GRAIDENT_DESCENT ALGORITHMS .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4bce0f42",
   "metadata": {},
   "source": [
    "# Importing Liabraries\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "601c4374",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import preprocessing\n",
    "from sklearn.metrics import mean_squared_error\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc6ca22d",
   "metadata": {},
   "source": [
    "# Loading Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6a47b987",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       area  bedrooms   price\n",
      "0    1056.0         2   39.07\n",
      "1    2600.0         5  120.00\n",
      "2    1440.0         2   62.00\n",
      "3    1521.0         3   95.00\n",
      "4    1200.0         2   51.00\n",
      "..      ...       ...     ...\n",
      "294  1425.0         2   70.00\n",
      "295  1450.0         3  100.00\n",
      "296  1847.0         3  105.00\n",
      "297  1100.0         2   45.00\n",
      "298   525.0         1   26.00\n",
      "\n",
      "[299 rows x 3 columns]\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv(\"Bengaluru_House_Data.csv\")\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3ece17d",
   "metadata": {},
   "source": [
    "# Scaling The Factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c0a9093c",
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The dataset should be Scaled before Training and dropping the target variable as Price\n",
    "\n",
    "\n",
    "sx=preprocessing.MinMaxScaler()\n",
    "sy=preprocessing.MinMaxScaler()\n",
    "\n",
    "scaled_X= sx.fit_transform(df.drop('price' , axis='columns'))\n",
    "scaled_X\n",
    "\n",
    "scaled_Y= sy.fit_transform(df['price'].values.reshape(df.shape[0],1))\n",
    "scaled_Y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83143199",
   "metadata": {},
   "source": [
    "# Batch Gradient Algorithm "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "02d30769",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weights: [0.90086202 0.88770941]\n",
      "Bias: -0.25552825290452735\n",
      "Final Cost: 0.03083080738651866\n"
     ]
    }
   ],
   "source": [
    "'''\n",
    "Gradient Batch takes the training samples one by one so lets say it takes the first sample (1056,2) , formulation for the \n",
    "calcuation can be stated as : Price = w1*Area + w2*Bedroom + bias .\n",
    "\n",
    "as the inital value of the variable w1,w2,bias is 1, so that it places the values in each context .\n",
    "    Price = 1*1056 + 1*2 + 1 = 1059\n",
    "    calculate the (Yi - Ypred) = (39,07,000 - 1059) = 3,905,941 \n",
    "    \n",
    "    so the value is the error one , similarly it calcultes all the erros and add it . \n",
    "    Error = err1 + err 2+.....+err n / total no of errors\n",
    "    \n",
    "    lastly it adds the partial Derivates w.r.t w1,w2,bias \n",
    "'''\n",
    "def gradient_batch(X, y_true, epochs, learning_rate=0.0011): #defining the learning rate  \n",
    "    \n",
    "    ''' If the learning rate is high lets say is 2.0 so after the 250th iteration or at any \n",
    "    significant iteration the cost will get increase so that learning rate should be between the 0 and 1 '''\n",
    "    \n",
    "    number = X.shape[1]\n",
    "    \n",
    "    w = np.ones(shape=(number))  # Initializing weights to 1 at starting \n",
    "    b = 0\n",
    "    \n",
    "    total_sam = X.shape[0]\n",
    "    \n",
    "    cost_list = []\n",
    "    epoch_list = []\n",
    "    \n",
    "    for i in range(epochs):\n",
    "        # Predictions\n",
    "        y_predicted = np.dot(X, w) + b\n",
    "        \n",
    "        # Gradients calculation Formulas \n",
    "        w_grad = -(2 / total_sam) * np.dot(X.T, (y_true - y_predicted))\n",
    "        b_grad = -(2 / total_sam) * np.sum(y_true - y_predicted)\n",
    "        \n",
    "        # Update weights and bias\n",
    "        w -= learning_rate * w_grad\n",
    "        b -= learning_rate * b_grad\n",
    "        \n",
    "        # Cost calculation\n",
    "        cost = np.mean(np.square(y_true - y_predicted))\n",
    "        \n",
    "        # Store cost and epoch for plotting\n",
    "        if i % 20 == 0:\n",
    "            cost_list.append(cost)\n",
    "            epoch_list.append(i)\n",
    "    \n",
    "    return w, b, cost, cost_list, epoch_list\n",
    "\n",
    "# Example usage\n",
    "w, b, cost, cost_list, epoch_list = gradient_batch(scaled_X, scaled_Y.reshape(-1,), 1000)\n",
    "print(f\"Weights: {w}\")\n",
    "print(f\"Bias: {b}\")\n",
    "print(f\"Final Cost: {cost}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cfc87b6",
   "metadata": {},
   "source": [
    "# Graph for Cost Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "58b42701",
   "metadata": {},
   "outputs": [
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fv4+ePXuiXr16RuMJDw/HF198gaSkJKN3ZUdFRZWpXsUpreldcXcOjxkzxuj0mJgYLFiwAHv37kV+fj7UajUOHTqEO3fuoHbt2kb/T46Ojhg+fDg+/fRTJCQkYMSIEQCAbdu2AQBGjBhR7u9hebaH9u3bQ61WY9myZWjSpIl83bSiMjIyAABubm6lli3c9E6n0+HKlSs4dOgQ1qxZAwBYunSp0bpfv34dmzdvRmpqKm7evIm8vDwAwNmzZwEAp0+fLlfMj/N9DwoKMvp56W+YLu91+5KcPHnS6A15Y8eORbNmzYpM19/oWJz8/Hzs3LkTSUlJ+Pvvv3H//n0I6cAUQNHPUX+9/ZlnnoGdnV2R9cXExOCVV14pa3Vw5MgRXLlyBQ0bNkSHDh2MltE3j0tKSjI639i2rtVq0aBBAxw5cgSXL1+Gj49PmWMqTL8N67fpsipXsq9Tpw4A4OrVq+V6E6Bg43Jzc4Ozs7PRMg0bNjQoCwCjR49GbGwsfvjhB0RFRUGtViMwMBBdu3bFkCFD0KNHj3LHUlbV0fypuB23/jMqfEPKxYsXAQBNmzat8pu+rl+/Lr+3/qbHRxn7fxVWnrqVpKLbDgCMGzcO77zzDlavXo2FCxfCwcEBALB8+XIAUoJUq9Vy+XPnzgGQbswp7TM21mmUh4fHY9/ZW9Gmd8X9n/TT79+/j+vXr8PDw0P+nIpbBjD+meq3QWM78dKUZ3to2LAhPvnkE0yfPh0TJ07ExIkT4efnh9DQUDz11FMYOnRoudq6Z2VlGbxXSYw1vbt16xaeeeYZ/Pjjj7h9+zY2btxoMP+rr77CK6+8grt37xa73uzs7DLHCzze972yvnsA5FY6xXWSpv//6DVq1Ej+cW6MsRsQ9c6ePYunn34ax48fL7bMo5/jX3/9BaD4bblWrVpwcXGRt4HS6PcBf/75Z4X2AUDlfv7FrePmzZvlWq5cyb5Dhw747rvvcPjwYfkIoarZ2Njg+++/x6xZs7B582YkJiYiMTERS5YswZIlS9C/f3+sX7++WmKpCJ1OV+J8GxvL7bHYFOqm7/ApPj4e69evx4gRI5CXlyffMT5u3DiD8vr/V6NGjdClS5cS120s4el/TJgq/dGREsq7PUyaNAnPPPMMNmzYgL1792Lv3r1YtWoVVq1ahTlz5mDPnj1lPtp3dXVFZmZmuRNu4eUXLFiA1q1bY9OmTTh+/DhatGgBQDoCf+GFF6BWq/HBBx+gf//+8PX1haOjI1QqFZYuXYoXXnihWj/7yvzutW/fHnv27Cm29U15lfQdGTJkCI4fP46nnnoKr732GgIDA+Hs7Aw7Ozvk5uaWqSXA49LvA7y8vBAZGVli2eKaK1flvk//o6VWrVrlWq5cyf6pp57CtGnTcOvWLWzYsKFcp5b0p0SvX7+O7Oxso7+w9b+ojJ0+DQwMRGBgIKZPnw4hBOLj4zFixAhs3LgR3377bZGddnWxs7NDXl4ebt++jZo1axaZr/91Xhn0vxbPnDkDIUSVHt27ublBq9UiJycH586dQ+vWrYuUKen/VZked9sZN24c4uPjsXz5cnmbuXbtGjp37lykaaj+1FrTpk3NrmOb8+fPG52u70nS3t5ePgWo/5yKWwYw/pnqt8FTp049drxl4enpieeeew7PPfec/L7PPvss9u3bhxkzZpS5PbeHhwcyMzOLbaZWFg0aNJDHT548KSf7tWvXQgiBSZMm4bXXXiuynP40fnlV5/e9JAMGDMCnn36K33//HampqWjZsmWVvM+pU6dw9OhReHh4YP369bC1NUxPxX2O+u2zuB5Tb926VeajeqBgH+Dm5maS+wD9Nuzp6Vmu5cr186Nhw4aIjo4GALz66qultnO9evWqfH2lfv368mlBYx+gEEKerm9/WhyVSoWePXvK1xFTUlLkefpTe9XVh7V+Qzt58mSReUePHkVaWlqlvVdQUBDc3d2RmZmJX375pUzLVPTzsLW1la8bF7fBL1u2DEDp/6/H9bjbTlRUFFxcXBAfH4+0tDT5FL6xH4g9e/aERqPBzp07K3S5Sknff/+90enffvstAOnygH4HGhQUJHdzumHDhiLL3L9/H6tWrQJg+Jnq72/48ccfSzxlXVWaNWuG119/HYDh9740+k5gHqdnt8Knpgtfs9fvB/38/Ios8+DBA/z8889G11fad7Mi3/eq0KNHD/l+lxdffBG5ublV8j76z9Hb27tIogeK3771XceuWbNGvk+iMP32X1bBwcFwd3fHiRMnSrycUJnKs59OTU0FgGLvJyhOuc81LFq0CI0aNcL58+fRtWtXubOFwnJzc7Fs2TK0a9fOIAn+85//BAC88847+P333+XpQgi8++67SElJgaurq/wrHpD+Ufq+mAu7ffu2fGNG4S+ZvgOU9PT0cnW6UVEREREAgLfffhs5OTny9AsXLiAmJqZST93Z2trijTfeAAA8//zzRntROnjwoHwNC5ASJSD9Kjb2RSjJq6++CgBYsmRJkV7DVqxYgQ0bNsDOzg5Tpkwp13oroiLbjp6DgwOGDx8OnU6HDz74ANu2bYOjoyOGDRtWpKynpycmTZqEu3fvon///jh27FiRMjk5OdiwYUO1Hd2WVXJyMj788EODaXv37pU74Ch8k5K9vT0mTJgAQPo/Fz4DlZeXhylTpiA9PR0BAQEGN1QNGDAA7dq1w5UrVzB06NAiR8oPHjzA1q1bH7su8fHx2LJlS5FtVgiBTZs2ATCeXIuj/8FSXGcopbl165a8DdauXdug51D9TW/ffPMNbt++LU9/8OABXn755WLPnpT23azI972q/PDDD3B3d0diYiJ69uxZ7A+t1NTUCj8krEmTJlCr1Th27FiRTm42btyITz75xOhyQ4YMQb169XDp0iXMnDnT4NJpamoq3n333XLFYWdnhzlz5kAIgaefftpojsvPz0d8fHylPfRHvy2U9uMiKysLJ06cgJOTk9GOi0pUrnv3/19GRoYIDw+XmxkEBASIgQMHiujoaNGjRw+5SY+zs7P47bff5OV0Op3cVt/W1lbudKRp06YCkDor2bJli8F7DRw4UAAQ3t7eom/fvmLkyJGib9++chOGli1bFmmHO2TIELkpRnR0tBg/fnyZ24iWt539uXPnhKurqwCkDlWioqLEE088IRwcHERERITo3LlziU3vimtqUVxzOJ1OJ1588UU5xnbt2onhw4eLvn37Gu1kQwght4tu2rSpGDlypBg/frxBxyBl7VSna9euYsSIEXJnIaV1qlPeupWkIttOYfv37zdoRjVmzJhiy+bl5YkRI0YIQOpQo127diIqKkoMGzZMdOnSRe68o3DHOo/b5FOIgqZ3DRs2NNqUST+8+eabBss92qlOixYt5M5K9J3qGOvE6MGDB3LzSgcHB9G3b18xbNgw4evrKwCpbbexpkcXLlyQP3dHR0fRu3dvER0dLZ544okSO9Upz/agby7l7OwswsPDxYgRI8TTTz8tN99ycXEpV6c66enpws7OTtStW9doh2CFm95FRUXJn/Xo0aNFRESEvL+xt7cXGzduNFj25s2bclxubm5i0KBBIioqSnh4eIiaNWuKKVOmCMB4/wmlfTfL+33XN70rrq+Gx9lOz549KzdXBaQ26AMHDhSjRo0SgwYNkrcJAKJr165Fmq4W17FNYfrPysbGRoSFhYno6Gh5f6PfFxnbN+/cuVM4OjrK35/hw4eLXr16CTs7OzF48OAKdaozffp0+f1atGghBg4cKIYPHy7Cw8Plff6SJUsMliktdxT3fps2bRIAhEajEU899ZR49tlnxfjx40ViYqJBuXXr1gkA4plnnin2PYpToWSvt3XrVjFmzBjRqFEj4eTkJOzs7ISXl5fo1auXWLhwobh+/brR5VauXCl/YHZ2dsLHx0eMHTtWnDp1qkjZ3bt3i6lTp4qOHTsKLy8vodFohJeXlwgNDRWLFi0Sd+7cKbLM9evXxQsvvCB8fX2FnZ1duZJ3eZO9EFJHEIMHDxa1atUSWq1WNG3aVLz77rsiNze31Hb2FU2IW7duFQMHDhSenp7Czs5O1KlTR3Ts2FG8/fbbRT73ixcvihEjRoi6desKW1vbIl/2srxX3759hZubm7C1tRVeXl5i6NChBj/kKrNuJSnPtvMofVvrkmIrbMuWLWLw4MGiXr16ws7OTri6usq9v61cuVLcvXtXLluZyb60oU2bNgbLFf684+LiRM+ePYWLi4twcHAQQUFBYsWKFcW+Z15envjiiy9Ep06d5I5CGjZsKCZNmlRsPwNCCHH79m3xwQcfiODgYFGzZk2h1WqFn5+fGDBggFi1alWx8RljbHv4448/xFtvvSV69uwpfH19hb29vahVq5Zo3bq1mDFjRrk6ZNLT/4Az9qOwpHb2NWrUEM2bNxcTJ04UZ8+eNbruzMxM8fLLL4uGDRsKrVYrvL29xahRo8TZs2dLTMClfTf1yvp9r8pkL4T042PdunVixIgRomHDhvJ+393dXXTq1ElMnTrVaJ8WQpQt2et0OvH111+LDh06CCcnJ+Hi4iK6du0qb1Ml7ZuPHTsmBg8eLGrXri20Wq1o3ry5mDt3rsjLy6tQshdCiMTERDFy5Ejh5+cntFqtqFmzpmjSpIkYNGiQ+O9//ytu3LhhUL6iyV4IqQfY9u3byz9aAMM+XYQQYsCAAQKA2LVrV7HvURzV/wdIRGaqtMdjkuTgwYPo2LEjBg8eXOx1dCJTlZ6eDl9fX7Rs2bJ6nnpHRGSOgoODMWLECKxfvx5Hjx5VOhyicnnnnXeQl5eHjz/+uELLM9kTkdX48MMP4ejoKPeySGQOzp07h6+++gpDhw6t8Nm7ausul4hIafXq1cOdO3eUDoOoXBo0aPDYTR55zZ6IiMjC8TQ+ERGRhWOyJyIisnC8Zm8i9I/SrFmzpmJ9YBMRVSYhBG7fvg1vb2+TeDCWNWOyNxFXrlyp8PONiYhMWVpamtwlLCmDyd5E6J+Yl5aWVqZnbhMRmbrs7Gz4+PgYfSIoVS8mexOhP3Xv7OzMZE9EFoWXJpXHiyhEREQWjsmeiIjIwjHZExERWTgmeyIiIgvHZE9ERGThmOyJiIgsHJM9ERGRhWOyJyIisnBM9kRERBaOyd6MrVkDxMQArVoBublKR0NERKaKyd6MbdwIfPstkJoKHDmidDRERGSqmOzNWOfOBeNJScrFQUREpo3J3owVTvb79ikXBxERmTYmezPWsiXg5CSNJyYCQigbDxERmSYmezOmVgOdOknjV64AaWnKxkNERKaJyd7M8bo9ERGVhsnezDHZExFRaZjszVxISME4kz0RERljlcl+8eLF8Pf3h729PUJCQnDgwIFiyx4/fhxRUVHw9/eHSqXCwoULS1z3vHnzoFKpMHXq1MoNuhiurkCLFtJ4Sgpw9261vC0REZkRq0v2q1evxrRp0zBnzhwcPnwYbdq0QWRkJK5evWq0/L1799CgQQPMmzcPXl5eJa774MGD+M9//oPWrVtXRejF0p/Kz88HDh6s1rcmIiIzYHXJ/uOPP8Zzzz2HcePGITAwEF9++SUcHR2xbNkyo+WDg4Px0UcfYfjw4dBqtcWu986dOxg5ciS++uor1KpVq6rCN4rt7YmIqCRWlexzc3ORnJyMiIgIeZqNjQ0iIiKw7zGz5IQJE9CvXz+DdZckJycH2dnZBkNF8SY9IiIqiVUl+2vXriE/Px+enp4G0z09PZGenl7h9a5atQqHDx/G3Llzy7zM3Llz4eLiIg8+Pj4Vfv/GjQE3N2k8KYmd6xARkSGrSvZVIS0tDVOmTMEPP/wAe3v7Mi83c+ZMZGVlyUPaY/SIo1IVHN3fuAGcOVPhVRERkQWyqmTv7u4OtVqNjIwMg+kZGRml3nxXnOTkZFy9ehXt27eHra0tbG1tsWvXLnz22WewtbVFfn6+0eW0Wi2cnZ0NhscRGlowzlP5RERUmFUle41Ggw4dOiAuLk6eptPpEBcXh9DC2bIcevbsiWPHjiElJUUegoKCMHLkSKSkpECtVldW+CXidXsiIiqOrdIBVLdp06YhJiYGQUFB6NixIxYuXIi7d+9i3LhxAIAxY8agXr168vX33NxcnDhxQh6/fPkyUlJS4OTkhEaNGqFmzZpo2bKlwXvUqFEDbm5uRaZXpeBgqa/8/HwmeyIiMmR1yX7YsGHIzMzE7NmzkZ6ejrZt22Lbtm3yTXuXLl2CjU3BCY8rV66gXbt28uv58+dj/vz5CAsLw86dO6s7/GI5OgLt2gGHDgEnTgA3bwLV3AKQiIhMlEoI3rttCrKzs+Hi4oKsrKwKX7+fMgX47DNpfOtWoE+fSgyQiKicKmO/RpXDqq7ZWzpetyciImOY7C0Ikz0RERnDZG9BfHyA+vWl8d9+Ax4+VDYeIiIyDUz2FkbfgvDOHSA1VdlYiIjINDDZWxieyiciokcx2VsYJnsiInoUk72FadsW0HfRz2RPREQAk73F0Wik3vQA4Px54K+/lI2HiIiUx2RvgcLDC8Z37VIsDCIiMhFM9hYoLKxg3IR69CUiIoUw2Vug0FDAzk4a55E9EREx2VsgR0cgJEQaP3sWuHxZ2XiIiEhZTPYWqvCpfB7dExFZNyZ7C8Wb9IiISI/J3kIVvm7Pm/SIiKwbk72FqlGjoL39mTPA338rGw8RESmHyd6C8VQ+EREBTPYWrXCy56l8IiLrxWRvwTp3BmxtpXEmeyIi68Vkb8EKX7c/fRpIT1c2HiIiUgaTvYXjdXsiImKyt3DsJ5+IiJjsLVyXLoBaLY3zyJ6IyDox2Vs4J6eC6/YnTwIZGcrGQ0RE1Y/J3grwuj0RkXVjsrcCfCgOEZF1Y7K3AoWv2/MmPSIi68NkbwVq1gSCgqTxEyeAq1eVjYeIiKoXk72VKHwqf/du5eIgIqLqx2RvJQrfpJeQoFgYRESkACZ7K1H4un18vLKxEBFR9WKytxLOzkCnTtL4qVPApUvKxkNERNWHyd6K9O5dMP6//ykXBxERVS8meyvCZE9EZJ2Y7K1IUBDg6iqN79gB5OcrGg4REVUTJnsrYmsLRERI4zdvAsnJysZDRETVg8neyvBUPhGR9WGytzK9ehWMM9kTEVkHq0z2ixcvhr+/P+zt7RESEoIDBw4UW/b48eOIioqCv78/VCoVFi5cWKTM3LlzERwcjJo1a8LDwwODBg3C6dOnq7AGFefvDzRpIo3v2wdkZysaDhERVQOrS/arV6/GtGnTMGfOHBw+fBht2rRBZGQkrhbTYfy9e/fQoEEDzJs3D15eXkbL7Nq1CxMmTMD+/fsRGxuLvLw89O7dG3fv3q3KqlSY/lT+w4d8MA4RkTVQCSGE0kFUp5CQEAQHB+Pzzz8HAOh0Ovj4+GDSpEmYMWNGicv6+/tj6tSpmDp1aonlMjMz4eHhgV27duGJJ54oU1zZ2dlwcXFBVlYWnJ2dy7RMRW3cCAwYII2//DKweHGVvh0RWanq3K9RyazqyD43NxfJycmI0N+SDsDGxgYRERHYt29fpb1PVlYWAKB27drFlsnJyUF2drbBUF3Cw6U78wFetycisgZWleyvXbuG/Px8eHp6Gkz39PREenp6pbyHTqfD1KlT0aVLF7Rs2bLYcnPnzoWLi4s8+Pj4VMr7l0XNmlJf+QDwxx/AuXPV9tZERKQAq0r21WHChAlITU3FqlWrSiw3c+ZMZGVlyUNaWlo1RSgp3AQvNrZa35qIiKqZVSV7d3d3qNVqZGRkGEzPyMgo9ua78pg4cSI2bdqEhIQE1K9fv8SyWq0Wzs7OBkN1Ynt7IiLrYVXJXqPRoEOHDoiLi5On6XQ6xMXFITQ0tMLrFUJg4sSJWL9+PeLj4xEQEFAZ4Vapdu0ANzdpPC5OujOfiIgsk1UlewCYNm0avvrqK3zzzTc4efIkXnrpJdy9exfjxo0DAIwZMwYzZ86Uy+fm5iIlJQUpKSnIzc3F5cuXkZKSgj/++EMuM2HCBHz//fdYuXIlatasifT0dKSnp+P+/fvVXr+yUqsLus7NygIOHlQ2HiIiqjq2SgdQ3YYNG4bMzEzMnj0b6enpaNu2LbZt2ybftHfp0iXY2BT8Brpy5QratWsnv54/fz7mz5+PsLAw7Pz/RupLliwBAISHhxu81/LlyzF27Ngqrc/j6N0bWL1aGt++HXiMkxtERGTCrK6dvalSoj3qX38B+kYAoaFAUlK1vC0RWQm2szcdVncanwrUrw8EBkrjv/0G3LqlaDhERFRFmOytnP6ufJ1OulGPiIgsD5O9lSvcBG/LFuXiICKiqsNkb+XCwwFHR2l882bpCJ+IiCwLk72Vc3AoeMZ9Rgab4BERWSIme0L//gXjGzcqFwcREVUNJntCv34F40z2RESWh8me4OUFdOwojR89Cly8qGw8RERUuZjsCQAwYEDBOI/uiYgsC5M9AeB1eyIiS8ZkTwCAVq0AX19pPCEByM5WNh4iIqo8TPYEAFCpCo7u8/L4jHsiIkvCZE8ynsonIrJMTPYkCw8HnJyk8S1bgPx8RcMhIqJKwmRPMq0WiIyUxq9dA/bvVzYeIiKqHEz2ZICn8omILA+TPRno21e6WQ8ANmxQNhYiIqocTPZkoE4dIDRUGj95EvjzT2XjISKix8dkT0WwNz0iIsvCZE9F8Lo9EZFlYbKnIpo3Bxo0kMZ37wZu3VI0HCIiekxM9lSESlVwKv/hQ2DTJmXjISKix8NkT0YNHlwwvnatcnEQEdHjY7Ino7p0AerWlca3b+eDcYiIzBmTPRllYwNERUnjOTm8UY+IyJwx2VOxhg4tGOepfCIi88VkT8Xq0gXw8pLGt23jqXwiInPFZE/FUqsNT+XzrnwiIvPEZE8l4ql8IiLzx2RPJeraFfD0lMa3bgVu31Y2HiIiKj8meyoRT+UTEZk/Jnsq1ZAhBeM8lU9EZH6Y7KlUTzwBeHhI41u3AnfuKBsPERGVD5M9lUqtLug+98EDnsonIjI3TPZUJrwrn4jIfDHZU5k88QRQp440vmULT+UTEZkTJnsqE1tbw1P5mzcrGw8REZUdkz2VGU/lExGZJyZ7KrOwMMDdXRrfsoV95RMRmQurTPaLFy+Gv78/7O3tERISggMHDhRb9vjx44iKioK/vz9UKhUWLlz42Os0V7a2BUf39+8D69YpGw8REZWN1SX71atXY9q0aZgzZw4OHz6MNm3aIDIyElevXjVa/t69e2jQoAHmzZsHL/0j4B5zneZszJiC8W+/VS4OIiIqO5UQQigdRHUKCQlBcHAwPv/8cwCATqeDj48PJk2ahBkzZpS4rL+/P6ZOnYqpU6c+9jpzcnKQk5Mjv87OzoaPjw+ysrLg7Oz8GDWsWkIATZsCZ88CKhVw4QLg66t0VERkirKzs+Hi4mLy+zVrYFVH9rm5uUhOTkZERIQ8zcbGBhEREdi3b1+1rnPu3LlwcXGRBx8fnwq9f3VTqYDRo6VxIYAfflA2HiIiKp1VJftr164hPz8fnvrHuP0/T09PpKenV+s6Z86ciaysLHlIS0ur0PsrYdSogvHvvpOSPhERmS6rSvamRKvVwtnZ2WAwFwEBQLdu0vjJk0BysrLxEBFRyawq2bu7u0OtViMjI8NgekZGRrE33ymxTnOgP5UPSEf3RERkuqwq2Ws0GnTo0AFxcXHyNJ1Oh7i4OISGhprMOs3B0KGAViuN//gjkJenbDxERFQ8q0r2ADBt2jR89dVX+Oabb3Dy5Em89NJLuHv3LsaNGwcAGDNmDGbOnCmXz83NRUpKClJSUpCbm4vLly8jJSUFf/zxR5nXaYlcXYEBA6TxzExg+3ZFwyEiohLYKh1AdRs2bBgyMzMxe/ZspKeno23btti2bZt8g92lS5dgY1PwG+jKlSto166d/Hr+/PmYP38+wsLCsHPnzjKt01KNGVPQbe633wJPPaVsPEREZJzVtbM3VebYHjUvD6hXTzqy12qB9HTpiJ+ICDDP/ZqlsrrT+FR57OyA6GhpPCeHD8chIjJVTPb0WAp3n8u78omITBOTPT2W9u2B5s2l8T17gPPnlY2HiIiKYrKnx6JSGR7df/+9crEQEZFxTPb02EaOlJI+ACxfDuh0ysZDRESGTDbZN2jQAJ999lmJZRYvXowGDRpUU0RUHB8foHdvafz8eSA2Vtl4iIjIkMkm+wsXLuDWrVsllrl16xYuXrxYPQFRiV54oWD8P/9RLg4iIirKZJN9WWRlZUGr77OVFPXUU0DdutL4hg3AlSvKxkNERAVMqge93bt3G7y+cOFCkWkAkJ+fj7S0NPzwww9o0qRJdYVHJbCzA8aPB959F8jPB5YtA/71L6WjIiIiwMR60LOxsYFKf6dXKYQQUKlUWLFiBUYXfgSbmbKEnqYuXpQefysE4OsLnDsHqNVKR0VESrGE/ZqlMKkj+9mzZ0OlUkEIgX//+98ICwtDeHh4kXJqtRq1a9dG9+7d0VzfyJsU5+cHPPkksGULcOmS9HCcvn2VjoqIiEzqyL6w7t27Y9y4cRhTuBG3BbOUX8C//goMGiSNDxggvSYi62Qp+zVLYLLJ3tpYypfi4UPA3x+4fBmwsZFO7devr3RURKQES9mvWQKTvRs/LS0N8fHxuHfvnjxNp9Phgw8+QJcuXRAREYHNmzcrGCEZY2sr3agHSJ3rLFumbDxERGTCR/Zjx47Fxo0bkZ6eDjs7OwDAO++8gzlz5shl1Go1kpKSEBwcrFSYlcaSfgGnpUlH9zqd1OHO+fO8UY/IGlnSfs3cmeyRfWJiIiIiIuREL4TA559/jmbNmuHSpUs4cOAAatSogY8++kjhSOlRPj4FN+alpQFbtyobDxGRtTPZZH/16lX4+fnJr1NSUpCZmYlJkyahfv36CAoKwqBBg3Dw4EEFo6TisEc9IiLTYbLJXqfTQVfoiSo7d+6ESqVCjx495Gn16tVDenq6EuFRKZ58UjrCB6SmeGlpysZDRGTNTDbZ+/r64sCBA/LrX375BXXr1kXTpk3laenp6XB1dVUgOiqNWg384x/SuE4HfPmlsvEQEVkzk032UVFRSExMxJAhQzBq1Cjs3bsXUVFRBmVOnDjBp96ZsH/8Q7o7H5CSfaGGFUREVI1MNtn/85//RHBwMNatW4eVK1eiVatWeOutt+T5Fy9exIEDB4z2sEemwdsbGD5cGr9xA/juO2XjISKyVibb9E4vNTUVANC8eXOoC7XfunjxIlJSUhAUFIR69eopFV6lsdQmKocPAx06SOPNmgHHj0ud7RCR5bPU/Zo5Mvlkby0s+UsRFgboH164ZYt08x4RWT5L3q+ZG5N6EE5xEhMTkZKSguzsbDg7O6Nt27bo0qWL0mFRGb3ySkGy//hjJnsioupm0sk+KSkJ48aNwx9//AGg4LG2ANC4cWMsX74coaGhSoZIZdC/P9CwIfDnn8COHcCxY0CrVkpHRURkPUw22R8/fhy9e/fGvXv30KtXL3Tv3h1169ZFeno6EhIS8L///Q+RkZHYv38/AgMDlQ6XSqBWA1OmAJMnS68XLgS+/lrRkIiIrIrJXrMfNmwY1q9fjw0bNqBPnz5F5m/btg0DBgzA4MGDsWrVKgUirFyWfm3rzh3p6XdZWYBGIz3v3tNT6aiIqCpZ+n7NnJjsfdE7d+7EkCFDjCZ6AOjTpw+GDBmChISEao6MKsLJCXj+eWk8NxdYskTZeIiIrInJJvusrCwEBASUWCYgIABZWVnVFBE9rkmTCp5+98UXwIMHysZDRGQtTDbZe3t7Y//+/SWW+e233+Dt7V1NEdHj8vEBhgyRxjMzgR9+UDYeIiJrYbLJfsCAAdi5cyfefPNNPHjkEPDBgweYM2cOEhISMHDgQIUipIp45ZWC8U8+AUzzjhEiIstisjfoXb9+HSEhITh//jzc3NzQsWNHeHp6IiMjAwcPHkRmZiYaNGiAAwcOoHbt2kqH+9is6UaWLl2ApCRpfPNmoG9fZeMhoqphTfs1U2eyR/Zubm7Yv38/YmJicOfOHWzZsgXLly/Hli1bcPv2bYwbNw779++3iERvbf75z4Lxd9/l0T0RUVUz2SP7wvLy8nDq1Cm5B71mzZrBzs5O6bAqlTX9AtbpgNatpX7yASAuDujRQ9mYiKjyWdN+zdSZ3JH9e++9h1mzZiEvL0+eZmdnh1atWqFLly5o1aoVhBB44403MG/ePAUjpYqysQHeeKPg9TvvKBcLEZE1MKlkv2PHDsyePRtubm4lHrlrNBq4ubnhjTfeYDt7M/XMM0DjxtL4zp3A3r2KhkNEZNFMKtl/++23qFWrFiZOnFhq2QkTJqB27dpYvnx5NURGlU2tBmbNKnj97rvKxUJEZOlMKtknJSUhIiICWq221LJarRYRERFITEyshsioKowcCfj7S+PbtwMHDyoaDhGRxTKpZH/lyhU0aNCgzOUDAgLw999/l/t9Fi9eDH9/f9jb2yMkJAQHDhwosfzatWvRrFkz2Nvbo1WrVtiyZYvB/Dt37mDixImoX78+HBwcEBgYiC+//LLccVkbOztg5syC1zy6JyKqGiaV7G1sbAxuzCtNXl4ebGzKV4XVq1dj2rRpmDNnDg4fPow2bdogMjISV69eNVo+KSkJ0dHRGD9+PI4cOYJBgwZh0KBBSE1NlctMmzYN27Ztw/fff4+TJ09i6tSpmDhxIjZs2FCu2KxRTIz0gBwA2LAB+P13ZeMhIrJEJpXsvb29DZJoaVJTU1GvXr1yvcfHH3+M5557DuPGjZOPwB0dHbFs2TKj5T/99FP06dMH06dPR/PmzfHOO++gffv2+Pzzz+UySUlJiImJQXh4OPz9/fH888+jTZs2pZ4xIECrBV57reD1e+8pFwsRkaUyqWTfrVs3xMfH48KFC6WWvXDhAuLj4/HEE0+Uef25ublITk5GRESEPM3GxgYRERHYt2+f0WX27dtnUB4AIiMjDcp37twZGzZswOXLlyGEQEJCAs6cOYPevXsXG0tOTg6ys7MNBmv1j38UPO72p5+AkyeVjYeIyNKYVLKfMGEC8vLyMGTIEFy7dq3YctevX8fQoUPx8OFDvPTSS2Ve/7Vr15Cfnw/PRx6k7unpifT0dKPLpKenl1p+0aJFCAwMRP369aHRaNCnTx8sXry4xB8ic+fOhYuLizz4+PiUuR6WxsGhoFc9IXh0T0RU2Uwq2bdv3x5Tp07F4cOHERgYiNmzZyMhIQFnz57F2bNn5QfjBAYGIjk5Ga+88grat2+vdNhYtGgR9u/fjw0bNiA5ORkLFizAhAkTsGPHjmKXmTlzJrKysuQhLS2tGiM2PS++CLi5SeM//gicOKFsPERElsRW6QAetWDBAtjb2+Ojjz7Ce++9h/ceOcwTQkCtVmPmzJl4t5y3b7u7u0OtViMjI8NgekZGBry8vIwu4+XlVWL5+/fvY9asWVi/fj369esHAGjdujVSUlIwf/78IpcA9LRabZmaGFoLJydg+nRgxgypO91Zs4BfflE6KiIiy2BSR/YAoFKp8P777+PUqVOYOXMmwsLC0LRpUzRt2hRhYWF44403cOrUKbz33ntQqVTlWrdGo0GHDh0QFxcnT9PpdIiLi0NoaKjRZUJDQw3KA0BsbKxcPi8vz2irALVaDZ1OV674rN2kSYC3tzT+668FT8YjIqLHJKzMqlWrhFarFStWrBAnTpwQzz//vHB1dRXp6elCCCFGjx4tZsyYIZdPTEwUtra2Yv78+eLkyZNizpw5ws7OThw7dkwuExYWJlq0aCESEhLEuXPnxPLly4W9vb344osvyhxXVlaWACCysrIqr7JmaOlSIaQr90J06yaETqd0RERUUdyvmQ6rS/ZCCLFo0SLh6+srNBqN6Nixo9i/f788LywsTMTExBiUX7NmjWjSpInQaDSiRYsWYvPmzQbz//77bzF27Fjh7e0t7O3tRdOmTcWCBQuErhyZil8KSV6eEE2bFiT8jRuVjoiIKor7NdNhFo+4tQZ8FGSBn38GhgyRxlu2BFJSpL70ici8cL9mOkzumj3R4MFAx47SeGoq8MMPysZDRGTumOzJ5KhUwLx5Ba9nzwZycpSLh4jI3DHZk0nq3h2IjJTGL14ElixRNh4iInPGZE8ma+7cgvH33gOsuEdhIqLHwmRPJqtdOyA6Whq/dg346CNl4yEiMldM9mTS3nlHeu49AMyfD5ThGUlERPQIJnsyaQ0bApMnS+MPHgDTpikbDxGROWKyJ5M3e3bBI3DXrwdiY5WNh4jI3DDZk8lzdgY++KDg9eTJQF6ecvEQEZkbJnsyC6NHA506SeOnTgGLFikbDxGROWGyJ7NgYyMleP2DDt96C0hPVzQkIiKzwWRPZiMoCBg/Xhq/fRuYMUPZeIiIzAWTPZmV998HXF2l8W++AfbvVzQcIiKzwGRPZqVOHeDf/y54PWkSoNMpFw8RkTlgsiez89JLQKtW0vihQ8DSpcrGQ0Rk6pjsyezY2gKffVbw+vXXgb/+Ui4eIiJTx2RPZik8HBg3ThrPzgZefhkQQtGQiIhMFpM9ma0FCwAvL2l840ZgzRpl4yEiMlVM9mS2atUCPv+84PWkSdLT8YiIyBCTPZm1qChg8GBpPDMTeOUVZeMhIjJFTPZk9j7/vKDt/fffA1u3KhoOEZHJYbIns1e3rnT9Xu+FF6Qe9oiISMJkTxZh3DigZ09pPC0NmDlT2XiIiEwJkz1ZBJVK6lzH0VF6vXgxEB+vbExERKaCyZ4sRoMGwHvvFbweMwa4fl25eIiITAWTPVmUyZOBHj2k8cuXpev37GyHiKwdkz1ZFBsb4Ntvgdq1pdc//wwsX65sTERESmOyJ4tTrx7w3/8WvJ48GTh7Vrl4iIiUxmRPFunpp4F//EMav3sXGDECyMtTNiYiIqUw2ZPF+uQToHFjafzQIeCttxQNh4hIMUz2ZLGcnICVK6VH4gLA3LnA7t3KxkREpAQme7JoQUHAO+9I40IAI0dKfegTEVkTJnuyeNOnA+Hh0vhffwHDhwMPHyoaEhFRtWKyJ4unVkun8728pNfx8cC//qVsTERE1YnJnqxC3brA2rUF1+8/+ABYt07ZmIiIqguTPVmNrl2B+fMLXo8dC5w+rVg4RETVhsmerMrkydI1e0B6DO7gwcCdO8rGRERU1ZjsyaqoVMBXXwEtWkivT5wAxo9n//lEZNmsMtkvXrwY/v7+sLe3R0hICA4cOFBi+bVr16JZs2awt7dHq1atsGXLliJlTp48iQEDBsDFxQU1atRAcHAwLl26VFVVoMfg5CRdr3d2ll6vWQMsWKBsTEREVcnqkv3q1asxbdo0zJkzB4cPH0abNm0QGRmJq1evGi2flJSE6OhojB8/HkeOHMGgQYMwaNAgpKamymX+/PNPdO3aFc2aNcPOnTtx9OhRvPnmm7C3t6+ualE5NWkiPTBH77XXgPXrlYuHiKgqqYSwrhOYISEhCA4Oxueffw4A0Ol08PHxwaRJkzBjxowi5YcNG4a7d+9i06ZN8rROnTqhbdu2+PLLLwEAw4cPh52dHb777rsKx5WdnQ0XFxdkZWXBWX/ISVXurbeAt9+Wxh0cgF27gOBgRUMishjcr5kOqzqyz83NRXJyMiIiIuRpNjY2iIiIwL59+4wus2/fPoPyABAZGSmX1+l02Lx5M5o0aYLIyEh4eHggJCQEv/zyS4mx5OTkIDs722Cg6jdnDjBqlDR+/z7Qvz9w8aKyMRERVTarSvbXrl1Dfn4+PD09DaZ7enoiPT3d6DLp6ekllr969Sru3LmDefPmoU+fPvjf//6Hp59+GoMHD8auXbuKjWXu3LlwcXGRBx8fn8esHVWESiU9DrdbN+l1RgbQrx+QlaVsXERElcmqkn1V0Ol0AICBAwfilVdeQdu2bTFjxgw89dRT8ml+Y2bOnImsrCx5SEtLq66Q6RFarXS9Xv+EvOPHgSFD+EhcIrIcVpXs3d3doVarkZGRYTA9IyMDXvq+VB/h5eVVYnl3d3fY2toiMDDQoEzz5s1LvBtfq9XC2dnZYCDluLkBW7ZIfwFgxw7gpZfYJI+ILINVJXuNRoMOHTogLi5OnqbT6RAXF4fQ0FCjy4SGhhqUB4DY2Fi5vEajQXBwME4/0hXbmTNn4OfnV8k1oKrUqBHw66+ARiO9/vrrgpv3iIjMmrAyq1atElqtVqxYsUKcOHFCPP/888LV1VWkp6cLIYQYPXq0mDFjhlw+MTFR2Nraivnz54uTJ0+KOXPmCDs7O3Hs2DG5zLp164SdnZ1YunSpOHv2rFi0aJFQq9Viz549ZY4rKytLABBZWVmVV1mqkB9/FEI6ppeGBQuUjojIPHG/ZjqsLtkLIcSiRYuEr6+v0Gg0omPHjmL//v3yvLCwMBETE2NQfs2aNaJJkyZCo9GIFi1aiM2bNxdZ59dffy0aNWok7O3tRZs2bcQvv/xSrpj4pTAtn3ximPCXLlU6IiLzw/2a6bC6dvamiu1RTc+//y01zQOku/ZXrizoV5+ISsf9mumwqmv2ROXx5pvAq69K40IAo0cDGzcqGxMRUUUw2RMVQ6UCPvoIeO456fXDh8DQoUB8vLJxERGVF5M9UQlUKmDJkoLT9zk5wIABwM6dioZFRFQuTPZEpVCrpYfm9O8vvb57F3jySWD7dmXjIiIqKyZ7ojKws5Mehduvn/T6wQPpCH/DBmXjIiIqCyZ7ojKytwfWrQOioqTXubnS+Nq1ysZFRFQaJnuictBogFWrgBEjpNcPH0rX8x/j6cZERFWOyZ6onGxtpWv448dLr3U6ICYGKOG5R0REimKyJ6oAtRpYuhSYOFF6LYT04Jw33+TDc4jI9DDZE1WQjQ3w2WfAa68VTHv3XekoPzdXubiIiB7FZE/0GFQq4IMPgIULpXFAun7fty+QlaVoaEREMiZ7okowZYp0V769vfQ6Lg7o2hVIS1M2LiIigMmeqNJERUlJ3s1Nep2aCoSGAikpioZFRMRkT1SZOncGkpKABg2k15cvS9NWrVI2LiKybkz2RJWsSRNg3z4gJER6ff8+EB0NTJ8utcsnIqpuTPZEVcDDQ3pYztixBdPmzwf69AGuX1cqKiKyVkz2RFXE3h5YtgxYvFjqiAeQrukHBfE6PhFVLyZ7oiqkUgEvvwzEx0tH+wBw4YJ0Hf/rr9kBDxFVDyZ7omrQrRuQnAx07Ci9vn8f+Mc/pGv5bI9PRFWNyZ6omtSvD+zaBbzwQsG01auBtm2B/fsVC4uIrACTPVE1sreXHpizdi3g6ipNu3BB6oBn7lwgP1/J6IjIUjHZEylgyBDpJr0uXaTX+fnArFlAr17AxYuKhkZEFojJnkghfn5S87w33yzoVz8hAWjZUjr65817RFRZmOyJFGRrC/z739Ld+vXrS9Pu3JEelxsRIZ3iJyJ6XEz2RCYgPFzqS/+55wqmxcdLR/lLlgA6nWKhEZEFYLInMhEuLsDSpcD27YCPjzTt7l2pnX737tKPASKiimCyJzIxvXtLib1wE73du4F27YB//hO4fVu52IjIPDHZE5kgZ2fpJr3YWKBhQ2naw4fAggVA8+bAmjW8gY+Iyo7JnsiERURIR/lvvy210Qekx+YOGwZERgInTyobHxGZByZ7IhNnbw/Mng0cPw7061cwPTYWaNUKePFFICNDufiIyPQx2ROZiQYNgI0bgV9+kdroA1JnPP/5D9CoEfDOO9INfUREj2KyJzIjKhUwcCBw4gTw/vtAzZrS9Dt3pKP/Jk2kp+k9fKhsnERkWpjsicyQoyMwcybwxx9S0zy1Wpp+5Yr0NL3AQOC779jXPhFJmOyJzJiHB7B4sXQT38CBBdPPngXGjJGS/sqVTPpE1o7JnsgCNGsmXcvfvVvqjU/vzBlg5EjpRr4ff+TpfSJrxWRPZEG6dZMeppOQADzxRMH0kyeBESOAxo2Bzz/njXxE1obJnsgChYdLT9SLiwO6di2YfuECMGmSdDf/W28BmZnKxEdE1YvJnshCqVRAjx7Sqf34eKBPn4J5169LHfX4+Unt9I8dUy5OIqp6TPZEFk6lkh6ks3UrkJICjBpVcPf+/ftSO/3WraWzAT/9BOTlKRktEVUFq0z2ixcvhr+/P+zt7RESEoIDBw6UWH7t2rVo1qwZ7O3t0apVK2zZsqXYsi+++CJUKhUWLlxYyVETPb42baQmeX/+CUydCjg5FczbtQsYOhQICADefVdqxkdElsHqkv3q1asxbdo0zJkzB4cPH0abNm0QGRmJq1evGi2flJSE6OhojB8/HkeOHMGgQYMwaNAgpBp53uj69euxf/9+eHt7V3U1iB6Lnx/wySdSP/uLFgFNmxbMu3wZePNN6TG7/fsD69fzaJ/I3KmEsK5nZ4WEhCA4OBiff/45AECn08HHxweTJk3CjBkzipQfNmwY7t69i02bNsnTOnXqhLZt2+LLL7+Up12+fBkhISHYvn07+vXrh6lTp2Lq1KnFxpGTk4OcnBz5dXZ2Nnx8fJCVlQVnZ+dKqClR2Qkh3cy3eDGwYQOg0xnO9/AARo8Gnn1WartPVBbZ2dlwcXHhfs0EWNWRfW5uLpKTkxERESFPs7GxQUREBPbt22d0mX379hmUB4DIyEiD8jqdDqNHj8b06dPRokWLMsUyd+5cuLi4yIOPj08FakRUOVQq6Ql769cD585JXe8W3iSvXpUer9uiBdC+PTB/PvDXX8rFS0TlY1XJ/tq1a8jPz4enp6fBdE9PT6SnpxtdJj09vdTyH3zwAWxtbTF58uQyxzJz5kxkZWXJQ1paWjlqQlR1/PykO/XPnwe2bweeeQbQaArmHzkCTJ8O+PpKN/599RVw44Zy8RJR6awq2VeF5ORkfPrpp1ixYgVUKlWZl9NqtXB2djYYiEyJWg307g2sXi3drPfpp0BwcMF8IaS2/M8/D3h6SmX/8x8+bpfIFFlVsnd3d4darUbGI3ujjIwMeHl5GV3Gy8urxPJ79uzB1atX4evrC1tbW9ja2uLixYt49dVX4e/vXyX1IKpubm7A5MnAgQNSF7xvvy09YU/v4UMgNlZqs1+3rtR736efSp34EJHyrCrZazQadOjQAXFxcfI0nU6HuLg4hIaGGl0mNDTUoDwAxMbGyuVHjx6No0ePIiUlRR68vb0xffp0bN++veoqQ6SQxo2la/qnTgGHDgHTpkmn/vWEAPbskZr2BQQALVsCM2ZI09g3P5EybJUOoLpNmzYNMTExCAoKQseOHbFw4ULcvXsX48aNAwCMGTMG9erVw9y5cwEAU6ZMQVhYGBYsWIB+/fph1apVOHToEJYuXQoAcHNzg5ubm8F72NnZwcvLC00Lt2cisjAqFdChgzTMnw8cPgysWwf8/DNw+nRBuePHpeGDD4BataSe/Pr0AXr1ks4CEFHVs7pkP2zYMGRmZmL27NlIT09H27ZtsW3bNvkmvEuXLsHGpuCER+fOnbFy5Ur861//wqxZs9C4cWP88ssvaNmypVJVIDI5hRP/u+9KD95Zvx7YvBnYv1862geAmzelp+/9+KP0umVLKen37i2d+nd0VK4ORJbM6trZmyq2RyVLlZkpddW7aZN0d392tvFydnZASIjUbW94OBAayuRv7rhfMx1M9iaCXwqyBnl5QFKSdDNfbKx0zf/RDnz07OyAjh2lI/4uXaTkX7t29cZLj4f7NdPBZG8i+KUga3TjhvREvthYICEBOHu25PLNm0uJv0sXoFMnqUWAjVXdZmxeuF8zHUz2JoJfCiKpX/5du6T2+zt3lp78nZ2ltv8dO0pDcDDg7S3dQ0DK437NdDDZmwh+KYiKunIFSEyUTv0nJkq995XWfM/TU+rSt1076W/79oC/P38AKIH7NdPBZG8i+KUgKt29e8DBg1LyP3hQ6uTn8uXSl3NxAVq3loZWraS/LVsCNWtWfczWjPs108FkbyL4pSCqmMuXCxL/gQPS0X9Z++r395ce7hMYKA0tWkj3BTg5VWnIVoP7NdPBZG8i+KUgqhxCAGlpUic/+uH338v3lL769YGmTYsOPj7SMwOobLhfMx1M9iaCXwqiqnXzJnDsGHD0aMFw4gRw+3bZ16HRAA0aSF0GN2pUMDRoID0FsPDTAYn7NVPCZG8i+KUgqn5CSEf8J05Iw/Hj0t/Tp8v/2F4bG+mMQIMG0jMBAgKkZwboh/r1AVsr67OU+zXTwWRvIvilIDIt165JSf/UKenvmTPAH38Af/4JPHhQ/vXZ2AD16klnAHx8DAdfX2lenTqW1W8A92umw8p+ZxIRlY27uzR06WI4XaeTbgr84w+pH4Bz54Dz5wv+Xr9ufH06nXQvQVpa8e9pZyc9HKhePWnw9paGunULBm9v6YFCbEpI5cEjexPBX8BEliE7W0r8Fy9Kw4ULBeMXL0pnDB6XRiP1J+DlVfDXywvw8JBee3gUjNeqpdzZAu7XTAeP7ImIKpGzM9C2rTQYc++edJ+A/ihfP1y+XDCU9oMgN7f0swR6ajXg5iZdItAP7u4Ff93cCs5iuLlJQ40aPHNgaZjsiYiqkaOj1Kd/kybFl8nJkXoPvHIF+Pvvgr/6IT1dGjIzCx4fXJz8fODqVWkoK41GeuiQm5vh348+4sOIzBVP45sInu4iovJ6+FA6C6BP/vqk/uiQmSkN9+8/3vvduCFdFigr7tdMB4/siYjMlK1twfX6srh7tyDxX7sm3UxY+K9+/MaNgr/37knL2thI3Q6TeWKyJyKyEjVqSIO/f9mXefBASvq3bllWs0Brw2RPRETFsrcvaAJI5ou/04iIiCwckz0REZGFY7InIiKycEz2REREFo7JnoiIyMIx2RMREVk4JnsiIiILx2RPRERk4ZjsiYiILByTPRERkYVjd7kmQv/wwezsbIUjISKqHPr9GR+uqjwmexNx+/ZtAICPj4/CkRARVa7bt2/DhY/MUxSfZ28idDodrly5gpo1a0KlUpV5uezsbPj4+CAtLc1inxdtDXUErKOe1lBHwDrqWZY6CiFw+/ZteHt7w4aPzFMUj+xNhI2NDerXr1/h5Z2dnS12p6JnDXUErKOe1lBHwDrqWVodeURvGvhTi4iIyMIx2RMREVk4Jnszp9VqMWfOHGi1WqVDqTLWUEfAOuppDXUErKOe1lBHS8Ib9IiIiCwcj+yJiIgsHJM9ERGRhWOyJyIisnBM9kRERBaOyd6MLV68GP7+/rC3t0dISAgOHDigdEhlNnfuXAQHB6NmzZrw8PDAoEGDcPr0aYMyDx48wIQJE+Dm5gYnJydERUUhIyPDoMylS5fQr18/ODo6wsPDA9OnT8fDhw+rsyplNm/ePKhUKkydOlWeZil1vHz5MkaNGgU3Nzc4ODigVatWOHTokDxfCIHZs2ejbt26cHBwQEREBM6ePWuwjhs3bmDkyJFwdnaGq6srxo8fjzt37lR3VYqVn5+PN998EwEBAXBwcEDDhg3xzjvvGPT7bm713L17N/r37w9vb2+oVCr88ssvBvMrqz5Hjx5Ft27dYG9vDx8fH3z44YdVXTV6lCCztGrVKqHRaMSyZcvE8ePHxXPPPSdcXV1FRkaG0qGVSWRkpFi+fLlITU0VKSkpom/fvsLX11fcuXNHLvPiiy8KHx8fERcXJw4dOiQ6deokOnfuLM9/+PChaNmypYiIiBBHjhwRW7ZsEe7u7mLmzJlKVKlEBw4cEP7+/qJ169ZiypQp8nRLqOONGzeEn5+fGDt2rPjtt9/EuXPnxPbt28Uff/whl5k3b55wcXERv/zyi/j999/FgAEDREBAgLh//75cpk+fPqJNmzZi//79Ys+ePaJRo0YiOjpaiSoZ9d577wk3NzexadMmcf78ebF27Vrh5OQkPv30U7mMudVzy5Yt4o033hDr1q0TAMT69esN5ldGfbKysoSnp6cYOXKkSE1NFT/++KNwcHAQ//nPf6qrmiSEYLI3Ux07dhQTJkyQX+fn5wtvb28xd+5cBaOquKtXrwoAYteuXUIIIW7duiXs7OzE2rVr5TInT54UAMS+ffuEENKOysbGRqSnp8tllixZIpydnUVOTk71VqAEt2/fFo0bNxaxsbEiLCxMTvaWUsfXX39ddO3atdj5Op1OeHl5iY8++kieduvWLaHVasWPP/4ohBDixIkTAoA4ePCgXGbr1q1CpVKJy5cvV13w5dCvXz/x7LPPGkwbPHiwGDlypBDC/Ov5aLKvrPp88cUXolatWgbb6+uvvy6aNm1axTWiwnga3wzl5uYiOTkZERER8jQbGxtERERg3759CkZWcVlZWQCA2rVrAwCSk5ORl5dnUMdmzZrB19dXruO+ffvQqlUreHp6ymUiIyORnZ2N48ePV2P0JZswYQL69etnUBfAcuq4YcMGBAUFYejQofDw8EC7du3w1VdfyfPPnz+P9PR0g3q6uLggJCTEoJ6urq4ICgqSy0RERMDGxga//fZb9VWmBJ07d0ZcXBzOnDkDAPj999+xd+9ePPnkkwAsp556lVWfffv24YknnoBGo5HLREZG4vTp07h582Y11Yb4IBwzdO3aNeTn5xskAADw9PTEqVOnFIqq4nQ6HaZOnYouXbqgZcuWAID09HRoNBq4uroalPX09ER6erpcxthnoJ9nClatWoXDhw/j4MGDReZZSh3PnTuHJUuWYNq0aZg1axYOHjyIyZMnQ6PRICYmRo7TWD0K19PDw8Ngvq2tLWrXrm0y9ZwxYways7PRrFkzqNVq5Ofn47333sPIkSMBwGLqqVdZ9UlPT0dAQECRdejn1apVq0riJ0NM9qS4CRMmIDU1FXv37lU6lEqVlpaGKVOmIDY2Fvb29kqHU2V0Oh2CgoLw/vvvAwDatWuH1NRUfPnll4iJiVE4usqzZs0a/PDDD1i5ciVatGiBlJQUTJ06Fd7e3hZVT7JMPI1vhtzd3aFWq4vctZ2RkQEvLy+FoqqYiRMnYtOmTUhISDB4xK+Xlxdyc3Nx69Ytg/KF6+jl5WX0M9DPU1pycjKuXr2K9u3bw9bWFra2tti1axc+++wz2NrawtPT0+zrCAB169ZFYGCgwbTmzZvj0qVLAAriLGl79fLywtWrVw3mP3z4EDdu3DCZek6fPh0zZszA8OHD0apVK4wePRqvvPIK5s6dC8By6qlXWfUxh23YGjDZmyGNRoMOHTogLi5OnqbT6RAXF4fQ0FAFIys7IQQmTpyI9evXIz4+vshpvg4dOsDOzs6gjqdPn8alS5fkOoaGhuLYsWMGO5vY2Fg4OzsXST5K6NmzJ44dO4aUlBR5CAoKwsiRI+Vxc68jAHTp0qVIs8kzZ87Az88PABAQEAAvLy+DemZnZ+O3334zqOetW7eQnJwsl4mPj4dOp0NISEg11KJ09+7dg42N4S5TrVZDp9MBsJx66lVWfUJDQ7F7927k5eXJZWJjY9G0aVOewq9OSt8hSBWzatUqodVqxYoVK8SJEyfE888/L1xdXQ3u2jZlL730knBxcRE7d+4Uf//9tzzcu3dPLvPiiy8KX19fER8fLw4dOiRCQ0NFaGioPF/fLK13794iJSVFbNu2TdSpU8ekmqU9qvDd+EJYRh0PHDggbG1txXvvvSfOnj0rfvjhB+Ho6Ci+//57ucy8efOEq6ur+PXXX8XRo0fFwIEDjTbhateunfjtt9/E3r17RePGjU2q6V1MTIyoV6+e3PRu3bp1wt3dXbz22mtyGXOr5+3bt8WRI0fEkSNHBADx8ccfiyNHjoiLFy9WWn1u3bolPD09xejRo0VqaqpYtWqVcHR0ZNO7asZkb8YWLVokfH19hUajER07dhT79+9XOqQyA2B0WL58uVzm/v374uWXXxa1atUSjo6O4umnnxZ///23wXouXLggnnzySeHg4CDc3d3Fq6++KvLy8qq5NmX3aLK3lDpu3LhRtGzZUmi1WtGsWTOxdOlSg/k6nU68+eabwtPTU2i1WtGzZ09x+vRpgzLXr18X0dHRwsnJSTg7O4tx48aJ27dvV2c1SpSdnS2mTJkifH19hb29vWjQoIF44403DJqUmVs9ExISjH4PY2JihBCVV5/ff/9ddO3aVWi1WlGvXj0xb9686qoi/T8+4paIiMjC8Zo9ERGRhWOyJyIisnBM9kRERBaOyZ6IiMjCMdkTERFZOCZ7IiIiC8dkT0REZOGY7ImIiCwckz0RPRZ/f3/4+/srHQYRlYDJnsgEXLhwASqVqsSBCZWIKorPsycyIQ0bNsSoUaOMznN1da3eYIjIYjDZE5mQRo0a4a233lI6DCKyMDyNT2SGVCoVwsPD8ddffyE6Ohru7u5wdHREly5dsGPHDqPLXLt2DVOnTkVAQAC0Wi08PDzwzDPPIDU11Wj53NxcfPLJJwgODkbNmjXh5OSEwMBATJs2DTdv3ixS/s6dO5gyZQq8vb2h1WrRunVr/PTTT5VabyKqGD71jsgEXLhwAQEBAYiMjMS2bdtKLa9SqdC6dWvcunULderUQUREBDIzM7F69Wo8ePAAP/30EwYNGiSXz8zMRGhoKP7880+Eh4ejU6dOOH/+PH766SdotVps374dXbt2lcvfv38fvXr1QmJiIho3bow+ffpAq9Xi7NmziI2NRWJiItq2bQtAukEvLy8Pfn5+uHnzJiIiInDv3j2sWrUK9+/fx7Zt29C7d+/K/siIqByY7IlMgD7Zl3TNvlOnTujTpw8AKdkDwIgRI/D999/Lr48ePYrg4GC4uLjg4sWLcHBwAAA8++yzWL58OWbOnIn3339fXueWLVvQr18/NGrUCKdPn4aNjXSy75///CcWLFiA0aNHY/ny5VCr1fIyWVlZUKvVcHJyAiAl+4sXL2LgwIFYs2YNNBoNACAuLg4RERFl/gFDRFWHyZ7IBOiTfUmmTJmChQsXApCSvVqtxp9//gk/Pz+Dcv/4xz/w9ddf46effkJUVBRyc3Ph4uKCGjVq4NKlS3B0dDQo37t3b8TGxmL37t3o1q0bHj58iNq1a8PGxgbnz59HrVq1SoxLn+zPnTtXpA7+/v64ffs2rl+/XsZPgoiqAq/ZE5mQyMhICCGMDvpEr+fr61sk0QNAt27dAABHjhwBAJw6dQoPHjxAx44diyR6AOjevTsAICUlRS5/+/ZtBAcHl5ro9VxdXY3+WKlfvz5u3bpVpnUQUdVhsicyU56eniVOz8rKAgBkZ2eXWL5u3boG5fTL1atXr8yxuLi4GJ1ua2sLnU5X5vUQUdVgsicyUxkZGSVO1ydgZ2fnEsunp6cblNO35798+XKlxUpEymKyJzJTly5dwsWLF4tM37NnDwCgXbt2AIBmzZrB3t4eBw8exL1794qU37lzJwDId9c3bdoUzs7OOHjwoNEmdkRkfpjsicxUfn4+Zs2ahcL32B49ehTfffcd6tSpg759+wIANBoNoqOjce3aNcydO9dgHdu2bcP27dvRqFEjdOnSBYB06v2FF15AVlYWpkyZgvz8fINlsrKycOfOnSquHRFVJt6NT2QCytL0DgBmzJgBe3v7EtvZ379/Hz///HORdvadOnXCuXPn0KNHD4SEhODChQtYu3YtNBpNkXb2Dx48QO/evbFnzx40btwYTz75JLRaLc6dO4dt27Zh7969Bu3s9XV4VHh4OHbt2gXuZogUJohIcefPnxcASh1u3rwphBACgAgLCxNpaWli2LBhonbt2sLe3l6EhoaK//3vf0bfIzMzU0yePFn4+fkJOzs74e7uLoYMGSKOHTtmtPyDBw/E/PnzRdu2bYWDg4NwcnISgYGB4tVXX5XjEEIIPz8/4efnZ3QdYWFhgrsZIuXxyJ7IDKlUKoSFhcnX24mISsJr9kRERBaOyZ6IiMjCMdkTERFZOD7PnsgM8VYbIioPHtkTERFZOCZ7IiIiC8dkT0REZOGY7ImIiCwckz0REZGFY7InIiKycEz2REREFo7JnoiIyML9H/DQjCSRqEC4AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set figure size\n",
    "plt.figure(figsize=(4, 4))\n",
    "\n",
    "plt.plot(epoch_list, cost_list, color='blue', linestyle='-', linewidth=2)\n",
    "\n",
    "#labels and title\n",
    "plt.xlabel('Epoch', fontsize=14)\n",
    "plt.ylabel('Cost', fontsize=14)\n",
    "plt.title('Cost Function over Epochs (Batch Gradient)', fontsize=16)\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n",
    "\n",
    "'''\n",
    "This method shows a steady decrease in cost over epochs. It starts with a higher cost, which gradually\n",
    "decreases but remains higher than the other methods throughout the epochs. This method takes the average \n",
    "of all gradients to update the weights, which can be slow but stable.\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "563f44ac",
   "metadata": {},
   "source": [
    "# Predict the values "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c08bffce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted Price: 491.4574974690325\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\anaconda3\\Lib\\site-packages\\sklearn\\base.py:439: UserWarning: X does not have valid feature names, but MinMaxScaler was fitted with feature names\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "def predict(area, bedrooms, w, b, sx, sy):\n",
    "    # Scale the input data\n",
    "    scaled_X = sx.transform([[area, bedrooms]])[0]\n",
    "    \n",
    "    # Predict the scaled price\n",
    "    scaled_price = np.dot(scaled_X, w) + b\n",
    "    \n",
    "    # Inverse transform to get the actual price\n",
    "    price = sy.inverse_transform([[scaled_price]])\n",
    "    \n",
    "    return price[0][0]\n",
    "\n",
    "# Example usage\n",
    "# Assume `w`, `b`, `sx`, and `sy` are already defined and fitted\n",
    "# Example inputs\n",
    "area = 1000  # Example area in square feet\n",
    "bedrooms = 8# Example number of bedrooms\n",
    "\n",
    "# Predict price\n",
    "predicted_price = predict(area, bedrooms, w, b, sx, sy)\n",
    "print(f\"Predicted Price: {predicted_price}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6774a1bb",
   "metadata": {},
   "source": [
    "# Stochastic Gradient Descent "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "bcf1856b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weights: [0.70037898 0.54822914]\n",
      "Bias: -0.18269786921195277\n",
      "Final Cost: 0.000297926440643927\n"
     ]
    }
   ],
   "source": [
    "def stochastic_gradient_batch(X, y_true, epochs, learning_rate=0.01):\n",
    "    number = X.shape[1]\n",
    "\n",
    "    # Initializing weights and bias\n",
    "    w = np.ones(shape=(number,))\n",
    "    b = 0\n",
    "\n",
    "    total_samples = X.shape[0]\n",
    "\n",
    "    cost_list = []\n",
    "    epoch_list = []\n",
    "\n",
    "    for i in range(epochs):\n",
    "        # Randomly pick a sample\n",
    "        random_index = np.random.randint(0, total_samples)\n",
    "        sample_x = X[random_index]\n",
    "        sample_y = y_true[random_index]\n",
    "        \n",
    "        # Predicted value\n",
    "        y_predicted = np.dot(sample_x, w) + b\n",
    "        \n",
    "        # Compute gradients\n",
    "        w_grad = -2 * sample_x * (sample_y - y_predicted)\n",
    "        b_grad = -2 * (sample_y - y_predicted)\n",
    "\n",
    "        # Update weights and bias\n",
    "        w -= learning_rate * w_grad\n",
    "        b -= learning_rate * b_grad\n",
    "\n",
    "        # Calculate cost\n",
    "        cost = np.square(sample_y - y_predicted)\n",
    "\n",
    "        if i % 100 == 0:  # Record cost every 100 iterations\n",
    "            cost_list.append(cost)\n",
