notebooks/graph-data-science/user_item_interaction_matrix.ipynb

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    "# Binary User-Item Interaction Matrix\n",
    "\n",
    "A **binary user-item interaction matrix** is a matrix where each row represents a user, and each column represents an item. The values in the matrix are binary ($0$ or $1$), where:\n",
    "\n",
    "- $1$ indicates that the user has interacted with the item (e.g., viewed, liked, purchased).\n",
    "- $0$ indicates no interaction with the item.\n",
    "\n",
    "Let there be $m$ users and $n$ items. The matrix $A$ is a binary user-item interaction matrix of size $m \\times n$, where:\n",
    "\n",
    "- Each row corresponds to a user.\n",
    "- Each column corresponds to an item.\n",
    "- The values in $A$ are binary ($0$ or $1$), indicating whether a user has interacted with an item.\n",
    "\n",
    "---\n",
    "\n",
    "## Example\n",
    "\n",
    "Let’s consider $3$ users and $4$ items.\n",
    "\n",
    "| User/Item | Item 1 | Item 2 | Item 3 | Item 4 |\n",
    "|-----------|--------|--------|--------|--------|\n",
    "| User 1    | 1      | 0      | 1      | 0      |\n",
    "| User 2    | 0      | 1      | 1      | 1      |\n",
    "| User 3    | 1      | 1      | 0      | 1      |\n",
    "\n",
    "In this example:\n",
    "- **User 1** interacted with **Item 1** and **Item 3**.\n",
    "- **User 2** interacted with **Item 2**, **Item 3**, and **Item 4**.\n",
    "- **User 3** interacted with **Item 1**, **Item 2**, and **Item 4**.\n",
    "\n",
    "---\n",
    "\n",
    "## Representing it with an Adjacency Matrix\n",
    "\n",
    "The binary user-item interaction matrix $A$ is similar to an **adjacency matrix** in graph theory, where:\n",
    "- **Users** can be seen as **nodes** in one set (e.g., left side).\n",
    "- **Items** can be seen as **nodes** in another set (e.g., right side).\n",
