXtqF+VSpmkhRtUhzpxBCVDFaa05m5lNoMGLUGgdbGzyc7XF3tLs4v+b+U1k8MieW5LN5fHRfK+5oWcfKUV9ZflExL/+4h592XNrxP8zPlQ4NfOkQ5kuHMB8C3K/e1yzxTC53TtuAn5sjSx7rjKuj5esjdiae4+7PNzK0XTBvDYq0ePmiZpHmTiGEqOIMxUZWxKXw9bqj7ErK/Md6GwWBns6E+Lqw/cRZPJ3tmf9wB9qG+Fgh2vJLycxn/Hcx7E7KZEzn+kQEeeDj6kDT2h7U9rz2GwDq+bjw6bA2jJqxlecX7eKz4W0s3j+tVT0vxnapz9frj3FHizpVeugSUXlJTZoQQlQBa+LTmLxsH8fSz1Pfz5UR7YPxc3NEKSgwGMnKK+JsbiFJZ/M4npFLLQ9H3rwrolw1TzdL7PEzTF62DwdbG4K8nbGzseF4xnniU7Ip1pqP72vFbc1rW2x/X649wtvLD/BM78ZM7NnIYuVekFdYTJ9P1qGA5U92xdmh9CZYIa5GatKEEKIKysgp4JWf9rAyLpUwP1e+GNmW25rVutisWVX8tucUT83fib+bI3W9nYk9fhZDsSbE14X+LQJ5sHN9mtR2t+g+x3cN40BKNh/+fpA6Xs4MsfCNBM4Otrx9dyTDv97Kx6sP8nK/cIuWL4QkaUIIUUkZjZon5+3k74QzvNCnCWO71MfRrurV1szalMCkZXG0Cfbm61FRN23aKaUU7w5uQVp2Pi8t3k2AuyNdG/tbdB+dGvgxrF0wX68/Srcm/nRq4GfR8kXNJjMOCCFEJfXtpgQ2HE7njTuaM6F7wyqZoP2y+yRvLI2jd3gtvh/X/qbPC+pgZ8N/R7alYYAbj86J5VRmnsX38Wr/cML83Xj8hx2cPGf58kXNZdUkTSnVRykVr5Q6rJR6qZT1jkqp+eb1W5VSoTc/SiGEuDn2nczis78OsycpkwMpWby74gC9wgMY1q6etUO7LrHHz/DMgl1Eh3ozdVjrMofNqGgeTvZ8PSoKg1Hz1m8HLF6+m6MdX97fliKDkUfmxJJfVGzxfYiayWpJmlLKFvgM6As0A4YppZpdttlY4KzWuiHwEfDuzY1SCCFujgJDMY//sJ33V8Zzx7QN9J+6AQ8nO94Z3KJCRs6vaMczzjNuVgxBXs58dX+U1RK0C+r5uPBwtwYs23WSrUczLF5+A383Pri3JbuTMvnXz3srdLJ3UXNYsyatHXBYa31Ua10IzAMGXrbNQGCW+fkioKeqiv+thBDiKqZvOMbR9PN8MrQVH9zTkjtb1mHqsNb4VcH5IbPzixg3KwYNzBgdjfdNbuIsy6PdGhDk5cwbS+MwFBstXv5tzWvzxK0NWRCTxA/bTli8fFHzWDNJCwISS7xOMi8rdRuttQHIBEodjEYpNV4pFaOUijl9+nQFhCuEEBUj+Vwen/5xmNua1WJgqyAGt63LR/e1qpKd0I1GzdPzd3I0/TyfD29TISP+Xy9nB1te7R/OgZRs5lZQEvVUr8Z0a+zPpKVxxB4/WyH7EDVHtblxQGv9ldY6Smsd5e9v2bt3hBCiomit+fcv+9BoXh9weY+PqkNrzcHUbF5dsofV+9N4vX84nRpWviSzb0RtOob5MmXVQc6cL7z6G66RrY3ik6GtCPR0ZsL3sZytgH2ImsOaSVoyULI3bF3zslK3UUrZAZ6A5TsTCCGEFWTmFvH4DztYvjeFx3s0pJ6Pi7VDui4bDqXT5d2/uO2jdczdlsgDHUN4oFOotcMqlVKKyQObk1NgYMqq+ArZh5eLA5+PaENqVgHfbz1eIfsQNYM1k7S/gUZKqfpKKQdgKLD0sm2WAg+Ynw8B/tTSG1MIUQ1sPpJBn0/WsTIuhedvb8Kj3RtaO6TrcjzjPBO+j8XJ3oa3BkWy+eVbmTwwolLf7NC4lkAzjhAAACAASURBVDujOoYwd9sJ9ib/c3otS4gI8uSWRn7M2XKCogro/yZqBqslaeY+Zo8DK4H9wAKtdZxS6v+UUneaN5sO+CqlDgPPAP8YpkMIIaqSQoORd5YfYPg3W3C2t+XHCZ14rEdDbKvYDAJgmhbpkTnbUUox88F2DG8fTKCns7XDKpenejXGx8WBSUvjKuxOzNGdQknJymdlXEqFlC+qP6vOOKC1/g347bJl/yrxPB+452bHJYQQlqC1vlijlJlXxB/7U5m+4RhxJ7MY1i6Y1weE4+JQNSd+MRo1L/24mwMpWXw7OrrKNdV6OtvzQp8mvLh4D8v3ptAvMtDi++jRJIAQXxdmbkxgQIs6Fi9fVH9V87+DEEJUIlprCgzGi2OBnTlfyHsrDrB4exKujnZ4OduTfC6PomJNkJczX97fltstOJH4zVZoMPLswl0s23WS529vQvcmAdYO6boMaVuPb9YfY8qqeG5rVgs7W8s2LtnYKEZ1DOXNX/axNzmTiCBPi5Yvqj9J0oQQ4jrlFRbz045kZm46xqG0HMJre9CynifL96aQnW9gcJsgnOxtOXO+kNua16ZvRG1a1fOq1P21rianwMAj38Wy4XA6L/VtysNdw6wd0nWztVE8e1sTHpkTy4/bk7k32vIzO9wTVZcPVsXz7cYEPri3pcXLF9WbJGlCCHEd9p3MYtSMbaTnFNAs0IOHuzZgT/I5luw4Sct6nky+M4Imtd2tHabFFBs1i2OT+OD3eNJzCnl/SAvuiaqa01WVdHvzWrSs58XHqw9yZ6s6Fp8ZwcPJnrvbBLEgJonXB4Tj5VI5BvYVVYMkaUIIcY32JGUycvpWXBxsmTe+A+3r+1ysHSvZD626OJZ+ngnfb2f/qSxa1fPi8xFtaBviY+2wLEIpxQu3N2HEN1v5fusJxnapb/F9DG8XwpwtJ1i8PblCyhfVV7UZzFYIIW6G3UnnGP7NFtwc7VjwcEc6hPlekpRVtwRt85EM7vpsI6lZ+Uwb3pqfJnSqNgnaBZ0b+tGpgS9frj1CgcHyk6M3q+NB62Avvt96XOb0FNdEkjQhhCinrPwiHp2zHQ8ne+Y/3KHK3dF4LbTWzNlynPunb8Xf3ZElEzozoEWdapeEXjChe0PSsgtYsuPyMdUtY0T7EI6ePs/WY2cqpHxRPUmSJoQQ5TR56T5OZebx6fDW1PWuvglaRk4B47+L5bUle+nU0I/Fj3Yi2Lf6Hi9A54a+NK/jwZfrjmI0Wr62a0CLQDyc7Ph+q0y8LspP+qQJIao9o1Ezc1MCf8WnUdfbhVBfFzRwNrcQR1sbxnYJw9PF/pL3bDiUzid/HKSwWDOmcyh2NjYs3p7EE7c2pE2wt3UO5CY4nJbDsK+3kJlbxGv9wxnTuT42VXCg3WullOLhbg2YOHcHq/encpuFh0hxsrdlcNu6zNlynPScZvi5OVq0fFE9SZImhKjW0rLyeXbhLtYfSifM35W9yZmczS0CwMHOBkOxkQUxSbw7pAURdTxYE3+aRbFJbD6aQZCXM072Njw5bycAEUEeTOzZyJqHU6Hyi4p57PvtFBs1Pz/emfBAD2uHdFP1i6jNe97OfLnuqMWTNIAR7YP5dmMC36w/xkt9m1q8fFH9SJImhKiWDMVG5v2dyAer4skrKuatQZEMa1cPpRRZ+UXY2Sic7W3Zm5zFMwt28sCMbSgFWkMtD0feuKMZw9sHY29jw+/7U/ll9yme6tUIewsPeFqZTF62j/jUbGY+GF3jEjQAO1sbHroljDeWxpkmjW/kZ9HyGwa4c3frIGZsPMaI9sHVuk+jsAxVHe80iYqK0jExMdYOQwhhBVpr/opP453lBziYmkO7+j68NSiChgFlj1mWX1TMjI3HKDQY6dm0Fs3reNSIJr6Sft6ZzJPzdvJo9wa82Kfm1vLkFxXT5+N1GIyaFU91xc3RsnUZJ8/lcesHa+jdrDafDmtt0bJF1aWUitVaR12+vPp+JRRC1Chaa37dfYp+UzcwZmYM+UVGvhjZhvnjO1wxQQNTf6EJ3RvyVK/GRNb1rHEJ2g9bT/Dsgl1EhXjzTO/G1g7HqpzsbZlyT0uSz+Xxn1/3W7z8Ol7OjL8ljGW7ThJ7/KzFyxfViyRpQogq78LQGI/9sJ2ComLeH9KCP57tRp+IwGo7ZIQlGIqNTF4Wxys/7aFLIz++fTC6WjfnlldUqA/jbwlj7rYTrD142uLlP9ytAf7ujkxaGkdeoeXHZRPVhzR3CiEqlZwCA3O3nmDu3yfwcLKnVT0vokK9uaWRP57O9v/YPu5kJo99v53Es3m82KcJY7uEYVvDasLKI7+omF2J5wj1cyXA3ZHle1OYsjKeo+nnGdulPq/0C5fzVkJ+UTF3fLqBlMx8Xh/QjHui6lo04V+x9xSPfr+dzg38+OaBKItPRyWqlrKaOyVJE0JUGgtjEnnzl31k5RtoF2oa1X538jnyi4zY2Sg6hPnSLzKQ/i0CcbK34bO/jvD5X4fxdXNg2vA2RIdWr5HwLSW/qJgR32y92LzmbG9LXlExjQLceLFPU3o1q2XlCCunxDO5PLdwF1uPnaFrY38+urclvhYcOmNhTCIvLN5Nt8b+fHl/WxztJFGrqSRJE0JUaj9uT+LZhbtoF+rDy/3CaVXPCzA1ye1KOsfv+9JYFZfC0fTzONjZ4O/mSPK5PAa1DuL1Ac3wcZWJq0tTbNRM+D6WVftSeb1/M2xtFIfSsmlVz5tBrYOk9uwqjEbN91uP8+av+7m9ueU7+8/ddoKXf9zDAx1DmDwwwqJli6qjrCRNhuAQQljdir2neG7hLjqG+TJjdPQlTT92tja0DfGhbYgPL/Zpwp7kTBbHJrH/VDb/HhRBjyYBVoy8ctNa8+Yv+1gZl8rrA5oxRib3vmY2Nor7O4ZyOqeQqX8cYnSnEIvOXTqsXTDxKdnM2pzAna2CaBtSfQdKFtdOatKEEFa15WgG90/fSmSQJ9+NbY+rhYc8qKnOFxh4ftEuftuTwtgu9Xl9QDNrh1Sl5RYa6DFlDbU9nPhpQmeL3gGcU2Dgtg/X4upox68Tb8HBTm7eqGmkJk0IUekkpJ/nkTmxBPu48O3odpKglUNuoYEFfyfy254U8g3FFBs1tjYKJ3tbXBxsqePlTD1vF37akcThtBxe6deUh