    "            epoch_list.append(i)\n",
    "\n",
    "    return w, b, cost, cost_list, epoch_list\n",
    "\n",
    "w_sgd, b_sgd, cost_sgd, cost_list_sgd, epoch_list_sgd = stochastic_gradient_batch(scaled_X, scaled_Y.reshape(scaled_Y.shape[0]), 1000)\n",
    "print(f\"Weights: {w_sgd}\")\n",
    "print(f\"Bias: {b_sgd}\")\n",
    "print(f\"Final Cost: {cost_sgd}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d04dc4cd",
   "metadata": {},
   "source": [
    "# Graph for Cost Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d2055976",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Lk5R58803AUAceXHhwoUmf9z9+vUDAPF0laurKwAYPNC3VJcuXbB7927U1taK8zZt2tTk9I+xbr75ZoSHhyMtLa1JPRvvn/4gfL19cXBwwNChQ/Htt9+Kp1UAIXjXrVuHwYMHNzk10xJBQUHo168f1q5dK6nTwYMH8dNPPzW50C4+Ph4+Pj5Yv3491q9fj+joaMmpJn9/f9xxxx14//33xYNVY2fPnm11nY1VVFQkjt4DhPP7n3zyCfr16yf2dY0YMQI5OTmSf4aqqqrwwQcfICwsTPzve9y4cSgvL8e7777bZDumtuiqq6ubXE3dpUsXuLu7X/cUbWxsLIgIubm5kvl79uwxGAQ5OTk4d+6c5HTcSy+9hPLyckybNs1gEJqyPw0NDZg7dy6OHDmCuXPnNvmdzM3NhUKhQGxsrNHrNBcejmslunTpgnXr1mHChAno0aOH5MrxXbt2ISMjAw8//DAAoG/fvkhKSsIHH3yAiooKxMXFIScnB2vXrsWYMWPEq17Xrl2L9957D2PHjkWXLl1QWVmJDz/8EB4eHuJBy8XFBT179sT69evRvXt3+Pj4oFevXq3qT3j00UexYcMGDBs2DOPHj8eJEyfw2WefSYZVmkKpVGLlypX417/+hX79+mHKlCkICgrC0aNHcejQIfz4448AhOGJgHBVe0JCAhwcHJq9Dcq///1vZGZmYvDgwXj88cfh6OiI999/HzU1NVi6dGnLdtyA119/HcOHD0dsbCymTp0qDsf19PRscoW7k5MT7r33XqSnp6OqqsrgfZlWrFiBwYMHo3fv3pg2bRoiIiJQWlqK7Oxs/PPPP9i3b1+r6puXl4fPPvusyfwuXbpIDlDdu3fH1KlTsXfvXgQEBODjjz9GaWkpVq9eLZZZsGABvvjiCwwfPhxz586Fj48P1q5di5MnT+Krr74Sh25PnjwZn3zyCZKTk5GTk4PbbrsNVVVV2Lp1Kx5//HGMHj3a6PofO3YMQ4YMwfjx49GzZ084Ojpi48aNKC0tve4tcQYPHgxfX19s3boVd911lzj/008/xeeff46xY8ciKioKKpUKR44cwccffwxnZ2fJ7UkeeOABHDx4EKmpqcjJycHEiRMRHh6OqqoqHDx4EF988QXc3d2bdMJrNBrx+15dXS1eOX7ixAlMnDgRr7zySpP6ZmZmYtCgQfD19TX6+2M2bT6Oi13TsWPHaNq0aRQWFkYqlYrc3d1p0KBBtHz5cskQzLq6Olq8eDGFh4eTk5MTderUqckFgHl5eZSYmEidO3cmtVpN/v7+NGrUKPr9998l29y1axdFRUWRSqUyywWARERvvPGGeEHfoEGD6Pfff292OO7V69IPvVy9erVk/s6dO+nuu+8WL9jr06cPLV++XFxeX19Pc+bMoY4dO5JCoTDqAsCEhARyc3MjV1dXuvPOO2nXrl2SMvphrVcPadbX/eeff77m94GIaOvWrTRo0CBycXEhDw8P+te//iW5ALCxzMxMAkAKhYLOnDljsMyJEydo8uTJFBgYSE5OThQSEkKjRo2iDRs2XLfezbnecNzGw6sbXwDYp08fUqvVFBkZafB3Qn8BoJeXFzk7O1N0dLTBCwCrq6vp+eefF3+fAwMD6b777hOHS1/rAsXGP9vy8nKaNWsWRUZGUocOHcjT05NiYmLoyy+/NOr7MHfuXOratatk3v79++npp5+mm2++mXx8fMjR0ZGCgoLo/vvvp7y8PIPr2b59O913330UFBRETk5O5OHhQQMGDKCUlBQqLi6WlI2Li5N8r93c3Khbt2704IMP0k8//WRw/RUVFaRSqej//u//jNovc1MQWVEPJGPM6oWFhaFXr17YtGmT3FUxu7/++guRkZH44YcfMGTIELmr06y0tDQsXboUJ06ckGUABPdxMMbY/0RERGDq1KlWfTfguro6vPnmm3jhhRdkGzXHfRyMMdbIypUr5a7CNTk5OeH06dOy1oFbHIwxxkzCfRyMMcZMwi0OxhhjJuHgYIwxZhLuHG8hnU6HoqIiuLu7y3KTMcYYMzciQmVlJYKDg6/5bB0OjhYqKioyy/2MGGPM2pw5cwY33HBDs8s5OFpIfzO5M2fOmOW+RowxJjetVotOnTpd92aZHBwtpD895eHhwcHBGLMr1zv9zp3jjDHGTMLBwRhjzCQcHIwxxkzCwcEYY8wkHByMMcZMYhXBsWLFCoSFhcHZ2RkxMTHIyclptuyHH36I2267Dd7e3vD29kZ8fHyT8kSEF198EUFBQXBxcUF8fHyT53OfP38ekyZNgoeHB7y8vDB16lRcvHjRIvvHGGP2RPbgWL9+PZKTk5GSkoK8vDz07dsXCQkJKCsrM1h++/btSExMxM8//4zs7Gx06tQJQ4cORWFhoVhm6dKleOedd7Bq1Srs2bMHHTp0QEJCguRZxJMmTcKhQ4eQmZmJTZs24ZdffsH06dMtvr+MMWbzZHnuYCPR0dE0a9Ys8X1DQwMFBwdTamqqUZ+vr68nd3d3Wrt2LRER6XQ6CgwMlDxisqKigtRqNX3xxRdERHT48OEmj9X84YcfSKFQUGFhocHtXL58mTQajTidOXOGAJBGozF5nxljzBppNBqjjmuytjhqa2uRm5uL+Ph4cZ5SqUR8fDyys7ONWkd1dTXq6urg4+MDADh58iRKSkok6/T09ERMTIy4zuzsbHh5eWHAgAFimfj4eCiVSuzZs8fgdlJTU+Hp6SlOfLsRxlh7JWtwlJeXo6GhAQEBAZL5AQEBKCkpMWodzz77LIKDg8Wg0H/uWussKSmBv7+/ZLmjoyN8fHya3e7ChQuh0WjE6cyZM0bVjwnq6oBdu4SvjDHbJnsfR2ssWbIE6enp2LhxI5ydnS26LbVaLd5ehG8zYrq0NGDQIOCdd+SuCWOstWQNDj8/Pzg4OKC0tFQyv7S0FIGBgdf87LJly7BkyRL89NNP6NOnjzhf/7lrrTMwMLBJ53t9fT3Onz9/3e2ylsnPl35ljNkuWYNDpVIhKioKWVlZ4jydToesrCzExsY2+7mlS5filVdewZYtWyT9FAAQHh6OwMBAyTq1Wi327NkjrjM2NhYVFRXIzc0Vy2zbtg06nQ4xMTHm2j3WiP7M3unT8taDMWYGbdRZ36z09HRSq9W0Zs0aOnz4ME2fPp28vLyopKSEiIgeeughWrBggVh+yZIlpFKpaMOGDVRcXCxOlZWVkjJeXl707bff0v79+2n06NEUHh5Oly5dEssMGzaM+vfvT3v27KGdO3dSt27dKDEx0eh6Gzv6gAnCwogA4StjzDoZe1yTPTiIiJYvX06dO3cmlUpF0dHRtHv3bnFZXFwcJSUlie9DQ0MJQJMpJSVFLKPT6WjRokUUEBBAarWahgwZQgUFBZJtnjt3jhITE8nNzY08PDxoypQpkvC5Hg4O4zU0EDk5CcHh6EhUXy93jRhjhhh7XFMQEcnW3LFhWq0Wnp6e0Gg03FF+HSUlQFDQlff//AOEhMhXH8aYYcYe12x6VBWzDVePXOZ+DsZsGwcHs7irg+Pvv+WpB2PMPDg4mMVxi4Mx+8LBwSyOg4Mx+8LBwSxOHxw33ih85eBgzLZxcDCL0wfHoEHCVw4OxmwbBwezOH1wDB4sfOXgYMy2cXAwi6qvB4qKhNf6FseFC0BlpXx1Yoy1DgcHs6jiYkCnAxwdga5dAS8vYT63OhizXRwczKL0p6lCQgClEujcWXjPwcGY7eLgYBb1zz/CV/0DEzk4GLN9HBzMovQtDg4OxuwHBwezKA4OxuwPBwezqKuDIzRU+Mr3q2LMdnFwMIviFgdj9oeDg1lUc8Hxzz9AQ4M8dWKMtQ4HB7OY2lqgtFR4rQ+OoCDAwUEIjeJi+erGGGs5Dg5mMYWFABHg7Az4+QnzHByAG24QXvPpKsZsEwcHsxj9aaobbgAUiivzuZ+DMdvGwcEspnFwNMYjqxizbRwczGKu7hjX4xYHY7aNg4NZzNW3G9Hj4GDMtnFwMIvhFgdj9omDg1kMBwdj9kn24FixYgXCwsLg7OyMmJgY5OTkNFv20KFDGDduHMLCwqBQKJCWltakjH7Z1dOsWbPEMnfccUeT5TNnzrTE7rVr1wuOigpAq23TKjHGzEDW4Fi/fj2Sk5ORkpKCvLw89O3bFwkJCSgrKzNYvrq6GhEREViyZAkCAwMNltm7dy+Ki4vFKTMzEwBw//33S8pNmzZNUm7p0qXm3bl27tIloLxceH11cLi7A97ewmtudTBme2QNjjfffBPTpk3DlClT0LNnT6xatQqurq74+OOPDZYfOHAgXn/9dUycOBFqtdpgmY4dOyIwMFCcNm3ahC5duiAuLk5SztXVVVLOw8PD7PvXnuk7xjt0uPLUv8b4dBVjtku24KitrUVubi7i4+OvVEapRHx8PLKzs822jc8++wyPPPIIFI2vQAPw+eefw8/PD7169cLChQtRXV19zXXV1NRAq9VKJta8xqeprvrWA+DgYMyWOcq14fLycjQ0NCAgIEAyPyAgAEePHjXLNr755htUVFTg4Ycflsx/4IEHEBoaiuDgYOzfvx/PPvssCgoK8PXXXze7rtTUVCxevNgs9WoPmuvf0OPgYMx2yRYcbeGjjz7C8OHDERwcLJk/ffp08XXv3r0RFBSEIUOG4MSJE+jSpYvBdS1cuBDJycnie61Wi07NHRUZBwdjdky24PDz84ODgwNK9bdP/Z/S0tJmO75N8ffff2Pr1q3XbEXoxcTEAAD+/PPPZoNDrVY326/CmmrudiN6HByM2S7Z+jhUKhWioqKQlZUlztPpdMjKykJsbGyr17969Wr4+/tj5MiR1y2bn58PAAgKCmr1dpngei0Ovl8VY7ZL1lNVycnJSEpKwoABAxAdHY20tDRUVVVhypQpAIDJkycjJCQEqampAITO7sOHD4uvCwsLkZ+fDzc3N3Tt2lVcr06nw+rVq5GUlARHR+kunjhxAuvWrcOIESPg6+uL/fv344knnsDtt9+OPn36tNGe27/mbjeip29xFBYC9fWAo12fNGXMzpDMli9fTp07dyaVSkXR0dG0e/ducVlcXBwlJSWJ70+ePEkAmkxxcXGSdf74448EgAoKCpps7/Tp03T77beTj48PqdVq6tq1Kz399NOk0WhMqrdGoyEAJn+uvfDyIgKIDh0yvLy+nsjRUShz+nTb1o0xZpixxzUFEZF8sWW7tFotPD09odFo+BqQq1y8KFzkBwhXhutfXy08HDh1Cti5Exg0qM2qxxhrhrHHNdlvOcLsj75/w9Oz+dAAuIOcMVvFwcHM7nod43ocHIzZJg4OZnbGBgePrGLMNnFwMLPjFgdj9o2Dg5kdBwdj9o2Dg5kdBwdj9o2Dg5nd9W43oqcPFo1GmBhjtoGDg5kVkfEtjsYPdNJ/hjFm/Tg4mFlpNEBVlfD6ei0OgEdWMWaLODiYWelbDr6+gKvr9ctzPwdjtoeDg5mVsaep9Dg4GLM9HBzMrDg4GLN/HBzMrDg4GLN/HBzMrDg4GLN/HBzMrEwNDv2oKv0DnRhj1o+Dg5mVqcERGAg4OQENDUBRkeXqxRgzHw4OZjZEVx4Za8w1HACgVF4py6erGLMNHBzMbMrLgcuXhdchIcZ/jvs5GLMtHBzMbPSnqQICALXa+M9xcDBmWzg4mNmY2r+hx8HBmG3h4GBmo+/fMDU49COrODgYsw0cHMxsWtvi4BsdMmYbODiY2fCpKsbaBw4OZjYtDQ59ea2WH+jEmC2QPThWrFiBsLAwODs7IyYmBjk5Oc2WPXToEMaNG4ewsDAoFAqkpaU1KfPSSy9BoVBIpsjISEmZy5cvY9asWfD19YWbmxvGjRuH0tJSc+9au9PS4HBzA3x8hNfc6mDM+skaHOvXr0dycjJSUlKQl5eHvn37IiEhAWVlZQbLV1dXIyIiAkuWLEFgYGCz673ppptQXFwsTjt37pQsf+KJJ/Ddd98hIyMDO3bsQFFREe69916z7lt7o9MJtw0BTA8OgE9XMWZTSEbR0dE0a9Ys8X1DQwMFBwdTamrqdT8bGhpKb731VpP5KSkp1Ldv32Y/V1FRQU5OTpSRkSHOO3LkCAGg7Oxso+uu0WgIAGk0GqM/Y8+KiogAIqWSqK7O9M+PHi18/r33zF41xpiRjD2uydbiqK2tRW5uLuLj48V5SqUS8fHxyM7ObtW6jx8/juDgYERERGDSpEk43ejf2NzcXNTV1Um2GxkZic6dO19zuzU1NdBqtZKJXaE/TRUUBDg6mv55HlnFmO2QLTjKy8vR0NCAgIAAyfyAgACUlJS0eL0xMTFYs2YNtmzZgpUrV+LkyZO47bbbUFlZCQAoKSmBSqWCl5eXSdtNTU2Fp6enOHVqyfkYO9bS/g09PlXFmO2QvXPc3IYPH477778fffr0QUJCAjZv3oyKigp8+eWXrVrvwoULodFoxOmM/kjJAHBwMNaetOCkgnn4+fnBwcGhyWim0tLSa3Z8m8rLywvdu3fHn3/+CQAIDAxEbW0tKioqJK2O621XrVZDbcoNmNoZDg7G2g/ZWhwqlQpRUVHIysoS5+l0OmRlZSE2NtZs27l48SJOnDiBoKAgAEBUVBScnJwk2y0oKMDp06fNut32pqW3G9HTBwc/0Ikx6ydbiwMAkpOTkZSUhAEDBiA6OhppaWmoqqrClClTAACTJ09GSEgIUlNTAQgd6ocPHxZfFxYWIj8/H25ubujatSsA4KmnnsK//vUvhIaGoqioCCkpKXBwcEBiYiIAwNPTE1OnTkVycjJ8fHzg4eGBOXPmIDY2FrfccosM3wX70NoWh/6BTnV1wgOd9EHCGLM+sgbHhAkTcPbsWbz44osoKSlBv379sGXLFrHD/PTp01AqrzSKioqK0L9/f/H9smXLsGzZMsTFxWH79u0AgH/++QeJiYk4d+4cOnbsiMGDB2P37t3o2LGj+Lm33noLSqUS48aNQ01NDRISEvDee++1zU7bqdYGh1IpfPavv4SRVRwcjFkvBRGR3JWwRVqtFp6entBoNPDw8JC7OrKqrxeev6HTCa2F/50VNNmddwLbtwOffQZMmmTWKjLGjGDscc3uRlWxtldcLISGk5PwEKeW4g5yxmwDBwdrNf1pqpAQ4ZRTS3FwMGYbODhYq+mD44YbWrceDg7GbAMHB2u11naM6/GTABmzDRwcrNXMFRyN71fFQzYYs14cHKzVzBUc+s9XVvIDnRizZhwcrNXMFRwdOgC+vsJrPl3FmPXi4GCt1trbjTTGHeSMWT8ODtYqtbWA/j6VHByMtQ8cHKxVCguFjmxnZ8DPr/Xr45FVjFk/Dg7WKo2v4VAoWr8+fhIgY9aPg4O1irk6xvX4VBVj1o+Dg7UKBwdj7Q8HB2sVc91uRE8fHEVFwrM5GGPWh4ODtYq5WxwBAYBKdeUW7Ywx68PBwVrF3MGhf6ATwKerGLNWHBysVcwdHACPrGLM2nFwsBarrgbOnRNeWyI4uMXBmHXi4GAtVlgofO3QAfDyMt96OTgYs24cHKzFGp+mMsfFf3ocHIxZNw4O1mKW6N8AODgYs3YcHKzFLBUc+vtV8QOdGLNOHBysxSwVHPr1XbzID3RizBpxcLAWM/dV43qurlfutMtDchmzPrIHx4oVKxAWFgZnZ2fExMQgJyen2bKHDh3CuHHjEBYWBoVCgbS0tCZlUlNTMXDgQLi7u8Pf3x9jxoxBQUGBpMwdd9wBhUIhmWbOnGnuXbN7lmpxANzPwZg1kzU41q9fj+TkZKSkpCAvLw99+/ZFQkICysrKDJavrq5GREQElixZgsDAQINlduzYgVmzZmH37t3IzMxEXV0dhg4diqqqKkm5adOmobi4WJyWLl1q9v2zdxwcjLVPjnJu/M0338S0adMwZcoUAMCqVavw/fff4+OPP8aCBQualB84cCAGDhwIAAaXA8CWLVsk79esWQN/f3/k5ubi9ttvF+e7uro2Gz7s+iorr/Q/cHAw1r7I1uKora1Fbm4u4uPjr1RGqUR8fDyys7PNth3N/45uPj4+kvmff/45/Pz80KtXLyxcuBDV