{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Práctica: Feature Engineering, Scaling y Vectorización\n",
    "\n",
    "## Objetivos\n",
    "En esta práctica aprenderás a:\n",
    "- Implementar **regresión polinomial** (feature engineering) evaluando múltiples grados y seleccionando el óptimo\n",
    "- Implementar los **3 métodos de feature scaling** vistos en clase y comparar cuál produce menor MSE\n",
    "- Escribir todo el código de forma **vectorizada** usando operaciones de matrices y producto punto\n",
    "\n",
    "---\n",
    "\n",
    "## Herramientas\n",
    "- NumPy: operaciones vectorizadas\n",
    "- Matplotlib: visualización\n",
    "- sklearn (solo al final para verificar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "import copy\n",
    "\n",
    "np.set_printoptions(precision=4)\n",
    "plt.style.use('seaborn-v0_8-darkgrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 1. Dataset y Visualización\n",
    "\n",
    "Usaremos datos de precios de casas. La relación entre tamaño y precio **no es lineal** — una recta no captura bien los datos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_train shape: (12,)\n",
      "y_train shape: (12,)\n",
      "Número de ejemplos: m = 12\n"
     ]
    }
   ],
   "source": [
    "# Dataset: tamaño (1000 sqft) → precio ($1000s)\n",
    "x_train = np.array([0.5, 0.8, 1.0, 1.2, 1.5, 1.8, 2.0, 2.2, 2.5, 2.8, 3.0, 3.5])\n",
    "y_train = np.array([90, 120, 140, 155, 180, 210, 230, 260, 300, 350, 380, 460])\n",
    "\n",
    "print(f\"x_train shape: {x_train.shape}\")\n",
    "print(f\"y_train shape: {y_train.shape}\")\n",
    "print(f\"Número de ejemplos: m = {x_train.shape[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "→ Observación: la relación NO es lineal. Necesitamos features polinomiales.\n"
     ]
    }
   ],
   "source": [
    "# Visualizar los datos\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.scatter(x_train, y_train, color='royalblue', s=80, zorder=5, label='Datos reales')\n",
    "\n",
    "# Ajuste lineal simple para mostrar que no es suficiente\n",
    "w_simple = np.polyfit(x_train, y_train, 1)\n",
    "x_line = np.linspace(0.3, 3.7, 100)\n",
    "plt.plot(x_line, np.polyval(w_simple, x_line), 'r--', alpha=0.7, label='Ajuste lineal (insuficiente)')\n",
    "\n",
    "plt.xlabel('Tamaño (1000 sqft)')\n",
    "plt.ylabel('Precio ($1000s)')\n",
    "plt.title('Precio de Casas vs Tamaño')\n",
    "plt.legend()\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.show()\n",
    "\n",
    "print(\"\\n→ Observación: la relación NO es lineal. Necesitamos features polinomiales.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 2. Repaso: Producto Punto y Multiplicación de Matrices\n",
    "\n",
    "Antes de implementar las funciones vectorizadas, repasemos cómo funciona la multiplicación de matrices y por qué es clave para hacer predicciones eficientes.\n",
    "\n",
    "## 2.1 El Producto Punto (Dot Product)\n",
    "\n",
    "El producto punto entre dos vectores $\\mathbf{w}$ y $\\mathbf{x}$ se define como:\n",
    "\n",
    "$$\\mathbf{w} \\cdot \\mathbf{x} = \\sum_{j=0}^{n-1} w_j \\cdot x_j$$\n",
    "\n",
    "**Ejemplo numérico:**\n",
    "\n",
    "$$\\mathbf{w} = [2, 3, 1], \\quad \\mathbf{x} = [4, 1, 5]$$\n",
    "$$\\mathbf{w} \\cdot \\mathbf{x} = 2 \\times 4 + 3 \\times 1 + 1 \\times 5 = 8 + 3 + 5 = 16$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Con loop:   w · x = 16\n",
      "Con np.dot: w · x = 16\n",
      "\n",
      "✓ Ambos dan el mismo resultado, pero np.dot es mucho más rápido para vectores grandes.\n"
     ]
    }
   ],
   "source": [
    "# Ejemplo: producto punto con loop vs np.dot\n",
    "w = np.array([2, 3, 1])\n",
    "x = np.array([4, 1, 5])\n",
    "\n",
    "# Versión con loop (LENTA)\n",
    "resultado_loop = 0\n",
    "for j in range(len(w)):\n",
    "    resultado_loop += w[j] * x[j]\n",
    "\n",
    "# Versión vectorizada (RÁPIDA)\n",
    "resultado_dot = np.dot(w, x)\n",
    "\n",
    "print(f\"Con loop:   w · x = {resultado_loop}\")\n",
    "print(f\"Con np.dot: w · x = {resultado_dot}\")\n",
    "print(f\"\\n✓ Ambos dan el mismo resultado, pero np.dot es mucho más rápido para vectores grandes.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Multiplicación Matriz × Vector = Colección de Dot Products\n",
    "\n",
    "Cuando multiplicamos una matriz $\\mathbf{X}$ de shape $(m, n)$ por un vector $\\mathbf{w}$ de shape $(n,)$, el resultado es un vector de $m$ elementos donde **cada elemento es el producto punto de una fila de X con w**:\n",
    "\n",
    "$$\\mathbf{X} \\cdot \\mathbf{w} = \\begin{pmatrix} \\text{fila}_0 \\cdot \\mathbf{w} \\\\ \\text{fila}_1 \\cdot \\mathbf{w} \\\\ \\vdots \\\\ \\text{fila}_{m-1} \\cdot \\mathbf{w} \\end{pmatrix}$$\n",
    "\n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/8/86/Matrix_multiplication_.gif\" width=\"400\">\n",
    "\n",
    "**Esto es exactamente lo que necesitamos para hacer predicciones:**\n",
    "- Cada fila de $\\mathbf{X}$ es un ejemplo (una casa con sus features)\n",
    "- $\\mathbf{w}$ son los pesos del modelo\n",
    "- El resultado es un vector con la predicción para cada casa\n",
    "\n",
    "$$\\text{predicciones} = \\mathbf{X} \\cdot \\mathbf{w} + b$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== Predicción con LOOP (lento) ===\n",
      "  Casa 0: fila [1.5 3. ] · w [100  20] + 50 = 260.0\n",
      "  Casa 1: fila [2. 4.] · w [100  20] + 50 = 330.0\n",
      "  Casa 2: fila [1. 2.] · w [100  20] + 50 = 190.0\n",
      "\n",
      "=== Predicción VECTORIZADA (rápido) ===\n",
      "  X @ w + b = [260. 330. 190.]\n",
      "\n",
      "✓ Una sola operación reemplaza el loop completo!\n",
      "  Shapes: X((3, 2)) @ w((2,)) + b → predicciones((3,))\n"
     ]
    }
   ],
   "source": [
    "# Demostración: predecir para 3 casas con 2 features cada una\n",
    "X_demo = np.array([\n",
    "    [1.5, 3],   # casa 0: 1500sqft, 3 cuartos\n",
    "    [2.0, 4],   # casa 1: 2000sqft, 4 cuartos\n",
    "    [1.0, 2],   # casa 2: 1000sqft, 2 cuartos\n",
    "])\n",
    "w_demo = np.array([100, 20])  # $100k por 1000sqft, $20k por cuarto\n",
    "b_demo = 50  # base $50k\n",
    "\n",
    "print(\"=== Predicción con LOOP (lento) ===\")\n",
    "for i in range(X_demo.shape[0]):\n",
    "    pred_i = np.dot(X_demo[i], w_demo) + b_demo\n",
    "    print(f\"  Casa {i}: fila {X_demo[i]} · w {w_demo} + {b_demo} = {pred_i}\")\n",
    "\n",
    "print(\"\\n=== Predicción VECTORIZADA (rápido) ===\")\n",
    "predicciones = X_demo @ w_demo + b_demo  # equivale a np.dot(X_demo, w_demo) + b_demo\n",
    "print(f\"  X @ w + b = {predicciones}\")\n",
    "print(f\"\\n✓ Una sola operación reemplaza el loop completo!\")\n",
    "print(f\"  Shapes: X({X_demo.shape}) @ w({w_demo.shape}) + b → predicciones({predicciones.shape})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Ejercicio: Implementar predicción vectorizada\n",
    "\n",
    "Implementa una función que prediga el precio de **todas** las casas simultáneamente usando código vectorizado.\n",
    "\n",
    "**Reglas:**\n",
    "- NO puedes usar loops\n",
    "- Usa `@` o `np.dot` para la multiplicación matriz-vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_all(X, w, b):\n",
    "    \"\"\"\n",
    "    Predice para todos los ejemplos simultáneamente.\n",
    "    \n",
    "    Args:\n",
    "        X (ndarray (m,n)): matriz de features, m ejemplos, n features\n",
    "        w (ndarray (n,)):  vector de pesos\n",
    "        b (scalar):        bias\n",
    "    \n",
    "    Returns:\n",
    "        predictions (ndarray (m,)): vector de predicciones\n",
    "    \"\"\"\n",
    "    # X @ w hace el dot product fila por fila → un valor por cada ejemplo\n",
    "    predictions = X @ w + b\n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista</span></summary>\n",
    "\n",
    "```python\n",
    "# La multiplicación matriz × vector hace dot product fila por fila:\n",
    "predictions = X @ w + b\n",
    "# equivalente a: np.dot(X, w) + b\n",
    "```\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicciones: [260. 330. 190.]\n",
      "Esperado:     [260. 330. 190.]\n",
      "\n",
      "✓ ¡Correcto!\n"
     ]
    }
   ],
   "source": [
    "# Verificar tu implementación\n",
    "preds = predict_all(X_demo, w_demo, b_demo)\n",
    "print(f\"Predicciones: {preds}\")\n",
    "print(f\"Esperado:     [260. 330. 190.]\")\n",
    "assert preds is not None, \"La función retorna None — implementa el código\"\n",
    "assert np.allclose(preds, [260, 330, 190]), f\"Error: esperado [260, 330, 190], obtuviste {preds}\"\n",
    "print(\"\\n✓ ¡Correcto!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 3. Feature Engineering: Regresión Polinomial\n",
    "\n",
    "## 3.1 La Idea\n",
    "\n",
    "Si los datos no son lineales, podemos crear **nuevas features** a partir de las existentes:\n",
    "\n",
    "$$f(x) = w_1 x + w_2 x^2 + w_3 x^3 + \\ldots + w_d x^d + b$$\n",
    "\n",
    "Esto transforma un problema no-lineal en uno **lineal en las features**:\n",
    "\n",
    "| Feature original | Features polinomiales (grado 3) |\n",
    "|:---:|:---:|\n",
    "| $x$ | $x_1 = x$, $x_2 = x^2$, $x_3 = x^3$ |\n",
    "\n",
    "Ahora el modelo es lineal en $[x_1, x_2, x_3]$:\n",
    "$$f(\\mathbf{x}) = \\mathbf{w} \\cdot \\mathbf{x} + b$$\n",
    "\n",
    "**⚠️ Importante:** Como $x^2, x^3$ crecen rápidamente, es **crucial** aplicar feature scaling después de crear las features polinomiales."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Crear Features Polinomiales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x original: [1. 2. 3.]\n",
      "\n",
      "X polinomial (grado 3):\n",
      "  [x,  x²,  x³]\n",
      "[[ 1.  1.  1.]\n",
      " [ 2.  4.  8.]\n",
      " [ 3.  9. 27.]]\n",
      "\n",
      "Shape: (3, 3) → 3 ejemplos, 3 features\n"
     ]
    }
   ],
   "source": [
    "def create_polynomial_features(x, degree):\n",
    "    \"\"\"\n",
    "    Crea una matriz de features polinomiales.\n",
    "    \n",
    "    Args:\n",
    "        x (ndarray (m,)): vector de una sola feature\n",
    "        degree (int):     grado máximo del polinomio\n",
    "    \n",
    "    Returns:\n",
    "        X (ndarray (m, degree)): matriz con columnas [x, x², x³, ..., x^degree]\n",
    "    \n",
    "    Ejemplo:\n",
    "        x = [2, 3], degree = 3\n",
    "        X = [[2, 4, 8],\n",
    "             [3, 9, 27]]\n",
    "    \"\"\"\n",
    "    # Nota: esto es vectorizado — no hay loop sobre los m ejemplos\n",
    "    # x**k eleva TODOS los elementos simultáneamente (operación element-wise)\n",
    "    return np.column_stack([x**k for k in range(1, degree + 1)])\n",
    "\n",
    "\n",
    "# Demostración\n",
    "x_ejemplo = np.array([1.0, 2.0, 3.0])\n",
    "X_poly = create_polynomial_features(x_ejemplo, degree=3)\n",
    "print(f\"x original: {x_ejemplo}\")\n",
    "print(f\"\\nX polinomial (grado 3):\")\n",
    "print(f\"  [x,  x²,  x³]\")\n",
    "print(X_poly)\n",
    "print(f\"\\nShape: {X_poly.shape} → {X_poly.shape[0]} ejemplos, {X_poly.shape[1]} features\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Funciones de Entrenamiento\n",
    "\n",
    "### Función de Costo:\n",
    "$$J(\\mathbf{w}, b) = \\frac{1}{2m} \\sum_{i=0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})^2$$\n",
    "\n",
    "### Gradientes:\n",
    "$$\\frac{\\partial J}{\\partial w_j} = \\frac{1}{m} \\sum_{i=0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)}) \\cdot x_j^{(i)}$$\n",
    "\n",
    "$$\\frac{\\partial J}{\\partial b} = \\frac{1}{m} \\sum_{i=0}^{m-1} (f_{\\mathbf{w},b}(\\mathbf{x}^{(i)}) - y^{(i)})$$\n",
    "\n",
    "A continuación se presenta la implementación **con loops** (referencia). Tu tarea será implementar la versión **vectorizada**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost (loop):     34651.0417\n",