    "- **Edges** between the user nodes and item nodes are represented by a $1$ if the user interacted with that item, and $0$ if there was no interaction.\n",
    "\n",
    "The adjacency matrix would look exactly the same as the binary interaction matrix $A$:\n",
    "\n",
    "| User/Item | Item 1 | Item 2 | Item 3 | Item 4 |\n",
    "|-----------|--------|--------|--------|--------|\n",
    "| User 1    | 1      | 0      | 1      | 0      |\n",
    "| User 2    | 0      | 1      | 1      | 1      |\n",
    "| User 3    | 1      | 1      | 0      | 1      |\n",
    "\n",
    "In this case, each row of the matrix corresponds to an edge from a user to an item, showing which items are connected (interacted with) by which users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "899dbb89-472b-4ebb-9829-39d225d03f2b",
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "plt.style.use('dark_background')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0a8192dc-e4f7-45f6-9a19-442d673e458f",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([\n",
    "    [1, 0, 1, 0, 1],  # User 1\n",
    "    [0, 1, 1, 1, 0],  # User 2\n",
    "    [1, 1, 0, 1, 1],  # User 3\n",
    "    [0, 0, 1, 1, 0]   # User 4\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5d4ab691-caa8-473f-b260-4a3d4e8918da",
   "metadata": {},
   "outputs": [],
   "source": [
    "userlabels = [\"User 1\", \"User 2\", \"User 3\", \"User 4\"]\n",
    "itemlabels = [\"Item 1\", \"Item 2\", \"Item 3\", \"Item 4\", \"Item 5\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eac538e7-895e-4cc6-bc49-465f97ea15fc",
   "metadata": {},
   "outputs": [
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OnUaPHj2K/T5ZeQ54ehtRcT9jd/craoqJiTHOnj3r1GZ2drbxyiuvGLVq1Sp23w4dOhjbtm1zeS0zZswo8biF3ZKQf+tQTk6O8cwzzxT5fQ8LCzM++eQTl/2/+eYbY/jw4eZyUlKSMWLEiCJraN68uREXF+fSzp///GdLf96efA9KexvR1V3sv/zyS6NFixZF7t++fftCx3P517/+Veq6PRkTqLCpKl0XDhw4YHzyySfGsGHDjPDwcLdef5MmTYyFCxe61PPFF1+4/T0MCgoytm7d6tJGZmam8corrxgRERElttGjRw9j1qxZRnp6erE/05LGDfJ0Ku1tREFBQcaOHTtc9j1z5owxZsyYIveLiIgw3nvvPZf9DMMwHnvsMbdqLnhLyNXvwbi4OGPAgAFF7lurVi3j66+/djn2vn37yvQ+8mQqKP82ovxp06ZNTl+fMmVKse01bNjQ5Vbkli1bml8vy21Eq1atMr755hvjnnvuKfH3Uv4UHR1tvPnmmy7Xht27d7v9PZo2bZpLzWX5nhc8Z66+3hw9etQYOnRokfv6+/sXeqtZQe6OjVWvXj0jMTHRad+8vDzj5ptvLnKfunXrGidPnnQ55m233VZu5y2TT0y2F8DExFSJp4oUtgwdOtRl+9/97nelOnZISEiJ2zz44IMux5s5c6ZHxxk3bpxLGyV9CJSKHvdk/fr1RlhYWLmeAxUpbNmwYYNTexcvXiz2j4SCU2BgoMu921lZWUajRo2K3a+o8R9yc3ONYcOGlXjcgIAAl3vc8/LyzMH/fvnll2IDh/ypWbNmLuPDHDhwoFzOAyvDlnz//ve/3QpKmzVr5jKeR1pamlvvY6vDlqp2XXA3YClseu6555zqyMvLM1q1auXWvn/7299cXkdqaqrRv39/j+uoXbt2sedCRQlbpk6d6rLfmTNn3B67569//avL/hkZGUaDBg1K3LfgH875tmzZUugAwwWnoKCgQsfp6N27d6m/j55MBRUMWwq+L/fv319se88884zT9j/88IPT18sStpTlPfW73/3O5biDBg1ya19vhy1Xf289GTOluJ+jJwOR33TTTS4B2enTpwt94IHD4TC+++47l+O5888VJiYPJ9sLYGJiqsRTRQpbJk6c6LTtpUuXvDZIn7+/v8sHja+++qpUbb3zzjtO7Zw6dcoICgoqdp/CpKamuvWh2uqpooQtAwcOdKlj1KhRHrcTHh7u8oSDkgbKKyps+etf/+r2cUeMGFFoG4ZhGDfeeKPb7cyaNctl/2bNmnn9PLA6bNm8ebNH79+///3vpfq+WRm2cF1wnbZs2eJUzyuvvFLiPpGRkS69FPPy8tz+o9LTqSKELQEBAYU+DSV/QFZ3p6+++sqljZdeeqnE/Qr7w/ns2bNG48aN3T72zTff7NLGiy++WC7nWUEFw5awsDDj4sWLTtv07NmzyPYKPrVrwoQJTl8v69OIyjItXrzY6biLFi1ya7/yCFuys7ONjh07WvZz9CRsKeo1rl+/3uV3yfPPP++y3aZNmzx6UhUTkzsTA+QCqDIK3rN+7tw5y++vzjd69GjFxMSYy5cvX9akSZNK1daLL76oy5cvm8v16tVTz549PW7n9ddf18mTJ0tVQ1Xw1FNPOS1///33Wrx4scftnD9/Xm+++abTuuHDh3vcTmpqqtOYLSVZvny5MjMzXdavWLFCq1evdrudTz75xGVd586d3d6/onjqqac8ev8WHARTkrp06WJlSSXiuuBq/vz5Tst9+vQpcZ9HH33U5Xr+zjvvaOXKlZbWVpHceeedatCggdO6L7/8UsuXL/eonYkTJ7qMNfE///M/LuMauePNN9/UiRMn3N5+xYoVOn36tNO68n4PFuXChQsu48cUHJMlX//+/dW8eXNz+eLFi1q0aJFX6/PEvHnznJbdeU+Vl/nz57s1Doy3vPjii/ruu++c1vXp08dp0PmbbrpJzzzzjNM2KSkpjNMCryBsAVBlpKSkOC3XrVvX6QOTlUaMGOG0vHbtWh05cqRUbSUkJGjPnj1O6/r16+dRG5cvX9Z7771XquNXBZGRkbrxxhud1s2ePbvU7X355ZdOyzExMS6DqJZk0aJFSk9Pd3v7zMxMHThwwGX9nDlzPDpuYYMltmrVyqM27Hbw4EGtW7fOo3327t2rixcvOq0r79fNdcHVoUOHnJY7d+5c4h/+BQd1vXz5smbMmGF5bRXJoEGDXNbNmjXL43aOHj2qb7/91mldrVq1ShW4vvvuux5tf/nyZf33v/91WleRrj0F3wujRo0q9AlXBUOYjz/+WJcuXfJqbZ4o+J5q0KCBGjdubFM1zjz9fWU1wzA0ZswYl4D5T3/6k4YOHap69epp4cKFLk+rHDdunOLj48uzVPgInkYEoMrYsmWL07Kfn5/+85//aPjw4R49AcMdffv2dVreuHFjmdo7duyYOnToYC536tTJo/0PHz6sX375pUw1VGZ9+/Z1ecxjWX4mx44dc1nXqVMnjz6Mff/99x4f9/jx407ngSStX7/eozZSU1N1/vx5p6faFHxSSEVXmu+dYRj6+eef1a5dO3Nd/tOMyosvXBdCQ0N1ww036LrrrlObNm0UHR2t8PBwhYaGFvqo1YJPeKtWrZrq1q1bZF1hYWEur3PTpk2lDq0qi969ezstX7x4Ud98802p2lq8eLFuueUWl/a3bt3qdhuHDx8uVY+ogj+n8n4PFmfdunU6fPiwWrRoIUkKDw/XiBEjnHqKhIeH684773Taz9uBZVBQkPr06aMOHTqoXbt2ql27tsLDw1WjRg2XUCB/+4KaNGniUS8kb0hPT9fmzZttrUGSTp8+rbvvvlurVq0yg10/Pz/NmzdPBw8eVN26dZ22nzFjhsc9yAB3EbYAqDJ27dql7du3O/0Hr2vXrjp48KAWL16sxYsXa/Xq1YXequGJ2NhYRUdHO60bO3asbr311lK3WbDXxNWPTnRHaR4LW5UU/ENFkpYsWaIrt6Rbw9OfSWkeC1vwEc3p6ek6depUqdq5OmypSH/wuKPgf27dde7cOafl8nzdVf260LlzZ/3pT3/SbbfdVmhvAE9EREQUGbZ0797dpefLhg0bynS8iq569epq2bKl07odO3Y43UbmiW3btrms87RnS2V8D7pj7ty5+utf/2ouT5gwwSlsufvuu53O74MHD+qHH37wSi3NmzfXn//8Z40YMaLMgXhFCNR3795d6nPWat9//72mTZvmdPtQdHS0y62YGzdu1NSpU8u7PPgQwhYAVcojjzyitWvXqlq1aua6kJAQjR07VmPHjlVWVpa2bdumzZs3a8uWLfr+++9d7jEvSaNGjVzWNW7c2NJuvAX/aCuJJ6/hhRdecOmmX5K3335b//73vz3apzwV9jMp2EOkrDz9maSmpnp8jJycnDK3UVg7gYGBpWrHLmfPni3Vfna+7sp+XShKQECA3njjDT388MOF/pe9NIr7A7zgf50ludxOVdVER0e79Arav39/qduLi4tTXl6e08/L06CuMr4H3TF37ly98MIL5vemX79+at68udkjp+AtRO+//75X6nj22Wf19NNPO31WKYuKEGpZcb2x0ssvv6y+ffvq5ptvLvTrKSkpGj16NOO0wKsIWwBUKVu2bNGtt96qjz76SLVr13b5enBwsPr06eM0oNy+ffv0ySefaOHChTp48GCJx/D0D57SCAkJ8Wj78+fPu71tkyZN1LFjR4/ar1evnkfbl7eK+DMp+EdHaVjRRmVUGV93RTwHPbkuFCYgIEAff/yxhg0bVqZ2CiruD/CoqCiXdaUNHSuLyMhIl3VpaWmlbs8wDJ0/f96p3cK+r8WpjO9Bd/zyyy9auXKl0x/g48eP1zPPPKM2bdqoe/fu5vrc3Fx98MEHltcwc+ZMPfroo5a2WRFCrbJeb7zh3nvv1Z49e1S/fn2n9ZcvX9bYsWNtv/UKVR8D5AIok8L+I2DVf2oK+8PCnf9ArFq1Sq1atdLLL7+s5OTkErdv06aNnnvuOe3fv18ff/yx09NEClPYB2O7+fp/ZirizwS+pSKeg2W9Ljz11FOFBi0JCQl66623NGbMGPXo0UONGjVSzZo1FRwcLIfD4TT179/fo2NefftbvoIDH1c1BZ+8JKnMA7IW3L+wY/iqgmOw/O53v5PD4dD999/vtP7bb78t1W2cxRkzZkyhQUtKSopmz56t8ePHq0+fPmratKkiIiJUrVo1l/dUSZ9R7FIRP4c0atSo0FusMjIyytR7DHAXPVsAlElh/30rOCBiaRXWjrv/4UxNTdVf/vIXPffcc7rppps0cOBA3XDDDerYsaOCg4ML3cfPz08jRozQoEGDNGrUKK1YsaLQ7TIyMlzW3X777Vq2bJlbtcF6BX8mqampHv8nFyiLqnZdqF27tstYBjk5OfrTn/6kmTNnuv1Ybit641j1O6WiKjhWk3RlIOKyKLh/YcfwVZ9//rlSUlLM3miNGzfWLbfconvvvddpO6sHxg0ICNCrr77qsv5vf/ubXnzxRbfHk/P0PeWrwsLC9PHHHxf6/QoNDdXixYvVq1cvZWdn21AdfAU9WwCUSWHhh1UDtRXWjqfdyfPy8rRixQpNmTJFPXr0UHh4uPr06aM///nPWrNmTaFdpWvWrKklS5bo2muvLbTNM2fOuKy75pprPKrLTuPHj3f5T1lJ0wsvvGB32cUq+DOJjIysEPeww3dU9utCQbfddpvLH+xPPfWU3nzzTbeDFsnz21dSUlJc1lXEXkNWsvr3qMPhcOkhVNoxWKqi7Oxsffjhh07r3n77bdWpU8dcTk5O1hdffGHpcfv166cGDRo4rfu///s/Pf300x4N3M8/Etzz7rvvFvk5TpK6dOmif/zjH+VYEXwRYQuAMinsD4zWrVuXud2wsDA1bNjQad3ly5fL/IExOztbGzZs0CuvvKIbb7xR9erV05QpU1w+7NaoUUPTp08vtI2kpCSXddddd12Z6kLZ8DOB3araOTho0CCn5bNnz2rmzJket9OsWTOPtk9MTHRZV5m/j+44c+aMy1NcYmNjS91eq1atXAYzLux3tS+bM2eO03LBzxsLFy60fNyagu+pvLw8p6fluMvT95Qvevjhh3XXXXc5rdu7d6/LGC0TJ050edQ3YCXCFgBlUtijRa34YNyuXTuXdXv37lVWVlaZ277a2bNn9dprr6lHjx4u3ddvvfVWBQUFueyze/dul1sGihrtHuVj69atLuuGDBliQyXwVVXtulDwKUpbtmwp1R+fBR+1WpJt27a5HKewR7tXJRkZGTpw4IDTuo4dO7o8ochd3bp1c1n33//+t1RtVVW7du3Sjh07ivy61bcQSa7vqYMHD5bqCT6evqd8TceOHfX66687rbt48aJGjBih0aNHu1xf5syZQ4AFryFsAVAmO3bscBmIr2XLlmrRokWZ2r311ltd1m3YsKFMbRbn4MGDLv/pCg0NVfPmzV22zcrK0g8//OC0rkGDBrrxxhu9Vl9VVXBAvdI+WnblypUu6+666y7LHlWLqquwQR1Lc95UtetCwUcFl6ZXYXR0tAYMGODRPhcvXnQJ8Xv06FHm3ynFseocKIuNGzc6LYeFhZU6rBs5cmSJ7aPoQOXHH3/0yuPGrXhPBQQElPrpYIWd56UN9Cqq/HFaCj6o4ZFHHlFcXJw2btyoZ5991ulrNWvW1OLFiwv95xpQVlXrHQag3OXl5Wn9+vUu6++7775St+nn56e7777bZf3q1atL3aY74uLiXNYVNe7H559/7rLu+eeft7qkKq/goI2lHQjz5MmT+vHHH53WNWvWTOPGjSttafARhQ0cWtrzsCpdFwqG6AX/UHTHo48+WqrBPD/99FOnZT8/P02ePNnjdtxl5TlQWt9++63Lut///vcetxMTE+MS0iQnJxfaC9XXLVy4sNCxUrzRq0Wy5j11zz33uIz74q6KcJ5725w5c1yC2Tlz5mj+/Pnm8iuvvKKvvvrKaRvGb4G3ELYAKLPC7uP/wx/+4NJl1l1PPPGEy8CSJ06ccPkAbrX69eu7rCvq0dFz5sxxeSRk3759NWXKFK/UVlUVHCunLAOKFnbv+4wZM4odIA8obHDS0nYpr0rXhYKvo1evXqpevbrb+7dp08blaUbu+te//qVz5845rXvwwQddxrywyoULF1xuLSjv