24Js3bYVZ6Lgx0v9mnKMwt2sWRnMne3qWuxst0c7fj3oAjGzIzhv2uO8GSv6jurhbg28h9RCGEVmXlFjJ31NwDTH4j+x9yZ4lL5RcV8ve4o0zce41xuEc3reBDg7oitjcJg1OQVFpOeU8CuxHOczS3C28We2WPaW3zU/JrsrlZBzNqUwLsrDtC7WS3cnSz3mb21aS3uaFmHz/46zP0dQ6SPpQAkSRNCWMGpzDwmfL+d4xm5fDe2PaF+rtYOqVJbvS+Vyb/EkXgmj55NA3i0ewOirnAna1Z+EQ62NjKsg4XZ2CgmD4xg0Ocb+WDVQSbd2dyi5T/c1TTI7cq4FIa1C7Zo2aJqkoZvIcRNtf7QafpP3UB8SjafDmtNxwa+1g6pUvti7RHGzY7Byc6WHx5qz/TR0VdM0AA8nOwlQasgrep5MapDCLM2J7DjhGVnDGhex4P6fq78uvuURcsVVZckaUKICpdXWMySHcmM/GYro2Zsw8/NgaWPd6FvZKC1Q6vUdpw4y/sr4+kXWZvfnryFTg2k6bIyeO72JtRyd+LlH/dQVGy0WLlKKfpHBrLpSDrpOQUWK1dUXZKkCSEqTFpWPu+tOECHt//gqfk7Scg4z5M9G7Hksc40DHCzdniVTk6Bgb3JmRQbNdn5RTw5bye1PZx4++4WMl1TJeLuZM+kO5tzICWb6RuOWbTsAS0DMWpYsTfFouWKqkn6pAkhLOZwWjYzNiZwOC2H9OwCEs/mYjBqbm9Wmwc6hdK+vk+Nm7y8vLTWTJy7gz8PpOHr6kCAhxNJZ3NZ8HDHUqfDEtbVJ6I2vZvV4uPVB+kfGUg9HxeLlNukljsN/F35ZfdJRnYIsUiZouqSJE0IccP2Jmfy2V+HWRGXgpOdLZF1PQmv40GfiNrcF12PEF+5MeBqVsal8ueBNIZG1yO3sJgNh9N57vYmV+1/Jqxn8p3N6f3hWl5dspdZD0ZbZG5PpRT9W9Th0z8PkZaVT4CHkwUiFVWVJGlCiOsWk3CGT/88zNqDp3F3suPxHg15sHN9GT7gGp0vMDB5WRxNa7vz77sisJOmzSqhjpczz93ehMnL9rF010kGtgqySLkDWgQy9Y9DLN11knEyxl2NJkmaEOKaJZ7J5T+/7mdFXAo+rg48f3sT7u8YgocFx42qST754xCnMvOZNry1JGhVzKiOoSzZkcybv+zjlkb+FvmC0riWO9Gh3kxZFU9kkCftw+QO6JpK/hsIIcpNa81X647Q88O1rD14mmd7N2bDiz14rEdDSdCug6HYyLQ/DzF9wzGGRtez6JyQ4uawtVG8M7gFWXkGXli0C0tNtfjFyLYEeTkzdlYMuxLPWaRMUfVIkiaEKJcCQzHPLtzFW78doEcTf/58rhtP9GyEi4NUyF+PY+nnuefLzUxZdZC+EbV5tX+4tUMS1yk80IOX+jZl9f405mw5bpEyfd0c+X5cB7xd7Xng222kZedbpFxRtUiSJoS4quz8IkZ8vZUftyfzTO/GfDGyLYGeztYOq0rSWvPdluP0+2Q9R9JymDqsNdOGt7HoFEPi5nuwcyjdm/jz71/3E5+SbZEya3s6MeOBaM7lFjF3a6JFyhRViyRpQoir+r9l+9h+4izThrdmYs9GFrmLraYxGjWbjqTzwLd/8/qSvUSFerPq6W7c2bKOtUMTFqCU4v0hLXF3smPi3B3kFxVbpNxGtdzp2tifH7Ydt+jAuaJqkHYKIcQVrYxLYWFsEo/3aMiAFpJQlIfWmh+3J7MoNgk7W4WLgy27kzI5lZmPm6Md/zewOfd3CJFkt5rxd3dkyj0tGf3t37z9234mD4ywSLmjOoQwbnYMq+JS6d9CZumoSaySpCmlfID5QCiQANyrtf7HJGhKqWJgj/nlCa31nTcrRiEEnM4u4OUf99C8jgcTezaydjiVUvK5PL7dcIzdyZm0CPIkIsiTH7aeYFvCGRr4u+LuZE9KZj7NAj14uV84vcNr4ewg82pWV92bBDC2S32mbzhG18b+9AyvdcNl9mgaQJCXM7M3J0iSVsNYqybtJeAPrfU7SqmXzK9fLGW7PK11q5sbmhA1l9aaL9cd5Yu1RwAoLtYUFBv56L5WONhJ74iSzhcYeH3JXn7edRKA8EB3Zm85TqHBiLeLPe/cHcm9UfVkhoUa6IU+Tdh0JIPnF+3m96e74uvmeEPl2dooRnYI4d0VB4hPyaZJbXcLRSoqO2slaQOB7ubns4A1lJ6kCSFukpwCA88v3MXyvSl0a+xPqK8LBQYjtzWvReNaclEoKSu/iAe//ZsdJ84ypnN9HuxSnyAvZwoMxcSnZBPi44qni9wIUFM52tny0X0t6fPxeuZuO8Hjt954LfR90fX4aPVBZm9O4D+DIm88SFElWCtJq6W1PmV+ngKUVR/spJSKAQzAO1rrJWUVqJQaD4wHCA4OtmSsQlR7scfP8vzCXRw/k8ur/cIZd0t96S9VhrPnCxk1Yxv7T2UxbXgb+kX+r/nJ0c6WFnW9rBidqCya1vagc0Nf5m5L5NHuDbG9wRpVH1cH7m4dxMLYJCb2bEQtmS6qRqiw9gul1Gql1N5SHgNLbqdNI/+VNfpfiNY6ChgOfKyUalDW/rTWX2mto7TWUf7+/pY7ECGqsdxCA//5dR9DvthEgcHInLHteahrmCRoZTAaNY9+H0t8ajZfjWp7SYImxOVGtg8h+Vwea+LTLFLehO4NKTZq/rvmiEXKE5VfhdWkaa17lbVOKZWqlArUWp9SSgUCpX6CtdbJ5p9HlVJrgNaAfDqFuEGZuUXM3pzAjI3HOJtbxIj2wbzcLxw3R7nh+0pmbDzGlqNneG9wC25teuMdwkX11qtZLQLcHZmz5bhFbiAI9nVhcJsg5m47wYTuDWTy9RrAWj2BlwIPmJ8/APx8+QZKKW+llKP5uR/QGdh30yIUoppKycyn54dr+OD3g7QO9mbxo534z6DIap+gFRqMHDmdQ3Z+EQDFRk1aVj5pWaWP5J5fVMzszQl8ve4oZ84XcjA1m/dWxtMrvBb3RNW9iZGLqsre1oah0fVYc/A0iWdyLVLm4z0aYTBq/rtW6itqAmv9V34HWKCUGgscB+4FUEpFAY9orccB4cCXSikjpmTyHa21JGlC3ACtNa/+tIecAgM/TehE62Bva4d0UxxMzebxH7ZzMDUHAFcHW/INRoqNGqVgbOf6PHtbE5wdbMkpMPDzzmQ+/eMwKeYEbsqqeLxc7HF3tOOdwZHSHCzKbWi7YKb9dZgftp3gxT5Nb7i8YF8X7m4dxA9bT/Bw1wbU9pTatOrMKkma1joD6FnK8hhgnPn5JkBuYRHCgpbsTOaPA2m81j+8RiRoWmvm/Z3I5GVxFweRzSssJiUrHxcHW2p7OLE/JZtvNhxj9f5UQv1c2XQ4g8JiI21DvPnovlb4ujkwc1MCK/em8N6QFvjd4HAKomap4+XMrU1rsTAmiWd6N8be9sYbsJ64tRG/7D7FxHk7+GFce+wsUKaonJSp3/4VNlDK15xUVRlRUVE6JibG2mEIUamkZefT+8N1NPB3ZeEjnW74brPKbt/JLCYtjWNbwhm6NPTjw/taEuBeeq3DpiPp/OvnOIqKjfQOr8VtzWsTHeotNWbCIn7fl8pDs2P4elQUvZtZpi/jkh3JPDV/Jw93DePlfuEWKVNYj1Iq1nyj5CXKU5O2RSm1E/gWWK6vltUJISoNrTW/7Unhtz2nWBOfRpFR896QltU6QUs8k8tnfx1mQUwiXi4OvH13JPddZVDZTg38WP1Mt5sYpahJujfxx8/NkQUxiRZL0u5qHUTs8bN8ue4orYO96BMhdxpXR+VJ0hoDvYAxwFSl1AJgptb6YIVGJoS4IVpr3l5+gK/WHcXf3ZGBrYO4p21dGga4WTu0CnHmfCHvLN/Pj9uTsVGKUR1DebpXYxlUVlidva0Ng9sE8c2GY5zOLsDf3TJN5q8NCGd30jle/nEPXRr5V/ubf2qiqzZka5PftdbDgIcw3Y25TSm1VinVscIjFEJcl49XH+KrdUe5v0MIW1/uyVuDIqttP7TY42fpP3U9S3acZGSHENa90INJdzaXBE1UGvdE1aXYqFmyI9liZTra2fJ/AyM4m1vEtxuOWaxcUXlcNe1WSvkCI4H7gVTgCUxDaLQCFgL1KzJAIUT55BYaWLE3heMZuRxKy+a3PSnc07Yuk+9sXqXmj9Ra8+eBNL5adxR7WxvC/F1pXMudWxr5EeLresm2xUbN9A1HeW9FPIFeTix+tBORdT2tFLkQZWsY4E6bYC8WxCRadEaPlvW86N2sFl+tP8qojqHyxaSaKU/d6GbgO+AurXVSieUxSqkvKiYsIUR5GY2axduTeH9lPGnZBSgFAe6OjOoYwht3VK0Ebd/JLF7/eS+xx88S7OOCt4s9P21PJrvAAECorwu9wmvRr0Ugns72vLhoNzHHz3J781q8N6Qlns5ygRKV1z1R9Xj5xz1sP3GWtiE+Fiv3md6N6fvJer5ef5Tnbm9isXKF9ZXn7s57tdYLLlt2j9Z6YYVGdgPk7k5REySfy+Pnncksjk3iyOnztKrnxUt9m9Im2BsHu6p3S/6h1Gzu+XIzdjY2PN27EfdG1cPe1gatNQkZuaw7eJo18WlsNA+RAeDhZMekO5szqHWQ3IkpKr2cAgO3vPsnTWt78MND7S36mX38h+38eSCN9S/0wFeGialyyrq7szxJ2natdZurLatMJEkT1U2xUbPu4GkWb0/icFoOqVn5nM01jZwfFeLNqE6h3NEisMomKsnn8hjy300YjJrFj3Qi2NelzG2z8otYvS+VI6dzGNUxVCaaFlXKrE0JvLE0jm9GRdHLQnd6AhxOy6H3R2t54tZGPNO7scXKFTfHNQ/BoZTqC/QDgpRSU0us8gAMlg9RCFGatQdP89Li3ZzKzMfX1YHWwd60DfEm2MeFvhGBV0xoqoJzuYXcP30rOQUGFjzc8arH4+Fkz91tZFomUTUNbx/MrM0JvPXbfro18bfI4LYADQPcuKWRPwtjEnmyZ6NqPcxOTXKlPmkngRjgTiC2xPJs4OmKDEoIYZKWnc9T83bg6+bIf0e0oWd4rSrZlFkWQ7GRJ+buIOlMHnPGtSc80MPaIQlRoextbXilbzjjZsfww9YTPNAp1GJlD4uux6Pfb2ftwTRubWq5WjphPWUmaVrrXcAupdT3WmupORPiJtNa8/LiPeQWFrNwZNtqOb7ZeyvjWX8onXcHR9KuvuU6UgtRmfUMD6BTA1+mrIqnXX0fi3056RleCz83B+ZuS5QkrZoo8yu5edBagB1Kqd2XP25SfELUWAtjkvjjQBov9GlaLRO0RbFJfLXuKKM6hnBfdLC1wxHiplFK8d6QFrg62DFqxjZOZORapFwHOxsGt63LnwfSSMvKt0iZwrqu1G7ypPnnAOCOUh5CiAqy/tBpJi+Lo0OYDw9asDmkMig2at5feYDnFu6iY5gvrw9oZu2QhLjp6nq78N3YdhQVGxk5fStp2ZZJqoZGB1Ns1CyMTbr6xqLSKzNJ01qfKrFNqtb6uNb6OJAGSI9EIa5BRk4Bmea7Ma9Ea81X647wwIxt1PV24aP7WlWpcc6u5mBqNg/O/JvP/jrC0Oh6fPtgtMU6TgtR1TSq5c63o6M5nV3AKz/usUiZ9f1c6RDmw9xtJ8gvKrZImcJ6yjOY7UKgU4nXxeZl0RUSkRDVhNaazUczmLUpgd/3pWLUEOLrQptgb8Z3DbvYDyU+JZvvtiRwPCOXE2dyOZ6RS9+I2ky5pyWu1WAuvqJiI0t3nmTO1uPsOHEOBzsb3r47kmHtpIlTiNbB3jzduxFv/XaAVXEp3Na89g2XOaF7Q0bN2MaUlfG8JjXVVVp5rgB2WuvCCy+01oVKKYcKjEmIKiO/qJhio8be1obzBQaOnM7hYGoOW49lsPFwOuk5hXi52PNQ1zA8ne3Zk5TJ6v2pLNmZzOA2dTEaNT/tTMbZ3pZGtdxpXseDcV3qM7JDSJUd8wxMsyAkn8tjTXwaX6w9SvK5PBr4u/Ja/3DublMXH1f5FyLEBQ92rs/i2GQmL9tHl0Z+uDjc2Jezro39GdkhmG82HOPWpgF0auhnoUjFzVaeT8JppdSdWuulAEqpgUB6xYYlhHXlFxWTdDaP5HN5NAxwI8jL+ZL15wsMTP3zEDM2HKOo+J8DQvu5OdKloR/dmvjTNyIQJ3vbi+vO5Rby+ZojzNyYgFIw/pYwHunWAO9qkLhsPJzOtD8PszPxHHnmppY2wV68eVdzejQJqNKJpxAVxd7Whv8MimDIF5v55I9DvNw3/IbLfLVfMzYdzuDZhbtY8WRXmdOziirPjAMNgO+BOpj6oiUCo7TWhys+vOsjMw6IG7Fs10menr8Tg9H0t+FgZ8P4W8KY0KMBp7ML+OuAqXYoJSufu1sH0aS2OwajxtHOhgb+boT5uxLs43LVhCQjpwClVLWoVdp+4ixTVsaz6UgGdTyduD2iNo0C3IkI8iAyyFOSMyHK4fmFu/hpRzJbX+lpkamddiWeY/B/N9EvMpCpw1pbIEJRUa55xoELtNZHgA5KKTfz65wKiE+ISiEzr4hJS+NoGujOuC5hBLg7siAmkWl/Hebr9UcpMJjmjIwM8uSzEW1oG+J93fuqDvPrHUjJYsrKg6zen4qvqwNv3NGMYe2CL6k5FEKUz4Od67MwNolV+1It0mezZT0vJvZsxIe/H6RneAADWwVZIEpxM11pWqiRWus5SqlnLlsOgNb6wwqOTYgKV2zUZOcX4eViqs36ePVBzuQWMmtMOyKCPAHo1NCPER1CWBSTRLM6HnRt7E+o79VryqqznAIDU1bGM3tzAq6Odjx3W2Me7Fy/WtzoIIS1hAe6E+LrwvK9KRa7sWZC9wb8FZ/Ga0v2Eh3qQ53Lum6Iyu1K/1FdzT/dS1l35TZSIaqI15bsYWFMEg92DuW25rWZvfk4I9oHX0zQLogO9SE6VEbEB9MYbi8s2k1KVj4j24fw7G2NLya5Qojrp5SiT0Rtpq8/RmZukUX6kdnZ2vDxfa3o+8l6nl2wi+/Hta9Ww/pUd1eaFupL89PVWuuNJdcppTpXaFRC3AQbDqUzd1sizQI9+GbDMb5efwxvF3ueu62JtUOrtOZtO8GrS/YS5ufKokc63VBzrxDin/pFBPLl2qP8vj+VIW3rWqTMEF9XXukXzmtL9rL20Gl6NAmwSLmi4pVnFMlPy7lMiCojt9DASz/uJszPlR8ndGLZ413o3awWbw2KlFqhUmit+fD3g7z04x66NPTjp8c6S4ImRAVoUdeTIC9nVuw9dfWNr8G9UfUIcHdkxoZjFi1XVKwr9UnriGkQW//L+qV5ANIrWFRpH6w6SNLZPOaP74CTvS0RQZ58PeofN9YIs7nbEpn6xyHujarLfwZFyiwBQlQQpRS3N6/NnC3Hyc4vwt3JMkNnONjZ8ECnUN5fGU98SjZNapfWk0lUNlf6T+sAuGFK5NxLPLKAIRUfmhAVY/W+VGZsPMaI9sG0D/O1djiVXuKZXP7z6z46N/TlnbtbSIImRAXrG1mbwmIjfx5Is2i5w9sF42RvI7VpVciV+qStBdYqpWaa5+xEKWUDuGmts25WgEJY0t7kTCbO20FEHU9e7X/jA0ZWd0aj5sXFu1FK8e7gFtLhWIiboG2wN3U8nfhg1UE6hvkS4OFkkXK9XR24u01dFsUm8XyfJvhVg2GAqrvyfCV+WynloZRyBfYC+5RSz1dwXEJYlKHYyIGULMbO+hsvZ3umPxB1w1OvVFeZuUXM3pzAxKio4AAAIABJREFUl2uP8MpPe9h0JIPX+odT19vF2qEJUSPY2CimjWhDek4Bo2ZsIzO3yGJlj+lcn0KDkVmbEixWpqg45blKNdNaZymlRgDLgZeAWOD9Co1MCAs4nJbN4z/s4HBaDgajxs3RjoWPdLTYN9Pq5sjpHMbNiuFY+vmLy/pHBnJfdD0rRiVEzdMm2Juv7o9izMy/eXDmNuaO74Cj3Y13B28Y4Eb/FoF8sfYIvcJr0bKelwWiFRWlPEmavVL/z959x2VV9g8c/1w3e29QmcpQcSvunSMzV9ku07JsWdl4nqfxtOvX096WtizLtG2ZmSNzL1TcooigiEyVvbl+f4CmqYhyH+4b+L5fr/slnHM41xcP48s1vpeyA8YB72uty5RSUidNWL2cwjLu+CKW/JJy7hrYilAfF3q29CbUx+XCH9wErdyXyX1ztmBvY+KbO3vRMcgDG5PCwdbUpAv3CmEp/SJ9efWajkybF8fvO9IY18U8Owa8NK49W5OPc/83W1nwQD/czbQ4QZhfbYY7ZwBJVBW3XamUCqVq8YAQVqu8opKp32zhyIkiPrqlG/+6vA3XxQRLgnYOhaXlPPvLLm79bCOBnk78fF9feof74OJgi6OdjSRoQljQmE4tCPVxZs6GQ2a7p6ezPe/e2IUjJ4p44scdXGgPb2E5F0zStNbvaq0DtdYjdZVkYHA9xCbEJamo1Dz9yy5W7c/ixXHtiZGdAs5r5b5MRr6zillrk5jYO5Qf7+1DsLfMPRPCWphMiht7hLAx6Rj70/PMdt+YMG8eHhbFgu1H+Tb2sNnuK8yrVjOnlVJXAu2A0yfyPG9IRA1AWk4xecVlRAZInRlrk1tcxv1ztrJiXyZ3Dwzn+u7m2f+usdmVmsPLC/eyOiGLEG9nvrmzF73DpRyJENbomm5BvLE4njkbD/HM6HZmu+/dA8NZeyCLZ37ZRZcQL6Lkd5rVuWCSppT6CHCmqvfsE6pqpG00OC6rVVmpuXbGWgI9nZg7pbelw2nyDh8r5N/fbycjr5gWnk4cPlZIyvEiXrqqPTf3DLV0eFZpb1ouV32wFhcHG54aFc0tvULMMiFZCGEMX1cHLm/XjB82p/CfEW1wtDPP96uNSfHW9Z0Z+c4qps7Zwi9T+5nt3sI8ajMnrY/W+lbguNb6OaA3EFWXRpVS1yqldimlKpVS5y3zrpQaoZSKV0olKKUeq0ub5mIyKW7tFcb6xGPEHT5h6XCatFX7Mxn9/mp2puYQ4e9KTlEZjnY2zJ7cUxK08yivqOTf32/HzdGWJQ8PZHK/lpKgCdEA3NQzhNzicn7bbt7tovzdHHnjus7sS8/nxd92m/Xeou5qk6QVVf9bqJRqAZQBzevY7k7gamDl+S5QStkAHwBXANHAjUqp6Dq2axY39gzB3dGWGSsOWDqUJqm0vJI3F8cz8bONBLg58svUfsyYEMMvU/uxaNoAGbarwaerD7I9JYfnxraTQpZCNCC9W/nQyteFL9YlmX2i/8AoP27rG8bXGw6x80iOWe8t6qY2SdoCpZQnVXXRtlC10vObujSqtd6jtY6/wGU9gAStdaLWuhSYC4ytS7vm4upgy4TeoSzalUZiZr6lw2n0VuzL5NVFe/lhcwor9mVy1fQ1vPtnAld1CeLHe/vQ0ldWbNbGvvQ83lyyj+HRAVzZoa5/Zwkh6pNSijsHtGJ7Sg6r9meZ/f7Thkbh6WTHi7/tltWeVuSCc9K01i9Uv/mDUmoB4Ki1ro9UOxA4fclJCtDzfBcrpaYAUwBCQoyfLD6pT0s+XnWQj1cl8vLVHQ1vrynKKSzjuQW7+HHLkTOO+7raM2NCNy5v18xCkTUcWmuWx2cwZ8Mhlsdn4upgy4vj2ktZDSEaoKu7BvLO0v28vzyBAVF+Zr23h5MdDw2L4un5u1i8O11+vlqJ8yZpSqmraziH1vrHmm6slFoKnOspP6m1nl/7EGtHaz0TmAkQExNj+J8Bfm4OXNstiO9iU3h4WGv83GToyJwSMvK4+ZMNZOeX8sBlEdwzKIIjJ4pIyiqga6gX3i72lg6xQfhoRSKvLNqLn5sDUwa04qYeIbLbghANlIOtDXcNbMVzv+5mQ2I2PVuZd2rHTT1C+HJdMi8v3MPg1v7Y29ZmsE0YqaaetNE1nNNAjUma1nroJUX0tyPA6XvRBFUfsxpjOwfy9YZD7D6ay0A38/5V05QdOVHEhE83UlEJP9/Xl/aBHkDVdiYR/q4Wjq7hmLvxEK8s2svoTi1487pO2NnID1whGrobuofwwfIE3l+eYPYkzdbGxJNXtuW2zzfx8apE7hscYdb7i4t33iRNa31bfQZyDpuASKVUS6qSsxuAmywb0pk8nKq20sgvLrdwJI3HsYJSJny6gfyScuZN6U10C3dLh9SgZOQWE5+eR9yhE7y1dB8Dovx441pJ0IRoLJzsbZjcrxWvLNrL+sRsepk5URvc2p+RHZrxztL9XN6umfxhbGHn/cmtlHr7tLcf/Me5WXVpVCl1lVIqhapyHr8ppf6oPt5CKbUQQGtdDkwF/gD2AN9qrXfVpV1zc3OsynHzS8osHEnjoLVm6pwtHDlexKcTu0uCdhGy80t4+Ns4evzfMiZ8upE3luyje5g3H93SVYYshGhkbu0dSqiPMw/Pi+N4QanZ7//smHY42dvwnx+2U1kpiwgsqaaf3gNOe3viP87Vaaa81vonrXWQ1tpBax2gtb68+niq1nrkadct1FpHaa3DtdYv1aVNI7hWJ2l50pNmFt9vTmHtgWyeHh1Nj5aylVNtFJVWMHtdEkPeXMGv21K5a0Ar5tzZk41PDmHulF4429dqUxEhRAPi4mDLezd2ITO/hH99v93sqzH93Rx5elQ0m5OP8+W6JLPeW1ycmn6Cq/O8Laq52EuSZi7Z+SW8tHAPMaFe3ChbOdWooKScnUdy+HNvBnM3HSanqIweYd68dFV72apMiCaiY5Anj13RlhcW7ObzNUnc3q+lWe9/dddAftmWyuuL9zGuSyCezrJYyxJqStJMSikvqnrbTr59MlmTEuVUbanh6mBLfokkabVVXFbBpqRj9IvwPaMMxEu/7aGgpJz/u7oDJpP8TfBPZRWVLNieyqy1yexIOUGlrvr6G9GuGZP6hhET6iVlNYRoYm7vG8aahCxeXxzP2M4t8DFjgWqlFI+PbMOIt1fx2eqDPDy8tdnuLWqvpiTNA9jM34nZltPOySB1NVcHW/KKZU5abb26KJ7P1hzkhbHtmNA7DIBFO9P4cesRpg6OkA1+z2HV/kz+9d120nKLifB3ZeplkXQJ9qRTsKeUIhGiCVNK8cTItgx/awUzVyby+Mi2Zr1/m2bujGjXjM/XJDG5Xys8nO3Men9xYTWt7gyrxzgaLFdH6UmrrYzcYr7ekIyDrYkXFuyhS4gXAA/Ni6NTsCdTL5Pl3v+UlV/Cg3Pj8HK24/NJ3RkY5Sc9jUKIUyL8XRnTqQVfrkvmzgGtzL7d2/1DIli0K43P1x5k2tA6bdstLoEs+6ojN0dbmZNWSx+uOEB5pWbeXb3xdrHnvjlbuOOLWLyc7fj41m442sko+um01jzx4w7yi8v58JZuDG7jLwmaEOIs9w+JpKS8gpkrE81+73YtPBgWHcBnqw+SK6NG9U6StDqqGu6UJO1CMnKLmbPhEOO7BtI52JP3bupCyvEi8orL+GRid/zdpAr+P/0cd4TFu9N5ZHiUDAMLIc4r3M+VsZ0D+XJdEpl5JWa//4NDIsktLufNxfvMfm9RM0nS6shNhjtr5YPlCZRXaqYOjgSge5g3n0yMYc6dvaQe2jlsPXScp+fvoluoF3f0b2XpcIQQVu6BIZGUlFcye32y2e/dPtCDSX3CmLU2id+2HzX7/cX51aqIklKqHxCptf5cKeUHuGqtDxobWsPg5mDXZHccKCqt4OXf93Awq4DUE0VoIMKvauumyABXIv3dyMovYfryA2xMOsYN3YMJ8XE+9fGDW/tbLngr9vuOo0ybF0eAuyNvX98ZGxniFEJcQEtfF/pH+vF97GEeHBJp9p8bT4xsy/aUE/z7+220buYmOxHUkwsmaUqpZ4AYoDXwOWAHfAX0NTa0hsHVsemu7vxtx1G+XJdMh0APogLc0BoSMvP5c28G5adVqW7u4cgzo6O5sUfTrX92stjk+cpkHMjMZ9PBY2w8eIyf4o7QOdiTT26NMeuSeiFE43ZdTBBT52xlTUIWA6LMu5+0va2JD27uyqh3V3PPV5v57YH+sptJPahNT9pVQBeqS3BorVOVUjJBppqrgy0FpRVUVOom1+OxYHsqgZ5O/DK17xnJR2l5JYeOFbA/PZ/ySs3wdgE42DbNRQHZ+SV8tf4Qs9cnU1BSTnMPR0J9nLmhRwjD2gaQXVDKi7/tZn5cKgCeznbc0D2YZ0a3k4UUQoiLMiw6AE9nO+bFHjZ7kgbQ3MOJ167tyO2zYpmzIZlJfc1bQFecrTZJWqnWWiulNIBSysXgmBqUk/t3FpSW4+7YdGrIHC8oZfX+LCb3a3lW75C9rYkIfzci/JtmLq+1ZuPBY3wbm8KC7amUlFdyWRt/Wvm6cDSnmLjDJ7hr9mZa+bqQlV9CcVklD1wWwbgugbT0dZGitEKIS+Jga8O4zoHM2XCI4wWleBlQR3Fwa3/6hPvw7p8JjO8WhFsT+r1nCbVJ0r5VSs0APJVSdwK3Ax8bG1bD4Xba/p1NKUn7Y1ca5ZWaUR1bWDoUiyouqyC7oJTjBaUcyMxnfWI2q/ZnkXK8CFcHW67uGsTkfmFnJKzlFZUs3JnG52sOEuztzFOjomV+hxDCLK6LCWbW2iR+jjvCbQb0dCml+M+INoz9YA0frzrIw8OkdpqRLpikaa1fV0oNA3Kpmpf2tNZ6ieGRNRCuDlWJWWNfPFBZqdmblkfb5m4opViw/SihPs60D2yaKzO11nyxNomXf99LSXnlqeNujrb0bOnDw8OiGNG+2Tk3OLe1MTGmUwvGdGraCa4QwvyiW7jTIdCDuRsPM7F3mCG1FTsFe3Jlh+Z8siqRCb1C8XOTubNGqc3CgYeBeZKYndvJnrT8ksa9eODtZft5d9l+bugezEPDolh7IIt7BoU32qG53OIyNicfZ3PScQK9nLi6a+CpeXWZeSU89sN2lu3NYHBrPy5v1wxPZ3uCvJxo29y9yc1NFEJYl9v7hfHQvG18sS7JkN40gEcvb82iXWlM/yuBZ0a3M6QNUbvhTjdgsVLqGDAP+E5rnW5sWA2Ha3WSltuIe9J2peYwfXkCrXxdmLvpMMvjM6jUNNqhzt93HOX+b7ZSXqkxKajU8O6y/VzTLYi4wydYeyAbG6V4dnQ0E/uENdpEVQjRMI3rHMgvcam8smgvA6P8aOVn/ukULX1dGNOpBd9uOsxDw6Ka1HSf+nTB9bNa6+e01u2A+4DmwAql1FLDI2sg3Byqe9IaaZJWVlHJo99tx8vFnh/v7cMr4zuQlV9KuJ8LbZo1voUBhaXlPPfrbqIC3JhzZ092PTeC2ZN7EOTlxHt/JpCcXcid/Vux8MH+TOp79qIJIYSwNKUU/xvfEQdbGx79bhsVp5VEMqfb+oZRUFrBd7Ephtxf1LKYbbUMIA3IBqQKabWTK1sa664D05cfYM/RXGZO6Iansz3Xdw+hXQsPHO1sGmWC8vHKg6TlFvPeTV3oHuYNQP9IP/pF+JJdUIqPi32j/LyFEI1LgLsjz41px7R5cXy8KpG7B4abvY2OQZ50C/Xii7VJTOoTJlM9DHDBnjSl1L1Kqb+AZYAPcKfWuqPRgTUUrqdWdza+OWkHswr4YHkCYzq1YHi7ZqeOtw/0aDSrEWOTjvHM/J3sT88jLaeYj1Yc4MoOzU8laCcppfB1dZAETQjRYIzt3ILL2wXw5uJ97EvPM6SN2/qGcehYIX/uzTDk/k1dbcoFBwPTtNbttNbPaq13Gx1UQ+JsZ4NSjXO48/lfd2Fva+K/o9paOhRDFJaW8+DcOL5Yl8zwt1cy/sO1VFRq/jOijaVDE0KIOlNK8dJVHXB1tOWRb7dRVlF54Q+6SCPaNaOFhyOz1spOkUY4b5KmlDpZW+E14JBSyvv0V/2EZ/1MJoWrgy15jWy4c9medJbHZzJtaCT+bo6WDscQ7/+ZwJETRcyY0I2pgyPIKy7j7kHhZ+wvKoQQDZmvqwMvjWvPjiM5TF9+wOz3t7UxMaF3GGsSslkuvWlmV9OctDnAKGAzoIHTx3k00MrAuBoUNwdb8hpRT1pxWQXPL9hNhL8rE/uEWTocQyRk5PHxqkTGdw3i8nbNuLxdMynKKIRolK7o0JwxnVrw3p/7ubprIMHe5v1DdFKfMBZsT+WBb7by0319muxuM0Y4b0+a1npU9b8ttdatqv89+ZIE7TSujraNarjzi7VJJGcX8uzodtjZNL4NdLXWPPXzLpzsbHh85N9Dm0opmXMmhGiUHruiDRqYvT7Z7Pd2srdh5q0xONiZmPxFLCcKS83eRlNVm4UDy2pzrClzc7RrNKs7C0vLmbEykQFRfvSL9LV0OIaY/tcB1iVm858r2uDrKpWyhRCNXwtPJ0a0b8bcjYcoLDX/76tATydmTOjG0RPFTJsXh9bGlP1oamqak+ZYPffMVynlddp8tDAgsL4CbAhcHWwbzerO2euSOVZQyrShkZYOxRB/7k3n9cXxjO3cgpt6hFg6HCGEqDe39w0jt7icH7ccMeT+3UK9efLKtvwVn8ncTYcNaaOpqakn7S6q5qO1qf735Gs+8L7xoTUcro6NY+FAYWk5M6t70bqGeFk6HLPbkZLDg9/EEd3cnf9d3VGGNoUQTUrXEC86BHowa22SYT1dE3qF0ifchxcX7ObwsUJD2mhKapqT9o7WuiXw6D/mpHXSWkuSdhr3RjIn7av1yWQXlPLgkMbTi1ZcVsGri/Zy2et/Mfr91djZmpgxoRtO9jaWDk0IIeqVUorb+oaRkJHPqv1ZhrRhMilevabqj+B/fb+NSoN2O2gqarMt1HtKqfZKqeuUUreefNVHcA2FayNY3VlRqZm5MpH+kb50C208vWhPz9/J9L8OEOjlxHNj2rHowf4EeUmJDSFE03Rlx+b4uTnw+uJ4SsvNXzcNIMjLmadGtWV94jFeWxxvSBtNRW0WDjwDvFf9Ggy8CowxOK4GxdXBjqKyCsr/UShQa91gJk8mZReQlV/K6E6NZ9P072IP821sClMHRzB7ck8m9gnD371x1nwTQojacLC14YWx7dieksNrf+w1rJ3rYoK5qWcIH/51gFlrpNDtpapNfYVrgCFAmtb6NqAT4GFoVA2MW/XWUAUlFWccn/7XAYa8saJBdPfGp1VtGdJYNk3fm5bLU/N30quVd6NdBCGEEJdiRPvmTOgVyserDvLn3nRD2lBK8cLY9gyPDuC5Bbv5dVuqIe00drVJ0oq01pVAefUuBBlUbRUlqp3cvzP3Hys8/9ybQWJWAfsyjNkzzZz2puVhUhDZCIoQJmUVMHlWLG6Odrx7YxdsG2GtNyGEqIsnr2xL2+buPPLtNtJyig1pw8akePfGLnQP9ebBuVv5ZuMhQ9ppzGrz2ytWKeUJfEzV6s4twDpDo2pg3ByqkrTTa6WVlFewIyUHgHUHsi0S18WIT8slzMelwU+oj0/L49oZ6ygsLefzSd0b7ZZWQghRF452Nrx/UxeKyyr51/fbDJua42hnw+e3dad/pB+P/7iDN5fsazDTgKxBTdtCAaC1vrf6zY+UUosAd631dmPDaljcHO2AM5O0Xam5lFbPUVt7IJvb+ra0SGy1FZ+WR9vm7he+0MpUVGqmL0849f+9Ofk4DrYm5t3Vm6iAht8rKIQQRgn3c+XJK9vy3593Mnt9Mrf2DjOkHRcHWz6ZGMPjP+7g3WX7cba34e6B4Ya01dicN0lTSnWt6ZzWeosxITU8J4c7Ty9ouyX5OACXtfFnfWI2FZUaG5N11uUqLC0n+Vgh47o0rBrF5RWVPPLdNubHpRLuV9UL2DnYk+fHtiPUx8XS4QkhhNW7uWcIS/ek838L99An3JcIf1dD2rGzMfHaNR3JKy7jzcX7GNLGn0j5Q/qCaupJe6OGcxq47FIbVUpdCzwLtAV6aK1jz3NdEpAHVADlWuuYS23TSK4OJ5O0v3vSth46QaCnE+O6BPLn3gx2pebQMcjTUiHWaH96Plo3rEUDJeUVPPDNVv7Ylc6/R7Tm3kERlg5JCCEaHKUUr47vyOVvr+Rf32/jh7v7YDKoQ0EpxUtXdWD4Wyt55Ltt/HhPH5kzfAE1FbMdXMPrkhO0ajuBq4GVtbh2sNa6s7UmaFBVzBbOHO7ccug4XUO96N3KB6ga8rRWJ1d2tm7WMIY7M/KKufnjDfyxK51nR0dLgiaEEHXg7+7IEyPbsvXQCX7dbuwqTF9XB14Y257tKTnMWJloaFuNwQXnpJ2vcK3W+stLbVRrvaf63pd6C6vy93BnVZKWeqKIoznFdA3xxM/NgagAV9YeyLbaMfg9abk42dkQ4m2dRV4rKjWHjhVSqTWpJ4p49Ltt5BaV8/5NXRjVsfHUdRNCCEsZ3zWIL9Yl8crvexke3czQRWRXdmzOwp3NeWvJPtoHejAwys+wthq6CyZpQPfT3nakqmbaFuCSk7SLoIHFSikNzNBazzzfhUqpKcAUgJCQ+t0428nOBhuTOrU11JZDVfPRTlbu7xPuy7xNhyktr8Te1vq6duPT8ogKcLXKOXNpOcXcNTuWbdUrZQGCvJz44Z4+RLdoGD1/Qghh7UwmxVNXRnP9zPV8siqR+w3eHvB/V3cgMbOAe77azLwpvekQJOVXz6U2qzvvP/396nIccy/0cUqppUCzc5x6Ums9v5bx9dNaH1FK+QNLlFJ7tdbnHCKtTuBmAsTExNTr+l6lFK4OtqeGO7ckn8DRznRqtWTvcB9mrU1iW8oJuod512dotRKflseQtv6WDuMsm5OPcdfsLRSVlvP0qGh8XO2xMSn6R/jh4Wxn6fCEEKJR6dnKhxHtmvHhigNc1z2YAAN3aHFztOOL27pz1fS13DZrIz/e05cQH+sczbGkS+nWKQAuWE9Caz1Ua93+HK/aJmhorY9U/5sB/AT0uIR464Wrg+2pYrZbDh2nY6AndtUTInu19MHWpHh6/i62HT5Rq/ul5xbzzPydZOSdu8jghsRsPl6ZWOd6M5l5JWQXlFrdfLTNyce5ceYGXBxs+Om+vtzeryVjOwcyqmMLSdCEEMIgj49sQ3ml5vlfdxvelr+7I19O7kFJeSXPLzC+vYaoNnt3/qqU+qX6tQCIpyphMpRSykUp5XbybWA4VQsOrJKboy35xeWk5RSzKzWHLqF/r+T0cLZj+s1dyc4vYdz0Nbz02+4zkquKSs2KfZkUl1VtK3W8oJQJn27gi3XJfLY66ay2vt+cws2fbOClhXvYfTS3TnFb43ZQxwpKmTpnCwEeDvx8b1+pdyaEEPUk1MeFBy6L4LcdR1my25gto04X7ufK5H4tWbon/dTvI/G32vSkvU5VOY43gJeBAVrrx+rSqFLqKqVUCtAb+E0p9Uf18RZKqYXVlwUAq5VS24CNwG9a60V1addIbo62bD18gmFvrsCkFCPbNz/j/PB2zVj2yEDGdQ7k41UHScwqOHXu122pTPxsI0PeWMG3sYeZ+PlGkrILaR3gxo9bUs7YuP3dZft59LttdAv1ws5G8eOWI3WKe29aVZLX2kqStMpKzUPz4sjOL2X6Td3wcrG3dEhCCNGkTBkQTptmbjz1884z6n8aZVKfMJztbfjwrwTD22poLpikaa1XaK1XAFuBPUChUqpOE6u01j9prYO01g5a6wCt9eXVx1O11iOr307UWneqfrXTWr9UlzaN5uFkR2ZeCR2DPfhj2gA6BZ9dE83N0Y77Blet8NycdPzU8Q0Hs3F1sMXT2Y5/f7+d3am5fHhzVx4aFkVGXgmr9mcBsGJfJm8u2cdVXQKZPbknQ9oEMD/uCGWnJXEX66/4TAI9nfB1dbjke5jTRysPsGJfJk+PjpaJpEIIYQH2tiZevroD6XnFvPZHvOHteTrbc0uvUH7Zlsqh7ELD22tIajPcOUUplQZsB2Kp2r/znMVnm7JHL2/Nx7fG8NXknoT5nr/afStfVzyd7YhNPnbq2MaDx+ge5sWvU/sx/eauzLqtB0PaBnBZG3+8Xez5bvNhyisqeXHBbkJ9nPnf+A7Y25q4umsgWfmlrNqfeUkx707NZXVCFrf0Cr2kjze3lOOFvLN0PyPaNePmnvW7QlcIIcTfuoR4cWuvUL5an0zSaSM/RrmjX0tsTSY+WnnA8LYaktoMd/4LaK+1DtNat9Jat9RatzI6sIamTTN3hkUHXLD2m8mk6BbiRWx1T1p2fgkHMgvo3tIbk0kxskNz+kX6AlV/zYzrHMiS3em8vzyB/Rn5PDmyLQ62VfVrBrX2x8vZjh8uccjzk1WJONvbcFMP60iI/vf7XpSCp0ZHN5oaekII0VDdd1kEdjYm3l9u/DCkv7sj18QE8X1sCvvSZW7aSbVJ0g4A0v9oRt3CvEjMKiA7v4TN1Xt8nq80x7UxQZRVaN5eup++ET4Miw44dc7e1sTY6iQup/Di5g0czSnil22pXN892CpWS25KOsaC7UeZMiCcQE8nS4cjhBBNnr+bIzf1DOGnrUfqZRhy2pBI3J1suffrLRSctoNPU1abJO1xYK1SaoZS6t2TL6MDa8xiQqsSss3Jx4lNPo69jYkOgeeef9W2uTvtA90xKXhq1Nk9TFd3DaS0vJK3l+2jsPTvL+qS8goqKs9fnmPW2iQqteb2vhespmK4yurl3s3cHbl7oHTSCiGEtbh7YDg2JsX0epjU7+/uyLs3dCExM58nftpR5xJTjUFtdhyYAfwJ7AAufYa6OKVjkAd2NorNycfZlHSMjkEeONqdfwuOl8Z14PDxQtqco5ZZh0APRnZoxudrkvjwZic9AAAgAElEQVR56xGu6NCc/el5bDucQ/9IXz6ZGHMqsducfIxftx0lM6+E5fEZXNGhOcH1vBVUQkYen6w6yGNXtMHTuWrl5udrk9hxJIe3r++Ms31tviSFEELUhwB3R27sHszXGw4x9bIIgryM/Z3RJ8KXh4ZG8caSffRq5cONVjIdx1Jq05Nmp7V+WGv9udb6i5MvwyNrxBztbOgQ6MHqhCx2Hskh5gK7EHQK9jzvHpVKKabf3I0f7ulNlxAvvos9TFmFZmBrP5btzThVouNAZj63frqRb2MPsyctl26hXjw6vLXZP7cLeWVRPHM3Heaer7ZQWl7JziM5/O/3PQyLDmBsZ9mHUwghrM3dg8IxmRRP/LSTyhpGaMzlvsER9Gzpzet/xFNUWmF4e9asNt0Wv1fvi/krUHLyoNb62Pk/RFxITJg3M1cmAtCjpVed79ct1JvPJnmjtUYpRWWl5toZ63h+wW56tPTmvq+3YG9rYuGD/WnuYZk5XwezCli6J51uoV6sS8zmsR+3E3foBD4uDrw6vqMsFhBCCCvU3MOJZ0ZH8+RPO3nvzwQeHGrsvp4mk+Jfl7fmmo/W8fWGZO7o33SnwdSmJ+1GquelUVV+Q0pwmMHJzdcBuoWYbz/Pk4mOyaR4ZXxHikorGPnuKuLT83jr+s4WS9AAPl2diJ3JxIe3dOX+yyL4ccsRDmYX8PYNnaVorRBCWLGbeoRwdddA3l62jxX7Lq3s08WICfOmT7gPM1YmntqNpymqTTHblud4Nd201kxOJmmtA9wMW10Z4e/Kg0MjySsuZ+rgCAa1ttwm6scLSvl+cwrjurTA382Rh4ZGcdfAVrwwtj29WvlYLC4hhBAXppTipXEdaB3gxrS5WzlRWGp4mw8MiSQzr4S5Gw8Z3pa1uuBwp1Lq1nMd11p/af5wmg5fVwd6tfKmZ0tjE5R7BobTq5U3nYPrPqRaF1+tT6a4rPJUt7XJpHj8irYWjUkIIUTtOdnb8Nb1nRn57io+XHHA8J/hvVr50KOlNx+uOMANPUJqXGDXWNVmuLP7aa/+wLPAGANjajLmTunNQ8OiDG3DZFJ0C/XGxmS5+V5Ldqczc1Uig1r7yWbpQgjRgLVt7s5VnQOZtSaJtJxiw9ubNiSS9NwS5mxomr1ptRnuvP+0151AV8DV+NBEQ1VcVkHqiSJ2pOTw2A/bufPLWIK9nHluTDtLhyaEEKKOHhoWRaXWvLNsv+Ft9YnwpW+EDx8sTyC/CRa4vZSiVAWA5SugCqsRn5bHx6sS2ZR0jOz80jO+kZSCeweFM21oFPa2tem4FUIIYc2CvZ25uWcos9cnc0f/loT7Gdtv86/L2zDugzV8uuqg4StLrU1t5qT9CpwsjGICooFvjQxKNAyFpeU88M1Wlu7JwMnOhsva+OPv7oCvqwPeLvb4uNgT7u9q+DewEEKI+jX1sgi+jT3M+38m8Nb1nQ1tq3OwJ5e3C+DjVYlM6B2KdxOqBlCbnrTXT3u7HEjWWqcYFI9oQBbtTGPpngymDo7gjv4tT+0gIIQQonHzdXXguphgvt6QzBMj2+Ln5mBoe48Ob82S3Sv5YHkCT42KNrQta3Le8SelVIRSqq/WesVprzVAqFIqvB5jFFZqye50AtwdeHhYlCRoQgjRxNzaO5SyCs039VAiIzLAjWu7BfPF2iT2puUa3p61qGmS0NvAuf4ncqvPiSasuKyCFfsyGdI2AJMFV44KIYSwjFZ+rgyI8uOr9cmUVRi/tfdjV7TB3cmOx3/cUS/bU1mDmpK0AK31jn8erD4WZlhEokFYn5hNYWkFw9oGWDoUIYQQFjKpTygZeSX8vjPN8La8XOx5alRbth46wdcbkg1vzxrUlKR51nDOcnsLCauwdE86TnY29A6X3QKEEKKpGhTlT6iPM1+sTaqX9sZ1DqR/pC+vLIrnaE5RvbRpSTUlabFKqTv/eVApdQdV+3eKJkprzdLdGQyI8m2SFaCFEEJUMZkUt/YOY3PycRbuOGp4e0opXhzXnopKzaPfbWv0w541JWnTgNuUUn8ppd6ofq0AJgMP1k94wlqUV1Syen8WRaUV7DySS1puMcOim1k6LCGEEBZ2S68QuoZ48si329idavyk/lAfF54ZHc2ahGw+XpVoeHuWdN4SHFrrdKCPUmow0L768G9a6z/rJTJhVWauSuTVRfG4O9oS5uuCScHg1n6WDksIIYSFOdja8NGEbox9fw13fhnL/Kl98XU1tiTH9d2DWbEvk9cXx9Mn3JcOQR6GtmcptdkWarnW+r3qlyRoTVBOURkf/XWAHmHeDIjyY3dqLr3DffAx+JtQCCFEw+Dv5sjMCTFk5ZfwwDdbDR+GVErx8tUd8HV14KFv4yivh9WlliD79IgL+nRVIrnF5TwzJpr3b+rKxieH8tEt3SwdlhBCCCvSIciD58a0Y+2BbGavN371paezPc+OaUdCRj4/bT1ieHuWIEmaqFF2fgmfrj7IlR2a065FVXeyt4s9bo52Fo5MCCGEtbm+ezCDWvvx8u97OJhVYHh7w6MD6BDowbt/7q+XWm31TZI0UaOPVhygqKyCh4ZFWToUIYQQVk4pxSvjO2JvY+LR77ZRUQ/Dng8Pi+LwsSK+39z4dqyUJE2cV3puMV+uS+aqLkFE+Msm6UIIIS4swN2R58e2Z3PycV5YsButjU3UBrX2o3OwJ+8t209JeYWhbdU3SdLEeb33534qtWba0EhLhyKEEKIBGdu5BZP7tWTW2iSm/3XA0LaUUjwyPIrUnGJmr2tcOxFIkibO6fCxQuZuPMz13YMJ9na2dDhCCCEaEKUUT45sy9jOLXjtj3jmbTJ2E/Z+Eb4MjPLjrSX7GtVOBJKkiXN6e+l+bEyKqYOlF00IIcTFM5kUr13TiQFRfvznhx18+NcBw4Y+T+1EoDXP/rLLkDYsQZI0cZaq5cwpTOgVSjMPR0uHI4QQooGytzUxc0I3RndqwSuL9vLkzzsNq2kW7O3MtKFR/LErncW7jN/wvT5IkibO8vHKROxtTdwzKNzSoQghhGjgHO1seOf6ztw3OJw5Gw7x2h/xhrU1uV9L2jRz4+n5u8jIKzasnfoiSZo4Q05hGfO3HeGqLoGyo4AQQgizMJkU/7q8DTf1DGHmqkRik44Z0o6djYnXr+1ETlEZk2fFUlBSbkg79cUiSZpS6jWl1F6l1Hal1E9KKc/zXDdCKRWvlEpQSj1W33E2Rd9tPkxxWSW39Aq1dChCCCEamSdGtiXIy4lHvttGYakxCVT7QA8+uLkLu1JzuPfrLQ26yK2letKWAO211h2BfcDj/7xAKWUDfABcAUQDNyqlous1yiamslLz1fpkuoV6ndpdQAghhDAXVwdbXrumE8nZhby8cK9h7VzWJoCXrurAin2ZvLVkn2HtGM0iSZrWerHW+mQKvR4IOsdlPYAErXWi1roUmAuMra8Ym6JVCVkkZRdya2/pRRNCCGGMXq18uKNfS2avTzZ0j88be4QwqmNzvlibRE5RmWHtGMka5qTdDvx+juOBwOHT3k+pPiYMMntdEr6u9oxo38zSoQghhGjEHruiDUPb+vP0/J0s3HHUsHbuHhhOQWkFX29omEVuDUvSlFJLlVI7z/Eae9o1TwLlwNdmaG+KUipWKRWbmZlZ19s1OQUl5fy5N4Px3YJwsLWxdDhCCCEaMVsbE+/d2JVuIV5MmxvHJoMWErQP9KB/pC+fr0miuKzhbRllWJKmtR6qtW5/jtd8AKXUJGAUcLM+d3W7I0Dwae8HVR87X3sztdYxWusYPz8/M34mTUNCRj6VGroEe1k6FCGEEE2Ak70Nn07sjr+7Ay8auMfn3QPDycwr4eet500hrJalVneOAP4NjNFaF57nsk1ApFKqpVLKHrgB+KW+Ymxq9qXnARAVIBupCyGEqB8eznbcMyicbSk5rDuQbUgbfcJ9aB/ozsyViVRWGrvZu7lZak7a+4AbsEQpFaeU+ghAKdVCKbUQoHphwVTgD2AP8K3WuvHs9WBl9mfkY29rIkT26RRCCFGPxncNws/NwbCN2JVS3DUgnMSsAhbvTjekDaPYWqJRrXXEeY6nAiNPe38hsLC+4mrK9qXn0crXBVsba1hLIoQQoqlwtLNhcr+W/O/3vWxPOUHHoHOWTq2TK9o3I9jbiY9WHODydgEopczehhHkN7IAYH96PlEBbpYOQwghRBN0c88Q3B1t+dCg3jRbGxN39m9F3OETbEo6bkgbRpAkTVBQUs6RE0UyH00IIYRFuDnacWvvMBbtSmNtQpYhbVzbLRhvF3tmrDAmETSCJGmC/Rn5AERKT5oQQggLuWdQOK18XXhg7lbSc82/ObqTvQ0Te4exbG/GqcVy1k6SNHHayk5J0oQQQliGi4MtH97SjYKSCu6fs5VyA/bcvLV3KE52Nry7bL/Z720ESdIE+9PzcJCVnUIIISwsKsCNl6/uwMakY7z7Z4LZ7+/lYs+UAa1YsP0oi3Yat9OBuUiSJtiXnk+4nys2poax2kUIIUTjNa5LIKM6NufjlYlk55eY/f5TL4ugQ6AHj/+4g4w88w+rmpMkaYL96XmyaEAIIYTVmDY0kuLyCj5ZfdDs97azMfHW9Z0pLK3gP99vN2ynA3OQJK2JyysuIzWnWBYNCCGEsBoR/m5c2aE5X65N4nhBqQH3d+WxK9qwPD6T+XGpZr+/uUiS1sSdXNkpiwaEEEJYkweGRFJQWsFna8zfmwYwsXcYHQI9+N/veyksLTekjbqSJK2JS0g/maTJcKcQQgjrERXgxsgOzZi1JokThebvTTOZFE+PjiYtt5gZKxLNfn9zkCStiduZmoOjnYkgL1nZKYQQwro8MCSS/NJyZq40JonqHubNlR2bM2PlAVJPFBnSRl1IktaElZRXsGD7US5r4y8rO4UQQlidNs3cGdOpBZ+vSTJsJebjV7ShUsP/ft9ryP3rQpK0Jmzp7gyOFZRyffcQS4cihBBCnNNDQ6MorajkAwPqpgEEeTlz98BwftmWysp9mYa0cakkSWvC5m46RAsPR/pF+Fo6FCGEEOKcwnxduC4mmDkbD3H4WKEhbdw7KJxWfi48+fMOq1pEIElaE5VyvJDVCVlcGxMsQ51CCCGs2oNDIlFK8eaSfYbc39HOhpev6sDhY0W8vdR6toySJK2J+i42BYBrY4IsHIkQQghRs2YejtzRryU/bT3C2gNZhrTRs5UPN/YI5pNView8kmNIGxdLkrQGqrJSk1dcdkkfm19Sznexh+kf6SerOoUQQjQIDwyJJNTHmSd+3EFxWYUhbTw2oi3eLg489uN2QzZ4v1iSpDVQbyyJp98ryzl2EZWYtdb8vPUIl73+F6k5xdzWN8y4AIUQQggzcrSz4aVxHUjKLuS9P40ZkvRwtuO5Me3YeSSXz9ckGdLGxZAkrQHKzi/hs9VJ5BSVXVTtmCd+2sG0eXE093Dkp3v7MLi1v4FRCiGEEObVL9KX8V2DmLEikd2puYa0MbJDM4a29efNJfsMW6hQW5KkNUCfrj5IcXkFMaFefLkuiez8krOuOZhVQEbu3zVldqXm8M3Gw0zsHcpP9/alS4hXPUYshBBCmMeTV7bFy8WeB+dupajU/MOeSimeH9sek6rq3LDkBuySpDUwJwpL+XJdMiPbN+d/4ztSXFZxRm+a1pqvNyQz/K0VXDV97akE7rU/4vFwsuPh4a0xyWpOIYQQDZS3iz1vXteJ/Rn5vPDbbkPaaOHpxL9HtCG3qIzcIsuV5JAkrYH5fE0S+SXlTL0sggh/V8Z0asGX65LZnZrLlkPH+c8P23nyp510DfEiM7+E++ZsYU1CFn/FZ3LvoHA8nOws/SkIIYQQddI/0o+7BrRizoZDLNp51JA2JvQK5cd7++LhbLnfm7YWa1lctPyScj5fc5Dh0QG0be4OwP1DIvllWyoj31116roHLovgwaFRzI87wsPfbiPu8CYC3B2Y2CfMQpELIYQQ5vXI8NasS8zmiZ920i/SD1cH86Y01jDqJD1pViotp5jxH649Y2Lkd7GHyS0u555B4aeOhfu58snEGF4Z34HPJ3Vn+aODeHh4a2xMiqu7BjG5X0uKyyp5cEgUjnY2lvhUhBBCCLOztzXx/Nj2HCsoZdaag5YOxxDSk2alPlmVyObk47y0cDdf39GLykrNF2uT6BLiedak/8vaBJz3Pk+MbMuVHZvTJdjT6JCFEEKIetU52JOhbf2ZuTKRCb3DGt2UHulJs0I5RWV8s/EQPi72rEnIZvX+LJbHZ5CUXcjtfVte1L1sTIquIV4oZfluWyGEEMLcHhoWRW5xOZ+uqn1JqoZCkjQrNGfDIQpKK/hkYgyBnk68+sdePl19kGbujoxo38zS4QkhhBBWo10LD0Z2aMZna5IuqsB7QyBJmpUpKa/g8zUH6RfhS5cQL6YNjWR7Sg5rD2Rza59Q7GzkkQkhhBCne2hoFAWl5byz1JgN2C1FfuNbmflxqWTklTBlQCsAru4aRIS/K452Jm7sHmLh6IQQQgjrExngxq29QvlyfTLbDp+wdDhmI0malSivqGTGigM8PX8n0c3d6R/pC1TNKfvolq58NrE7Xi72Fo5SCCGEsE6PXN4afzcHHv9xh1Vsjm4OkqRZgWMFpYx5fw0v/76XfhF+fDop5oyJ/hH+bvSJ8LVghEIIIYR