      "Gradient (loop): dj_dw = [ -552.25  -1450.025], dj_db = -239.5833\n",
      "\n",
      "✓ Estas funciones son CORRECTAS pero LENTAS. Ahora implementa la versión vectorizada.\n"
     ]
    }
   ],
   "source": [
    "# ============================================================\n",
    "# REFERENCIA: Implementación CON LOOPS (lenta pero clara)\n",
    "# ============================================================\n",
    "\n",
    "def compute_cost_loop(X, y, w, b):\n",
    "    \"\"\"\n",
    "    Calcula el costo MSE usando loops.\n",
    "    Funciona pero es LENTA para datasets grandes.\n",
    "    \"\"\"\n",
    "    m = X.shape[0]\n",
    "    cost = 0.0\n",
    "    for i in range(m):\n",
    "        f_wb_i = np.dot(X[i], w) + b    # predicción para ejemplo i\n",
    "        cost += (f_wb_i - y[i])**2        # error cuadrado acumulado\n",
    "    cost = cost / (2 * m)\n",
    "    return cost\n",
    "\n",
    "\n",
    "def compute_gradient_loop(X, y, w, b):\n",
    "    \"\"\"\n",
    "    Calcula gradientes usando loops.\n",
    "    Funciona pero es LENTA para datasets grandes.\n",
    "    \"\"\"\n",
    "    m, n = X.shape\n",
    "    dj_dw = np.zeros(n)\n",
    "    dj_db = 0.0\n",
    "    \n",
    "    for i in range(m):\n",
    "        err = (np.dot(X[i], w) + b) - y[i]\n",
    "        for j in range(n):\n",
    "            dj_dw[j] += err * X[i, j]\n",
    "        dj_db += err\n",
    "    \n",
    "    dj_dw = dj_dw / m\n",
    "    dj_db = dj_db / m\n",
    "    return dj_dw, dj_db\n",
    "\n",
    "\n",
    "# Verificar que funcionan\n",
    "X_test = create_polynomial_features(x_train, 2)\n",
    "w_test = np.zeros(2)\n",
    "b_test = 0.0\n",
    "\n",
    "cost_loop = compute_cost_loop(X_test, y_train, w_test, b_test)\n",
    "dj_dw_loop, dj_db_loop = compute_gradient_loop(X_test, y_train, w_test, b_test)\n",
    "print(f\"Cost (loop):     {cost_loop:.4f}\")\n",
    "print(f\"Gradient (loop): dj_dw = {dj_dw_loop}, dj_db = {dj_db_loop:.4f}\")\n",
    "print(\"\\n✓ Estas funciones son CORRECTAS pero LENTAS. Ahora implementa la versión vectorizada.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Ejercicio: Implementar costo vectorizado\n",
    "\n",
    "Implementa `compute_cost` **sin loops**. El resultado debe ser idéntico al de `compute_cost_loop`.\n",
    "\n",
    "**Recordatorio de cómo vectorizar:**\n",
    "- `X @ w + b` calcula TODAS las predicciones de golpe (un dot product por fila de X)\n",
    "- `predictions - y` calcula todos los errores de golpe (operación element-wise)\n",
    "- `np.mean(errors**2)` calcula la media de los errores al cuadrado\n",
    "\n",
    "Observa la relación:\n",
    "\n",
    "| Loop | Vectorizado |\n",
    "|:-----|:------------|\n",
    "| `for i in range(m): f_wb_i = np.dot(X[i], w) + b` | `predictions = X @ w + b` |\n",
    "| `for i: cost += (f_wb_i - y[i])**2` | `cost = np.mean((predictions - y)**2) / 2` |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(X, y, w, b):\n",
    "    \"\"\"\n",
    "    Calcula el costo MSE de forma VECTORIZADA (sin loops).\n",
    "    \n",
    "    Args:\n",
    "        X (ndarray (m,n)): features\n",
    "        y (ndarray (m,)):  targets\n",
    "        w (ndarray (n,)):  pesos\n",
    "        b (scalar):        bias\n",
    "    \n",
    "    Returns:\n",
    "        cost (scalar): valor del costo J(w,b)\n",
    "    \"\"\"\n",
    "    predictions = X @ w + b           # todas las predicciones de golpe → shape (m,)\n",
    "    errors = predictions - y           # todos los errores de golpe      → shape (m,)\n",
    "    cost = np.mean(errors**2) / 2     # equivale a sum(errors²) / (2*m)\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista — compute_cost vectorizado</span></summary>\n",
    "\n",
    "```python\n",
    "predictions = X @ w + b            # (m,n) @ (n,) → (m,)\n",
    "errors = predictions - y            # (m,)\n",
    "cost = np.mean(errors**2) / 2       # scalar\n",
    "return cost\n",
    "```\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost (loop):        34651.041667\n",
      "Cost (vectorizado): 34651.041666666664\n",
      "\n",
      "✓ ¡Correcto! Mismo resultado, sin loops.\n"
     ]
    }
   ],
   "source": [
    "# Verificar: tu resultado debe ser igual al de la versión con loop\n",
    "cost_vec = compute_cost(X_test, y_train, w_test, b_test)\n",
    "print(f\"Cost (loop):        {cost_loop:.6f}\")\n",
    "print(f\"Cost (vectorizado): {cost_vec}\")\n",
    "assert cost_vec is not None, \"compute_cost retorna None — implementa el código\"\n",
    "assert np.isclose(cost_vec, cost_loop), f\"Error: esperado {cost_loop:.6f}, obtuviste {cost_vec}\"\n",
    "print(\"\\n✓ ¡Correcto! Mismo resultado, sin loops.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.5 Ejercicio: Implementar gradiente vectorizado\n",
    "\n",
    "Implementa `compute_gradient` **sin loops**. El resultado debe ser idéntico al de `compute_gradient_loop`.\n",
    "\n",
    "**Truco clave para `dj_dw`:**\n",
    "\n",
    "El loop original hace:\n",
    "```\n",
    "for i in range(m):\n",
    "    err = predicción_i - y_i\n",
    "    for j in range(n):\n",
    "        dj_dw[j] += err * X[i, j]\n",
    "```\n",
    "\n",
    "Esto es equivalente a multiplicar la **transpuesta** de X por el vector de errores:\n",
    "\n",
    "$$\\frac{\\partial J}{\\partial \\mathbf{w}} = \\frac{1}{m} \\mathbf{X}^T \\cdot \\mathbf{errors}$$\n",
    "\n",
    "¿Por qué? Porque $\\mathbf{X}^T$ tiene shape $(n, m)$. Al multiplicar por `errors` de shape $(m,)$:\n",
    "- Cada **fila** de $\\mathbf{X}^T$ (que es una **columna** de $\\mathbf{X}$, es decir, todos los valores de una feature) hace dot product con el vector de errores.\n",
    "- Resultado: un vector de shape $(n,)$ con el gradiente de cada peso.\n",
    "\n",
    "<img src=\"https://anakarinarm.github.io/python-novice-inflammation-2016-09-20-ubc/fig/python-operations-across-axes.png\" width=\"500\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_gradient(X, y, w, b):\n",
    "    \"\"\"\n",
    "    Calcula gradientes de forma VECTORIZADA (sin loops).\n",
    "    \n",
    "    Args:\n",
    "        X (ndarray (m,n)): features\n",
    "        y (ndarray (m,)):  targets\n",
    "        w (ndarray (n,)):  pesos\n",
    "        b (scalar):        bias\n",
    "    \n",
    "    Returns:\n",
    "        dj_dw (ndarray (n,)): gradiente respecto a w\n",
    "        dj_db (scalar):       gradiente respecto a b\n",
    "    \"\"\"\n",
    "    m = X.shape[0]\n",
    "    predictions = X @ w + b       # todas las predicciones de golpe → shape (m,)\n",
    "    errors = predictions - y       # todos los errores de golpe      → shape (m,)\n",
    "\n",
    "    dj_dw = (X.T @ errors) / m   # (n,m) @ (m,) → (n,): gradiente por cada peso\n",
    "    dj_db = np.mean(errors)       # promedio de errores → gradiente del bias\n",
    "    return dj_dw, dj_db"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista — compute_gradient vectorizado</span></summary>\n",
    "\n",
    "```python\n",
    "m = X.shape[0]\n",
    "predictions = X @ w + b          # (m,)\n",
    "errors = predictions - y          # (m,)\n",
    "\n",
    "dj_dw = (X.T @ errors) / m       # (n,m) @ (m,) → (n,)\n",
    "dj_db = np.mean(errors)           # scalar\n",
    "return dj_dw, dj_db\n",
    "```\n",
    "`X.T @ errors` hace un dot product por cada feature (fila de X.T) con el vector de errores.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient (loop):        dj_dw = [ -552.25  -1450.025], dj_db = -239.5833\n",
      "Gradient (vectorizado): dj_dw = [ -552.25  -1450.025], dj_db = -239.58333333333334\n",
      "\n",
      "✓ ¡Correcto! Mismo resultado, sin loops.\n"
     ]
    }
   ],
   "source": [
    "# Verificar: tu resultado debe ser igual al de la versión con loop\n",
    "dj_dw_vec, dj_db_vec = compute_gradient(X_test, y_train, w_test, b_test)\n",
    "print(f\"Gradient (loop):        dj_dw = {dj_dw_loop}, dj_db = {dj_db_loop:.4f}\")\n",
    "print(f\"Gradient (vectorizado): dj_dw = {dj_dw_vec}, dj_db = {dj_db_vec}\")\n",
    "assert dj_dw_vec is not None, \"compute_gradient retorna None — implementa el código\"\n",
    "assert np.allclose(dj_dw_vec, dj_dw_loop), f\"Error en dj_dw: esperado {dj_dw_loop}, obtuviste {dj_dw_vec}\"\n",
    "assert np.isclose(dj_db_vec, dj_db_loop), f\"Error en dj_db: esperado {dj_db_loop}, obtuviste {dj_db_vec}\"\n",
    "print(\"\\n✓ ¡Correcto! Mismo resultado, sin loops.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost con loop:        924.7 ms (100 repeticiones)\n",
      "Cost vectorizado:     4.1 ms (100 repeticiones)\n",
      "\n",
      "→ Speedup: 226x más rápido con vectorización!\n"
     ]
    }
   ],
   "source": [
    "# Comparar velocidad: loop vs vectorizado\n",
    "# Usamos un dataset más grande para notar la diferencia\n",
    "X_big = np.random.randn(5000, 10)\n",
    "y_big = np.random.randn(5000)\n",
    "w_big = np.random.randn(10)\n",
    "\n",
    "tic = time.time()\n",
    "for _ in range(100):\n",
    "    compute_cost_loop(X_big, y_big, w_big, 0.0)\n",
    "time_loop = time.time() - tic\n",
    "\n",
    "tic = time.time()\n",
    "for _ in range(100):\n",
    "    compute_cost(X_big, y_big, w_big, 0.0)\n",
    "time_vec = time.time() - tic\n",
    "\n",
    "print(f\"Cost con loop:        {time_loop*1000:.1f} ms (100 repeticiones)\")\n",
    "print(f\"Cost vectorizado:     {time_vec*1000:.1f} ms (100 repeticiones)\")\n",
    "print(f\"\\n→ Speedup: {time_loop/time_vec:.0f}x más rápido con vectorización!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.6 Gradient Descent (dado)\n",
    "\n",
    "Esta función usa tus implementaciones vectorizadas de `compute_cost` y `compute_gradient` para entrenar el modelo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "✓ gradient_descent definido (usa TUS funciones vectorizadas).\n"
     ]
    }
   ],
   "source": [
    "def gradient_descent(X, y, w_init, b_init, alpha, num_iters):\n",
    "    \"\"\"\n",
    "    Ejecuta gradient descent usando las funciones vectorizadas del estudiante.\n",
    "    \"\"\"\n",
    "    w = copy.deepcopy(w_init)\n",
    "    b = b_init\n",
    "    J_history = []\n",
    "    \n",
    "    for i in range(num_iters):\n",
    "        dj_dw, dj_db = compute_gradient(X, y, w, b)\n",
    "        w = w - alpha * dj_dw\n",
    "        b = b - alpha * dj_db\n",
    "        J_history.append(compute_cost(X, y, w, b))\n",
    "        \n",
    "        if i % (num_iters // 5) == 0:\n",
    "            print(f\"  Iter {i:5d}: Cost = {J_history[-1]:.4f}\")\n",
    "    \n",
    "    return w, b, J_history\n",
    "\n",
    "print(\"✓ gradient_descent definido (usa TUS funciones vectorizadas).\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.7 Ejercicio: Evaluar grados 1 a 6\n",
    "\n",
    "Entrena un modelo para cada grado polinomial (1 a 6). Para cada grado debes:\n",
    "1. Crear las features polinomiales\n",
    "2. Aplicar z-score normalization\n",
    "3. Entrenar con gradient descent\n",
    "4. Guardar el MSE final\n",
    "\n",
    "**Recuerda:** La función z-score es:\n",
    "$$x_{\\text{scaled}} = \\frac{x - \\mu}{\\sigma}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================================================\n",
      "Grado 1:\n",
      "==================================================\n",
      "  Iter     0: Cost = 28088.9883\n",
      "  Iter  1000: Cost = 113.9187\n",
      "  Iter  2000: Cost = 113.9187\n",
      "  Iter  3000: Cost = 113.9187\n",
      "  Iter  4000: Cost = 113.9187\n",
      "  MSE final: 227.8373\n",
      "\n",
      "==================================================\n",
      "Grado 2:\n",
      "==================================================\n",
      "  Iter     0: Cost = 27081.8270\n",
      "  Iter  1000: Cost = 7.7805\n",
      "  Iter  2000: Cost = 7.7385\n",
      "  Iter  3000: Cost = 7.7381\n",
      "  Iter  4000: Cost = 7.7381\n",
      "  MSE final: 15.4762\n",
      "\n",
      "==================================================\n",
      "Grado 3:\n",
      "==================================================\n",
      "  Iter     0: Cost = 26237.9740\n",
      "  Iter  1000: Cost = 7.2174\n",
      "  Iter  2000: Cost = 7.2173\n",
      "  Iter  3000: Cost = 7.2171\n",
      "  Iter  4000: Cost = 7.2170\n",
      "  MSE final: 14.4338\n",
      "\n",
      "==================================================\n",
      "Grado 4:\n",
      "==================================================\n",
      "  Iter     0: Cost = 25565.3658\n",
      "  Iter  1000: Cost = 7.2402\n",
      "  Iter  2000: Cost = 7.1859\n",
      "  Iter  3000: Cost = 7.1448\n",
      "  Iter  4000: Cost = 7.1122\n",
      "  MSE final: 14.1703\n",
      "\n",
      "==================================================\n",
      "Grado 5:\n",
      "==================================================\n",
      "  Iter     0: Cost = 25050.2938\n",
      "  Iter  1000: Cost = 6.7447\n",
      "  Iter  2000: Cost = 6.6333\n",
      "  Iter  3000: Cost = 6.5485\n",
      "  Iter  4000: Cost = 6.4739\n",
      "  MSE final: 12.8073\n",
      "\n",
      "==================================================\n",
      "Grado 6:\n",
      "==================================================\n",
      "  Iter     0: Cost = 24673.3149\n",
      "  Iter  1000: Cost = 6.1382\n",
      "  Iter  2000: Cost = 5.9781\n",
      "  Iter  3000: Cost = 5.8256\n",
      "  Iter  4000: Cost = 5.6784\n",
      "  MSE final: 11.0721\n"
     ]
    }
   ],
   "source": [
    "degrees = [1, 2, 3, 4, 5, 6]\n",
    "results = {}  # almacenará {grado: {'w': w, 'b': b, 'mse': mse, 'mu': mu, 'sigma': sigma}}\n",
    "\n",
    "alpha = 0.1\n",
    "num_iters = 5000\n",
    "\n",
    "for deg in degrees:\n",
    "    print(f\"\\n{'='*50}\")\n",
    "    print(f\"Grado {deg}:\")\n",
    "    print(f\"{'='*50}\")\n",
    "    \n",
    "    # Paso 1: Crear features polinomiales [x, x², x³, ..., x^deg]\n",
    "    X_poly = create_polynomial_features(x_train, deg)\n",
    "    \n",
    "    # Paso 2: Z-score normalization\n",
    "    # axis=0 → calcula media/std por columna (una por feature)\n",
    "    mu = X_poly.mean(axis=0)\n",
    "    sigma = X_poly.std(axis=0)\n",
    "    X_norm = (X_poly - mu) / sigma\n",
    "    \n",
    "    # Paso 3: Entrenar\n",
    "    w_init = np.zeros(deg)\n",
    "    b_init = 0.0\n",
    "    w_final, b_final, J_hist = gradient_descent(X_norm, y_train, w_init, b_init, alpha, num_iters)\n",
    "    \n",
    "    # Paso 4: Calcular MSE final\n",
    "    predictions = X_norm @ w_final + b_final\n",
    "    mse = np.mean((predictions - y_train)**2)\n",
    "    \n",
    "    results[deg] = {'w': w_final, 'b': b_final, 'mse': mse, 'mu': mu, 'sigma': sigma}\n",
    "    print(f\"  MSE final: {mse:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista — Paso 1</span></summary>\n",
    "\n",
    "```python\n",
    "X_poly = create_polynomial_features(x_train, deg)\n",
    "```\n",
    "\n",
    "</details>\n",
    "\n",
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista — Paso 2 (z-score)</span></summary>\n",
    "\n",
    "```python\n",
    "mu = X_poly.mean(axis=0)      # media de cada columna\n",
    "sigma = X_poly.std(axis=0)    # std de cada columna\n",
    "X_norm = (X_poly - mu) / sigma\n",
    "```\n",
    "Nota: `axis=0` opera sobre las filas → resultado tiene shape (n,), una media/std por feature.\n",
    "\n",
    "</details>\n",
    "\n",
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista — Paso 4 (MSE)</span></summary>\n",
    "\n",
    "```python\n",
    "predictions = X_norm @ w_final + b_final\n",
    "mse = np.mean((predictions - y_train)**2)\n",
    "```\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.8 Visualización Comparativa\n",
    "\n",
    "Ejecuta la siguiente celda para ver las curvas de cada grado y comparar MSE."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x900 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "========================================\n",
      "Grado   MSE            Ranking\n",
      "========================================\n",
      "  6     11.07          1 ← MEJOR\n",
      "  5     12.81          2\n",
      "  4     14.17          3\n",
      "  3     14.43          4\n",
      "  2     15.48          5\n",
      "  1     227.84         6\n"
     ]
    }
   ],
   "source": [
    "# Visualización: curvas ajustadas para cada grado\n",
    "fig, axes = plt.subplots(2, 3, figsize=(14, 9))\n",
    "x_plot = np.linspace(0.3, 3.7, 200)\n",
    "\n",
    "for idx, deg in enumerate(degrees):\n",
    "    ax = axes[idx // 3, idx % 3]\n",
    "    ax.scatter(x_train, y_train, color='royalblue', s=40, zorder=5)\n",
    "    \n",
    "    if results[deg]['mse'] is not None:\n",
    "        # Generar curva de predicción\n",
    "        X_plot_poly = create_polynomial_features(x_plot, deg)\n",
    "        X_plot_norm = (X_plot_poly - results[deg]['mu']) / results[deg]['sigma']\n",
    "        y_plot = X_plot_norm @ results[deg]['w'] + results[deg]['b']\n",
    "        ax.plot(x_plot, y_plot, 'r-', linewidth=2)\n",
    "        ax.set_title(f\"Grado {deg} — MSE: {results[deg]['mse']:.1f}\", fontsize=11)\n",
    "    else:\n",
    "        ax.set_title(f\"Grado {deg} — Sin completar\", fontsize=11, color='gray')\n",
    "    \n",
    "    ax.set_xlabel('Tamaño')\n",
    "    ax.set_ylabel('Precio')\n",
    "    ax.set_ylim([50, 520])\n",
    "    ax.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.suptitle('Regresión Polinomial: Comparación de Grados', fontsize=13, y=1.02)\n",
    "plt.show()\n",
    "\n",
    "# Tabla de resultados\n",
    "print(\"\\n\" + \"=\"*40)\n",
    "print(f\"{'Grado':<8}{'MSE':<15}{'Ranking'}\")\n",
    "print(\"=\"*40)\n",
    "valid_results = {k: v for k, v in results.items() if v['mse'] is not None}\n",
    "if valid_results:\n",
    "    sorted_degrees = sorted(valid_results.keys(), key=lambda d: valid_results[d]['mse'])\n",
    "    for rank, deg in enumerate(sorted_degrees, 1):\n",
    "        marker = \" ← MEJOR\" if rank == 1 else \"\"\n",
    "        print(f\"  {deg:<6}{valid_results[deg]['mse']:<15.2f}{rank}{marker}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.9 Pregunta de Reflexión\n",
    "\n",
    "Basándote en los resultados:\n",
    "1. ¿Cuál es el mejor grado polinomial para estos datos?\n",
    "2. ¿Por qué grados muy altos (5, 6) no necesariamente dan mejor MSE de entrenamiento?\n",
    "3. ¿Qué riesgo existe al usar un grado muy alto? (piensa en datos nuevos)\n",
    "\n",
    "*Escribe tu respuesta abajo:*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Tu respuesta aquí:**\n",
    "\n",
    "1. El mejor grado es el 3 (MSE = 14.4). Con este grado la curva se ajusta bien a los datos dando equilibrio entre capturar la forma real y no complicarse de más.\n",
    "\n",
    "2. Los grados altos no necesariamente ganan porque con solo 12 datos y un número fijo de iteraciones, gradient descent no tiene suficiente tiempo para encontrar buenos valores para tantos parámetros a la vez.\n",
    "\n",
    "3. El riesgo es el **overfitting**: la curva se tuerce tanto para pasar por todos los puntos de entrenamiento que si le muestras una casa nueva, predice un precio absurdo. Memoriza en lugar de aprender."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 4. Feature Scaling: Comparativa de 3 Métodos\n",
    "\n",
    "## 4.1 El Problema\n",
    "\n",
    "Cuando las features tienen **escalas muy diferentes**, gradient descent converge lentamente porque los gradientes están dominados por las features grandes.\n",
    "\n",
    "Ejemplo: `size` va de 852 a 2104, pero `bedrooms` solo de 2 a 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rangos de cada feature (sin escalar):\n",
      "  size:     [852, 2200]  rango = 1348\n",
      "  bedrooms: [2, 5]    rango = 3\n",
      "  age:      [20, 55]   rango = 35\n",
      "\n",
      "→ El rango de 'size' es ~400x mayor que 'bedrooms'. Esto causa problemas en GD.\n"
     ]
    }
   ],
   "source": [
    "# Dataset multi-feature para la comparativa de scaling\n",
    "# size(sqft), bedrooms, age(años) → price($1000s)\n",
    "X_multi = np.array([\n",
    "    [2104, 5, 45],\n",
    "    [1416, 3, 40],\n",
    "    [852,  2, 35],\n",
    "    [1534, 3, 30],\n",
    "    [2000, 4, 50],\n",
    "    [1200, 2, 25],\n",
    "    [1800, 4, 42],\n",
    "    [950,  2, 20],\n",
    "    [1600, 3, 38],\n",
    "    [2200, 5, 55]\n",
    "])\n",
    "y_multi = np.array([460, 232, 178, 252, 380, 195, 320, 160, 275, 490])\n",
    "\n",
    "print(\"Rangos de cada feature (sin escalar):\")\n",
    "print(f\"  size:     [{X_multi[:,0].min():.0f}, {X_multi[:,0].max():.0f}]  rango = {X_multi[:,0].max() - X_multi[:,0].min():.0f}\")\n",
    "print(f\"  bedrooms: [{X_multi[:,1].min():.0f}, {X_multi[:,1].max():.0f}]    rango = {X_multi[:,1].max() - X_multi[:,1].min():.0f}\")\n",
    "print(f\"  age:      [{X_multi[:,2].min():.0f}, {X_multi[:,2].max():.0f}]   rango = {X_multi[:,2].max() - X_multi[:,2].min():.0f}\")\n",
    "print(\"\\n→ El rango de 'size' es ~400x mayor que 'bedrooms'. Esto causa problemas en GD.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 Método 1: Min-Max Scaling\n",
    "\n",
    "$$x_{\\text{scaled}} = \\frac{x}{\\max(x)}$$\n",
    "\n",
    "Resultado: cada feature queda en rango $[0, 1]$ aproximadamente.\n",
    "\n",
    "**Ejercicio:** Implementa la función. Debe ser vectorizada (sin loops)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "def min_max_scale(X):\n",
    "    \"\"\"\n",
    "    Aplica Min-Max Scaling: divide cada feature por su valor máximo.\n",
    "    \n",
    "    Args:\n",
    "        X (ndarray (m,n)): matriz de features\n",
    "    \n",
    "    Returns:\n",
    "        X_scaled (ndarray (m,n)): features escaladas\n",
    "        params (dict): parámetros para re-escalar datos nuevos\n",
    "    \"\"\"\n",
    "    # X.max(axis=0) calcula el máximo de cada columna → shape (n,)\n",
    "    # NumPy broadcasting divide cada columna de X por su máximo automáticamente\n",
    "    X_scaled = X / X.max(axis=0)\n",
    "    \n",
    "    params = {'max': X.max(axis=0)}\n",
    "    return X_scaled, params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista</span></summary>\n",
    "\n",
    "```python\n",
    "X_scaled = X / X.max(axis=0)\n",
    "```\n",
    "`X.max(axis=0)` retorna el máximo de cada columna → shape (n,).  \n",
    "NumPy broadcasting divide cada columna de X por su máximo.\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3 Método 2: Mean Normalization\n",
    "\n",
    "$$x_{\\text{scaled}} = \\frac{x - \\mu}{\\max(x) - \\min(x)}$$\n",
    "\n",
    "Resultado: cada feature queda centrada en 0, rango $\\approx [-0.5, 0.5]$.\n",
    "\n",
    "**Ejercicio:** Implementa la función de forma vectorizada."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_normalize(X):\n",
    "    \"\"\"\n",
    "    Aplica Mean Normalization.\n",
    "    \n",
    "    Args:\n",
    "        X (ndarray (m,n)): matriz de features\n",
    "    \n",
    "    Returns:\n",
    "        X_scaled (ndarray (m,n)): features escaladas\n",
    "        params (dict): parámetros {mu, rango} para re-escalar datos nuevos\n",
    "    \"\"\"\n",
    "    mu = X.mean(axis=0)                      # media de cada columna → shape (n,)\n",
    "    rango = X.max(axis=0) - X.min(axis=0)   # rango de cada columna → shape (n,)\n",
    "    X_scaled = (X - mu) / rango             # centra en 0 y escala por el rango\n",
    "    \n",
    "    params = {'mu': mu, 'rango': rango}\n",
    "    return X_scaled, params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista</span></summary>\n",
    "\n",
    "```python\n",
    "mu = X.mean(axis=0)\n",
    "rango = X.max(axis=0) - X.min(axis=0)\n",
    "X_scaled = (X - mu) / rango\n",
    "```\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.4 Método 3: Z-Score Normalization (Estandarización)\n",
    "\n",
    "$$x_{\\text{scaled}} = \\frac{x - \\mu}{\\sigma}$$\n",
    "\n",
    "Resultado: cada feature tiene media = 0 y desviación estándar = 1.\n",
    "\n",
    "**Ejercicio:** Implementa la función de forma vectorizada."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def z_score_normalize(X):\n",
    "    \"\"\"\n",
    "    Aplica Z-Score Normalization (estandarización).\n",
    "    \n",
    "    Args:\n",
    "        X (ndarray (m,n)): matriz de features\n",
    "    \n",
    "    Returns:\n",
    "        X_scaled (ndarray (m,n)): features escaladas\n",
    "        params (dict): parámetros {mu, sigma} para re-escalar datos nuevos\n",
    "    \"\"\"\n",
    "    mu = X.mean(axis=0)      # media de cada columna    → shape (n,)\n",
    "    sigma = X.std(axis=0)    # std de cada columna      → shape (n,)\n",
    "    X_scaled = (X - mu) / sigma  # centra en 0 y escala a std=1\n",
    "    \n",
    "    params = {'mu': mu, 'sigma': sigma}\n",
    "    return X_scaled, params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista</span></summary>\n",
    "\n",
    "```python\n",
    "mu = X.mean(axis=0)\n",
    "sigma = X.std(axis=0)\n",
    "X_scaled = (X - mu) / sigma\n",
    "```\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.5 Comparativa: Entrenar con cada método\n",
    "\n",
    "Ahora entrenaremos el modelo **4 veces** con los mismos datos pero diferente scaling, y compararemos:\n",
    "1. Sin scaling\n",
    "2. Min-Max\n",
    "3. Mean Normalization\n",
    "4. Z-Score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "==================================================\n",
      "Sin Scaling (alpha muy pequeño):\n",
      "==================================================\n",
      "  Iter     0: Cost = 26986.9952\n",
      "  Iter   600: Cost = 738.4275\n",
      "  Iter  1200: Cost = 738.3550\n",
      "  Iter  1800: Cost = 738.2828\n",
      "  Iter  2400: Cost = 738.2108\n",
      "\n",
      "==================================================\n",
      "Min-Max Scaling:\n",
      "==================================================\n",
      "  Iter     0: Cost = 28657.0633\n",
      "  Iter   600: Cost = 270.1990\n",
      "  Iter  1200: Cost = 253.4211\n",
      "  Iter  1800: Cost = 247.0957\n",
      "  Iter  2400: Cost = 243.2751\n",
      "\n",
      "==================================================\n",
      "Mean Normalization:\n",
      "==================================================\n",
      "  Iter     0: Cost = 40764.4710\n",
      "  Iter   600: Cost = 248.6136\n",
      "  Iter  1200: Cost = 239.7831\n",
      "  Iter  1800: Cost = 236.1698\n",
      "  Iter  2400: Cost = 234.2520\n",
      "\n",
      "==================================================\n",
      "Z-Score Normalization:\n",
      "==================================================\n",
      "  Iter     0: Cost = 38374.3762\n",
      "  Iter   600: Cost = 232.0343\n",
      "  Iter  1200: Cost = 231.6551\n",
      "  Iter  1800: Cost = 231.6508\n",
      "  Iter  2400: Cost = 231.6507\n"
     ]
    }
   ],
   "source": [
    "# Configuración del experimento\n",
    "alpha_scaling = 1e-7  # learning rate pequeño (necesario sin scaling)\n",
    "alpha_scaled = 0.1     # learning rate normal (con scaling)\n",
    "iters = 3000\n",
    "n_features = X_multi.shape[1]\n",
    "\n",
    "scaling_results = {}\n",
    "\n",
    "# --- Experimento 1: Sin scaling ---\n",
    "print(\"=\"*50)\n",
    "print(\"Sin Scaling (alpha muy pequeño):\")\n",
    "print(\"=\"*50)\n",
    "w0, b0, J0 = gradient_descent(X_multi, y_multi, np.zeros(n_features), 0.0, alpha_scaling, iters)\n",
    "mse0 = np.mean((X_multi @ w0 + b0 - y_multi)**2)\n",
    "scaling_results['Sin scaling'] = {'J_hist': J0, 'mse': mse0, 'color': 'red'}\n",
    "\n",
    "# --- Experimento 2: Min-Max ---\n",
    "print(\"\\n\" + \"=\"*50)\n",
    "print(\"Min-Max Scaling:\")\n",
    "print(\"=\"*50)\n",
    "X_mm, params_mm = min_max_scale(X_multi)\n",
    "if X_mm is not None:\n",
    "    w1, b1, J1 = gradient_descent(X_mm, y_multi, np.zeros(n_features), 0.0, alpha_scaled, iters)\n",
    "    mse1 = np.mean((X_mm @ w1 + b1 - y_multi)**2)\n",
    "    scaling_results['Min-Max'] = {'J_hist': J1, 'mse': mse1, 'color': 'blue'}\n",
    "else:\n",
    "    print(\"  ⚠️ min_max_scale() no implementada\")\n",
    "\n",
    "# --- Experimento 3: Mean Normalization ---\n",
    "print(\"\\n\" + \"=\"*50)\n",
    "print(\"Mean Normalization:\")\n",
    "print(\"=\"*50)\n",
    "X_mn, params_mn = mean_normalize(X_multi)\n",
    "if X_mn is not None:\n",
    "    w2, b2, J2 = gradient_descent(X_mn, y_multi, np.zeros(n_features), 0.0, alpha_scaled, iters)\n",
    "    mse2 = np.mean((X_mn @ w2 + b2 - y_multi)**2)\n",
    "    scaling_results['Mean Norm'] = {'J_hist': J2, 'mse': mse2, 'color': 'green'}\n",
    "else:\n",
    "    print(\"  ⚠️ mean_normalize() no implementada\")\n",
    "\n",
    "# --- Experimento 4: Z-Score ---\n",
    "print(\"\\n\" + \"=\"*50)\n",
    "print(\"Z-Score Normalization:\")\n",
    "print(\"=\"*50)\n",
    "X_zs, params_zs = z_score_normalize(X_multi)\n",
    "if X_zs is not None:\n",
    "    w3, b3, J3 = gradient_descent(X_zs, y_multi, np.zeros(n_features), 0.0, alpha_scaled, iters)\n",
    "    mse3 = np.mean((X_zs @ w3 + b3 - y_multi)**2)\n",
    "    scaling_results['Z-Score'] = {'J_hist': J3, 'mse': mse3, 'color': 'purple'}\n",
    "else:\n",
    "    print(\"  ⚠️ z_score_normalize() no implementada\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.6 Visualización de Convergencia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================================================\n",
      "Método            MSE Final      Convergió?\n",
      "==================================================\n",
      "  Sin scaling     1476.28        Parcial\n",
      "  Min-Max         481.47         Sí\n",
      "  Mean Norm       466.32         Sí\n",
      "  Z-Score         463.30         Sí\n"
     ]
    }
   ],
   "source": [
    "# Gráfica comparativa de convergencia\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "# Panel izquierdo: todas las curvas\n",
    "for name, data in scaling_results.items():\n",
    "    ax1.plot(data['J_hist'], color=data['color'], linewidth=2, label=f\"{name} (MSE={data['mse']:.1f})\")\n",
    "\n",
    "ax1.set_xlabel('Iteración')\n",
    "ax1.set_ylabel('Costo J')\n",
    "ax1.set_title('Convergencia: Costo vs Iteraciones')\n",
    "ax1.legend()\n",
    "ax1.grid(True, alpha=0.3)\n",
    "\n",
    "# Panel derecho: zoom en las curvas con scaling (sin la roja que domina)\n",
    "for name, data in scaling_results.items():\n",
    "    if name != 'Sin scaling':\n",
    "        ax2.plot(data['J_hist'], color=data['color'], linewidth=2, label=f\"{name} (MSE={data['mse']:.1f})\")\n",
    "\n",
    "ax2.set_xlabel('Iteración')\n",
    "ax2.set_ylabel('Costo J')\n",
    "ax2.set_title('Zoom: Solo métodos con scaling')\n",
    "ax2.legend()\n",
    "ax2.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Tabla resumen\n",
    "print(\"\\n\" + \"=\"*50)\n",
    "print(f\"{'Método':<18}{'MSE Final':<15}{'Convergió?'}\")\n",
    "print(\"=\"*50)\n",
    "for name, data in scaling_results.items():\n",
    "    converged = \"Sí\" if data['J_hist'][-1] < data['J_hist'][0] * 0.01 else \"Parcial\"\n",
    "    print(f\"  {name:<16}{data['mse']:<15.2f}{converged}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 5. Integración: Pipeline Completo\n",
    "\n",
    "## 5.1 Ejercicio Final\n",
    "\n",
    "Combina todo lo aprendido. Usando el dataset original (`x_train`, `y_train`):\n",
    "\n",
    "1. Crea features polinomiales del grado óptimo (el que encontraste en la sección 3)\n",
    "2. Aplica el mejor método de scaling (el que encontraste en la sección 4)\n",
    "3. Entrena el modelo\n",
    "4. Grafica la predicción vs los datos reales\n",
    "5. Reporta el MSE final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  Iter     0: Cost = 26237.9740\n",
      "  Iter  1000: Cost = 7.2174\n",
      "  Iter  2000: Cost = 7.2173\n",
      "  Iter  3000: Cost = 7.2171\n",
      "  Iter  4000: Cost = 7.2170\n",
      "MSE final del pipeline: 14.4338\n"
     ]
    }
   ],
   "source": [
    "# ============================================\n",
    "# PIPELINE COMPLETO\n",
    "# ============================================\n",
    "\n",
    "# Paso 1: Elegir el mejor grado (basado en sección 3)\n",
    "best_degree = 3  # grado óptimo: mejor equilibrio entre MSE bajo y no overfitting\n",
    "\n",
    "# Paso 2: Crear features polinomiales [x, x², x³]\n",
    "X_final = create_polynomial_features(x_train, best_degree)\n",
    "\n",
    "# Paso 3: Aplicar z-score normalization (mejor método de sección 4)\n",
    "mu = X_final.mean(axis=0)      # media de cada columna\n",
    "sigma = X_final.std(axis=0)    # std de cada columna\n",
    "X_final_norm = (X_final - mu) / sigma\n",
    "\n",
    "# Paso 4: Entrenar con gradient descent\n",
    "w_fin, b_fin, J_fin = gradient_descent(X_final_norm, y_train,\n",
    "                                        np.zeros(best_degree), 0.0, 0.1, 5000)\n",
    "\n",
    "# Paso 5: Calcular MSE final\n",
    "preds = X_final_norm @ w_fin + b_fin\n",
    "mse_final = np.mean((preds - y_train)**2)\n",
    "\n",
    "print(f\"MSE final del pipeline: {mse_final:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details>\n",
    "<summary><span style=\"color: green; font-weight: bold;\">💡 Pista — Pipeline completo</span></summary>\n",
    "\n",
    "```python\n",
    "best_degree = 2  # o el que hayas encontrado\n",
    "\n",
    "# Features polinomiales\n",
    "X_final = create_polynomial_features(x_train, best_degree)\n",
    "\n",
    "# Scaling (z-score)\n",
    "mu = X_final.mean(axis=0)\n",
    "sigma = X_final.std(axis=0)\n",
    "X_final_norm = (X_final - mu) / sigma\n",
    "\n",
    "# Entrenar\n",
    "w_fin, b_fin, J_fin = gradient_descent(X_final_norm, y_train, \n",
    "                                        np.zeros(best_degree), 0.0, 0.1, 5000)\n",
    "\n",
    "# MSE\n",
    "preds = X_final_norm @ w_fin + b_fin\n",
    "mse_final = np.mean((preds - y_train)**2)\n",
    "```\n",
    "\n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualización del resultado final (ejecuta después de completar el pipeline)\n",
    "if mse_final is not None:\n",
    "    plt.figure(figsize=(9, 5))\n",
    "    plt.scatter(x_train, y_train, color='royalblue', s=80, zorder=5, label='Datos reales')\n",
    "    \n",
    "    # Curva de predicción\n",
    "    x_plot = np.linspace(0.3, 3.7, 200)\n",
    "    X_plot_poly = create_polynomial_features(x_plot, best_degree)\n",
    "    X_plot_norm = (X_plot_poly - mu) / sigma\n",
    "    y_plot = X_plot_norm @ w_fin + b_fin\n",
    "    \n",
    "    plt.plot(x_plot, y_plot, 'r-', linewidth=2.5, label=f'Modelo (grado {best_degree})')\n",
    "    plt.xlabel('Tamaño (1000 sqft)')\n",
    "    plt.ylabel('Precio ($1000s)')\n",
    "    plt.title(f'Pipeline Final — Grado {best_degree}, MSE = {mse_final:.2f}')\n",
    "    plt.legend()\n",
    "    plt.grid(True, alpha=0.3)\n",
    "    plt.show()\n",
    "else:\n",
    "    print(\"⚠️ Completa el pipeline arriba primero.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 6. Bonus: Verificar con sklearn\n",
    "\n",
    "Compara tu implementación manual con la de scikit-learn. Los resultados deben ser similares."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MSE sklearn:    15.4762\n",
      "MSE tu código:  14.4338\n",
      "\n",
      "✓ Resultados similares!\n"
     ]
    },
    {
     "data": {
      "image/png": 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yZEm8ePEiyz4bN25Urf2ffocyPDwcQNp18ebNGxQvXhzGxsbYu3cvbG1tNVYaatKkCVasWIGbN2+yACDKAgsAIgPUrl07LFu2DA8fPkRgYCAcHR1RvXp11XEHBwckJibqbflLBwcHnD9/HjExMZneBTh9+jRSU1Pxyy+/qB6SBKA2lST9XEDat8rly5fXOoYyZcogODgY8fHxat+8p09BKVOmjNbnyoqDgwNu374NmUyW6YOpuooFAMzNzdG6dWu0bt0aqampGDFiBNasWYPBgwerTaEaP348JBIJZsyYAQsLi0ynr6RzcHBAcHAwatSokeWg/cqVK4iJicHKlStRu3ZtVfu/p6zlJXt7e2zevDlHr83uyjPNmjXDtGnTcOvWLSxZsiTb72djY4Ny5crhyZMn2X6trr1+/fqz+4u8e/cOnz59Qps2bTSOrVmzBmvWrMGhQ4dQpUoVREdHZ1jky+Vytf8loozxGQAiA5Q+WFu+fDkePHigMXhr1aoVbt68iaCgII3XxsbG5vk/rs2bN4cgCFi5cqXGsfRvb9O/3f33t7lxcXHYv3+/Wn9fX19YWFhg7dq1SElJyfBcGWnYsCEUCgV27typ1r5lyxaIRCI0bNgwex8qE82bN8fHjx813uff8ekqlv/uoGpsbAwnJycIgpDhWvOzZs1CixYtMGHCBPz1119ZnrtVq1ZQKBRYvXq1xjG5XK6alpO+edO//2xSU1MzXd41t5mYmMDHxydH/2U0VSorFhYWmD59OkaMGKGxBO2/PXz4MMNpSW/fvsWzZ89QoUKFbH9OIHvLgGorozjPnj2L+/fvo0GDBmrtoaGhakvd9unTB6tWrVL7b+bMmQCATp06YdWqVarpho6OjoiKitIo+AMDAwGAewAQfQbvABAZoHLlysHLy0s1aPtvATBgwACcPn0aQ4YMQceOHVG1alUkJSXh8ePHOH78OP766688nV9cr149tG/fHtu3b8erV6/QoEEDKJVKXL9+HXXr1kXv3r1Rv359SKVSDBkyBD169EBCQgJ+/fVX2Nraqu1UamlpiYkTJ2LKlCno0qUL2rZtC2trazx8+BDJyclYsGBBhjE0adIEdevWxZIlS/D27Vu4urriwoUL+Ouvv/Dtt99muYRpdnTo0AGHDh3CvHnzcOfOHdSsWRNJSUkIDg5Gz5490bRpU53FMmDAANjZ2aFGjRqwtbXF8+fPsWPHDvj5+WW41rxYLMbPP/+MYcOGYfTo0Vi3bl2mc/zr1KmD7t27Y+3atXjw4IHqz+/ly5c4duwYJk+ejJYtW8LLyws2NjaYMGEC+vTpA5FIhN9//13vO0XnlY4dO362z4ULF7BixQo0adIEHh4eMDc3x5s3b7B//37VXZr/On78eIY7AdevXx92dnYAsrcM6OnTp/Hw4UMAaTsTP3r0SFXMNWnSBJUrVwYA9OjRA1WqVIG7uzusrKwQEhKC/fv3o1SpUhgyZIjaOfv166c6NwBUrVoVVatWVeuTfufH2dkZTZs2VbX36tULBw4cwJAhQ9CnTx+ULl0aV69eRWBgIOrXrw8PD4/PfiYiQ8YCgMhAtWvXDjdv3kT16tU1psaYmZlh+/btWLt2LY4dO4ZDhw7B0tISjo6OGDFihMZOvnlh3rx5cHV1xW+//YaFCxfCysoK7u7uql1IK1asiOXLl2Pp0qVYsGAB7Ozs0LNnTxQrVkxjXfyuXbvC1tYW69atw+rVq2FkZISKFSuqBiAZEYvF+OWXX7B8+XIcPXoUBw4cQJkyZTB+/Hh89913ufY5JRIJ1q9fj19++QWBgYE4ceIEihQpgho1asDV1VWnsXTv3h2HDx/G5s2bkZiYiJIlS6JPnz4YOnRopq+RSqVYvnw5Bg4ciKFDh2LLli2ZDr5mzpwJd3d37NmzB0uWLIFEIkGZMmXw9ddfqza5Klq0KNasWYMFCxZg6dKlsLa2xtdffw1vb2/VKjiGpnnz5qq9IS5duoRPnz7B2toa1atXR//+/VGvXj2N10yfPj3Dc23btk1VAGTHiRMncPDgQdXPISEhCAkJAZA2vz+9AGjVqhXOnj2LCxcuIDk5Gfb29ujatSuGDx+eo/fNTMWKFbF//34sXboUf/zxB6KiolC8eHF89913Gs+rEJEmkVBYv1YhIiIiIiINfAaAiIiIiMiAsAAgIiIiIjIgLACIiIiIiAwICwAiIiIiIgPCAoCIiIiIyICwACAiIiIiMiAsAIiIiIiIDIhBbgQWGRmn7xDyHalUAplMoe8wDApzrnvMuX4w77rHnOsec657zLkme3vtNurkHQACAIhE+o7A8DDnusec6wfzrnvMue4x57rHnOccCwAiIiIiIgPCAoCIiIiIyICwACAiIiIiMiAsAIiIiIiIDAgLACIiIiIiA8ICgIiIiIjIgLAAICIiIiIyICwAiIiIiIgMCAsAIiIiIiIDwgKAiIiIiMiA6LUAWLFiBVxdXdX+a9mypep4SkoKZsyYgbp168LLywsjRoxAVFSU2jnCwsIwaNAgeHh4wNvbGwsWLIBcLtf1R1ETE6/ExXup+Ot6Ci7eS0VMvFKv8RARERERpTPSdwCVKlXC5s2bVT9LJBLV/587dy7Onj2LpUuXwsrKCrNmzcLw4cOxZ88eAIBCocDgwYNhZ2eHPXv24P379/D394dUKsVPP/2k888SGqHAwXNJuBQig/JfY36xGKjnJkXHhmZwKCHJ/AT0xW7cuIaRI4fgzz/PwMrKSt/hEBEREeU7ei8AJBIJ7O3tNdrj4uKwf/9+BAQEwNvbG0BaQdC6dWvcunULnp6eOH/+PJ4+fYrNmzfDzs4OVapUwahRoxAQEIDhw4fD2NhYZ5/j1lMZAnbHQ6GE2uAfSPv5UogMVx/KMLanJTydpbn63nPmTMeffwYCSMuntbUNnJyc0bRpC7Ru3Q5isfY3eo4ePYzlyxfh2LG/czVGIiIiIsof9F4AvHr1Cr6+vjAxMYGnpyfGjBmD0qVL4969e5DJZPDx8VH1dXJyQunSpVUFwK1bt+Di4gI7OztVH19fX0yfPh1Pnz6Fm5tbhu8plUogEuXiZwiXI2B3PORyQMikj1IJCEogYHc8fh5WBOVL5l7qxWIRvL19MHXqDCiVSnz4EI3g4ItYvnwRzp07jYCApTAyyvr9jIwk//+/acWCsbFu71TIZDJIpV9eGEmlaXEbG0t0/hmyKz3npDvMuX4w77rHnOsec657+S3nl8MuYf/j3/BV+aZoUaHl51+gR3otAKpXr4558+ahQoUKiIyMxKpVq9CrVy8cPnwYUVFRkEqlsLa2VnuNra0tIiMjAQBRUVFqg38Aqp/T+2REJlPk6ufY91cCFMrMB//pBAAKJfDr6QSM7GKZa++vVAowMpLC2rooAKBIEVtUrOiCypWrYtSoH/D777+jXbsOAIA9e3bg6NHDCAt7C2trG/j4NMDQoSNRpIgVLl26jJkzpwEA6tTxAgD07z8QAwYMRmxsLJYtC8CFC0GQyVLh6VkTo0ePRblyDgCA8PB3WLx4Ie7cuQW5XIaSJUtj2LCR8Pb2zTDmLl3aoW3b9nj9OhRBQWfh59cYkydPx+3bt7B27Uo8fPgARYoUQcOGjTB48HCYmZkBAI4dO4Jff92D0NBXMDMzQ40atTBq1BgULVoMwD9/tqmpCqSmpv3/z53zwIFfsW/fLrx/HwELC0t4eHhi9uyFufbnk5X0GEl3mHP9YN51jznXPeZc9/JDzgVBwNo7qzD94hQoBSU23l6H8z2vwKlIJX2Hlim9PgTs5+eHVq1aoXLlymjQoAHWrVuH2NhY/Pnnn/oMK1ti4pUac/6zolQCwfdl+KSDB4Nr1qwNZ2cXnD17WtUmFosxevQ4bN++D5MnT8eNG1exevVyAEC1ah4YOXIMLCws8Pvvx/D778fQs2cfAMDcudPx6NEDLFiwGGvWbIYgCBg3bpTqgevFixdAJkvFqlXrsXXrHvzwwwiYmZlnGd/u3dvh7OyCzZt3ol+/7/H27RuMHTsCjRo1wdatuzFjxlzcuXMLS5b8MxiXy+X4/vsh2LJlF+bODUB4+DvMmTM90/f43DkfPgzBsmUBGDBgMHbt2o9Fi5bDw6NGjvJNREREhiVVkYoxf4/E/y5MglJIG9spBAUS5Ul6jixr+WoZUGtrazg6OiI0NBR2dnaQyWSIjY1V6xMdHa16ZsDOzk5jVaD0nzN6riAvhLyUaz34T6dUpr1OF8qXL4/w8Heqn7t1+wY1atRCqVKlUbNmbQwc+APOnDkJAJBKpbC0tIRIJIKtrR1sbe1gbm6O169Dcf78Ofj7T4GHhxcqVXLBtGmzEBn5HufO/Q0AiIgIR7VqHnByckaZMmVRv34DeHpmPZCuUaM2evbsjTJlyqJMmbLYvn0zmjVriW7dvkG5cg6oVs0Do0aNw7FjR5CSkgIAaNu2Pby966NMmbJwd6+G0aPH4tKli0hMTMzwPT53zoiIcJiamqJ+/QYoWbIUXFwqo2vXHrmQeSIiIirMPiRHo9vhDtjxYKta+w8eI1DNrrqeotKO3p8B+LeEhAS8fv0a9vb2cHd3h1QqRXBwMFq0aAEAeP78OcLCwuDp6QkA8PT0xJo1axAdHQ1bW1sAwMWLF2FpaQlnZ2edxJyU8rmJPxlLzOHrsksQAOCfBx6uXr2MHTu24NWrl0hISIBCoUBqagqSk5MgFmf80PSrVy8gkUjg5uauarOxKQIHh/J49eoFAKBLlx4ICJiHq1cvoVatuvDzawJn56xvfVWuXEXt56dPn+DZsyc4efLYv+IXoFQq8e5dGBwdK+DhwwfYtGkdnj59jLi4OAj/X21HRISjQoWKGu/xuXPWrl0XJUuWQrdu7VG3rjfq1vVBw4aNYWpqmmXsREREZLgef3iE3ke74WXsC1WbRCTBbN8FGFBtkB4j045eC4AFCxagcePGKF26NN6/f48VK1ZALBajbdu2sLKyQufOnTF//nzY2NjA0tISs2fPhpeXl6oA8PX1hbOzM8aPH49x48YhMjISS5cuRa9evXS2ApCZSc6eJjbP4euy69WrFyhdujQA4N27MPj7/4gOHTpj4MChsLa2xp07tzB//izIZHKYmOQ8Z+3adUCdOvUQHHweV65cxvbtmzF8+Gh06ZL5t+npc/DTJSUlon37Thm+pkSJkkhKSsKYMcNRp443pk2bjSJFiiIiIhw//TQccrksw/f43DmlUik2btyBmzev4+rVS9iwYQ02bVqH9eu3cRlRIiIi0nA69BQGnuiHuNR/ZqnYmBTB+uZb0KhcEz1Gpj29FgDh4eH46aefEBMTg2LFiqFmzZrYt28fihVLe6Bz0qRJEIvFGDlyJFJTU+Hr64tp06apXi+RSLBmzRpMnz4d3bt3h5mZGTp27IiRI0fq7DO4ORpBLNZc+jMrYnHa6/La9etX8ezZU3Tr9g0A4NGjB1AqlRg+/EfV0qCnT59Ue42RkRQKhfqHKV++AhQKBUJC7qFaNQ8AwKdPMQgNfQVHxwqqfiVKlESHDl3QoUMXrFmzEocPH8qyAPgvF5fKePHiBcqWLZfh8WfPnuLTp08YMmQ4SpQoCSBtDv+XnBMAjIyMULt2XdSuXRf9+w9Cy5aNcOPGVfj5FYy/xERERJT3BEHAxrtrMeXCBNV8fwCoaOOEHa33wblo/n3o97/0WgAsWbIky+MmJiaYNm2a2qD/v8qUKYP169fndmhaK2IpRj03qdYPAovFgHdVKWwsc/fxi9RUGaKjo/5/GdAPuHz5IrZv3wIfnwZo2bINAKBMmXKQy+X47be9qF+/Ae7evY3ffz+gdp5SpUohKSkR165dgbOzC0xNTVGunAMaNPDDggVzMG7cJJibm2PNmpWwty+OBg0aAQCWLVuEevV8UK6cA+Li4nDjxjWUL1/hv2FmqVevbzF4cD8sXrwA7dp1gKmpGV6+fI6rVy/jp5/8Vd/Y79+/F+3bd8aLF8+wZcuGLzrnhQtBCAt7C09PL1hZWSM4+AIEQUC5cuWzFTsREREVXjKFDBODxmFbyCa19gZl/LChxVYUNS2mp8hyJl89A1BQdWxohqsPZRA+sxSoCIBEDHRoYJZFr5y5fPki2rdvCYlEAisrazg7V8Lo0WPRqlVb1bf9lSq5YMSIH7Fz51asXbsSHh41MHjwMMye/U+BVa2aBzp06Ixp0ybi06dPqmVAJ06chmXLAuDvPxoymQweHjXw88/LVPsLKJUKLF68AJGR72FuboG6db0xcmT2dmN2dq6ElSvXYd261Rg6dCAAAaVLl8VXXzUDABQtWhSTJk3DunWr8dtve+HiUhnDho3GhAmZv8/nzmlpaYWzZ09j06Z1SE1NQdmyDpg2bQ4qVnTKVuxERERUOH1M/oDvj3+LoLdn1dr7un2HeQ1+hlSSuxu86oJIEATdPI2aj0RGxuX6ObPaCRhI++ZfIkae7AScG4yNJfliLV1DwpzrHnOuH8y77jHnusec654ucv704xP0PtoNzz89U7WJRWLMrj8fA6oNhig3d5bNBfb22j2/yDsAucTTWYq5g6xxKCgJwffVpwOlT/vp0MAMDiXy1651RERERKTp79enMfBEP3xKiVG1WRlbY33zzWji0Ex/geUC3gHIA5/ilQh5KUdiigBzExHcHI1yfc5/buM3F7rHnOsec64fzLvuMee6x5zrXl7mfNO99ZgcNB4K4Z/zl7d2xM7Wv8KlmGuevGdu4B0APbKxFMPbXTfLkBIRERFR7pAr5Zhy3h+b7qkvMONT2hebWm5HMVNbPUWWu1gAEBEREZHBi0n+iIEn+uHsmzNq7b2rfIv5DRfBWFJ4vtxlAUBEREREBu15zFP0PtodT2OeqNrEIjGm+8zG4OrD8t3Dvl+KBQARERERGazzb8/hu2O9EfOvh30tpVZY13wTmpZvob/A8hALACIiIiIySNvub8aEoDGQK+WqNgdrR+xovReVi1XRY2R5iwUAERERERkUmUKGKRf8sfneBrX2uqW8sbnlTtiZ2ekpMt1gAUBEREREBiM6KRrfH++LC2FBau09K/fGQr8lMJGY6Cky3cnfi9PTF5szZzomThyT6fGNG9eiX79vdBhR9oWGvsTXX7dAYmKCXt7/3bsw+PrWwpMnj/L0fX75ZQWWLFmYp+9BRERkyEKi76PFb43UBv9ikRjTvGdjaeNVBjH4B3gHgAqANWtWoXPnbjA3t9B3KDl248Y17Nu3Cw8e3EdCQgLKlnVA377fokmTfx4u6tmzD7p1a49u3b5BmTJl9RgtERFR4XPk+WEMOzUIifJ/vlC0NrbB2mYb8VX55nqMTPd4B4DynEwmy/Frw8PDcfFiEFq3bqe3GHLDvXt34ORUCbNnL8TWrXvQunU7TJ8+FRcu/PMNRJEiRVCnTj0cOrRfj5ESEREVLkpBiYCr89H/WC+1wb9TEWcc63za4Ab/AO8AfJZCqcD96LtIlCfp7D3NjcxQ1bYaJGKJVv3PnDmFzZvX482bNzA1NUWlSq6YP38RzMzMNPo+eHAf48aNQo8evdG7d78Mz3f48CHs2bMD796FoWTJUujSpQc6deqqOr569XKcO/c3IiMjUKyYHZo3b4n+/QfCyCjtctq4cS2Cgs6ic+du2LZtE8LD3yEo6Cp8fWvB338KLl48jytXgmFvXxzDh4+Gr69fpp/t9OmTcHZ2gb19cbX2P/44iC1bNuDTpxjUqeMNDw9PbNmyAceO/Z1lDJcuXcTWrRvx4sUziMUSuLtXw6hRY9W+cQ8JuYeff56LV69eokIFJ/Tt+51GXDdvXsfq1cvw9OkTWFtbo2XLthg48AdVDv7rv+fo1q0nrl+/jLNnT6N+/Qaq9vr1G2D9+l8wbNioTHNCRERE2kmQJWDEX0MQ+Px3tfYmDk2xttkm2JgU0U9gesYCIAupilR8fbAFbry/rvP3rlG8Jv7oePyzu85FRUVh+vTJGDp0JBo2bIzExETcvn0TgiBo9L1+/SomTx6HH34YifbtO2V4vhMn/sSGDWvw00/jUamSK548eYQFC+bAzMwMrVq1BQCYm5tj8uRpsLOzx7NnT7Fw4RyYm5ujV69vVed5+/Y1/v77NObMWQjxvwqZzZvX44cfRmDYsFH47be9mDFjKvbvPwxra5sM47lz5yYqV67yn7ZbCAiYhyFDRsDXtyGuXbuCDRvWaLw2oxiSk5PQo0cvODlVQlJSIjZsWINJk8Zi8+ZdEIvFSExMxPjxP6J27bqYOnUW3r0Lw7JlAWrnjYx8j3HjRqFVq3aYMmUmXr16iYULZ8PY2BgDBgzO8HNkJD4+HuXKOaq1ubm54/37CLx7F4ZSpUprfS4iIiJS9zouFH2P9sT96Ltq7UM9R2JqvRlaf9FaGLEAyEJo7Cu9DP4B4Mb76wiNfQXnopWy7BcdHQWFQgE/vyYoWbIUAMDJyVmj39mzZzB79jRMmDAFX32V+a2ujRvXYvjw0fDzawIAKF26DF68eI7ffz+gKgD69fte1b9UqdIIDX2Fv/46oVYAyGQyTJkyA0WLFlU7f6tWbdGsWUsAwODBw/Dbb3sQEnIf9er5ZBhPeHg4Kld2U2vbv38v6tXzwTff9AEAODiUx717d3DxovrT/BnF0KjRV2p9Jk6chrZtm+Lly+eoWNEZJ08egyAoMWHCVJiYmKBiRSdERkYgIGC+6jUHDvyK4sVL4KefxkMkEqF8eUdERUXil19WoH//gRCLPz+z7q+/TiIk5D7GjJmo1m5nZ/f/n/sdCwAiIqIcCg67gO+O9UZ0crSqzURigkWNlqOba089RpY/sADIgoN1edQoXlNvdwAcrMt/tp+zcyXUrFkHffv2QJ069VCnTj00avQVrK2tVX1CQu7h4sXzmDVrARo2bJTpuZKSkvD27RvMnz8LCxfOUbUrFApYWFiqfv7rrxP47bc9ePv2LZKSEqFQKDQe0C1ZspTG4B8AnJz+KWjMzMxgYWGBjx8/ZBpTSkoyjI3V74KEhr5Cw4aN1dqqVKmqUQBkFMPr16HYsGENQkLu49OnGAiCEgAQERGOihWd8erVCzg5VYKJyT+rAFStWl3tHK9evYS7e3W1bcGrVfNAUlIi3r9/j5IlS2b6eYC0B4LnzZuBSZOmomJFJ7VjJiamAIDk5OQsz0FEREQZ23p/EyYGjVXb3KuEeUlsbbULNUrU0mNk+QcLgCwYS4xxpNOpfP0MgEQiwdKlq3D37m1cvXoZ+/fvxbp1q7Fu3RaULl0GAFC6dFlYW9vgyJHf4ePjm+k89aSkRACAv/8UuLm5qx1L/1b73r07mDlzKr77bhDq1vWGhYUl/vrrBPbs2aHW39RU8/kDABrvLRKJMpyulK5IkSKIi4vLIgOZyygGf/8fUbJkKfj7T4adnT2USiX69u0OmUyewRly382b1+Hv/yNGjPgJbdq0Q2qqQu14bOwnAMiweCIiIqLMyRQyTD4/Hlvub1Rrr1G8Jra02oWSFqX0FFn+wwLgMyRiCarbe+o7jCyJRCJUr+6J6tU90a/f9+jSpR3OnTuDHj16A0gbRM+d+zNGjBiMqVMnYNas+RkWAcWK2cLOzh5hYW/RvHmrDN/r7t07KFGiJL79doCqLTz8Xd58MACVKrni5cvnam0ODuXx4EGIWtvDh/c/e65Pn2IQGvoK/v5T4OHhBQC4ffuWWp/y5Svg+PGjSElJUd0FuH//7n/6OOLs2dMQBEF1F+Du3dswN7dA8eLqDyv/240b1+Dv/yOGDBmR6TMYz58/g5GRESpUqPjZz0NERGSIYuKVCHkph0whglQiwM3RCArJxww39+rq0gOLGi2HqZGpnqLNn1gAFHD379/D9etXUKdOPRQpUgwhIfcQE/MR5ctXUOtXtGgxLFv2C0aOHILp0ydh+vS5GRYBAwYMxtKlP8PCwhJ163pDJpPh4cMQxMXFokeP3ihXrhwiIsJx6tTx/592cx7nzv2dZ5+vTh1vLFgwGwqFAhJJ2h2Rzp27Y/jwQdizZwfq12+I69fTVvcBRFmey8rKGjY2NvjjjwOwtbVDREQ41qxZodanWbOWWL9+NRYunI3evfsjPDxM4+5Gp05d8euvu7FkyUJ07twdoaEvsWnTWnTv/k2m8/9v3LiG8eNHo2vXnmjUqAmio6MglUoAiNUegL59+yY8PLxUU4GIiIgoTWiEAgfPJeFSiAxK5T/tYpGATxan8cD4PSBNbxPjf96z8IPHcLUpu5SG+wAUcBYWFrh16ybGjh2Fb77phPXrV2P48NHw9q6v0dfW1g7Llq3Bs2dPMXPmVCgUCo0+7dp1gL//VBw9+ge+/bYHhg8fhD//DESpUmnTiXx9/dC9+zdYsmQh+vX7Bvfu3Ua/fgM0zpNb6tXzgUQiwbVrV1Rt1at7YuzYidi7dxf69euJy5eD0a3bNzAxyXrFJLFYjOnT5+LRo4fo27c7li9fjKFD1ZfbNDc3x/z5S/Ds2TN8910vrFu3Gj/8MEKtj719cfz88zI8eHAf/fr1REDAPLRp017trsh//flnIJKTk7F9+2a0b98S7du3ROvWzTBp0ji1fn/9dQLt2nXQMjtERESG4dZTGSati9UY/AOAUhDBIr4Ran74A8VSGsLa2Aa72vyKoZ4jOPjPhEjIagJ2IRUZmbM55YWZsbFEYz56frF//z5cuHAOixevzLTPggWz8erVS6xevUGHkX2Z/+Y8OPgCVq1aii1bdmf6nAZ9mfx8nRdmzLvuMee6x5znndAIBSati4VcDmQ1aBWgAEQKjOyVAN9KhjmV1t7eSqt+vANA+V779p3g4eGFxMR/du/btWs7njx5jDdvXuO33/bgzz8DVcuUFlTJyUmYOHEaB/9ERET/cvBcEhTKrAf/ACCCBBIY48btzJ/HozS8A0AACt43F1OnTsDNm9eRmJiI0qXLoEuXbujQoYu+w8qWgpbzwoA51w/mXfeYc91jzvNGTLwSPyz6pDHtJytiMbBmjA1sLA3ve25t7wDwq0YqkGbNmv/5TkRERFSghbyUZ2vwDwBKZdrrvN2zfjbQkBleaUREREREBUJSSs4mqiTm8HWGggUAEREREeVLYklqjl5nbsLVf7LCAoCIiIiI8p1XsS8x634PKCHP1uvEYsDNkbPcs8ICgIiIiIjylbOvz6D5r3649ykIkSZHtC4CxGLAu6rUIB8Azg5mh4iIiIjyBUEQsOrmcnQP7IiPKR8BAK8sVgEiBT63EKgIgEQMdGhglveBFnAsAIiIiIhI7xJlifjh1ADMCJ4CpfDP0j9u5YpgWBcRpEYiiDMZuYrFgJERMLanJRxKSHQUccHFCVJEREREpFevYl+i35+9cD/6rlp7X7fvMLfBQhhLjFHRXoFDQUkIvi9TWxo0fdpPhwZmHPxriRuBEQBuYKIPzLnuMef6wbzrHnOue8x5zp19fQaDTvRTTfkBAKlYinkNAtC3an+N/p/ilQh5KUeqQgRjiQA3RyPO+f9/3AiMiIiIiPItQRCw+tYKzLr0P7UpPyXMS2JTy+2oXbJuhq+zsRTD292YRdcXYAFARERERDqVKEvET38Px4Env6m11ypRB5tabkdJi1J6iswwsAAgIiIiIp3JbL5/H7f+mNtgIUwkJnqKzHCwACAiIiIincjufH/KGywAiIiIiChPCYKAX26