2wo+/fRT/fLLL07rfvvb33p8O+Q///lPBQYGOq3797//XSEfy2u31NRUNWzYUPXq1XOa3nnnHa8cr+B7qlWrVmratKnb+9epU0czZswo9fGtvNZVRBMnTnTp1bVnzx5NnDjRZdvf/e53jN+CckHYAqDMvvzyS+3bt89pXVhYmD755BOPR80fPHhwoQPTvvnmmyV+WHziiSc0cOBAj46XLywszKUXRFpamuLj4wvdPjMzs9A/7l9++WU9+uijpapBuvL633rrrVLvX9kU7KodERGhXr16laqtzz77TNu2bXNp7+uvv1abNm1K1WaNGjU0efJkjRkzplT7o+L76aefXNYNHTq0VG1VpetCwR6LYWFhmjZtmlv7Nm3aVMuWLXPpyu+u8+fP680333Ra5+fnp0WLFqlfv34et1e7du1ie9gYhuHyO2zw4MFyOBweH6u0cnNzC/3HxQcffOD2YLkvvPCCyy24GRkZmjVrliU1VkVnz55VUlKS0+TJ07Y8UVgv4FdeecWtfSMjI7V8+XLVrl271Mcv7Nao0l7rKprOnTu7BFEXL17UqFGjCu29lJKSorvvvpvxW+B1hC0ALPHggw+6/NLq3r27tmzZojvuuKPE/SMiIjR9+nQtW7bM5b+n27Zt0z//+c8S2+jXr59WrlypPXv2aOrUqWrVqpVbtbdp00bfffedYmJinNYvWrSo2AEh33rrLX322WdO6/z9/TVz5kwtXbrU7YGCY2JiNGXKFO3atUvffPONbrjhBrf2qwoKG0fgvffeU//+/Uv1h87dd9/t8ujY5s2ba8uWLXr66addHodaGIfDof79++tf//qX4uPj9dprr6levXoe14LKITU1Vfv373daN378eD3xxBNunS8FVZXrwpIlS1z+6JwyZYpefPHFYsczGT16tDZt2mSOd1Wwh4q7/vrXv2rTpk1O6yIjI/Xtt9/qb3/7m1uPRu7WrZveeust/fzzz06P9S1MwWtR69atNXv2bDVp0sTj2kvrH//4h8ugrbVr19batWtdnqxytZo1a+rdd9/Vc8895/K1p556yqVHBezxzTffuAzEf9ddd+ndd98tttfYoEGDtHnzZnPg49K+p3766SeXfadOnaqxY8eWOhitCMLDw7V48WIFBwc7rX/44YcLvT0834YNGwodv2XRokWM3wLLBNhdAICqYePGjXrqqadcRoBv0aKFlixZovj4eK1evVq7du1SSkqK0tPTFRkZqbp166p3797q27dvofcOp6SkaOTIkcrOzna7lnbt2unll1/Wyy+/rGPHjmnHjh3atWuXkpKSlJaWptzcXIWHh6tFixbq27evevfu7TJI3JkzZ9z6L+69996rH374QR07dnRaP3z4cA0fPlw7d+7U2rVrdejQITMEiIiIUK1atXTdddepS5cuhQ7C6yu2bt2qvXv3qm3btua6Vq1aac2aNUpPT1dCQoLS09Nd9hs6dGihf0AcOXJEo0aN0ldffeX0watGjRp66aWXNHXqVP3www/asGGDTp06pbS0NFWvXl0RERFq3LixOnfurM6dOysyMtI7LxgV0nvvvafXXnvNXA4ICNAbb7yhf/zjH0pISNC5c+dcgoe3335b//73vwttrypcFw4dOqQFCxZo7NixTuufffZZjRs3Tp988ol2796tixcvKioqSq1atdJtt93mNF7CpUuX9NRTT+ntt9/2+Pg5OTkaOXKktm7d6jRGRXBwsP785z/rscce07p167R+/XolJibq/PnzCgsLU926ddWxY0f16tXLo6Dkvffe08MPP+y0bsKECZowYYJOnz6t5ORkl/D9xx9/1IMPPujxaytKTk6O7rnnHm3dulVhYWHm+jp16ug///mPpk2bps8++0yHDx/WhQsXVLduXV1//fW67bbbCg0Gly9f7tY/KlA+0tLS9MYbb7h8tnjggQc0bNgwffzxx9q+fbtSU1MVERGhZs2a6dZbb3UKaHNzc/X4449r7ty5Hh8/NzdXCxYscOplV6NGDc2dO1ezZ8/WiRMndOHCBZfHkD/33HP64osvPD5eeXnvvfdcrpezZ8/WggULStz3lVde0Q033ODUw6dr1676xz/+oUmTJlleK3yTwcTExGTV9MgjjxhZWVmGFfbv32+0bt3a7WN/+umnlhw3NTXV6Nu3r9vHrVGjhvHxxx9bcmzDMIw9e/aUeMyCpk2bZtvPvGnTpi71rFmzxu39BwwYYOTk5Hj0PWratGmxbXbr1s04fvx4aX8ELp588slijzd27FiPayxsev/9953aOHbsWKl+JseOHXNq5/333/f6eVDY98Cd87Kw82fs2LGlqmHNmjVO7bh7HoaEhBh79uzx6Jwo6bVVhetCeHi4sW/fvlLVm5WVZQwZMsTo16+fy9f69evndg2NGjUyduzYUaoarubO+3HOnDketVnU+VXW19ylSxcjMTGxTK/3k08+MYKDg8v9mjFt2jSXWspyDro7FbRy5UqvHm/MmDEux3TnuhUQEOBynXJXXl6e8eCDD5bpmlm3bl3j5MmTHh23qLa98XumoJKuYY899pjLPrt37zaqVavm9jGjo6ON+Ph4l3buvPPOcjl3mar2xG1EACw1a9Ys9e/fX1u3bi11G1lZWXrnnXfUvXv3YruAFpSYmFjqY+Zbv369evXqVei91UW5ePGiRo4cqd///vdKSEgo0/GPHz+u999/v0xtVDZr1qzR8OHDLfn55du2bZs6d+6s9957z6NeUQVdvnxZa9as8eh8QOWTkZGhwYMHa8WKFZa1WRWuC+fPn9fAgQNdbucpyS+//KKBAwfq66+/LnMNCQkJ6t27t/7v//6v0LEX3HHu3Dm39n344Yf1v//7v14bs8Nd//3vf9WzZ89CH2lfkosXL+q5557TyJEjlZWV5YXqUBa5ubm6/fbbPe4pkpqaqlGjRundd98t0/GTkpJ04403ujy9rzLq2rWrXn31Vad1+dddT64VRY3fMnv27DIN2g9IjNkCwAs2bdqk66+/XgMGDNB//vMfnTx5ssR98vLytGvXLv3tb3/TNddco4ceeqjQxxQW5+GHH1bTpk31yCOP6OOPP3b7D5z09HR9/PHH+u1vf6sbbrjBZfwGd/373/9Ws2bN9MADD2jlypUuj3ksTF5enrZv365XX31V/fv3V0xMjMutWL5g+fLliomJ0ciRIzV79mxt2bJFp06d0sWLF126NLsrJSVF999/v1q0aKHXXntNP/30k1ttnT9/XsuXLzefinXjjTeWKTxE5XDy5EkNHjxYnTt31t/+9jd98803OnbsmFJTU4sdu6kklf26cPLkSd1www169NFHdeTIkWK3/fnnn/XMM8+odevWlgaU6enpevzxx3Xttdfq9ddf18GDB0vc59KlS/rqq6/0wAMPqEGDBkpKSipxn+zsbP3hD39QTEyM/vSnP2nJkiWKi4vTmTNnyj24OHbsmH7zm99o0KBBWrZsmS5evFjs9keOHNHrr7+uFi1aaPr06TIMo5wqhafOnz+v2267Tffcc4927dpV7LZJSUl69dVX1apVKy1ZssSS48fFxalbt2664YYb9MYbb2j16tU6ceKEzp07V2meWlWzZs1Cx2n5/e9/rwMHDnjcXmHjt0RERGjx4sWM34IycehKFxcA8KrmzZurTZs2ioqKUlRUlEJCQnTu3DnzSQA//vijy8BxVqhXr55atGihmJgYRUVFKTQ0VJcvX9aFCxd05swZ7d27V3FxcV75T2ZgYKC6dOmiRo0aqVatWoqMjFRubq557IMHD+rgwYOl/m8tPFerVi116dJFtWvXVnR0tGrUqKFLly7pwoULSkhIUFxcnI4fP253majCKvt14dprr1X37t1Vu3ZthYaG6tKlS0pISNDu3bvdCkGs0qRJE3Xo0MF8L/v7++