1c3e049nR7dh9NJdZa5MsHY5ZSAkOK7Bwx1F2H83lnRs6M6ZTC1mJKYQQQlyCEe2bMaSNP68vjicmzJvODbz8lPSkWYE9R3Nxc7SVBE0IIYSoA6UUL4/vgJ+bA7fP2sTBrAJLh1QnFknSlFKvKaX2KqW2K6V+UkqdM9VVSiUppXYopeKUUrH1HWd92X00l7bN3SVBE0IIIerI382RL2/vCcCtn20gI7fYwhFdOkv1pC0B2mutOwL7gMdruHaw1rqz1jqmfkKrXxWVmvi0PKKr9+IUQgghRN209HXh80ndycor5dlfd1k6nEtmkSRNa71Ya11e/e56IMgScViD5OwCCksrJEkTQgghzKhTsCe39wvj951pJDXQYU9rmJN2O/D7ec5pYLFSarNSako9xmSYxMx83l22n8pKDcCeo3kARLeQJE0IIYQwp4l9wrAzmfi4gW4ZZViSppRaqpTaeY7X2NOueRIoB74+z236aa27AlcA9ymlBtTQ3hSlVKxSKjYzM9Osn8ul2p2ay+z1yWhdlZBVVmoe/W4bby7ZR1xKVbG93UdzsDEpIvxdLRmqEEII0ej4uzkyvlsg321OISu/xNLhXDTDkjSt9VCtdftzvOYDKKUmAaOAm/XJLObsexyp/jcD+AnoUUN7M7XWMVrrGD8/P7N/Ppdi1tqDPPXzTuZtOgzAz3FH2HKoKjn7fcdRoKonLcLPFUc7G4vFKYQQQjRWd/RvRVlFJV82wNppllrdOQL4NzBGa114nmtclFJuJ98GhgM76y/KujtyogiAp3/ZxcaDx3j59710CvZkUGs/Fu5IQ2vN7tRc2jZ3s3CkQgghROMU7ufK8OgAvliXTEFJ+YU/wIqo83RiGduoUgmAA5BdfWi91vpupVQL4BOt9UilVCuqes+gqujuHK31S7W5f0xMjI6NNbZix6BBg846dt1113HvvfdSWFjIyJEjSek0GdvSPMocvamwdwFl4qd7+xCXmMZzixIJ2PMd6W2vxSv5LzyObuKee+7h+uuv5/Dhw0yYMOGs+z/yyCOMHj2a+Ph47rrrrrPO//e//2Xo0KHExcUxbdq0s87/3//9H3369GHt2rU88cQTZ51/++236dy5M0uXLuXFF1886/yMGTNo3bo1v/76K2+88cZZ52fPnk1wcDDz5s3jww8/POv8999/j6+vL7NmzWLWrFlnnV+4cCHOzs5Mnz6db7/99qzzf/31FwCvv/46CxYsOOOck5MTv/9eNbXxhRdeYNmyZWec9/Hx4YcffgDg8ccfZ926dWecDwoK4quvvgJg2rRpxMXFnXE+KiqKmTNnAjBlyhT27TtzE9/OnTvz9ttvA3DLLbeQkpJyxvnevXvz8ssvAzB+/Hiys7PPOD9kyBCeeuopAK644gqKiorOOD9q1CgeffRRoHZfe/80adIkJk2aRFZWFtdcc81Z5+VrT772QL725Guv8X7tjZr0AGntb8Y7aRnuaVuA2n/t1Qel1OZzVbGwyI4DWuuI8xxPBUZWv50IdKrPuMxJA+UO7jgfT8Dz8GrSom+gs2cRXUK8cFclUFnB8eB+ANgXZlg2WCGEEKIRc8xPxSE3hZzmMbilx6F0w9jb0yI9aUarj560C8nIK6bHS8t4bkw7JvYJI/VEEf5uDtjaVI0wT/xsIyv2VS1wiP3vUHxdHSwZrhBCCNGoLd2dzh1fxvLODZ0Z2znQ0uGc4Xw9adZQgqNRSj1RVeE40NMJgBaeTqcSNICRHZoB4O/mIAmaEEIIYbDL2vgT7ufCjBWJNJQOKknS6qC8opL5cUeoqDz7YR85XjW23qI6SfunYdHNsDEpqY8mhBBC1AOTSXHXgHB2H81ldUKWpcOpFUnS6uCXbak8ODeODYnZZ51LrV7ZGeh17iTN28Wep65sy539WxkaoxBCCCGqjO3SAn83B15fvI/yCuuflyZJWh38tr2q1ll63tmbtx45UYSbgy0eTnbn/fhJfVvSN8LXsPiEEEII8TcHWxv+OyqabYdPMP2vA5YO54IkSbtEOYVlrNxfNfE/K6/0rPMpx4vOO9QphBBCCMsY06kFYzu34J1l+9l2+ISlw6mRJGmXaPHuNMoqquainWuridQTRecd6hRCCCGE5Tw/pj3+bg48NC+OotIKS4dzXpKkXaLfdhwlyMuJ5h6OZJ4jSTtyoogWno4WiEwIIYQQNfFwtuONazuRmFXAhyusd9hTkrRLcKKwlNX7s7iyY3P83BzIyj9zuDO/pJycojICPZ0tFKEQQgghatInwpfRnVowY8WBU9s4WhtJ0i7B4l3plFdqRnVoga+rA1l5Z/akXWhlpxBCCCEs7z8jWgPw6qK9Fo7k3CRJuwQLdhwlxNuZ9oHu+Lrak11wZpJ2skZaoAx3CiGEEFYryMuZKQNaMT8ulc3Jxy0dzlkkSbtIWmvaNndjQq9QlFL4ujqQnV9K5WkFbU92m8pwpxBCCGHd7h4YToC7A8/9usvqaqdJknaRlFI8fkVb7hxQVYTW19WB8kpNTlHZqWuOnCjCzkbh7ybbPQkhhBDWzMXBlv9eGc32lBw+W3PQ0uGcQZK0OvKtTsROL8OReqKIZh6OmEzKUmEJIYQQopZGdWzO8OgA3li8j8TMfEuHc4okaXXk62oPcEYZjiPHi05trC6EEEII66aU4sVx7XG0s+Hf328/YwqTJUmSVke+rid70v4uw1FVI02SNCGEEKKh8Hd35OlR0cQmH2f2+mRLhwNIklZnp5K06jIcZRWVpOcWEyRJmhBCCNGgXN01kP6Rvrz2RzxpOWfvy13fJEmrI08nO2xM6tSctKMniqnUUiNNCCGEaGhODnuWVVTy/IJdlg5HkrS6MpkUPi72ZFcPd8an5wEQ4e9mybCEEEIIcQlCfVx4YEgkC3ek8efedIvGIkmaGfi6OpzqSYtPywWgdTNJ0oQQQoiG6M7+rYj0d+Wpn3dRWFpusThsLdZyI+Lr9neStictjxBvZ1wd5L9WCCGEaIjsbU3839UdWJuQjY0Fy2lJJmEGvq72HMioqquy92iu9KIJIYQQDVz3MG+6h3lbNAYZ7jQDP1cHMvNLKC6r4GBWAW0lSRNCCCFEHUmSZga+rg6Ulley9dAJKjW0buZu6ZCEEEII0cBJkmYGPtW7DqxOyASgTXPpSRNCCCFE3UiSZgYnC9qu3p+Fg62JMB8XC0ckhBBCiIZOkjQzOJmk7TiSQ1SAm0VXggghhBCicZAkzQx83aqGO6vmo8lQpxBCCCHqTpI0M/B2tkdVd561kSRNCCGEEGYgSZoZ2NqY8Hau6k1r21xWdgohhBCi7iRJM5OT89JkuFMIIYQQ5iA7DpiJr5s92QUOp5I1IYQQQoi6kCTNTG7pGUpWQamlwxBCCCFEI2Gx4U6l1AtKqe1KqTil1GKlVIvzXDdRKbW/+jWxvuOsrSs6NGdCr1BLhyGEEEKIRsKSc9Je01p31Fp3BhYAT//zAqWUN/AM0BPoATyjlPKq3zCFEEIIIeqfxZI0rXXuae+6APocl10OLNFaH9NaHweWACPqIz4hhBBCCEuy6Jw0pdRLwK1ADjD4HJcEAodPez+l+pgQQgghRKNmaE+aUmqpUmrnOV5jAbTWT2qtg4Gvgal1bGuKUipWKRWbmZlpjvCFEEIIISzG0J40rfXQWl76NbCQqvlnpzsCDDrt/SDgr/O0NROYCRATE3OuoVMhhBBCiAbDkqs7I097dyyw9xyX/QEMV0p5VS8YGF59TAghhBCiUbPknLT/KaVaA5VAMnA3gFIqBrhba32H1vqYUuoFYFP1xzyvtT5mmXCFEEIIIeqP0rrxjQzGxMTo2NhYS4chhBBCCHFBSqnNWuuYfx6XvTuFEEIIIayQJGlCCCGEEFZIkjQhhBBCCCskSZoQQgghhBWSJE0IIYQQwgo1ytWdSqlMqsp6GMkXyDK4DXFx5JlYJ3ku1keeiXWS52J96uuZhGqt/f55sFEmafVBKRV7ruWywnLkmVgneS7WR56JdZLnYn0s/UxkuFMIIYQQwgpJkiaEEEIIYYUkSbt0My0dgDiLPBPrJM/F+sgzsU7yXKyPRZ+JzEkTQgghhLBC0pMmhBBCCGGFJEm7AKXUCKVUvFIqQSn12DnOOyil5lWf36CUCqv/KJuWWjyTh5VSu5VS25VSy5RSoZaIs6m50HM57brxSimtlJJVbAarzTNRSl1X/f2ySyk1p75jbIpq8TMsRCm1XCm1tfrn2EhLxNlUKKU+U0plKKV2nue8Ukq9W/28toqyX0YAAAeOSURBVCulutZXbJKk1UApZQN8AFwBRAM3KqWi/3HZZOC41joCeAt4pX6jbFpq+Uy2AjFa647A98Cr9Rtl01PL54JSyg14ENhQvxE2PbV5JkqpSOBxoK/Wuh0wrd4DbWJq+b3yX+BbrXUX4AZgev1G2eTMAkbUcP4KILL6NQX4sB5iAiRJu5AeQILWOlFrXQrMBcb+45qxwBfVb38PDFFKqXqMsam54DPRWi/XWhdWv7seCKrnGJui2nyvALxA1R8yxfUZXBNVm2dyJ/CB1vo4gNY6o55jbIpq81w04F79tgeQWo/xNTla65XAsRouGQt8qausBzyVUs3rIzZJ0moWCBw+7f2U6mPnvEZrXQ7kAD71El3TVJtncrrJwO+GRiSgFs+leoggWGv9W30G1oTV5nslCohSSq1RSq1XStXUmyDMozbP5VngFqVUCrAQuL9+QhPncbG/d8zGtj4aEcISlFK3ADHAQEvH0tQppUzAm8AkC4cizmRL1RDOIKp6nFcqpTporU9YNCpxIzBLa/2GUqo3MFsp1V5rXWnpwET9kp60mh0Bgk97P6j62DmvUUrZUtU1nV0v0TVNtXkmKKWGAk8CY7TWJfUUW1N2oefiBrQH/lJKJQG9gF9k8YChavO9kgL8orUu01ofBPZRlbQJ49TmuUwGvgXQWq8DHKnaQ1JYRq1+7xhBkrSabQIilVItlVL2VE3g/OUf1/wCTKx++xrgTy3F54x0wWeilOoCzKAqQZM5NvWjxueitc7RWvtqrcO01mFUzRUco7WOtUy4TUJtfn79TFUvGkopX6qGPxPrM8gmqDbP5RAwBEAp1ZaqJC2zXqMUp/sFuLV6lWcvIEdrfbQ+GpbhzhporcuVUlOBPwAb4DOt9S6l1PNArNb6/9u7txCrqjiO49+fIpl4eaheMkOUQMhy7EaGUlJEaWZRUWEX7cYQJklJSWkF2UO9KcGQ1UyZ2UVHkx6SqAQtMi1HnZTSMnzpwQcrQQPTfw9rDZ6m03jOcc6crf0+MMw+6+x12We//M9/rX3WWuANUip6D2nh4V2NG/Hpr8J78gowGPgwP8OxLyJubtig/wcqvC/Whyq8J+uA6yXtBI4C8yLCMwF1VOF9eQJYKmku6SGCmf7yXz+SVpC+rJyd1wE+BwwAiIgW0rrAKcAe4BAwq8/G5vtuZmZmVjye7jQzMzMrIAdpZmZmZgXkIM3MzMysgBykmZmZmRWQgzQzMzOzAnKQZmZ1JekcSRsldUq6paT8I0nn1tDWJklbJU0qKV8tqUPSHkm/5+MOSVfVOOaRkg6XtNMh6b783i/5N8WqbXNmJdebz9ufr3G3pHW1XoeZndr8O2lmVm93Ay1AO+n3htZImgZsjYhqN46+FtgREQ+VFkbErQCSrgGejIibTnrU8FNENPVCO11mAp1Utln2+xExG0DSZKBd0uSI2NWL4zGzgnMmzczq7QgwCDgDOJq3T3scePm/KuRM1ueStkv6TNL5kppynek5s3VmT52WayOXt0lqkbRF0o+Sag7oJK2R9K2k7yU9ksv65z46Je2QNFfS7aR9ZJdXMvZSEfEF8BrQ1f7DkjZL2iZplaRBkoZI2itpQD5naNdrSXMk7cyfw3u1XquZ9T0HaWZWb+8C04FPgZeAR4FlEXGohzpLgLci4mJgObA4IjqAhaQsU1NEHD5Bv/9qo+S9kcAVwFSgRdLAMvVHd5vunFTmnAci4lJSADZH0llAEzA8IsZGxEVAa0SsBLYAMyoce3ffAWPycXtEXB4R44BdwIMRcRBYn68H0s4n7RFxBHgaGJ8/h+Yq+zWzBnKQZmZ1lfftnBoRl5GCjWnASklLJa2UNKFMtQmk4A5gGTCxhq57auODiDgWEbtJe1WO6V6ZPN1Z8rehzDlzJG0j7UU6grQ5+c/AKElLJN0A/FHD2LtTyfFYSRsk7QBmABfm8tc5vl3NLKA1H28nZfDuAf7qhbGYWR9xkGZmfWkBsIi0Tm0jcD/wfAPG0X0/vKr3x8vr364DJuSs1lZgYEQcAMaRMlvNpODpZI0nZc0A2oDZOUv3AmnzbSLiS2BkHlf/iOjM508FXgUuATbn6WYzOwU4SDOzPiHpAuC8iFhPWqN2jBQclVuf9RVpyg5StqhcFutEemrjDkn9JI0GRgE/1ND+MOBARBySNAa4EiA/+dkvIlYBz5KCI4CDwJBqO5F0NWk92tJcNAT4Na8/m9Ht9LdJ2cPWXLcfMCKva3sqj3lwtWMws8bwNyoz6yuLgGfy8QpgDWm91MIy5z4GtEqaB+zn+DReNXpqYx/wDTAUaI6IP8vUHy2po+T1mxFRuq7tE6BZ0i5SkPd1Lh+e++36Ejw//28jrX87TJqKnQ9siYi1Zfq+U9JEUjC7F7it5MnOBcCmfE2b+Gfgtxx4kfT5AvQH3pE0jDRlujgifivTn5kVkCKqzvKbmZ2yJLUBH+fF/KeV/BTp9Ii4t9FjMbOT50yamdlpQNIS4EZgSqPHYma9w5k0MzMzswLygwNmZmZmBeQgzczMzKyAHKSZmZmZFZCDNDMzM7MCcpBmZmZmVkAO0szMzMwK6G+uAiSbSiPtdgAAAABJRU5ErkJggg==\n" }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "source": [ "Observar como el IC es cada vez más pequeño a medida que acumulamos más datos. Esto se debe a que el tamaño de la muestra aumenta." ], "metadata": { "id": "LnIVyVtO6fHw" } }, { "cell_type": "code", "source": [ "def cumulative_gain_ci(dataset, prediction, y, t, min_periods=30, steps=100):\n", " size = dataset.shape[0]\n", " ordered_df = dataset.sort_values(prediction, ascending=False).reset_index(drop=True)\n", " n_rows = list(range(min_periods, size, size // steps)) + [size]\n", " return np.array([elast_ci(ordered_df.head(rows), y, t) * (rows/size) for rows in n_rows])" ], "metadata": { "id": "2tuLJ4RB6z7T" }, "execution_count": 34, "outputs": [] }, { "cell_type": "code", "source": [ "plt.figure(figsize=(10,6))\n", "\n", "cumu_gain = cumulative_gain_ci(prices_rnd_pred, \"elast_m_pred\", \"sales\", \"price\", min_periods=50, steps=200)\n", "x = np.array(range(len(cumu_gain)))\n", "plt.plot(x/x.max(), cumu_gain, color=\"C0\")\n", "\n", "plt.plot([0, 1], [0, elast(prices_rnd_pred, \"sales\", \"price\")], linestyle=\"--\", label=\"Random Model\", color=\"black\")\n", "\n", "plt.xlabel(\"% of Top Elast. Days\")\n", "plt.ylabel(\"Cumulative Gain\")\n", "plt.title(\"Cumulative Gain for elast_m_pred with 95% CI\")\n", "plt.legend();" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 404 }, "id": "WmDf2AC_658W", "outputId": "3c7312e7-a07d-4c9f-e15f-16645be1d2b1" }, "execution_count": 35, "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "
" ], "image/png": 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\n" }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "source": [ "Aca el intervalo de confianza es pequeño al principio aunque el grupo sea pequeño tambien, esto pasa porque el $\\frac{k}{N}$ (que no depende de $\\hat{\\beta_1}$) achica todo." ], "metadata": { "id": "KV0l_SML7Zw-" } }, { "cell_type": "markdown", "source": [ "# Referencias y material recomendado" ], "metadata": { "id": "o2Mva_vw8Dh8" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "* [Causal Inference for The Brave and True](https://matheusfacure.github.io/python-causality-handbook/landing-page.html), de la parte dos de este libro salio todo el material, en especial parte 18 y 19\n", "* [Causal Inference in the Wild: Elasticity Pricing](https://towardsdatascience.com/causal-inference-example-elasticity-de4a3e2e621b) Trata un tema parecido, lamentablemente no me dio el tiempo de leerlo mucho.\n", "\n", "* [Documentacion de statsmodel](https://www.statsmodels.org/dev/generated/statsmodels.regression.linear_model.OLS.html) No entre en mucho detalle de como funciona pero la documentacion esta bastante completa\n", "\n", "\n", "* [Modelos lineales](https://hastie.su.domains/ISLR2/ISLRv2_website.pdf) An Introduction to Statistical\n", "Learning capitulo 3. Material de regresion lineal hay de sobra pero si algo no se entendio este libro que es gratis tiene un capitulo dedicado a regresion lineal.\n", "\n", "* [Libreria DoWhy](https://www.kaggle.com/code/adamwurdits/causal-inference-with-dowhy-a-practical-guide) Cuando estaba decidiendo el tema dar vi este post sobre una libreria en python que parece interesante\n", "\n", "\n" ], "metadata": { "id": "eOogq23F8EYR" } } ] }