1dXXXE9NTQ20Wq1kas/0rQ1PT8Dd3fzr5ycBMma9ZGtxlJeXo6GhAQEBAZL5AQEBOHr0qFm2odPpMH/+fAwaNAi9evUS5z/wwAMIDQ1FcHAw9u/fj2effRYFBQX4+uuvm11XamoqFi9ebJZ62QNLnqYCuMXBmDWT9VSVpc2aNQsHDx7Ezp07JfOnT58uvu7duzeCgoIwZMgQnDhxAl26dDG4roULFyI5OVl8r9Vq0clSR00b8M8/wldLBwePqmLM+sgWHH5+fnBwcEBpaalkfmlpqVn6HmbPno1Nmzbhl19+wQ3XGS8aExMDAPjzzz+bDQ61Wg21Wt3qetmLtmpx6B/o5ORkme0wxkwnWx+HSqVCVFQUsrKyxHk6nQ5ZWVmIjY1t8XqJCLNnz8bGjRuxbds2hIeHX/cz+fn5AICgoKAWb7e9sXRw+PsLD3QiunIzRcaYdZD1VFVycjKSkpIwYMAAREdHIy0tDVVVVeIoq8mTJyMkJASpqakAhA71w4cPi68LCwuRn58PNzc3dO3aFYBwemrdunX49ttv4e7ujpKSEgCAp6cnXFxccOLECaxbtw4jRoyAr68v9u/fjyeeeAK33347+vTpI8N3wTZZOjj0D3Q6cULo5wgLs8x2GGMtQDJbvnw5de7cmVQqFUVHR9Pu3bvFZXFxcZSUlCS+P3nyJAFoMsXFxYllDC0HQKtXryYiotOnT9Ptt99OPj4+pFarqWvXrvT000+TRqMxqd4ajYYAmPw5exEZSQQQZWVZbht33SVs49NPLbcNxtgVxh7XFER8G7mW0Gq18PT0hEajgYeHh9zVaVNEwhDcqiqgoADo3t0y25kyBVizBnj1VeC55yyzDcbYFcYe12S/5QizPRUVQmgA5r9PVWM8soox68TBwUym79/w9RVuSGgpfC0HY9aJg4OZzNId43ocHIxZJw4OZjI5goN74hizHhwczGRtHRwXLwr9Kowx68DBwUxm6duN6Lm4AB07Cq/5dBVj1oODg5msrVocAI+sYswacXAwk8kRHNziYMx6cHAwkxC13akqgIODMWvEwcFMUl4OXL4svA4Jsfz2ODgYsz4cHMwk+tNUAQHC3WstjZ8EyJj14eBgJmnL/g2AWxyMWSMODmYSuYKjqAiorW2bbTLGro2Dg5mkrYOjY0dAreYHOjFmTTg4mEnaOjj0D3QC+HQVY9aCg4OZpK2DA+B+DsasDQcHM0lbXsOhxyOrGLMuLQqOl19+GdXV1U3mX7p0CS+//HKrK8Wsk053pZ+BWxyMtV8tCo7Fixfj4sWLTeZXV1dj8eLFra4Us06lpUBdndDvEBTUdtvl+1UxZl1aFBxEBIVC0WT+vn374OPj0+pKMeuk798IDgYcHdtuu9ziYMy6mPTn7+3tDYVCAYVCge7du0vCo6GhARcvXsTMmTPNXklmHfTBYcnnjBty9QOdDPzPwhhrQyYFR1paGogIjzzyCBYvXgxPT09xmUqlQlhYGGJjY81eSWYd5BhR1Xh7VVXAhQsAN2oZk5dJwZGUlAQACA8Px6BBg+DYlucrmOzkCg4XF8DfHygrE1odHByMyatFfRzu7u44cuSI+P7bb7/FmDFj8Nxzz6GW7wtht+QKDoD7ORizJi0KjhkzZuDYsWMAgL/++gsTJkyAq6srMjIy8Mwzz5i1gsx6WENw8MgqxuTXouA4duwY+vXrBwDIyMhAXFwc1q1bhzVr1uCrr74yaV0rVqxAWFgYnJ2dERMTg5ycnGbLHjp0COPGjUNYWBgUCgXS0tJatM7Lly9j1qxZ8PX1hZubG8aNG4fS0lKT6t0eWUNwcIuDMfm1eDiuTqcDAGzduhUjRowAAHTq1Anl5eVGr2f9+vVITk5GSkoK8vLy0LdvXyQkJKCsrMxg+erqakRERGDJkiUIDAxs8TqfeOIJfPfdd8jIyMCOHTtQVFSEe++91+h6t0f19UBxsfCag4Oxdo5a4M4776TJkyfTJ598Qk5OTnT8+HEiItq+fTuFhoYavZ7o6GiaNWuW+L6hoYGCg4MpNTX1up8NDQ2lt956y+R1VlRUkJOTE2VkZIhljhw5QgAoOzvb6LprNBoCQBqNxujP2LLTp4kAIicnooaGtt/+hg3C9m+5pe23zVh7YexxrUUtjrS0NOTl5WH27Nl4/vnn0bVrVwDAhg0bcOuttxq1jtraWuTm5iI+Pl6cp1QqER8fj+zs7JZUy6h15ubmoq6uTlImMjISnTt3vuZ2a2pqoNVqJVN7oj9NFRIiXDne1vh+VYxZjxaNp+3Tpw8OHDjQZP7rr78OBwcHo9ZRXl6OhoYGBAQESOYHBATg6NGjLamWUessKSmBSqWCl5dXkzIlJSXNrjs1NbVd305Fzv4N4MqpquJi4YFObfHYWsaYYa26ECM3N1ccltuzZ0/cfPPNZqmUNVq4cCGSk5PF91qtFp3kOorKQO7g0D/QqaZGuNFieLg89WCMtTA4ysrKMGHCBOzYsUP8z72iogJ33nkn0tPT0bFjx+uuw8/PDw4ODk1GM5WWljbb8W2OdQYGBqK2thYVFRWSVsf1tqtWq6FWq1tUL3sg1+1G9BQKodVx/LgwJJeDgzH5tOhs9Zw5c3Dx4kUcOnQI58+fx/nz53Hw4EFotVrMnTvXqHWoVCpERUUhKytLnKfT6ZCVldXi25YYs86oqCg4OTlJyhQUFOD06dN8u5RrkLvFAfDIKsasRYtaHFu2bMHWrVvRo0cPcV7Pnj2xYsUKDB061Oj1JCcnIykpCQMGDEB0dDTS0tJQVVWFKVOmAAAmT56MkJAQpKamAhA6vw8fPiy+LiwsRH5+Ptzc3MQO+uut09PTE1OnTkVycjJ8fHzg4eGBOXPmIDY2FrfccktLvh3tAgcHY0yvRcGh0+ng5OTUZL6Tk5N4fYcxJkyYgLNnz+LFF19ESUkJ+vXrhy1btoid26dPn4ay0RCeoqIi9O/fX3y/bNkyLFu2DHFxcdi+fbtR6wSAt956C0qlEuPGjUNNTQ0SEhLw3nvvmfptaFesITh4ZBVj1kFBRGTqh0aPHo2Kigp88cUXCA4OBgAUFhZi0qRJ8Pb2xsaNG81eUWuj1Wrh6ekJjUYDDw8PuatjUTU1gLOz8LqsTOiolsPq1cAjjwAJCcCWLfLUgTF7ZuxxrUV9HO+++y60Wi3CwsLQpUsXdOnSBeHh4dBqtVi+fHmLK82sk/5xsc7OgJ+ffPXgU1WMWYcWnarq1KkT8vLysHXrVvH6iB49ekguqmP2o/GIKjkfotT4Rof8QCfG5GNSi2Pbtm3o2bMntFotFAoF7r77bsyZMwdz5szBwIEDcdNNN+HXX3+1VF2ZTP75R/gq92Ur+qHA1dXA+fPy1oWx9syk4EhLS8O0adMMnvvy9PTEjBkz8Oabb5qtcsw6WEPHOHDlgU4An65iTE4mBce+ffswbNiwZpcPHToUubm5ra4Usy7WEhwAj6xizBqYFBylpaUGh+HqOTo64uzZs62uFLMucl813hh3kDMmP5OCIyQkBAcPHmx2+f79+xEUFNTqSjHrYk0tDg4OxuRnUnCMGDECixYtwuXLl5ssu3TpElJSUjBq1CizVY5ZB2sMDn6ELGPyMWk47gsvvICvv/4a3bt3x+zZs3HjjTcCAI4ePYoVK1agoaEBzz//vEUqyuRRXQ2cOye8tqbg4BYHY/IxKTgCAgKwa9cuPPbYY1i4cCH0F50rFAokJCRgxYoVTZ6FwWybfihuhw7AVY8wkQUHB2PyM/kCwNDQUGzevBkXLlzAn3/+CSJCt27d4O3tbYn6MZk1Pk1lDRfc6UdVFRcLt0Jpx3e6Z0w2LX6Qk7e3NwYOHGjOujArZE39G4BwyxNnZ+DyZeFWKBERcteIsfZHhqdHM1tibcGhf6ATwKerGJMLBwe7Jmu53UhjPLKKMXlxcLBrsrYWB8AtDsbkxsHBromDgzF2NQ4Odk3WdLsRPb5fFWPy4uBgzaqsBDQa4TW3OBhjehwcrFn61oanJ+DuLm9dGmscHKY/+Jgx1locHKxZ1ti/AUgf6KS/HQpjrO1wcLBmWWtwODsD+jvb8OkqxtoeBwdrlrUGB8D9HIzJiYODNcuag4NHVjEmHw4O1ixrDg5ucTAmH6sIjhUrViAsLAzOzs6IiYlBTk7ONctnZGQgMjISzs7O6N27NzZv3ixZrlAoDE6vv/66WCYsLKzJ8iVLllhk/2wVBwdjzBDZg2P9+vVITk5GSkoK8vLy0LdvXyQkJKCsrMxg+V27diExMRFTp07FH3/8gTFjxmDMmDGSR9oWFxdLpo8//hgKhQLjxo2TrOvll1+WlJszZ45F99WWEFnnfar0+H5VjMlHQSTvSPiYmBgMHDgQ7777LgBAp9OhU6dOmDNnDhYsWNCk/IQJE1BVVYVNmzaJ82655Rb069cPq1atMriNMWPGoLKyEllZWeK8sLAwzJ8/H/Pnz29RvbVaLTw9PaHRaODh4dGidVizCxcAHx/hdVUV4Ooqb32ulpsLDBgABAYKz+ZgjLWescc1WVsctbW1yM3NRXx8vDhPqVQiPj4e2dnZBj+TnZ0tKQ8ACQkJzZYvLS3F999/j6lTpzZZtmTJEvj6+qJ///54/fXXUV9f32xda2pqoNVqJZM905+m8vW1vtAArrQ4SkqEBzoxxtpOix/kZA7l5eVoaGho8rjZgIAAHD161OBnSkpKDJYvKSkxWH7t2rVwd3fHvffeK5k/d+5c3HzzzfDx8cGuXbuwcOFCFBcX48033zS4ntTUVCxevNjYXbN51ty/AQgPdHJxAS5dEk6pdekid40Yaz9kDY628PHHH2PSpElwdnaWzE9OThZf9+nTByqVCjNmzEBqairUBp5HunDhQslntFotOlnrUdUMrD049A90KigQOsg5OBhrO7KeqvLz84ODgwNKS0sl80tLSxEYGGjwM4GBgUaX//XXX1FQUIBHH330unWJiYlBfX09Tp06ZXC5Wq2Gh4eHZLJn1h4cAI+sYkwusgaHSqVCVFSUpNNap9MhKysLsbGxBj8TGxsrKQ8AmZmZBst/9NFHiIqKQt++fa9bl/z8fCiVSvj7+5u4F/bJloKDR1Yx1rZkP1WVnJyMpKQkDBgwANHR0UhLS0NVVRWmTJkCAJg8eTJCQkKQmpoKAJg3bx7i4uLwxhtvYOTIkUhPT8fvv/+ODz74QLJerVaLjIwMvPHGG022mZ2djT179uDOO++Eu7s7srOz8cQTT+DBBx+Et7e35XfaBthScHCLg7G2JXtwTJgwAWfPnsWLL76IkpIS9OvXD1u2bBE7wE+fPg2l8krD6NZbb8W6devwwgsv4LnnnkO3bt3wzTffoFevXpL1pqeng4iQmJjYZJtqtRrp6el46aWXUFNTg/DwcDzxxBOSPoz2joODMdYc2a/jsFX2fB0HkTBiqaYG+OsvIDxc7hoZ9vPPwF13ATfeCDQzCI8xZgKbuI6DWaezZ4XQUCiAkBC5a9M8fqATY/Lg4GBN6G81EhAAqFTy1uVa9A90unSJH+jEWFvi4GBN6Ps39Adma6VWC7ccAbifg7G2xMHBmrCFjnE9HpLLWNvj4GBN2GJwcIuDsbbDwcGasKXg4CcBMtb2ODhYE7YUHNziYKztcXCwJjg4GGPXwsHBJBoagMJC4TUHB2PMEA4OJlFaCtTXA0olEBQkd22ur/EDnS5flrcujLUXHBxMQn+aKjgYcJT9TmbX5+sr3B4FuHLhImPMsjg4mIQt9W8Awm1ReGQVY22Lg4NJ6P9rt5XgALifg7G2xsHBJGzldiONcXAw1rY4OJiErZ2qAjg4GGtrHBxMwpaDg+9XxVjb4OBgErYcHNziYKxtcHAwUX09UFwsvLal4Gg8qoof6MSY5XFwMFFREaDTAU5OwkOcbEVIiDAs9/JloLxc7towZv84OJhIf5oqJES4ctxW8AOdGGtbNnR4YJZmi/0betzPwVjb4eBgInsIDh5ZxZjlcXAwkT0EB7c4GLM8Dg4m0t9uxJauGtfj+1Ux1nasIjhWrFiBsLAwODs7IyYmBjk5Odcsn5GRgcjISDg7O6N3797YvHmzZPnDDz8MhUIhmYYNGyYpc/78eUyaNAkeHh7w8vLC1KlTcfHiRbPvmy3hFgdjzBiyB8f69euRnJyMlJQU5OXloW/fvkhISEBZWZnB8rt27UJiYiKmTp2KP/74A2PGjMGYMWNw8OBBSblhw4ahuLhYnL744gvJ8kmTJuHQoUPIzMzEpk2b8Msvv2D69OkW20+9gweBbdssvpkW4eBgjBmFZBYdHU2zZs0S3zc0NFBwcDClpqYaLD9+/HgaOXKkZF5MTAzNmDFDfJ+UlESjR49udpuHDx8mALR3715x3g8//EAKhYIKCwuNqrdGoyEApNFojCpPRPTNN0QAUZcuRPX1Rn+sTVy+LNQNICork7s2pisvv1L/S5fkrg1jtsnY45qsLY7a2lrk5uYiPj5enKdUKhEfH4/s7GyDn8nOzpaUB4CEhIQm5bdv3w5/f3/ceOONeOyxx3Du3DnJOry8vDBgwABxXnx8PJRKJfbs2WNwuzU1NdBqtZLJVPHxgI8PcOIE8O23Jn/covSPi3V2Bvz85K1LS/j4AK6uwmt9y4kxZhmyBkd5eTkaGhoQcNVlygEBASgpKTH4mZKSkuuWHzZsGD755BNkZWXhtddew44dOzB8+HA0NDSI6/D395esw9HRET4+Ps1uNzU1FZ6enuLUqQXnczp0AB5/XHi9bJnJH7eoxrdTVyjkrUtLKBR8uoqxtiJ7H4clTJw4Effccw969+6NMWPGYNOmTdi7dy+2b9/e4nUuXLgQGo1GnM608N/a2bMBlQrIzgZ27WpxdczOlvs39HhkFWNtQ9bg8PPzg4ODA0pLSyXzS0tLEai/h8RVAgMDTSoPABEREfDz88Off/4pruPqzvf6+nqcP3++2fWo1Wp4eHhIppYICAAmTxZev/FGi1ZhEfYQHNziYKxtyBocKpUKUVFRyMrKEufpdDpkZWUhNjbW4GdiY2Ml5QEgMzOz2fIA8M8//+DcuXMICgoS11FRUYHc3FyxzLZt26DT6RATE9OaXTJKcrLwdeNG4H9ZJjsODsaY0dqos75Z6enppFarac2aNXT48GGaPn06eXl5UUlJCRERPfTQQ7RgwQKx/G+//UaOjo60bNkyOnLkCKWkpJCTkxMdOHCAiIgqKyvpqaeeouzsbDp58iRt3bqVbr75ZurWrRtdvnxZXM+wYcOof//+tGfPHtq5cyd169aNEhMTja53S0ZVNTZypDAC6PHHW/Rxsxs1SqjPqlVy16Tl1q4V9iE+Xu6aMGabjD2uyR4cRETLly+nzp07k0qloujoaNq9e7e4LC4ujpKSkiTlv/zyS+revTupVCq66aab6PvvvxeXVVdX09ChQ6ljx47k5OREoaGhNG3aNDGI9M6dO0eJiYnk5uZGHh4eNGXKFKqsrDS6zq0Njp9/Fg5yLi5EZ8+2aBVm1bevUJ9G30qbo/+edusmd00Ys03GHtcURPzom5bQarXw9PSERqNpUX8HETBwIJCbC7z8MrBokQUqaQI/P+DcOWDfPqBPH3nr0lJ//QV06SLcZv3SJdscHcaYnIw9rtnlqCpboFAATz0lvH73XeEhRHKprhZCA7DtPg79UOKaGuDsWblrw5j94uCQ0X33CR26ZWXAZ5/JVw/9zQ07dAC8vOSrR2upVMD/xj9wBzljFsTBISNHR2D+fOH1G28Ij22VQ+MRVbZ+eodHVjFmeRwcMnv0UcDTEzh6FLjqJr9txh6G4upxcDBmeRwcMnN3B2bMEF7LdRsSewwOfhIgY5bDwWEF5s4VTlvt2AHs3dv227fH4OAWB2OWw8FhBUJCgAceEF7LcRsSewoOvl8VY5bHwWElnnxS+LphA3DqVNtu256Cg1scjFkeB4eV6NMHuPtuoKEBePvttt22PQZHWZlwESBjzPw4OKyI/oLADz8ELlxom21qtcIECBfQ2Tpvb+F6FODK9SmMMfPi4LAid98N9O4NVFUBH3zQNtvUH1w9PYURXraOH+jEmOVxcFiRxrcheecdoLbW8tu0p9NUejwklzHL4uCwMhMnAsHBQFERkJ5u+e3ZY3DwyCrGLIuDw8qoVMC8ecLrZcuEu+hakj0GB5+qYsyyODis0PTpgJsbcOAAkJlp2W1xcDDGTMXBYYW8vIR7WAGWvw0JBwdjzFQcHFZq3jzAwUFocezbZ7nt2Htw8GPKGDM/Dg4rFRYG3H+/8NpStyEhss/gCAm58kCnsjK5a8OY/eHgsGL625B88YVlLma7cEF4+h9gHxf/6alUwsg0gE9XMWYJHBxWbMAA4I47gPp6YPly869f39rw8wNcXMy/fjlxPwdjlsPBYeX0rY5Vq67cGsRc9MFhT60NPQ4OxiyHg8PKjRgBREYKofHRR+Zdt/70lz31b+hxcDBmORwcVk6pvNLqSEsD6urMt2577BjX4+BgzHI4OGzAgw8C/v7CQXDDBvOttz0EB9+vijHz4+CwAc7OwJw5wmtz3obEnoOD71fFmOVYRXCsWLECYWFhcHZ2RkxMDHJycq5ZPiMjA5GRkXB2dkbv3r2xefNmcVldXR2effZZ9O7dGx06dEBwcDAmT56MoqIiyTrCwsKgUCgk05IlSyyyf+bw2GPCyKe8POHZ5OZgz8Ghb3GcPcsPdGLM3GQPjvXr1yM5ORkpKSnIy8tD3759kZCQgLJmrtzatWsXEhMTMXXqVPzxxx8YM2YMxowZg4MHDwIAqqurkZeXh0WLFiEvLw9ff/01CgoKcM899zRZ18svv4zi4mJxmqP/t94K+foCU6YIr81xGxIi++4c9/IS7vcFXAlIxpiZkMyio6Np1qxZ4vuGhgYKDg6m1NRUg+XHjx9PI0eOlMyLiYmhGTNmNLuNnJwcAkB///23OC80NJTeeuutFtdbo9EQANJoNC1eh6mOHydSKIgAokOHWreu0lJhPQoFUU2NeepnbXr2FPYxM1PumjBmG4w9rsna4qitrUVubi7i4+PFeUqlEvHx8cjOzjb4mezsbEl5AEhISGi2PABoNBooFAp4eXlJ5i9ZsgS+vr7o378/Xn/9ddTX1ze7jpqaGmi1WsnU1rp2BcaOFV6/+Wbr1qX/LzwgQLjS2h7xyCrGLEPW4CgvL0dDQwMCAgIk8wMCAlBSUmLwMyUlJSaVv3z5Mp599lkkJibCw8NDnD937lykp6fj559/xowZM/Cf//wHzzzzTLN1TU1Nhaenpzh1kun8jv4JgZ9+CjSzy0ax5/4NPR5ZxZhlyN7HYUl1dXUYP348iAgrV66ULEtOTsYdd9yBPn36YObMmXjjjTewfPly1NTUGFzXwoULodFoxOmMTCfOY2OBW28VHiu7YkXL12PPV43r8cgqxixD1uDw8/ODg4MDSktLJfNLS0sRGBho8DOBgYFGldeHxt9//43MzExJa8OQmJgY1NfX49SpUwaXq9VqeHh4SCa56C8IfO89oKqqZetoTy0ODg7GzEvW4FCpVIiKikJWVpY4T6fTISsrC7GxsQY/ExsbKykPAJmZmZLy+tA4fvw4tm7dCl9f3+vWJT8/H0qlEv7+/i3cm7YzejTQpQtw/jywZk3L1mHPI6r0ODgYs5C26atvXnp6OqnValqzZg0dPnyYpk+fTl5eXlRSUkJERA899BAtWLBALP/bb7+Ro6MjLVu2jI4cOUIpKSnk5OREBw4cICKi2tpauueee+iGG26g/Px8Ki4uFqea/w0f2rVrF7311luUn59PJ06coM8++4w6duxIkydPNrrecoyqamzFCmHEUEQEUX296Z8fPFj4fHq6+etmLU6eFPZRrSZqaJC7NoxZP2OPa7IHBxHR8uXLqXPnzqRSqSg6Opp2794tLouLi6OkpCRJ+S+//JK6d+9OKpWKbrrpJvr+++/FZSdPniQABqeff/6ZiIhyc3MpJiaGPD09ydnZmXr06EH/+c9/6PLly0bXWe7gqKoi8vUVDowbNpj++dBQ4bO//Wb2qlmN2torw5f/938IY+wajD2uKYj44ZotodVq4enpCY1GI1t/x4svAq+8AtxyC3CN0chNNDQItzGprxdO49jz6aobbgAKC4E9e4DoaLlrw5h1M/a4ZtejquzdrFmAWg3s3g3s2mX850pLhdBQKoGgIMvVzxrwyCrGzI+Dw4YFBAAPPSS8NuU2JPoRVcHBgKOj+etlTbiDnDHz4+CwccnJwtdvvgGOHzfuM+1hKK4eBwdj5sfBYeN69ABGjRJuWvjWW8Z9hoODMdYaHBx2QH8bktWrhduIXw8HB2OsNTg47MDttwMDBgCXLwNX3VnFoPZwuxE9vl8VY+bHwWEHFIorrY533xUC5FraU4tDP6qqvByorpa3LozZCw4OOzFunHCQPHtWuHPutbSH243oeXoC7u7Ca36gE2PmwcFhJxwdgfnzhddvvAHodIbL1dcDxcXC6/YQHAoF93MwZm4cHHZk6lThP+yCAuD77w2XKSoSQsXJSbgOpD3g4GDMvDg47Ii7OzBzpvC6uQsC9adrQkKEK8fbAw4OxsyrnRw62o85c4TWxC+/AHv3Nl3enjrG9XhkFWPmxcFhZ0JCgAceEF6/8UbT5e0xOPQjqw4cAM6dk7cujNkDDg47pL8NSUYGcPUDDdtjcHTtKnzNywMCA4ERI4BPPgE0GnnrxZit4uCwQ336AEOHCp3gaWnSZe0xOKKjgXfeAfr3F0aV/fADkJQkDA4YOxZYv77lj+BlrD3i4LBT+gsC/+//gAsXrsxvT1eN6ykUQt9PXh5w9CiweDEQGQnU1Ag3h5w4EfD3BxIThffXu4CSsfaOg8NOxccLLY+qKuD996/Mb48tjsZuvFF4ANbhw8C+fcBzzwEREcJV5enpQgskIAB4+GFgyxagrk7uGjNmnPPnge++A559Frj11iunrC2BnwDYQtbwBMDr+fRTYPJk4WFNp04Jd9B1dhaWlZUBHTvKWj2rQQT8/rsQHOvXC08M1PP1Be67D5gwQbgnmIODfPVkTI9IGF7+66/Azp3CdOiQtEyfPsI/R6Yw9rjGwdFCthActbXCf9OFhcCaNcDgwUJHsbOz8B+2QiF3Da2PTic8TTE9XRhcUFZ2ZVlgIDB+vHBq65Zb+PvH2o5OBxw8eCUkfv31yq2DGouMFP7OBw8GbrtN+Ps3BQeHhdlCcADA0qVC07VXL2D5cuDOO4XwMPahT+1ZfT2wfbsQIl99BVRUXFkWGiq0QiZMEDrdOUSYOV2+LLSC9S2K335rOgrQ0RG4+WYhIAYPBgYNav1ZBA4OC7OV4KioEPozLl4EHnwQ+OwzITy2bZO7ZralthbIzBRC5JtvhO+nXrduQitk4kSgZ0/ZqshsWEWFEA761sTevcLvXGNubkBs7JXWRHQ00KGDeevBwWFhthIcgNBJ1vjpgJMnA2vXylcfW3fpErB5sxAimzZJR2H16iUEyIQJV64fYexqZ85cCYmdO4XTUFcfiQMCroTE4MFA375CK8OSODgszJaC4++/gS5dgIYG4f3zzwP//re8dbIXlZXCSJb09KajsAYMEEJk/Pj2O4qNCf0TR45cCYlffzV837Tu3aX9E126tP0pUA4OC7Ol4ACE25B88YXwetUqYMYMeetjjy5cADZuFEJk27YrQQ0Ip7C8vIQbURo7ublJ3/OILstpaBD6tOrqmk4tnX/2rHD66bffpNdSAcLPsn9/af+ENdyt2qaCY8WKFXj99ddRUlKCvn37Yvny5YiOjm62fEZGBhYtWoRTp06hW7dueO211zBixAhxOREhJSUFH374ISoqKjBo0CCsXLkS3bp1E8ucP38ec+bMwXfffQelUolx48bh7bffhpubm1F1trXgyM0V/gMGhFuuN/p2MQsoKxM61NPThf8wzfFX5uJieti4uwMeHsLt9r28hMnDw7ZDiEho6ZWXCwfnxl+vfl1ZadwB39JHQVdXaf9ETIzws7I2NhMc69evx+TJk7Fq1SrExMQgLS0NGRkZKCgogL+/f5Pyu3btwu23347U1FSMGjUK69atw2uvvYa8vDz06tULAPDaa68hNTUVa9euRXh4OBYtWoQDBw7g8OHDcP7fhQzDhw9HcXEx3n//fdTV1WHKlCkYOHAg1q1bZ1S9bS04AKFzfMcOYWy3j4/ctWk/CguFMfYXLwoHsutNV5ezxEWIV4eJfjI07+r5np7CHZjNpbb2yoG+uRBoPK+8vGnHsSU4Ogr76eQkfX311NyyDh2EDuzBg4F+/cz7PbMUmwmOmJgYDBw4EO+++y4AQKfToVOnTpgzZw4WLFjQpPyECRNQVVWFTZs2ifNuueUW9OvXD6tWrQIRITg4GE8++SSe+t99NzQaDQICArBmzRpMnDgRR44cQc+ePbF3714M+N+/4Vu2bMGIESPwzz//IDg4+Lr1tsXgIOJho7aopsb4kGlu0miEkTvmeu56hw7GBY+Hh7DN5loEZ88CWm3L6uDqCvj5CUNQ/fwMv/bwMO4gf/UyR8f2+bdi7HHNwn3011ZbW4vc3FwsXLhQnKdUKhEfH4/s7GyDn8nOzkbyVdfSJyQk4JtvvgEAnDx5EiUlJYiPjxeXe3p6IiYmBtnZ2Zg4cSKys7Ph5eUlhgYAxMfHQ6lUYs+ePRg7dmyT7dbU1KCmpkZ8r23pb7uM2uMfgj1Qq4XJz6/166qtvRIi+q9XT4bm6+dVVgrrqaoSpqKi1tcJEB4qpj/gNxcGjef5+QnBweQha3CUl5ejoaEBAVf1CgUEBODo0aMGP1NSUmKwfElJibhcP+9aZa4+Debo6AgfHx+xzNVSU1OxePFiI/eMMeukUgkH4JZeKFZfL7QQrhcwjd8b0zLw8mo/T6S0B7IGhy1ZuHChpKWj1WrRicdYsnbG0VHoH+M+svZN1oz38/ODg4MDSktLJfNLS0sRGBho8DOBgYHXLK//er0yZY1vQgSgvr4e58+fb3a7arUaHh4ekokxxtojWYNDpVIhKioKWVlZ4jydToesrCzExsYa/ExsbKykPABkZmaK5cPDwxEYGCgpo9VqsWfPHrFMbGwsKioqkJubK5bZtm0bdDodYmJizLZ/jDFml0hm6enppFarac2aNXT48GGaPn06eXl5UUlJCRERPfTQQ7RgwQKx/G+//UaOjo60bNkyOnLkCKWkpJCTkxMdOHBALLNkyRLy8vKib7/9lvbv30+jR4+m8PBwunTpklhm2LBh1L9/f9qzZw/t3LmTunXrRomJiUbXW6PREADSaDRm+C4wxpj8jD2uyR4cRETLly+nzp07k0qloujoaNq9e7e4LC4ujpKSkiTlv/zyS+revTupVCq66aab6Pvvv5cs1+l0tGjRIgoICCC1Wk1DhgyhgoICSZlz585RYmIiubm5kYeHB02ZMoUqKyuNrjMHB2PM3hh7XJP9Og5bZYvXcTDG2LUYe1zjAXCMMcZMwsHBGGPMJBwcjDHGTMLBwRhjzCQcHIwxxkzCwcEYY8wkfK+qFtKPYrbFu+Qyxpgh+uPZ9a7S4OBoocr/3V+ab3TIGLM3lZWV8PT0bHY5XwDYQjqdDkVFRXB3d4fChAdd6O+qe+bMmXZ14WB73W+A97097rut7jcRobKyEsHBwVBe4z733OJoIaVSiRtuuKHFn2+vd9htr/sN8L63x323xf2+VktDjzvHGWOMmYSDgzHGmEk4ONqYWq1GSkoK1Gq13FVpU+11vwHe9/a47/a+39w5zhhjzCTc4mCMMWYSDg7GGGMm4eBgjDFmEg4OxhhjJuHgaEMrVqxAWFgYnJ2dERMTg5ycHLmr1CqpqakYOHAg3N3d4e/vjzFjxqCgoEBS5vLly5g1axZ8fX3h5uaGcePGobS0VFLm9OnTGDlyJFxdXeHv74+nn34a9fX1bbkrrbZkyRIoFArMnz9fnGfP+15YWIgHH3wQvr6+cHFxQe/evfH777+Ly4kIL774IoKCguDi4oL4+HgcP35cso7z589j0qRJ8PDwgJeXF6ZOnYqLFy+29a4YraGhAYsWLUJ4eDhcXFzQpUsXvPLKK5L7Otnjfhtkweees0bS09NJpVLRxx9/TIcOHaJp06aRl5cXlZaWyl21FktISKDVq1fTwYMHKT8/n0aMGEGdO3emixcvimVmzpxJnTp1oqysLPr999/plltuoVtvvVVcXl9fT7169aL4+Hj6448/aPPmzeTn50cLFy6UY5daJCcnh8LCwqhPnz40b948cb697vv58+cpNDSUHn74YdqzZw/99ddf9OOPP9Kff/4pllmyZAl5enrSN998Q/v27aN77rmHwsPD6dKlS2KZYcOGUd++fWn37t3066+/UteuXSkxMVGOXTLKq6++Sr6+vrRp0yY6efIkZWRkkJubG7399ttiGXvcb0M4ONpIdHQ0zZo1S3zf0NBAwcHBlJqaKmOtzKusrIwA0I4dO4iIqKKigpycnCgjI0Msc+TIEQJA2dnZRES0efNmUiqVVFJSIpZZuXIleXh4UE1NTdvuQAtUVlZSt27dKDMzk+Li4sTgsOd9f/bZZ2nw4MHNLtfpdBQYGEivv/66OK+iooLUajV98cUXRER0+PBhAkB79+4Vy/zwww+kUCiosLDQcpVvhZEjR9IjjzwimXfvvffSpEmTiMh+99sQPlXVBmpra5Gbm4v4+HhxnlKpRHx8PLKzs2WsmXlpNBoAgI+PDwAgNzcXdXV1kv2OjIxE586dxf3Ozs5G7969ERAQIJZJSEiAVqvFoUOH2rD2LTNr1iyMHDlSso+Afe/7f//7XwwYMAD3338//P390b9/f3z44Yfi8pMnT6KkpESy756enoiJiZHsu5eXFwYMGCCWiY+Ph1KpxJ49e9puZ0xw6623IisrC8eOHQMA7Nu3Dzt37sTw4cMB2O9+G8I3OWwD5eXlaGhokBwgACAgIABHjx6VqVbmpdPpMH/+fAwaNAi9evUCAJSUlEClUsHLy0tSNiAgACUlJWIZQ98X/TJrlp6ejry8POzdu7fJMnve97/++gsrV65EcnIynnvuOezduxdz586FSqVCUlKSWHdD+9Z43/39/SXLHR0d4ePjY7X7vmDBAmi1WkRGRsLBwQENDQ149dVXMWnSJACw2/02hIODmcWsWbNw8OBB7Ny5U+6qtIkzZ85g3rx5yMzMhLOzs9zVaVM6nQ4DBgzAf/7zHwBA//79cfDgQaxatQpJSUky185yvvzyS3z++edYt24dbrrpJuTn52P+/PkIDg626/02hE9VtQE/Pz84ODg0GVFTWlqKwMBAmWplPrNnz8amTZvw888/S241HxgYiNraWlRUVEjKN97vwMBAg98X/TJrlZubi7KyMtx8881wdHSEo6MjduzYgXfeeQeOjo4ICAiw230PCgpCz549JfN69OiB06dPA7hS92v9vgcGBqKsrEyyvL6+HufPn7fafX/66aexYMECTJw4Eb1798ZDDz2EJ554AqmpqQDsd78N4eBoAyqVClFRUcjKyhLn6XQ6ZGVlITY2VsaatQ4RYfbs2di4cSO2bduG8PBwyfKoqCg4OTlJ9rugoACnT58W9zs2NhYHDhyQ/DFlZmbCw8OjycHJmgwZMgQHDhxAfn6+OA0YMACTJk0SX9vrvg8aNKjJsOtjx44hNDQUABAeHo7AwEDJvmu1WuzZs0ey7xUVFcjNzRXLbNu2DTqdDjExMW2wF6arrq5u8nAjBwcH6HQ6APa73wbJ3TvfXqSnp5NaraY1a9bQ4cOHafr06eTl5SUZUWNrHnvsMfL09KTt27dTcXGxOFVXV4tlZs6cSZ07d6Zt27bR77//TrGxsRQbGysu1w9JHTp0KOXn59OWLVuoY8eOVj8k1ZDGo6qI7Hffc3JyyNHRkV599VU6fvw4ff755+Tq6kqfffaZWGbJkiXk5eVF3377Le3fv59Gjx5tcFhq//79ac+ePbRz507q1q2bVQ9LTUpKopCQEHE47tdff01+fn70zDPPiGXscb8N4eBoQ8uXL6fOnTuTSqWi6Oho2r17t9xVahUABqfVq1eLZS5dukSPP/44eXt7k6urK40dO5aKi4sl6zl16hQNHz6cXFxcyM/Pj5588kmqq6tr471pvauDw573/bvvvqNevXqRWq2myMhI+uCDDyTLdTodLVq0iAICAkitVtOQIUOooKBAUubcuXOUmJhIbm5u5OHhQVOmTKHKysq23A2TaLVamjdvHnXu3JmcnZ0pIiKCnn/+ecnQaXvcb0P4tuqMMcZMwn0cjDHGTMLBwRhjzCQcHIwxxkzCwcEYY8wkHByMMcZMwsHBGGPMJBwcjDHGTMLBwRhjzCQcHIzZKYVCgW+++UbuajA7xMHBmAU8/PDDUCgUTaZhw4bJXTXGWo2fx8GYhQwbNgyrV6+WzFOr1TLVhjHz4RYHYxaiVqsRGBgomby9vQEIp5FWrlyJ4cOHw8XFBREREdiwYYPk8wcOHMBdd90FFxcX+Pr6Yvr06bh48aKkzMcff4ybbroJarUaQUFBmD17tmR5eXk5xo4dC1dXV3Tr1g3//e9/LbvTrF3g4GBMJosWLcK4ceOwb98+TJo0CRMnTsSRI0cAAFVVVUhISIC3tzf27t2LjIwMbN26VRIMK1euxKxZszB9+nQcOHAA//3vf9G1a1fJNhYvXozx48dj//79GDFiBCZNmoTz58+36X4yOyT37XkZs0dJSUnk4OBAHTp0kEyvvvoqEQm3pJ85c6bkMzExMfTYY48REdEHH3xA3t7edPHiRXH5999/T0qlUnyGS3BwMD3//PPN1gEAvfDCC+L7ixcvEgD64YcfzLafrH3iPg7GLOTOO+/EypUrJfN8fHzE11c//TE2Nhb5+fkAgCNHjqBv377o0KGDuHzQoEHQ6XQoKCiAQqFAUVERhgwZcs069OnTR3zdoUMHeHh4NHl0KWOm4uBgzEI6dOjQ5NSRubi4uBhVzsnJSfJeoVCIjzplrKW4j4MxmezevbvJ+x49egAAevTogX379qGqqkpc/ttvv0GpVOLGG2+Eu7s7wsLCJM+3ZqytcIuDMQupqalBSUmJZJ6joyP8/PwAABkZGRgwYAAGDx6Mzz//HDk5Ofjoo48AAJMmTUJKSgqSkpLw0ksv4ezZs5gzZw4eeughBAQEAABeeuklzJw5E/7+/hg+fDgqKyvx22+/Yc6cOW27o6zd4eBgzEK2bNmCoKAgybwbb7wRR48eBSCMeEpPT8fjjz+OoKAgfPHFF+jZsycAwNXVFT/++CPmzZuHgQMHwtXVFePGjcObb74prispKQmXL1/GW2+9haeeegp+fn6477772m4HWbvFzxxnTAYKhQIbN27EmDFj5K4KYybjPg7GGGMm4eBgjDFmEu7jYEwGfIaY2TJucTDGGDMJBwdjjDGTcHAwxhgzCQcHY4wxk3BwMMYYMwkHB2OMMZNwcDDGGDMJBwdjjDGT/D+ONS7+OybJ4AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4,4))\n",