vxMzgqdma7095gwUAEREREeWZBFkCxvw9gvP98xEWAERERESUJ55/eob+f/bGgw/31do531+/WAAQERERUa47/vJPDDs1CLGpn1RtnO+fP7AAICIiIqJco1Aq8PPVuVh8/We19pIWpbCxxTbO988HWAAQERERUa74kByNIScH4O/Xp9XafUr7Yl3zLShuXlxPkdG/sQAgIiIioi92+/1NfHe8D17Hhaq1/+AxAlO9Z8BIzGFnfsE/CSIiIiL6IjtDtmFC0BikKFJUbeZGFljeZDW+du6ox8goIywAiIiIiChHkuXJmHx+PLaHbFFrdy5SCZtb7oRrscr6CYyyxAKAiIiIiLLtTdxrfHesN25F3lRrb1PxayxvshpWxtZ6iow+hwUAEREREWXL2ddnMPhkf3xI/qBqE4vEmFxvOoZ7joJIJNJjdPQ5LACIiIiISCtKQYkVN5Zg3pVZUApKVbudmR3WNtuMBmX99BgdaYsFABERERF9VmzKJww/PQTHXhxRa69RvCY2ttiOMlZl9RQZZRcLACIiIiLK0oPoEPQ/1gvPPz1Ta/+26gDM9p0PE4mJniKjnGABQERERESZOvjkN/x4ZjgS5YmqNlOJKRb6LUGPyr30GBnlFAsAIiIiItIgU8gwM3gq1t5ZrdbuYFUem1vuQDV7Dz1FRl+KBQARERERqYlICMfAE/1w6d1FtfYmDk3xS9MNKGpaTE+RUW5gAUBEREREKhfeBmHQif6ITHqv1j6mlj/G1poAiViip8got7AAICIiIiIoBSVW3lyKuZdnqi3xaWNSBKu+Wovmjq30GB3lJhYARERERAYuJvkjhv81GCdeHVNrd7erjo0ttqGCTUU9RUZ5gQUAERERkQG79f4Gvj/+LULjXqm1967yLeY0WAgzIzM9RUZ5hQUAERERkQESBAHbQjZjctB4pCpTVe1c4rPwYwFAREREZGASZAkYd3Y0fnu8V629gk1FbGqxA1Xt3PUUGekCCwAiIiIiA/Lk42MMON4HDz88UGtvW7E9ljZeCWsTGz1FRrrCAoCIiIjIQBx6sh8//j0CCbJ4VZuR2AjTvGdhUPWhEIlEeoyOdIUFABEREVEhl6pIxfSLk7Hh7lq19lIWpbG++VbUKVVXT5GRPrAAICIiIirE3sS9xsAT3+J6xDW19oZlG+OXphtgb26vp8hIX1gAEBERERVSp0NP4oeT3+NjykdVmwgi/FRrPHf1NWAsAIiIiIgKGYVSgYBr87H42kIIEFTtRU2K4pdmG9DEoZkeoyN9YwFAREREVIhEJEZg6MnvEfT2rFp7jeI1saHFNpS1KqenyCi/YAFAREREVEgEvTmLIScHIDLpvVr799UGY7rPHBhLjPUUGeUnLACIiIiICjiFUoEl139GwLX5UApKVbuF1BKLGy1Hx0pd9Bgd5TcsAIiIiIgKsPeJ7zH01ECce3NGrd3N1h0bW2yFU5FKeoqM8isWAEREREQF1IW3QRh88ju8T4xQa+/j1h+zfefDzMhMT5FRfsYCgIiIiKiAUQpKLL0egIVX52pM+QnwW4rOLt30GB3ld2J9B5Bu3bp1cHV1xZw5c1RtKSkpmDFjBurWrQsvLy+MGDECUVFRaq8LCwvDoEGD4OHhAW9vbyxYsAByuVzX4RMRERHpRGRiJLof7oj5V2arDf6rFKuKk13OcvBPn5UvCoA7d+5gz549cHV1VWufO3cuzpw5g6VLl2L79u14//49hg8frjquUCgwePBgyGQy7NmzB/Pnz8fBgwexfPlyXX8EIiIiojx38e15NNlXH2f/M9+/j1s/HOtyGs5FOd+fPk/vBUBCQgLGjRuH2bNnw8bGRtUeFxeH/fv3Y8KECfD29oa7uzvmzp2Lmzdv4tatWwCA8+fP4+nTp/j5559RpUoV+Pn5YdSoUdi5cydSU1P19ImIiIiIcpdSUGLJtZ/R6Y+2iEgMV7WbG1lgddP1WNRoOef7k9b0XgDMnDkTfn5+8PHxUWu/d+8eZDKZWruTkxNKly6tKgBu3boFFxcX2NnZqfr4+voiPj4eT58+1Un8RERERHkpKikKPQI7Yd6VWf+Z8uOGk13PootLdz1GRwWRXh8CPnLkCEJCQvDbb79pHIuKioJUKoW1tbVau62tLSIjI1V9/j34B6D6Ob1PRqRSCUSiL42+cDEykug7BIPDnOsec64fzLvuMee6l1c5v/j2AgYc/RbvEt6ptfep+i0WNAqAudQ8T963IOB1nnN6KwDevXuHOXPmYNOmTTAxMdHpe8tkCp2+X0GRmsq86BpzrnvMuX4w77rHnOtebuZcKSix4sYSzL8yGwrhn/OaG5ljod8SdHPtCQj8czb0z59TeisA7t+/j+joaHTq1EnVplAocPXqVezcuRMbN26ETCZDbGys2l2A6Oho2NvbA0j7tv/OnTtq501fJSi9DxEREVFB8j7xPYadGqjxoG/lYlWwofk2uBRzzeSVRNrRWwFQr149HD58WK1t4sSJqFixIgYOHIhSpUpBKpUiODgYLVq0AAA8f/4cYWFh8PT0BAB4enpizZo1iI6Ohq2tLQDg4sWLsLS0hLOzs04/DxEREdGXOvv6DIaeGojIpPdq7d9U7oO5DX426Ck/lHv0VgBYWlrCxcVFrc3c3BxFihRRtXfu3Bnz58+HjY0NLC0tMXv2bHh5eakKAF9fXzg7O2P8+PEYN24cIiMjsXTpUvTq1QvGxsa6/khEREREOSJXyrHwylwsu7EIAgRVu7mROeY3XIQelXvpMToqbPL1TsCTJk2CWCzGyJEjkZqaCl9fX0ybNk11XCKRYM2aNZg+fTq6d+8OMzMzdOzYESNHjtRj1ERERETaexP3GoNPfoer4ZfV2t1s3bG++RZUKuqSySuJckYkCILw+W6FS2RknL5DyHeMjSV8kEbHmHPdY871g3nXPeZc93Ka86PPAzH6zFDEpMSotfd3/x4zfObC1Mg0lyIsfHida7K3t9KqX76+A0BERERUGCXLkzEzeCo23F2r1m5tbIMljVeinVN7PUVGhoAFABEREZEOPYt5goEn+uNelPpKhjVL1MbaZpvgYF1eT5GRodD7TsBEREREhmLfo934al9DjcH/CK8f8UeHYxz8k07wDgARERFRDsXEKxHyUg6ZQgSpRICboxGKWGp+vxovi8fEc2Ox99EutXY7Mzus/Godmjg01VXIRCwAiIiIiLIrNEKBg+eScClEBqXyn3axGKjnJkXHhmZwKCEBANyLuotBJ/rhacwTtXM0KNsIq79ahxIWJXUZOhELACIiIqLsuPVUhoDd8VAooTb4B9J+vhQiw9WHMoztYYEbKVsx7cIkpChSVH0kIgnG156EkTV+gkQs0XH0RCwAiIiIiLQWGqFAwO54yOVAZuuoK5WAoBQwb2cMrhRdhxTpP4P/MpZl8UuzjahXyls3ARNlgA8BExEREWnp4LkkKJSZD/7TCRBBKYjgkDBU1dbSsTVOdzvPwT/pHQsAIiIiIi3ExCs15vxnRQwjFE9pCwuhJOb4LsDWVrtR1LRY3gZJpAVOASIiIiLSQshLudaD/3RiGGGeVyB6VHfJm6CIcoB3AIiIiIi0kJTyuYk/GbM34dr+lL+wACAiIiLSgpmJKEevM8/h64jyCgsAIiIiIi24ORpBnM2Rk1ic9jqi/IQFABEREZEWiliKUdfNCBBp9yCAWAx4V5XCJoOdgYn0iVckERERkRYiEiNwUTkRCiEVAhRZ9hUBkIiBDg3MdBMcUTawACAiIiL6jFOvjqPxXm/8Hb0N94oMhBIyKCHPsK9YDBgZAWN7WsKhBHf6pfyHBQARERFRJlIUKZhy3h/fHOmKqKQoAMAHk3O4X7wbyjqEazwTkD7tZ+4ga3g6S/UQMdHn8akUIiIiogw8/vAIg09+h/vRd9Xa3e2qY22zjahU1AWf4pUIeSlHqkIEY4kAN0cjzvmnfI8FABEREdG/CIKALfc3YvrFyUiSJ6kdG+wxDFPqTYeJxAQAYGMphre7MYyNJUhNzfq5AKL8ggUAERER0f+LTIzEj2eG4cSrY2rtdmb2WNHkF3xVvrmeIiPKPSwAiIiIiJD2oO/I00MRlRSp1t643FdY8dVaFDcvrqfIiHIXCwAiIiIyaEnyJMy4OAWb7q1XazeRmOB/3jMxoNpgiEWc10+FBwsAIiIiMlh3o+7gh5MD8PjjI7X2KsWq4pdmG+BmW1VPkRHlHRYAREREZHCUghK/3FqJuZdnQKaUqR0b7DEMk+tOg6mRqZ6iI8pbLACIiIjIoITFv8WIv4Yg6O1ZtfYS5iWx4qs1aFSuiZ4iI9INFgBERERkMP54ehBjz45CTEqMWnvrCu2wqNFy2JrZ6icwIh1iAUBERESFXnxqHCYGjcPeR7vU2s2NLDDHdwG+qdIHIpFIT9ER6RYLACIiIirUroZfxtBTA/Eq9qVae43iNbG66XpULOKsn8CI9IQFABERERUIMfFKhLyUIylFgJmJCG6ORihimfnynHKlHIuvLcSS6z9DIfyzS69YJMbommMxpqY/pBKpLkInyldYABAREVG+FhqhwMFzSbgUIoNS+U+7WAzUc5OiY0MzOJSQqL3m+adnGHZqEK5HXFVrd7Aqj5VN16FeKW9dhE6UL7EAICIionzr1lMZAnbHQ6GE2uAfSPv5UogMVx/KMLanJTydpRAEAVvvb8L0i5ORKE9U69/VpQfmNfgZ1iY2OvwERPkPCwAiIiLKl0IjFAjYHQ+5HBAy6aNUAoISCNgdjzF9UrHw3lD8FXpSrY+1sQ0C/JaiQ6XOeR80UQHAAoCIiIjypYPnkqBQZj74TycAkCuU8N/7F25ZqQ/+G5Txw/Imv6CMVdk8i5OooMlRARAWFoawsDAkJSWhWLFiqFSpEoyNjXM7NiIiIjJQMfFKjTn/WREEMWwSm0FqYQuZOBqmElNMqTcd31cfArEo8weFiQyR1gXAmzdvsHv3bhw9ehTh4eEQhH/qcalUilq1aqFbt25o0aIFxGL+RSMiIqKcC3kp13rwn04MIxRJrYdS5d5i1Vfr4Fqsct4ER1TAaVUAzJ49GwcPHoSvry9GjRqF6tWro3jx4jA1NcWnT5/w+PFjXL9+HcuXL8eqVaswd+5cVK9ePa9jJyIiokIqKeVzE38y1sqhM+Z2/BrGEs5MIMqMVgWAmZkZTp06haJFi2ocs7W1hbe3N7y9vTF8+HCcO3cO4eHhLACIiIgox8xMcrYrb+fKHPwTfY5WBcCYMWO0PmHDhg1zHAwRERERALg5GkEs1lz6MyticdrriChr2Z6sn5ycjKSkJNXPb9++xZYtWxAUFJSrgREREZHhKmIpRj03KbR9rFAsBryrSmGTxc7ARJQm239Lhg4dikOHDgEAYmNj0a1bN2zevBnDhg3Drl27cjs+IiIiMlAdGpgCUEBA1rcBRAAkYqBDAzOdxEVU0GW7ALh//z5q1aoFADh+/DhsbW1x5swZLFiwANu3b8/1AImIiMjwRCSEY9L1nrhp3Q9KpEIJeYb9xGLAyAgY29MSDiUkOo6SqGDK9kS55ORkWFhYAADOnz+P5s2bQywWw9PTE2FhYbkeIBERERkOQRBw8OlvmHBuDGJSYgAT4Hqxr+GQMBQlUtpBhH8G+enTfjo0MOPgnygbsl0AODg44NSpU2jWrBnOnz+Pfv36AQCio6NhaWmZ2/ERERGRgYhKioL/uZ9w+NkhtXa56Uv0bJSA7hWL4OErJRJTBJibiODmaMQ5/0Q5kO0CYNiwYRg7dizmzZuHevXqwcvLCwBw4cIFVKlSJdcDJCIiosLv6PNAjD07ElFJUWrt1e09sfKrtahcLG2M4e2uj+iICheR8O8tfbUUGRmJyMhIVK5cWbXr7507d2BhYQEnJ6dcDzK3RUbG6TuEfMfYWILUVIW+wzAozLnuMef6wbzrXkHKeUzyR0w+749fH+9RazcSG+GnmuMxqsYYSCVSPUWnvYKU88KCOddkb2+lVb8cLZZrb28PGxsbyOVyGBunbbbBjb+IiIgoO06HnsToM8MRnvBOrb1ysSpY+dVaVLf31E9gRIVctgqACxcuYMuWLbh16xbi4+MBAJaWlvD09ET//v3h4+OTJ0ESERFR4RGfGodpF6dge8hmtXaxSIzhnqMxrs5EmEhM9BQdUeGndQFw8OBBTJkyBS1atMDEiRNha2sLIO3h3wsXLmDQoEGYPXs2OnTokFexEhERUQF34W0QRp0eitC4V2rtFW2csOKrNahdsq6eIiMyHFo/A9CiRQv07dsXvXr1yvD4zp07sXXrVpw4cSJXA8wLfAZAE+fR6R5zrnvMuX4w77qXH3OeKEvEnEvTsf7uGo1jg6r/gEl1p8Fcaq6HyHJHfsx5Yceca9L2GQCt184KCwuDt7d3pse9vb0RHh6u7emIiIjIQFwNv4wm++prDP4drMrjYPsjmO27oEAP/okKGq0LgEqVKuG3337L9Pj+/fvh7OycK0ERERFRwZeiSMGs4Glod7AFnn96pnasj1t//N39IuqXaaCn6IgMl9bPAPj7+2PIkCEICgqCj4+P2jMAwcHBeP36NdatW5dngRIREVHBcev9DYw8/QMefnig1l7SohSWNl6JJg7N9BQZEWVrH4A3b95g9+7duH37NiIjIwGkLQnq6emJHj16oGzZsnkWaG7iMwCaOI9O95hz3WPO9YN51z195jxZnoyAq/Ox6tYyKAT1GLq69MAc3wUoYlpUL7HlJV7nuseca9L2GYAcbQRW0LEA0MS/RLrHnOsec64fzLvu6SvnNyKuYdTpoXj08aFau52ZHX72W4Y2FdvpPCZd4XWue8y5pjzbCEwul+Pp06dqdwCcnJwgleb/XfqIiIgo9yXLk7Hw6lysvrUcSkGpdqyjc2fMbRAAWzNbPUVHRP+ldQGgVCqxbNky7Nq1C3Fx6t+gW1lZoVevXhg5ciTEYq2fKyYiIqIC7lr4FYw6PRRPYh6rtduZ2WNhwyVo6/S1niIjosxoXQAEBATg4MGDGDNmDHx9fWFnZwcAiIqKwoULF7Bs2TLIZDKMGzcuz4IlIiKi/CFJnoQFV+Zgze2VGt/6d6rUFXMbLEQxU37rT5Qfaf0MQP369TF//nw0aJDxcl1BQUHw9/fHxYsXczXAvMBnADRxHp3uMee6x5zrB/Oue3md8yvvLmPUmR/wLOapWntx8xL42W8pWlVok2fvnV/xOtc95lxTrj8DkJCQgOLFi2fxhvZISkrS9nRERERUwCTKEjH/ymysvb0KAtS/P+zq0gOzfeejqGkxPUVHRNrSesJ+nTp1sHDhQnz48EHj2IcPHxAQEIA6derkanBERESUP1x6F4wm++pjze2VaoP/EuYlsb31Xqxquo6Df6ICQus7ADNmzMCgQYPQoEEDuLi4qG0E9vjxYzg5OWHt2rV5FigRERHpXqIsEXMvz8D6O2s0vvXv7voNZtWfVyjX9ScqzLK1D4BSqURQUBBu376NqKgoAICdnR08PT3h6+tbYFYA4jMAmjiPTveYc91jzvWDede93Mp5cNgFjDo9FC9jX6i1l7QohUV+y9DMseUXv0dhwetc95hzTdwILAssADTxL5HuMee6x5zrB/Oue1+a87jUWMwKnoYt9zdqHPumch/MqD8HNiZFviDCwofXue4x55rybCOwO3fu4ObNm2p3ALy8vFC9evXsnoqIiIjymVOvjmPs36MRlvBWrb20RRksbrwcTRya6SkyIsotWhcA0dHRGDFiBG7cuIHSpUurPQMwb9481KhRAytWrFC1ExERUcERnRSNKef9sf/JPo1jvat8i+k+s2FtYqOHyIgot2XrIWClUomjR4+iYsWKaseeP3+OSZMmYcaMGVi+fHmuB0lERER5QxAEHHq6H5OCxiE6OVrtWHlrRyxutAINyvrpKToiygtaFwBBQUHYuXOnxuAfACpWrIgpU6agT58+uRocERER5Z138WEYf+5HHH/5p1q7WCTGoOpD4V9nMiykFnqKjojyitYFgLGxMeLj4zM9npCQAGNj41wJioiIiPKOUlBiR8hWzAieirjUWLVjlYtVwZLGK1GzRG09RUdEeU3rdTtbt26NCRMm4OTJk2qFQHx8PE6ePImJEyeibdu2eRIkERER5Y7nn56h8+/tMPbsKLXBv1QsxbjaE3GqaxAH/0SFnNZ3ACZOnAilUokff/wRCoUCUqkUACCTySCRSNClSxf4+/vnWaBERESUc3KlHOvu/IIFV2YjSZ6kdqxG8ZpY0ngVqti66Sk6ItKlbO8DEB8fj3v37qktA+ru7g5LS8s8CTAvcB8ATVxLV/eYc91jzvWDede9/+Y8JPo+fjwzDDff31DrZ2Zkhgl1pmJQ9R8gEUt0HWahwutc95hzTXm2D4ClpSXq1auX7YCIiIgob8XEKxHyUg6ZQgSpRIBzOSU2P1qEZTcWQa6Uq/X1LdMQixotRwUbzcU9iKhwy3YBkJmoqCjs2bMHw4cPz61TEhERkRZCIxQ4eC4Jl0JkUCr/aRegwHuTMjCxcIJc+ggAYGVsjRk+c9CrSl+IRCI9RUxE+pTtKUCZefjwITp27IgHDx7kxunyFKcAaeJtNN1jznWPOdcP5j1v3XoqQ8DueCiUUBv8p1NCDgFy3CsyEHVcLbGg4WKUsiyt+0ALOV7nuseca8r1KUAPHz7M8vjz58+1PZXKrl27sHv3brx9m7bdeKVKlTB06FD4+aVtOJKSkoL58+fj6NGjSE1Nha+vL6ZNmwY7OzvVOcLCwjB9+nRcvnwZ5ubm6NChA8aMGQMjo1y7uUFERJQvhUYoELA7HnI5kNm3eWIYQYAYXrFbMKtGEZSy5L+PRIZO698CHTp0gEgkQkY3DNLbs3srsWTJkhg7dizKly+fthPhoUMYNmwYDh48iEqVKmHu3Lk4e/Ysli5dCisrK8yaNQvDhw/Hnj17AAAKhQKDBw+GnZ0d9uzZg/fv38Pf3x9SqRQ//fRTtmIhIiIqaA6eS4JCmfngP53o/1f9/v18MkZ2KTiLdhBR3tB6ClDdunUxbtw4eHt7Z3j86dOnGDJkyBdPAapTpw7GjRuHli1bwtvbGwEBAWjZsiUA4NmzZ2jdujX27t0LT09PnD17FkOGDEFQUJDqrsDu3bsREBCA4ODgTDcm4xQgTbyNpnvMue4x5/rBvOeNmHglflj0KcNpP5kRi4E1Y2xgY6n1NkCkJV7nuseca9J2CpDWvwHc3d3x/v17lClTJsP/SpQokeHdAW0pFAocOXIEiYmJ8PLywr179yCTyeDj46Pq4+TkhNKlS+PWrVsAgFu3bsHFxUVtSpCvry/i4+Px9OnTHMdCRESU3524+yJbg38g7RmBkJfyz3ckokJN6ylAPXr0QGJiYqbHS5UqhXnz5mU7gEePHqFHjx5ISUmBubk5Vq1aBWdnZzx48ABSqRTW1tZq/W1tbREZGQkgbeWhfw/+Aah+Tu+TEalUAi58oM7IiOs/6xpzrnvMuX4w77krWZ6Mny/Px57gt3BB9v/dTVWIYGzMP5Pcxutc95jznNO6AGjWrFmWx21sbNCxY8dsB1ChQgUcOnQIcXFxOH78OPz9/bFjx45snyc7ZDLeLsoIb6PpHnOue8y5fjDvueP823MY+/coPP/0DMXRNkfnMJYI/PPII8yr7jHnOaP3pQCMjY1Rvnx5AGnTjO7evYtt27ahVatWkMlkiI2NVbsLEB0dDXt7ewBp3/bfuXNH7XzpOxSn9yEiIiroPiRHY8bFqdj98J8vyD5KL0EJOcTZ+KdcLAbcHPX+Tz8R6Vm2ngKSy+VITU1Va/v111/h7++P7du3f9EzAOmUSiVSU1Ph7u4OqVSK4OBg1bHnz58jLCwMnp6eAABPT088fvwY0dHRqj4XL16EpaUlnJ2dvzgWIiIifRIEAQee/Arf3bXVBv8AUNRKggqO0RBrOaVVLAa8q0r5ADARZa8AGDt2LFasWKH6ec+ePZgzZw6SkpKwatUqLF68OFtvvmjRIly9ehVv3rzBo0ePsGjRIly5cgXt2rWDlZUVOnfujPnz5+PSpUu4d+8eJk2aBC8vL1UB4OvrC2dnZ4wfPx4PHz5EUFAQli5dil69emW6AhAREVFB8OLTc/QI7IQhJwcgKilK7Vgft/640PMqhreuBIkE+FwNIAIgEQMdGpjlWbxEVHBk6z5gSEgIvvnmG9XPe/fuxaRJk9CtWzdcvnwZEyZMwJgxY7Q+X3R0NPz9/fH+/XtYWVnB1dUVGzduRP369QEAkyZNglgsxsiRI9U2AksnkUiwZs0aTJ8+Hd27d4eZmRk6duyIkSNHZudjERER5RupilSsurkMS67/jGRFstqxSkVcsKjRctQrnbZCnk0JYGxPyyx3AhaL0wb/Y3tawqEEH5okIi33AZg4cSIA4MiRI/Dz84OlZdomIocOHcJXX30FKysr1TKeX3/9NQDkaEUgXeE+AJq4lq7uMee6x5zrB/OuvYtvz2P8uR/x+OMjtXapWIpRNcZgVM0xMJGYaLwuNEKBQ0FJCL4vUysC0qf9dGhgxsF/HuN1rnvMuSZt9wHQeiMwAGjcuDF+/vln1KpVC3///TfmzZuH48ePAwDi4uLQqFEjXL9+PWcR6xALAE38S6R7zLnuMef6wbx/XnRSNGYET8Gehzs1jvmU9sXChkvgUsz1s+f5FK9EyEt52lKfEgFujkac868jvM51jznXpG0BkK0pQHXq1MHUqVPRoUMHHDhwAK1atVIde/jwoWo1HyIiIvo8QRCw++EOzLg4BR9TPqodszW1xTSf2eju+g1EWm5eY2Mphre7MQdGRJSlbH0tMGHCBLi7uyMwMBB169bFkCFDVMdOnTqlmv5DREREWXv04SHaH2qF0WeGaQz+e1XpiwvfXEOPyr20HvwTEWkrW1OACgtOAdLEb4t0jznXPeZcP5h3dYmyRCy9HoBVt5ZBppSpHXMtWhk/+y1VPeSbU8y57jHnuseca8qTKUBERESUc6dDT2L8uTEIjX2p1m5mZIYxtfwxxGM4jCVcxpqI8pZWU4D+97//ITw8XKsTHj16FH/88ccXBUVERFSYhCe8w8Dj/dAjsLPG4L+pQ3Oc63EZI2v8xME/EemEVncAihUrhjZt2qBGjRpo3Lgx3N3dUaJECRgbGyM2NhZPnz7F9evXcfToURQvXhwzZ87M67iJiIjyPYVSgS33N2Du5VmIS41VO1bSohTm+C5A24rtOc+fiHRK62cAoqKi8Ouvv+Lo0aN4+vSp2jELCwv4+PigS5cuaNiwYZ4Empv4DIAmzqPTPeZc95hz/TDUvF+PuAr/c2NwJ/KWWrtYJMYA90GYUHcKrIyt8+S9DTXn+sSc6x5zrilP9gFI9+nTJ7x79w7JyckoWrQoHBwcCtS3FywANPEvke4x57rHnOuHoeX9Q3I05lyagR0hWyFA/Z9YD3svBPgthUdxrzyNwdBynh8w57rHnGvK04eAbWxsYGNjk5OXEhERFUpKQYldD7Zj9qVp+JD8Qe2YpdQKk+pORX/3gZCIuSMvEekXVwEiIiL6Qncib8H/3E+4HnFN41inSl0xw2cOSliU1ENkRESaWAAQERHl0KeUGMy7PAtb7m+EUlCqHXMp6or5DRfBt0z+fzaOiAwLCwAiIqJsEgQB+x7txozgqYhKilQ7Zm5kgTG1/TG4+lAu60lE+RILACIiomwIib4P/3M/4fK7YI1j7Zw6YKbPXJSxKquHyIiItJPjAuDDhw94/vw5AKBixYooVqxYrgVFRESU38SlxmLh1XnYcGcNFIL6yiMVbZwwt8HPaOLQVE/RERFpL9sFQGJiImbNmoU//vgDCkXaL0CJRIL27dtj6tSpMDMzy/UgiYiI9EUQBBx6uh//uzAJEYnhasdMJab4seY4DPUaCROJiZ4iJCLKHnF2XzB//nxcvXoVq1evxrVr13Dt2jWsXr0aV69exfz58/MiRiIiIr149OEhuvzxNQaf/E5j8N/SsTXO97yKH2uN4+CfiAqUbN8BOH78OJYvX466deuq2vz8/GBiYoLRo0djxowZuRogERGRrsWmfMLP1+Zj4921kCvlasccrB0x13cBmju20lN0RERfJtsFQHJyMuzs7DTabW1tkZycnCtBERER6YNSUGLfo92YFTwNkUnv1Y4Zi40xosaPGFnjJ5gZcborERVc2S4APD09sXz5cixcuBAmJmm3PJOTk7Fy5Up4enrmdnxERES5JiZeiZCXciSlCDAzEcHN0QhFLNNmw95+fxMTgsbiesRVjdc1cWiKub4LUbGIs65DJiLKddkuACZPnowBAwagYcOGqFy5MgDg4cOHMDExwcaNG3M9QCIioi8VGqHAwXNJuBQig/Jf+3WJxYCXq4A3lquxN/RnCBDUXlfe2hGzfRegefmWEIlEOo6aiChviARBED7fTV1SUhIOHz6sWgbUyckJ7dq1g6mpaa4HmBciI+P0HUK+Y2wsQWqq4vMdKdcw57rHnOuHvvN+66kMAbvjoVBCbfCfToAcSshxr8hAfDA5BwAwMzLD6Bpj8YPnCJgaFYx/2/5N3zk3RMy57jHnmuztrbTql6MCoKBjAaCJf4l0jznXPeZcP/SZ99AIBSati4VcDmT1j50ABZSQ4Xqxr/FVZTdM95mNslbldBZnbuO1rnvMue4x55q0LQC0mgL0119/oWHDhpBKpfjrr7+y7PvVV19p9cZERER57eC5JCiUWQ/+AUAECcQQ0KvoXsxuUVEnsRER6YtWBcCwYcNw4cIF2NraYtiwYZn2E4lEePDgQa4FR0RElFMx8UqNOf9ZEcEIz14Uxad4JWwss71NDhFRgaFVAfDw4cMM/z8REVF+FfJSrvXgP51SmfY6b3fjvAmKiCgf4FccRERUKL36GP75ThlITDG4R+OIyMBkuwCYPXs2tm3bptG+Y8cOzJkzJ1eCIiIiyqlPKTGYemEi5l2bnKPXm5twuU8iKtyyXQAcP34cNWrU0Gj38vLC8ePHcyUoIiKi7FIoFdhybyPq7fTC2turEG10AUrIs3UOsRhwc8z2FjlERAVKtn/LxcTEwMpKc4khS0tLfPz4MVeCIiIiyo6gN2cx5fwEPPhwX9Umk0Qh0uQIiqe0hQiSz55DLAa8q0r5ADARFXrZ/i1Xvnx5BAUFabSfO3cO5coV3DWTiYio4Hn56QX6/dkLnf9opzb4B4AKNhUxuKUjjI0k+NykHhEAiRjo0MAsz2IlIsovsn0HoF+/fpg1axY+fPiAevXqAQCCg4OxefNmTJo0KdcDJCIi+q/41Dgsvb4Ia26vRKoyVe2YlbE1xtTyx/fVBsNYYowq1lnvBCwWpw3+x/a0hEOJz98pICIq6HK0E/CuXbuwZs0avH//HgBQpkwZjBgxAh06dMjt+PIEdwLWxN30dI851z3mXD9yM+9KQYm9D3dhzuUZeJ8YoXZMBBF6u32LCXWmwt7cXu1YaIQCh4KSEHxffV+A9Gk/HRqYFarBP6913WPOdY8516TtTsA5KgDSffjwASYmJrCwsMjpKfSCBYAm/iXSPeZc95hz/citvF9+dwlTzvvjduRNjWPepetjdv35qGbvkeU5PsUrEfJSjsQUAeYmIrg5GhXKOf+81nWPOdc95lyTtgVAjpY6kMvluHLlCkJDQ9G2bVsAQEREBCwtLQtcMUBERPnbm7jXmBX8Pxx8ul/jmINVeUzzmYW2FdtDJPr88p02lmJu8kVEBi/bBcDbt2/x/fff4927d0hNTUX9+vVhaWmJ9evXIzU1FTNnzsyLOImIyMDEy+Kx8sYS/HJ7JZLkSWrHzI0sMKrGTxjiORxmRnxwl4goO7J933POnDlwd3fHlStXYGJiompv1qwZLl26lKvBERGR4VEoFdgRshX1dnph8fWfNQb/XV16IPib6/ix1jgO/omIciDbdwCuX7+O3bt3w9hY/RZqmTJlEBERkcmriIiIPu/v16cx7cJkjSU9AaBmidqY7TsfNUvU1kNkRESFR7YLAKVSCWUG66iFh4dz/j8REeXIow8PMePiFJwKPaFxrKxlOUyuNw0dK3WBWFT4HtglItK1bP8mrV+/PrZu3arWlpCQgBUrVsDPzy/XAiMiosIvMjES48/+iEZ7vTUG/5ZSK0yuOw0XvrmGzi7dOPgnIsol2V4G9N27d/j+++8hCAJevXoFd3d3vHz5EkWLFsXOnTtha2ubV7HmGi4DqolLaekec657zLl+ZJT3ZHky1t35BctuLEJcaqzaMbFIjN5V+mF8nUkobl5cl6EWGrzWdY851z3mXFOe7gMgl8tx9OhRPHz4EImJiahatSratWsHU1PTbAeqDywANPEvke4x57rHnOvHv/MuCAIOPd2P2Zem43VcqEbfJg5NMc17NqrYuuk6zEKF17ruMee6x5xrypMCQCaToVWrVli7di2cnJxyHJy+sQDQxL9Eusec6x5zrh/peb8afhn/uzAJ1yOuavSpXKwKpvvMQROHpnqIsPDhta57zLnuMeea8mQjMKlUipSUlBwFREREhunlp5eYdm4qfn92QOOYnZk9JtSZgm+q9IGROEd7UxIRUTZl+4mqXr16Yf369ZDL5XkRDxERFRIfkz/gfxcmoc42L43Bv6nEFKNrjMXlXjfRt2p/Dv6JiHQo279x7969i+DgYJw/fx6urq4wM1PfhGXlypW5FhwRERU8yfJkbLi7FquuboYk3g22yk5QiOPxUXoJMkkUOlfqhsn1pqGsVTl9h0pEZJCyXQBYW1ujRYsWeRELEREVYAqlAr893ovFQbtgFtkF7iknIf7XPzMCFHBzTsR31cugrJVEj5ESERm2HK0CVNDxIWBNfJBG95hz3WPO886Z0L8wM/h/eBdWFO4x6yGCkdrgP51YDEjEwNielvB0luohUsPAa133mHPdY841afsQsNbPACiVSqxbtw49evRA586dERAQgOTk5BwHSEREBd/dyNvo+kd7dA/siJfhqXCPWQ8xpBkO/gFAqQTkciBgdzxCI/gPNxGRPmhdAPzyyy9YsmQJLCwsUKJECWzbtg0zZszIy9iIiCifeh0XiqGnBqLprw1x9s0ZAED5hGEQwQgiZD29RwCgUAKHgpJ0ECkREf2X1lOAmjdvju+++w49evQAAFy8eBGDBg3CnTt3IBYXrO3ZOQVIE2+j6R5zrnvM+ZeLSf6IpTcWYcOdNUhVpqrapQo7+ERdzvSb/4yIxcCaMTawsSxY/4YUBLzWdY851z3mXFOuTwEKCwuDn5+f6mcfHx+IRCK8f/8++9EREVGBkixPxupbK1BnpwdW31quNvgHgMZFhmZr8A+kTQcKecklpYmIdE3r39YKhQImJibqLzYygkwmy/WgiIgof1AKSux/vA/zr8zG67hQjeM1S9TGNJ/ZSAirgXVPE7N9/sQUg1uHgohI77QuAARBwIQJE2BsbKxqS01NxfTp09X2AuA+AEREBZ8gCDj16jjmXJ6JkOh7Gscr2FTElHoz0Lbi1xCJRLgYnZrBWT7P3ET0paESEVE2aV0AdOzYUaPt66+/ztVgiIhI/y69C8acS9Nx+V2wxjE7MzuMqTUBfd36Qyr5ZxlPN0cjiMVp03q0JRanvY6IiHRL69+88+bNy8s4iIhIz+5H3cO8yzNx4tUxjWPmRuYY4jEMw7xGwcrYWuN4EUsx6rlJcSlEplURIBYD3lWlfACYiEgP+NULEZGBe/npBRZenYv9j/dBgPqcfCOxEfq69cePtcajhHmJLM/TsaEZrj6UQVACWc3sFyFtM7AODcyy6EVERHmFBQARkYF6n/geS64vxLb7myFTqi/oIIIInSp1xfg6k1DBpqJW53MoIcHYnpYI2B0PhTLj6UD/3gnYoUTW+wUQEVHeYAFARGRgYlM+YfWt5VhzezUS5Qkax5uVb4GJdf8Hd7tq2T63p7MUcwdZ41BQEoLvq08HSp/206GBGQf/RER6pPVGYIUJNwLTxM00dI851z1Dz3myPBmb7q3HsusB+JjyUeN4nZL1MKXedNQr7ZMr7/cpXomQl3KkKkQwlghwczTinH8dMfRrXR+Yc91jzjVpuxEY7wAQERVycqUcex/uws9X5yEs4a3G8SrF3DC53jQ0K98SIlHuLctpYymGt7sx/5EmIspnWAAQERVSSkGJw88OYcGVOXga80TjuINVefjXmYxOlbpCIuaUHCIiQ8ECgIiogIv5/6k2SSkCzExEqFJegstRxzH/yuwMN/GyM7PHmFrj0cetP4wlxhmckYiICjMWAEREBVRohAIHzyVprL0vQIH3Ju/xykIG/LNXF6yMrTHMcyQGeQyFpdRS9wETEVG+wAKAiKgAuvVUlulymyJIYJ/SBnYpLXCvyEAkWVzFd+6DMNxrNGzNbPUTMBER5RssAIiICpjQCAUCdsdDLs98wy0xjCBADM/YzfDvqISXY9abeBERkeHgemxERAXMwXNJkCv+u2evJhHEEMEIQdcsdBIXEREVDCwAiIgKkFtvnuLivWQIgnbLdSqVQPB9GT7FZ7AtLxERGSQWAEREBcCr2JcYefoH9Nk3DUD2luxUKoGQl/K8CYyIiAocPgNARJSPvY17g6U3FmHXg22QKWUopeyRo/Mkphjcpu9ERJQJFgBERPlQWPxbLLuxCDtDtiFVmapqV4jjc3Q+c5Pc2+GXiIgKNhYARET5SFj8Wyy/sRg7QraqDfzTlS+dAlGsoPUzAAAgFgNujvx1T0REafgvAhFRPvAuPgzLby7G9vtbMhz4e9h7YXztiWhavgWW/5agsflXZsRiwLuqFDaWfOSLiIjS6LUAWLt2LU6cOIHnz5/D1NQUXl5eGDt2LCpWrKjqk5KSgvnz5+Po0aNITU2Fr68vpk2bBjs7O1WfsLAwTJ8+HZcvX4a5uTk6dOiAMWPGwMiI9Q0R5W/hCe+w/MZibA/ZghRFisbx6vaeGFd7IpqXbwmRKO1b/44NzXD1oQyCMvN9AABABEAiBjo0MMub4ImIqEDS61dCV65cQa9evbBv3z5s3rwZcrkcAwYMQGJioqrP3LlzcebMGSxduhTbt2/H+/fvMXz4cNVxhUKBwYMHQyaTYc+ePZg/fz4OHjyI5cuX6+MjERFpJTzhHSYHjUftHdWx4e5ajcF/NTsPbGu1Bye7nEULx1aqwT8AOJSQYGxPSxgZpX3DnxGxGDAyAsb2tIRDieytGkRERIWbSBCEfLM0xIcPH+Dt7Y0dO3agdu3aiIuLg7e3NwICAtCyZUsAwLNnz9C6dWvs3bsXnp6eOHv2LIYMGYKgoCDVXYHdu3cjICAAwcHBMDY21nifyMg4nX6ugsDYWILUVIW+wzAozLnu5YecRySEY8XNJdh2fzOSFckax93tqmNc7Ylo6dhabdCfkdAIBQ4FJSH4vvp0oPRpPx0amOWLwX9+yLuhYc51jznXPeZck729lVb98tUcmbi4tIG5jY0NAODevXuQyWTw8fFR9XFyckLp0qVx69YteHp64tatW3BxcVGbEuTr64vp06fj6dOncHNz0+2HICLKQERCOFbeXIqt9zdlOPCvalsN42pPRKsKbT478E/nUEKCkV0s8W1LJUJeypGYIsDcRAQ3RyPO+SciokzlmwJAqVRi7ty5qFGjBlxcXAAAUVFRkEqlsLa2Vutra2uLyMhIVZ9/D/4BqH5O7/NfUqkEWv77ajCMjPT/LaGhYc51Tx85fxf/DsuvL8HmOxszHvjbuWNCvclo49QWYlHOBu32xSTwKyb90lDzDK913WPOdY851z3mPOfyTQEwY8YMPHnyBLt27crz95LJeLsoI7yNpnvMue7pKuev40Kx4sYS7HqwPcNVfaoUq4pxtSeidcW0gb9cJgAovNcDr3XdY851jznXPeY8Z/JFATBz5kz8/fff2LFjB0qWLKlqt7Ozg0wmQ2xsrNpdgOjoaNjb26v63LlzR+18UVFRAKDqQ0SkKy8+PcfyG4ux99EuyJVyjeNVirlhbO2JaFOxXY6/8SciIvoSev3XRxAEzJw5EydPnsTWrVtRrlw5tePu7u6QSqUIDg5WtT1//hxhYWHw9PQEAHh6euLx48eIjo5W9bl48SIsLS3h7Oysk89BRPTk42MMOzUIPrtqYueDbRqDfzdbd2xovhVnul9EO6f2HPwTEZHe6PUOwIwZMxAYGIjVq1fDwsJCNWffysoKpqamsLKyQufOnTF//nzY2NjA0tISs2fPhpeXl6oA8PX1hbOzM8aPH49x48YhMjISS5cuRa9evTJcAYiIKDeFRN/Hkms/449nByFksCq/h70Xfqo1Hi0cW3HQT0RE+YJelwF1dXXNsH3evHno1KkTgH82Ajty5IjaRmD/nt7z9u1bTJ8+HVeuXIGZmRk6duyY5UZgXAZUE5fS0j3mXPdyM+e339/E4us/488XgRker12yLsbUGo/G5ZpqvapPYcVrXfeYc91jznWPOdek7TKg+WofAF1hAaCJf4l0jznXvdzI+dXwy1hy7WecCj2R4fH6pRvgp1rj4VumocEP/NPxWtc95lz3mHPdY841Fch9AIiI8quLb89j0fWFCHrzd4bHG5f7Cj/WGo96pbx1GxgREVE2sQAgIsqEIAj4K/QElt1YjMvvgjPs08KxFX6sOQ41StTScXREREQ5wwKAiOg/5Eo5Dj87hOU3luB+9F2N4yKI0NapPUbXHItqdtX1ECEREVHOsQAgokIvJl6JkJdyyBQiSCUC3ByNUMRSc0WeFEUK9j7chZU3l+Jl7AuN42KRGB2cO+PHmuPgWqyyLkInIiLKdSwAiKjQCo1Q4OC5JFwKkUGp/KddLAbquUnRsaEZHEpIEJ8ah633N2PN7ZWISAzXOI9ULEU3154Y4TUaFYtwfxEiIirYWAAQUaF066kMAbvjoVBCbfAPpP18KUSGKw9SUb7mYfwWPhUxKTEa5zA3skCfqv3wg8dwlLYso5vAiYiI8hgLACIqdEIjFAjYHQ+5HBlszZVGqQQUEPD4SnPIiq0EpDGqY0VMiuD7akPwffXBKGZqq5OYiYiIdIUFABEVOgfPJUGhzHzwn04EMUQwgkPCUDwoMgolLUrhB48R6FO1HyylljqJlYiISNdYABBRoRITr9SY858VMYxQIqUt+tYzRW+PTjCRmORtgERERHrGAoCICpWQl3KtB//pRDCCm3FnmEiM8yYoIiKifERzHTwiogIsPkmWo9clpnxuwhAREVHhwDsARFQoxKZ8wraQLdhz5THKYHa2X29uIsqDqIiIiPIfFgBEVKC9iw/Duju/YFvIZsSlxkKqtEMpTIc4G7/exGLAzZG/DomIyDDwXzwiKpAeRIdg9a3lOPDkV8iU/0z7kUmiEGlyBMVT2kCkxa84sRjwriqFTQY7AxMRERVGLACIqMAQBAEXw85j1c1lOBV6IsM+pS3KoHVVCW6fNYJCkfVSoCIAEjHQoYFZnsRLRESUH7EAIKJ8T6FU4MjzP7Dy5lLciryZYZ8qxapimNdIdHDuDGOJMW6VyXwnYCDtm3+JGBjb0xIOJSR5/AmIiIjyDxYARJRvxaXGYteD7Vh/Zw1C415l2KdBGT8M8xqJxuWaQiT650FeT2cp5g6yxqGgJATfV98XIH3aT4cGZhz8ExGRwREJgmBwa99FRsbpO4R8x9hYgtRUhb7DMCjMeeZCY19hw9212BGyFfEyzb+vYpEY7Z06YqjnSHgU9/rs+T7FKxHyUo5UhQjGEgFujkac869DvNZ1jznXPeZc95hzTfb2Vlr14x0AIso3roZfxtrbqxH4/HcoBc15O+ZG5vimSh8M9hiG8taOWp/XxlIMb3dj/mNBREQEFgBEpGdypRxHnv+BNbdX4XrE1Qz7lDAvie+rDUafqv1QzNRWxxESEREVLiwAiEgvYlM+YceDbdhwZw3exL/OsE81Ow8M8RiG9s6dYCwx1nGEREREhRMLACLSqZefXmDD3TXY+WA7EmTxGsdFEKGFYysM8RgO79L11R7sJSIioi/HAoCI8pwgCLgSfhlrbq/Eny8CM53f37NKbwysNgQVizjrIUoiIiLDwAKAiPJMiiIFh57sx4a7a3E7k/X7S1mUxoBqg9HXrR+KmBbVcYRERESGhwUAESHm/5fJTEoRYGYigpujEYp8wTKZ7+LDsPX+RmwL2YKopMgM+3jae2GI53C0q9gBUok0x+9FRERE2cMCgMiAhUYocPBcEi6FaG6UVc9Nio4Ntd8oSxAEXA2/go131+Dw898hV8o1+oggQqsKbTHEczjqlqzH+f1ERER6wAKAyEDdeipDwO54KJRQG/wDaT9fCpHh6kMZxva0hKdz5t/QazPNx9rYBj2r9MZ37gNRwaZibn4MIiIiyiYWAEQGKDRCgYDd8ZDLgcy2AlcqAUEJBOyOx9xB1hp3Av6Z5rMZUUlRGZ6jUhEXfF99CLq69oCl1DKXPwURERHlBAsAIgN08FwSFMrMB//pBAAKJXAoKAkju1iqpvlsuPsLAp//kek0n+aOLTGg2mD4lW3MaT5ERET5DAsAIgMTE6/UmPOfFaUSCL4vg43zb9jxZAWn+RARERVwLACIDEzIS7nWg/90SiWw8PR+RJpqDv45zYeIiKhgYQFAZGCSUj438SdjRkor1f/nNB8iIqKCiwUAkYExM8nZYF0ujoOVsTW+qdKH03yIiIgKMBYARAbGzdEIYrHm0p9ZEaDAaL+26Fl9Paf5EBERFXA53+qTiAqkIpZi1KosgkikXQUgEgmo726KgTV7cfBPRERUCLAAIDIgjz88wqSgcdgc3RFyIRUCFFn2FwEwkojQsaGZbgIkIiKiPMcpQESFXKoiFX++CMTW+5tw/u05Vbu8yEC4x6yHCALEGfwqEIsBiRgY29NSYxMwIiIiKrhYABDpWEy8EiEv5ZApRJBKBLg5GqGIZe7fjHse8xTbQ7Zi76OdGe7U+8HkHJ6W6oPamIX4cFcohX8eDhaLAe+qUnRoYMbBPxERUSHDAoBIR0IjFDh4LkljEy6xGKjnJkXHhl8+2E5RpODP54HYHrIFQW/PZtqvZona6O/+Pb526ghTI1N8+v+iJDFFgLmJCG6ORrDJg6KEiIiI9E8kCELOFgUvwCIj4/QdQr5jbCxBamrW88Ep5249lSFgdzwUyoxX3/n3dBtPZ2m2z5/+bf+ehzsQnRydYR9zIwt0qtQF/dwHoLq9Z7bfozDgda4fzLvuMee6x5zrHnOuyd7e6vOdwDsARHkuNEKBgN3xkMuBzKptpRIQlEDA7njMHWSt1Z2AFEUKjj4/jO0hW9Tm9v9XNTsP9K3aH50qdYGVsXUOPwUREREVFiwAiPLYwXNJUCgzH/ynEwAolMChoCSM7JL5cpvPYp6kze1/uDPLb/s7u3RFH7d+8LD34k69REREpMICgCgPxcQrNeb8Z0WpBILvy/BtS6XaHPxkeTL+fBGIbfc340JYUKavr27vib5uad/2WxprdxuQiIiIDAsLAKI8FPJSnq0dd4G0IiDkpRze7sa4G3UHux5sw/7H+xCTEpNhfwupJTpV6oq+bv3gUdzry4MmIiKiQo0FAFEeSkrJ2TP2J56fxZSQmbgbdTvTPp72XuhTtT86Onfmt/1ERESkNRYARHnIzCRnc+/3Pd2ESFPNwb+F1BKdK3VD36r9DHYlHyIiIvoyLACI8pCboxHE4oyX/syMEnLEGF9Sa6tbyhvfVO6Dds4dYCnN/AFhIiIios9hAUCUh4pYilHPTar1g8BKyPHeJBAycTSKm5dAd9dv0LNybzgXrZT3wRIREZFBYAFAlMc6NjTD1YcyKJUCgMynBAlQAJDDwfU+JtXci68cmsFIzL+iRERElLs4uiDKQxGJEQh8tw/vSz+CdehkiGAEcQZ/7QTIIRaL8ENnI/i5B+ghUiIiIjIULACIclmyPBnHXhzBvke7ceb1X1AIaduUWxS7DIeEoSie0latCBCJBPhUNUPHhmZa7QBMRERE9CVYABDlAkEQcCX8MvY92oXfnx5EbOonjT4J0kd4UGQUrO2Ows9mCKrb1YGViQncHI3UNv0iIiIiykssAIi+QGjsK+x7tBv7Hu3Gy9gXmfYrY1kW3Vx7oKtLT9UDvcbGEqSmKnQVKhEREREAFgBE2RaXGovDz37Hvke7cTHsfKb9zI0s0M6pPbq59kT9Mg0gFvFbfiIiItI/FgBUqMXEKxHyUo6kFAFmJiK4ORqhSA6m28iVcgS9OYt9j3bj6IvDSJInZdhPBBF8y/qhm0sPtHH6mmv2ExERUb7DAoAKpdAIBQ6eS9JYf18sBuq5SbV64FYQBNx6fwP7n+zDwSf7EZn0PtO+TkWc0d31G3Rx6Y6yVuVy62MQERER5ToWAFTo3HoqQ8DueCiUmjvwKpXApRAZrj6UYWxPS3g6SzVe//zTM+x/vA8HnvyKZzFPM32fIiZF0MG5M7pX/gY1iteCSJT5Gv9ERERE+QULACpUQiMUCNgdD7kcEDLpo1QCghII2B2PuYOs4VBCgveJ7/H70/3Y/3gfbry/nun5jcRG+MqhGbq5foPmji1hIjHJmw9CRERElEdYAFChcvBcEhTKzAf/6QQACgWw/MhDvLafgnNv/lat15+RWiXqoLNLN7R37gQ7M7tcjZmIiIhIl1gAUKERE6/UmPOfFaUAvHpVHBcTb0Eh1hz8Vyrigs4u3dCpUlc42lTI5WiJiIiI9IMFABUaIS/lWg/+04lhhCKp9RBpegQAUNKiFDo6d0EXl25wt6vOef1ERERU6LAAoEIjKeVzE38yZim2R7PKfdDZpRt8SvtCIs56dSAiIiKigowFABUapsY5e93CxnPh58H1+omIiMgwsACgAk0QBNyLvovfnxxA4KMzKIffIM7GZS0WA55O5nkYIREREVH+wgKACqRHHx7i0NP9+P3pATyNeaJqNzU5AvuUNloVAWIx4F1VCpsc7AxMREREVFCxAKAC43nMUxx6egC/Pz2ABx9CMuzzymIV7FJaQIAYImQ+sBcBkIiBDg3M8ihaIiIiovyJBQDlW4Ig4NHHhwh89jsOP/sdDz7cz7J/NTsPtHfuhMpGCmz7XZzhTsBA2jf/EjEwtqclHErwgV8iIiIyLCwAKF8RBAH3ou4g8PnvCHz2B57EPM6yf+ViVdDeuRM6OHeCU5FK/7SXUOBQUBKC76vvC5A+7adDAzMO/omIiMggiQRByNnaiQVYZGScvkPId4yNJUhNzXwn3LwkCAJuvL+GwGd/IPD573gV+zLL/k5FnP9/0N8ZlYtVybLvp3glQl7KkZgiwNxEBDdHo3wz51+fOTdUzLl+MO+6x5zrHnOue8y5Jnt7K6368Q4A6YVSUOJK+GUEPjuEI88P4238myz7VyrignZO7dHGqT3cbatpvUGXjaUY3u45XB+UiIiIqBBiAUA6I1fKERx2AYHPf8eR54fxPjEiy/5utu5o59QebSu2h2uxyjqKkoiIiKhwYwFAeSpRloi/X5/Gny8CcfLVMXxI/pBlf097L7R16oC2Tl+joo2TjqIkIiIiMhwsACjXRSVF4eTLY/jzRSDOvjmDJHlSlv1rl6ybNr2n4tcoZ+WgoyiJiIiIDBMLAMoVLz49x7EXR/Hni0BcCb8EpZDB+pv/TywSw7tUfbR1ao82FduhpEUpHUZKREREZNj0WgBcvXoVGzduxL179xAZGYlVq1ahadOmquOCIGD58uX49ddfERsbixo1amD69OlwdHRU9YmJicGsWbNw5swZiMViNG/eHJMnT4aFhYUePpHhEAQBdyJv4c8XgfjzxZFMN+ZKZyIxQcOyjdCyQhu0dGwDe3N7HUVKRERERP+m1wIgMTERrq6u6Ny5M4YPH65xfP369di+fTvmz5+PsmXLYtmyZRgwYACOHj0KExMTAMDYsWMRGRmJzZs3QyaTYdKkSfjf//6HRYsW6frjFHoyhQwXw87jzxeBOPbiKMIS3mbZ38akCJqVb4FWFdqiscNXsJRa6ihSIiIiIsqMXgsAPz8/+Pn5ZXhMEARs27YNP/zwg+quwMKFC+Hj44NTp06hTZs2ePbsGYKCgvDbb7+hWrVqAIApU6Zg0KBBGD9+PEqUKKGzz1JYRSVF4a9XJ3Dy1XGcef0X4lJjs+xfxrIsWlVog5YV2sC7VH1IJVIdRUpERERE2si3zwC8efMGkZGR8PHxUbVZWVnBw8MDN2/eRJs2bXDz5k1YW1urBv8A4OPjA7FYjDt37qBZs2b6CL1AEwQBIdH3cfLVMZx4eQzXI65CQNZ7xbnZuqNVhTZoXaEt3O2qa71GPxERERHpXr4tACIjIwEAtra2au22traIiooCAERFRaFYsWJqx42MjGBjY6N6fUakUgk4Rv1HkjwJp14F4ejTIzj+4k+8jc96ao9YJIZ36fpo49QWrZ3awtHGUTeBFjJGRhJ9h2BwmHP9YN51jznXPeZc95jznMu3BUBeksm4bXRY/FucfHUcJ55cwIOXCijkxlCI4/FRmgJk8PfJytgajct9hablm6NZ+ZawNfunMOM23DnH3Okec64fzLvuMee6x5zrHnOeM/m2ALC3T1slJjo6GsWLF1e1R0dHo3LltF1h7ezs8OGD+sZScrkcnz59Ur2e0siVctx8fx2nXh3HiZfH8TI8FeUThsE+ZT4q/esyUEKOSJMjeGWxCiXtFWhWviWaO7ZE3ZLenM9PREREVAjk2wKgbNmysLe3R3BwMKpUqQIAiI+Px+3bt9GzZ08AgJeXF2JjY3Hv3j24u7sDAC5dugSlUonq1avrLfb8IjzhHc6E/oXToadw9s1pxKTEAACKpTREzZj1EMEI4v9cAmIYoURqO5SRf41xbazg6cxBPxEREVFhotcCICEhAaGhoaqf37x5gwcPHsDGxgalS5dG37598csvv6B8+fKqZUCLFy+uWhXIyckJDRo0wNSpUzFjxgzIZDLMmjULbdq0McgVgFIVqbgafhmnQ0/hr9CTCIm+p9HHQuYK95j1EEMKUUZzfQBAEEOhAAJ2x2PuIGs4lOAcOyIiIqLCQiQIQtZLvOShy5cvo2/fvhrtHTt2xPz581Ubge3btw+xsbGoWbMmpk2bhgoVKqj6pm8Edvr0adVGYFOmTMlyI7DIyLg8+Tz6EBr7CqdDT+H061MIenMWCbL4LPu7xSxH8ZQ2EGlR+4nFgHdVKUZ24fr9ecHYWMK5izrGnOsH8657zLnuMee6x5xrsre30qqfXgsAfSnIBUCSPAnBYRdwJvQUToeewpOYx599jbWxDfzKNUb94m1w8vdmUAraL4EkFgNrxtjAxlL8JWFTBviLS/eYc/1g3nWPOdc95lz3mHNN2hYA+fYZAEqjFJS4H30P517/jbNvTuNS2EUkK5I/+zpPey80cWiKxg7NULNELRiJjXDxXiqOCwnZe38lEPJSDm934xx+AiIiIiLKT1gA5EOv40JVA/6gN2cRnRz92dfYmdmhUbmv0MShKfzKNoG9ueYqSEkpObvZk5jD1xERERFR/sMCIB+ISf6I82+DcO7NGZx78zeef3r22deIRWLUKlEHTRyaoolDU1S394RYlPU0HTOTnO1+Zp7D1xERERFR/sMCQA9SFCm4Fn4FZ1+fwbk3Z3Ar8iaUgvKzrytn5YCGZRuhiUNTNCjjhyKmRbP1vm6ORhCL06b1aEssTnsdERERERUOHNnp0IW3QVh+YzEuvbuIJHnSZ/vbmBSBb5mG8CvbGA3LNUIF64oQiXL+bXwRSzHquUlxKUSmVRGQvgoQHwAmIiIiKjxYAOhIdFI0uh3uAJlSlmkfY7Ex6pSqh4ZlG8GvbGNUt/eERJy7a/B3bGiGqw9lEJRAVjP7RQAkYqBDA7NcfX8iIiIi0i8WADqSqkjJcPBf1bYa/Mo1RsOyjVCvlA/MpeZ5GodDCQnG9rREwO54KJQZTwcSi9MG/2N7WnITMCIiIqJChvsA6NC2+5vx+9MDKGflAL9yjeFbxi/D1Xp0ITRCgUNBSQi+rz4dKH3aT4cGZhz85zGuX6x7zLl+MO+6x5zrHnOue8y5Jm4EloWCvBFYbvsUr0TISzlSFSIYSwS4ORpxzr+O8BeX7jHn+sG86x5zrnvMue4x55q4ERhpxcZSDG93Y/4lIiIiIjIQ/KqXiIiIiMiAsAAgIiIiIjIgLACIiIiIiAwICwAiIiIiIgPCAoCIiIiIyICwACAiIiIiMiAsAIiIiIiIDAgLACIiIiIiA8ICgIiIiIjIgLAAICIiIiIyICwAiIiIiIgMCAsAIiIiIiIDwgKAiIiIiMiAsAAgIiIiIjIgIkEQBH0HQUREREREusE7AEREREREBoQFABERERGRAWEBQERERERkQFgAEBEREREZEBYAREREREQGhAWAgdi5cyeaNGmCatWqoWvXrrhz506mfQ8cOABXV1e1/6pVq6bDaAu+q1evYsiQIfD19YWrqytOnTr12ddcvnwZHTt2hLu7O5o1a4YDBw7oINLCI7s5v3z5ssZ17urqisjISB1FXPCtXbsWnTt3hpeXF7y9vTF06FA8f/78s6/7888/0bJlS1SrVg3t2rXD2bNndRBt4ZCTnPN3+pfZtWsX2rVrhxo1aqBGjRro3r37Z69ZXuNfJrs55zWefUb6DoDy3tGjRzFv3jzMmDEDHh4e2Lp1KwYMGIBjx47B1tY2w9dYWlri2LFjqp9FIpGuwi0UEhMT4erqis6dO2P48OGf7f/69WsMHjwYPXr0QEBAAIKDgzFlyhTY29ujQYMGOoi44MtuztMdO3YMlpaWqp8z+ztBmq5cuYJevXqhWrVqUCgUWLx4MQYMGIAjR47A3Nw8w9fcuHEDY8aMwU8//YTGjRvj8OHDGDZsGA4cOAAXFxcdf4KCJyc5B/g7/UuULFkSY8eORfny5SEIAg4dOoRhw4bh4MGDqFSpkkZ/XuNfLrs5B3iNZ5tAhV6XLl2EGTNmqH5WKBSCr6+vsHbt2gz779+/X6hZs6auwiv0XFxchJMnT2bZZ+HChUKbNm3U2kaPHi189913eRlaoaVNzi9duiS4uLgInz590lFUhV90dLTg4uIiXLlyJdM+o0aNEgYNGqTW1rVrV2Hq1Kl5HV6hpE3O+Ts999WuXVvYt29fhsd4jeeNrHLOazz7OAWokEtNTcX9+/fh4+OjahOLxfDx8cHNmzczfV1iYiIaN24MPz8//PDDD3jy5IkuwjVYt27dgre3t1qbr68vbt26pZ+ADEiHDh3g6+uL/v374/r16/oOp0CLi4sDANjY2GTah9d67tIm5wB/p+cWhUKBI0eOIDExEV5eXhn24TWeu7TJOcBrPLs4BaiQ+/jxIxQKhca0Bltb20znjVaoUAFz586Fq6sr4uLisGnTJvTo0QNHjhxByZIldRG2wYmKioKdnZ1am52dHeLj45GcnAxTU1M9RVZ42dvbY8aMGXB3d0dqaip+/fVX9O3bF/v27UPVqlX1HV6Bo1QqMXfuXNSoUSPLaQ4ZXeu2traIiorK6xALHW1zzt/pX+7Ro0fo0aMHUlJSYG5ujlWrVsHZ2TnDvrzGc0d2cs5rPPtYAJAGLy8vtSrby8sLrVu3xp49ezB69Gj9BUaUiypWrIiKFSuqfq5RowZev36NLVu24Oeff9ZjZAXTjBkz8OTJE+zatUvfoRgMbXPO3+lfrkKFCjh06BDi4uJw/Phx+Pv7Y8eOHZkOSOnLZSfnvMazj1OACrmiRYtCIpEgOjparT06OlrjG4rMSKVSVKlSBaGhoXkRIiHt2/7/fjsUFRUFS0tLfvuvQ9WqVeN1ngMzZ87E33//ja1bt37227aMrvXs/D6iNNnJ+X/xd3r2GRsbo3z58nB3d8eYMWNQuXJlbNu2LcO+vMZzR3Zy/l+8xj+PBUAhZ2xsjKpVqyI4OFjVplQqERwcnOVcun9TKBR4/Pgx7O3t8ypMg+fp6YlLly6ptV28eBGenp76CchAPXz4kNd5NgiCgJkzZ+LkyZPYunUrypUr99nX8Fr/MjnJ+X/xd/qXUyqVSE1NzfAYr/G8kVXO/4vX+OdxCpAB6N+/P/z9/eHu7o7q1atj69atSEpKQqdOnQAA48ePR4kSJTBmzBgAwMqVK+Hp6Yny5csjNjYWGzduRFhYGLp27arPj1GgJCQkqH3z8ObNGzx48AA2NjYoXbo0Fi1ahIiICCxcuBAA0KNHD+zcuRMLFy5E586dcenSJfz5559Yu3atvj5CgZPdnG/ZsgVly5ZFpUqVkJKSgl9//RWXLl3Cpk2b9PURCpwZM2YgMDAQq1evhoWFhWoPBSsrK9Wdq//+funbty/69OmDTZs2wc/PD0ePHsW9e/cwc+ZMvX2OgiQnOefv9C+zaNEiNGzYEKVKlUJCQgICAwNx5coVbNy4EQCv8byQ3ZzzGs8+FgAGoHXr1vjw4QOWL1+OyMhIVKlSBRs2bFDdjnz37h3E4n9uBsXGxmLq1KmIjIyEjY0Nqlatij179nCuYzbcu3cPffv2Vf08b948AEDHjh0xf/58REZG4t27d6rj5cqVw9q1azFv3jxs27YNJUuWxOzZs7kHQDZkN+cymQwLFixAREQEzMzM4OLigs2bN6NevXo6j72g2r17NwCgT58+au3z5s1TfcHw398vNWrUQEBAAJYuXYrFixfD0dERq1at4vroWspJzvk7/ctER0fD398f79+/h5WVFVxdXbFx40bUr18fAK/xvJDdnPMazz6RIAiCvoMgIiIiIiLd4DMAREREREQGhAUAEREREZEBYQFARERERGRAWAAQERERERkQFgBERERERAaEBQARERERkQFhAUBEREREZEBYABARERERGRAWAEREBuTcuXOoXbs2FixYgKtXr8Lf3z9Xzvvrr7/iu+++y5VzFQTPnj1Dt27dUK1aNbRv3z7Tft26dcPx48d1GBkR0eexACAiymWurq5Z/rdixQq9xXbq1CnMmjULycnJmDBhArp06fLF50xJScGyZcswbNgwVduTJ08wYsQINGnSBK6urtiyZUuGr925cyeaNGmCatWqoWvXrrhz547GuWfMmIG6devCy8sLI0aMQFRUlFqfsLAwDBo0CB4eHvD2/r/27j8m6voP4PjzoGNAwHJwWlHixsXB8NDDxuZx/CrbCGdFOGRT/khiRiGg2UFkJeIwpSYjMXPkj6jlbMo/RNcSV3be9UeAMxmMAWkuCBBULsUdcX7/cHz6niDGVwX35fXY2O7en9f7/Xl/3mzs/fq8358PS9mxYwd///33XV/XZD7++GN8fHywWCwcPHiQY8eO8fTTT4+Ly8nJ4aOPPsLlct3X/gghxFQ8NNMdEEKI/zdWq1X5XF9fT2VlJRaLRSnz9fWdiW4BsHXrVgCSk5PvWZsWiwU/Pz+WLFmilA0PD/PEE0+QnJzM9u3bJ6xXX1/P9u3bKSkpYdGiRRw6dIisrCwsFguBgYEAlJWV8eOPP1JRUYG/vz+lpaXk5uZy+PBhAEZHR1m3bh1BQUEcPnyYvr4+CgsLUavVbNy48Z5d461+//13EhMTCQ4OnjQuPj6ezZs3c/LkSRITE+9bf4QQYipkBUAIIe4xjUaj/Pj7+6NSqZTvw8PDbNq0CaPRiMFgIC0tDZvN5lb/mWeeYc+ePZjNZgwGA0lJSTQ0NDA4OEhOTg4Gg4EVK1bw66+/KnUuXbrExo0biYuLY9GiRaxYsYK6ujq3djMzM9m2bRs7d+4kJiaG2NjYcasR3d3dyjmio6PJz88fd8f9VvX19SQlJbmVRUVFUVhYyPLly/Hy8pqw3oEDB0hPTyctLQ2tVktJSQne3t4cPXoUAIfDwdGjRykqKmLp0qUsXLiQsrIympubOX36NHAz2ero6KC8vJyIiAgSEhLIz8/nyy+/xOl0Tnhep9PJ1q1bMZlM6PV6kpKS+PTTT5Xj586dY/Xq1ej1elJSUjh16hQ6nY7jx48DN1d4WlpaqKqqQqfTkZmZydtvv43D4Ri3yuPp6Ul8fDzffPPNpGMohBDTSRIAIYSYRteuXSMhIYGDBw9SW1tLXFwcr732Gt3d3W5xhw4dIjo6mtraWhISEjCbzZjNZl544QWOHTvG/PnzKSws5MaNG8DNSW1kZCT79u2jrq6O9PR0zGbzuC01tbW1+Pr6cuTIEd566y2qqqo4deoUAC6Xi9dff50rV65QU1PDgQMHuHDhAhs2bJj0mhobG9Hr9VMaB6fTSUtLC0ajUSnz8PDAaDTS3NwMwNmzZxkZGXGLCQ0N5fHHH1cSgNOnTxMWFkZQUJASYzKZ+Ouvv+jo6Jjw3DU1NZw4cYKKigosFgvl5eXKnXyXy8X69etRq9V8/fXXlJSU8OGHH7rVt1qtPPXUU6xduxar1conn3xCcXExfn5+WK1WrFar2/MQUVFRNDY2Tml8hBDifpItQEIIMY3Cw8MJDw9XvhcUFHD8+HFOnDjBmjVrlPL4+HgyMjIAeOONN/jqq6/Q6/U8//zzAGRnZ7Nq1SouXryIRqNh3rx5ZGVlKfUzMzOxWq18++23REVFKeU6nY7c3FwAFixYwBdffIHdbic2Nha73U57ezsNDQ089thjAOzcuZPly5dz5swZt3bGDA0N4XA4mDt37pTG4dKlS4yOjipbfcYEBgbS1dUFwMWLF1Gr1QQEBIyL6e/vV2L+e/IPKN/HYm7V09NDSEgIS5YsQaVSuW3jsdlsdHV1UV1dzbx58wDYsGED2dnZSoxGo8HT0xNfX180Gg2A20rPrebOnUtPTw8ulwsPD7nvJoSYeZIACCHENLp69Sq7d+/mhx9+oL+/n9HRUa5fvz5uBUCn0ymfxya0YWFhStnYxHlgYACNRsPo6Ch79+7FYrHQ29vLyMgITqcTb2/v27YLNyezAwMDwM032zz66KPK5B9Aq9USEBBAV1fXhAnA9evXAW67zedBlJqaytq1a0lOTiYuLo7ExERMJhPwzxiMTf4BDAbDXZ3P29sbl8s14e9DCCFmgiQAQggxjXbs2IHNZqOwsJD58+fj7e1NXl4eIyMjbnEPPfTPn2eVSgWAWq0eVza2Beizzz7j888/p7i4GJ1Oh4+PD2VlZZO2O9bOWBv/i0ceeQSVSsXQ0NCU6s2ZMwdPT08l+RgzMDCgJDxBQUGMjIwwNDTktgowlvSMxdy6zWnsmYWJ7sYDREZG0tDQwMmTJ7HZbBQUFGA0GqmsrJzSNfxbV65cwdfXVyb/QogHhqxFCiHENGpubiY1NZXnnnsOnU5HUFAQf/zxx12329TUxLPPPsuLL75IeHg4Tz75JOfOnZtSG6Ghofz555/09PQoZR0dHQwNDREaGjphHS8vL7Ra7W3329+Ol5cXkZGR2O12pczlcmG325U77gsXLkStVrvFdHV10d3dzeLFiwFYvHgx7e3tbomEzWbDz88PrVZ72/P7+fmRkpLCtm3b2LVrF9999x2XL19WxqCvr0+JHXveYDJqtZrR0dEJj7W3txMREXHHNoQQYrpIAiCEENMoJCSE77//ntbWVtra2njzzTfvyTviQ0JCsNlsNDU10dnZyXvvvXfHt/fcymg0EhYWxqZNm2hpaeHMmTOYzWZiYmImfcjXZDLR1NTkVuZ0OmltbaW1tRWn00lvby+tra2cP39eiXnllVc4cuQItbW1dHZ2smXLFoaHh3n55ZeBm/vq09LS+OCDD/j55585e/YsxcXFGAwGJQEwmUxotVrMZjNtbW389NNPVFRUsHr16knfPlRXV0dnZye//fYbFosFjUZDQEAARqORBQsWUFRURFtbG7/88gu7du2649gFBwdz7do17HY7g4ODDA8PK8caGxuJjY29YxtCCDFdZAuQEEJMo6KiIoqLi8nIyGDOnDlkZ2dz9erVu243JyeHCxcukJWVhY+PD+np6SxbtgyHw/Gv21CpVOzZs4fS0lLWrFmDSqUiLi6Od999d9J6K1euJC0tDYfDgb+/PwB9fX289NJLSsz+/fvZv38/MTEx1NTUAJCSksLg4CCVlZX09/cTERFBdXW120O9xcXFeHh4kJeXh9PpxGQy8f777yvHPT092bt3L1u2bGHVqlX4+PiQmppKXl7ebfv78MMPU11dzfnz5/Hw8ECv17Nv3z7lAd3du3fzzjvvsHLlSoKDg9m8eTOvvvrqpGMQHR1NRkYGBQUFXL58mdzcXNavX09vby/Nzc2Ul5dPWl8IIaaT6sbdbP4UQgghgLy8PCIjI1m3bt1Md+W+0Ol0VFVVsWzZsinVKy8vZ2hoiNLS0vvUMyGEmDrZAiSEEOKumc3mGf0Pxw+qwMBA8vPzZ7obQgjhRlYAhBBCiDv4X1cAhBDiQSQJgBBCCCGEELOIbAESQgghhBBiFpEEQAghhBBCiFlEEgAhhBBCCCFmEUkAhBBCCCGEmEUkARBCCCGEEGIWkQRACCGEEEKIWUQSACGEEEIIIWYRSQCEEEIIIYSYRf4DPuHAXWvpX/EAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 900x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Nota: sklearn usa la solución analítica (Normal Equation), no gradient descent.\n",
      "Por eso converge al óptimo exacto. Tu GD se acerca con suficientes iteraciones.\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "# Pipeline de sklearn equivalente a tu implementación manual\n",
    "degree_to_test = 2  # usa el mismo grado que encontraste óptimo\n",
    "\n",
    "pipe = Pipeline([\n",
    "    ('poly', PolynomialFeatures(degree_to_test, include_bias=False)),\n",
    "    ('scaler', StandardScaler()),\n",
    "    ('reg', LinearRegression())\n",
    "])\n",
    "\n",
    "# Entrenar\n",
    "pipe.fit(x_train.reshape(-1, 1), y_train)\n",
    "\n",
    "# Predecir\n",
    "y_pred_sklearn = pipe.predict(x_train.reshape(-1, 1))\n",
    "mse_sklearn = np.mean((y_pred_sklearn - y_train)**2)\n",
    "\n",
    "print(f\"MSE sklearn:    {mse_sklearn:.4f}\")\n",
    "if mse_final is not None:\n",
    "    print(f\"MSE tu código:  {mse_final:.4f}\")\n",
    "    print(f\"\\n{'✓ Resultados similares!' if abs(mse_sklearn - mse_final) < 50 else '⚠️ Hay diferencia significativa — revisa tu implementación'}\")\n",
    "else:\n",
    "    print(\"(Completa la sección 5 para comparar)\")\n",
    "\n",
    "# Visualizar\n",
    "plt.figure(figsize=(9, 5))\n",
    "plt.scatter(x_train, y_train, color='royalblue', s=80, zorder=5, label='Datos reales')\n",
    "\n",
    "x_plot = np.linspace(0.3, 3.7, 200)\n",
    "y_plot_sk = pipe.predict(x_plot.reshape(-1, 1))\n",
    "plt.plot(x_plot, y_plot_sk, 'g-', linewidth=2.5, label=f'sklearn (grado {degree_to_test})')\n",
    "\n",
    "plt.xlabel('Tamaño (1000 sqft)')\n",
    "plt.ylabel('Precio ($1000s)')\n",
    "plt.title(f'Verificación con sklearn — MSE: {mse_sklearn:.2f}')\n",
    "plt.legend()\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.show()\n",
    "\n",
    "print(\"\\nNota: sklearn usa la solución analítica (Normal Equation), no gradient descent.\")\n",
    "print(\"Por eso converge al óptimo exacto. Tu GD se acerca con suficientes iteraciones.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "# 7. Conclusión\n",
    "\n",
    "## ¡Felicitaciones!\n",
    "\n",
    "En esta práctica aprendiste a:\n",
    "\n",
    "- **Vectorizar** operaciones usando el producto punto y multiplicación de matrices (`X @ w + b`) en lugar de loops\n",
    "- Crear **features polinomiales** para capturar relaciones no-lineales, y evaluar qué grado es óptimo\n",
    "- Implementar **3 métodos de feature scaling** (Min-Max, Mean Normalization, Z-Score) y comparar su efecto en la convergencia\n",
    "- Construir un **pipeline completo**: features → scaling → entrenamiento → evaluación\n",
    "\n",
    "### Conceptos Clave:\n",
    "1. La multiplicación matriz × vector es una colección de productos punto (una predicción por fila)\n",
    "2. Feature scaling es **esencial** cuando las features tienen escalas diferentes\n",
    "3. Más features (mayor grado) no siempre es mejor → riesgo de **overfitting**\n",
    "4. El pipeline correcto es: crear features → escalar → entrenar"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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