    "plt.plot(epoch_list_sgd, cost_list_sgd, 'b-')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Cost')\n",
    "plt.title('Cost Function over Epochs (SGD)')\n",
    "plt.show()\n",
    "\n",
    "'''\n",
    "This method shows a rapid initial decrease in cost but with significant fluctuations. \n",
    "The cost decreases quickly at first but varies due to the random selection of a single \n",
    "data point for each update. Over time, the cost reduces but is less stable compared to the \n",
    "other methods.\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35c46ec0",
   "metadata": {},
   "source": [
    "# Mini-batch Gradient Descent "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "02fd288f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mini-Batch Weights: [0.51656012 0.17169604]\n",
      "Mini-Batch Bias: -0.03588356114580012\n",
      "Mini-Batch Final Cost: 0.006220655697930686\n"
     ]
    }
   ],
   "source": [
    "\n",
    "\n",
    "def gradient_mini_batch(X, y_true, epochs, batch_size, learning_rate=0.01):\n",
    "    number = X.shape[1]\n",
    "    w = np.ones(shape=(number,))  # Initializing weights\n",
    "    b = 0\n",
    "    \n",
    "    total_samples = X.shape[0]\n",
    "    \n",
    "    cost_list = []\n",
    "    epoch_list = []\n",
    "    \n",
    "    for epoch in range(epochs):\n",
    "        # Shuffle the data\n",
    "        indices = np.arange(total_samples)\n",
    "        np.random.shuffle(indices)\n",
    "        X_shuffled = X[indices]\n",
    "        y_shuffled = y_true[indices]\n",
    "        \n",
    "        # Iterate over mini-batches\n",
    "        for start in range(0, total_samples, batch_size):\n",
    "            end = min(start + batch_size, total_samples)\n",
    "            X_batch = X_shuffled[start:end]\n",
    "            y_batch = y_shuffled[start:end]\n",
    "            \n",
    "            # Predictions for the mini-batch\n",
    "            y_predicted = np.dot(X_batch, w) + b\n",
    "            \n",
    "            # Compute gradients\n",
    "            w_grad = -(2 / len(y_batch)) * X_batch.T.dot(y_batch - y_predicted)\n",
    "            b_grad = -(2 / len(y_batch)) * np.sum(y_batch - y_predicted)\n",
    "            \n",
    "            # Update weights and bias\n",
    "            w -= learning_rate * w_grad\n",
    "            b -= learning_rate * b_grad\n",
    "        \n",
    "        # Compute cost for the entire dataset\n",
    "        y_predicted_final = np.dot(X, w) + b\n",
    "        cost = np.mean(np.square(y_true - y_predicted_final))\n",
    "        \n",
    "        if epoch % 10 == 0:\n",
    "            cost_list.append(cost)\n",
    "            epoch_list.append(epoch)\n",
    "    \n",
    "    return w, b, cost, cost_list, epoch_list\n",
    "\n",
    "# Example usage\n",
    "w_mb, b_mb, cost_mb, cost_list_mb, epoch_list_mb = gradient_mini_batch(scaled_X, scaled_Y.reshape(scaled_Y.shape[0],), epochs=1000, batch_size=5)\n",
    "\n",
    "print(\"Mini-Batch Weights:\", w_mb)\n",
    "print(\"Mini-Batch Bias:\", b_mb)\n",
    "print(\"Mini-Batch Final Cost:\", cost_mb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "791cab58",
   "metadata": {},
   "source": [
    "# Graph for Cost Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "1c297e0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plt.figure(figsize=(4, 4))\n",
    "plt.plot(epoch_list_mb, cost_list_mb, 'b-')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Cost')\n",
    "plt.title('Cost Function over Epochs (Mini-Batch Gradient Descent)')\n",
    "plt.show()\n",
    "\n",
    "'''\n",
    "This method also shows a rapid initial decrease in cost but with fewer fluctuations than Stochastic \n",
    "Gradient Descent. The cost reaches a lower value faster and stabilizes more quickly. This method \n",
    "balances the stability of Batch Gradient Descent and the speed of Stochastic Gradient Descent by \n",
    "updating weights using a small random subset of data.\n",
    "'''"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cc8b926",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "1262efe8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "# Plot cost function over epochs for each method\n",
    "plt.figure(figsize=(4,4))\n",
    "\n",
    "# Batch Gradient Descent\n",
    "plt.plot(epoch_list, cost_list, label='Batch Gradient Descent', color='blue')\n",
    "\n",
    "# Mini-Batch Gradient Descent\n",
    "plt.plot(epoch_list_mb, cost_list_mb, label='Mini-Batch Gradient Descent', color='green')\n",
    "\n",
    "# Stochastic Gradient Descent\n",
    "plt.plot(epoch_list_sgd, cost_list_sgd, label='Stochastic Gradient Descent', color='red')\n",
    "\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Cost')\n",
    "plt.title('Cost Function over Epochs for Different Gradient Descent Methods')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d1dc23a",
   "metadata": {},
   "source": [
    "# Calculating Metrics "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "7632edff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Batch - MSE: 0.03082305268190736, MAE: 0.11717196061532824, R2: -1.0853323559518153\n",
      "Stochastic Gradient Descent - MSE: 0.012631340325295762, MAE: 0.07549584351502758, R2: 0.14542719206914712\n",
      "Mini-Batch Gradient Descent - MSE: 0.0062206676904994, MAE: 0.043427038902897445, R2: 0.5791409843634047\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score\n",
    "\n",
    "def calculate_metrics(y_true, y_pred):\n",
    "    mse = mean_squared_error(y_true, y_pred)\n",
    "    mae = mean_absolute_error(y_true, y_pred)\n",
    "    r2 = r2_score(y_true, y_pred)\n",
    "    return mse, mae, r2\n",
    "\n",
    "# Gradient Batch\n",
    "w, b, _, _, _ = gradient_batch(scaled_X, scaled_Y.reshape(-1,), epochs=1000)\n",
    "y_pred_batch = np.dot(scaled_X, w) + b\n",
    "mse_batch, mae_batch, r2_batch = calculate_metrics(scaled_Y, y_pred_batch)\n",
    "print(f\"Gradient Batch - MSE: {mse_batch}, MAE: {mae_batch}, R2: {r2_batch}\")\n",
    "\n",
    "# Stochastic Gradient Descent\n",
    "w_sgd, b_sgd, _, _, _ = stochastic_gradient_batch(scaled_X, scaled_Y.reshape(-1,), epochs=1000)\n",
    "y_pred_sgd = np.dot(scaled_X, w_sgd) + b_sgd\n",
    "mse_sgd, mae_sgd, r2_sgd = calculate_metrics(scaled_Y, y_pred_sgd)\n",
    "print(f\"Stochastic Gradient Descent - MSE: {mse_sgd}, MAE: {mae_sgd}, R2: {r2_sgd}\")\n",
    "\n",
    "# Mini-Batch Gradient Descent\n",
    "w_mb, b_mb, _, _, _ = gradient_mini_batch(scaled_X, scaled_Y.reshape(-1,), epochs=1000, batch_size=5)\n",
    "y_pred_mb = np.dot(scaled_X, w_mb) + b_mb\n",
    "mse_mb, mae_mb, r2_mb = calculate_metrics(scaled_Y, y_pred_mb)\n",
    "print(f\"Mini-Batch Gradient Descent - MSE: {mse_mb}, MAE: {mae_mb}, R2: {r2_mb}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e9a76a3",
   "metadata": {},
   "source": [
    "# Cost Variance and Cost SD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "fa18c4ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost Variance: 0.003446224116606266\n",
      "Cost Standard Deviation: 0.058704549368905526\n"
     ]
    }
   ],
   "source": [
    "cost_variance = np.var(cost_list_sgd)\n",
    "print(f\"Cost Variance: {cost_variance}\")\n",
    "\n",
    "cost_std_dev = np.std(cost_list_sgd)\n",
    "print(f\"Cost Standard Deviation: {cost_std_dev}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f93e0bf",
   "metadata": {},
   "source": [
    "# Plotting Linear Regression Line on Mini-batch Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "8dd2541e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the linear regression line\n",
    "plt.figure(figsize=(4,4))\n",
    "\n",
    "# Scatter plot of actual data\n",
    "plt.scatter(scaled_X[:, 0], scaled_Y, color='blue', label='Actual Data')\n",
    "\n",
    "# Generate predictions for plotting\n",
    "y_pred_mb = predict(scaled_X, w_mb, b_mb)\n",
    "\n",
    "# Plot the linear regression line\n",
    "plt.plot(scaled_X[:, 0], y_pred_mb, color='red', linewidth=2, label='Mini-Batch Gradient Descent Line')\n",
    "\n",
    "plt.xlabel('Area')  # Adjust if needed for your feature\n",
    "plt.ylabel('Price')\n",
    "plt.title('Linear Regression Line with Mini-Batch Gradient Descent')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}