vChQtKSkrSgQMHFBcXV6aQrKIJDAzU9ddfr8aNG5vf+5SUFCUnJ+unn37SoUOH7C4RpdS4cWP17NlTdevWVXh4uDIzM3Xy5Ent3btXu3fvtrs8AGVA2AIAAAAAAGAhbiMCAAAAAACwEGELAAAAAACAhQhbAAAAAAAALETYAgAAAAAAYCHCFgAAAAAAAAsRtgAAAAAAAFiIsAUAAAAAAMBChC0AAAAAAAAWImwBAAAAAACwEGELAAAAAACAhQhbAAAAAAAALETYAgAAAAAAYCHCFgAAAAAAAAsRtgAAAAAAAFiIsAUAAAAAAMBChC0AAAAAAAAWImwBAAAAAACwEGELAAAAAACAhQhbAAAAKqhjx47JMAynKScnRw0aNLC7NAAAUAzCFgAAgApo4MCBiomJcVkfEBCgcePGlXs9AADAfYQtAAAAFdD9999f5NcmTJhQjpUAAABPOSQZdhcBAACAX0VGRurkyZOqVq1akdsMGDBAa9euLb+iAACA2+jZAgAAUMHce++9LkHL5cuXnZaL6/kCAADsRdgCAABQwRS8TejgwYNaunSp07o77rhD4eHh5VkWAABwE2ELAABABdKlSxd17NjRad28efP0wQcfOK2rXr267rnnnnKsDAAAuIuwBQAAoAIpeHvQ5cuXNX/+fH399ddKSkoqdlsAAFAxELYAAABUENWqVdPdd9/ttO77779XfHy88vLy9OGHHzp9rWvXrrruuuvKs0QAAOAGwhYAAIAKYsSIEYqIiHBad/XtQwVvJZJ4DDQAABURj34GAACoINasWaP+/fuby5cuXVK9evV08eJFc93OnTvVoUMHczklJUUNGjRQdnZ2eZYKAACKQc8WAACACqB58+a64YYbnNZ99tlnTkGL5Nq7JTo6WsOGDfN2eQAAwAOELQAAABXAhAkT5Ofn/NGssNuGFi5cqNzcXKd1DJQLAEDFwm1EAAAANvPz81N8fLwaNmxorvvll1/UuHFjGYbrR7Xly5frlltuMZfz8vLUrFkzxcfHl0u9AACgePRsAQAAsNmQIUOcghZJWrBgQaFBi+Ta48Xf31/jxo3zVnkAAMBD9GwBAACw2dKlSzV8+HCndW3bttW+ffsK3T4oKEiJiYmKjIw01/38889q1qxZkQENAAAoP/RsAQAAsFHt2rWdbgmSpP/+979FBi2SlJ2drUWLFjmti4mJ0U033eSVGgEAgGcIWwAAAGw0duxYBQUFOa0rbGDcgubNm+eyjoFyAQCoGLiNCAAAwEb79u1TbGysuZyTk6MGDRrozJkzJe574MABtWzZ0lzOzMxUgwYNlJqa6pVaAQCAe+jZAgAAYJNevXo5BS2S9PXXX7sVtEiuvVuqVaumMWPGWFYfAAAoHcIWAAAAmxR22487txDlmz9/vi5fvlximwAAoHxxGxEAAIANQkNDlZiYqBo1apjrzp49q/r16ys7O9vtdlatWqUbb7zRaV2XLl20fft2y2oFAACeoWcLAACADUaPHu0UtEjSokWLPApapMJ7wtC7BQAAe9GzBQAAwAYbN25Uz549vdJ2amqqGjRooMzMTK+0DwAAikfPFgAAgHIWGxvrtaBFkiIjI3XHHXd4rX0AAFA8whYAAIByVh63+XArEQAA9uE2IgAAgHIUEBCgX375RXXq1DHXZWVlaf/+/WVqt3HjxoqOjjaXL1++rBYtWujYsWNlahcAAHguwO4CAAAAfMltt93mFLRI0qeffqq77767TO3+/ve/17/+9S9z2c/PT+PHj9dzzz1XpnYBAIDnuI0IAACgHBV2e8+CBQvK3O6iRYuUlZXltG7cuHFyOBxlbhsAAHiGsAUAAKCcNGjQQL/5zW+c1p0+fVrffPNNmdtOTU3V119/7bSucePGGjx4cJnbBgAAniFsAQAAKCfjx49XQIDzXdyLFi1SXl6eJe0X1kOGgXIBACh/DJALAABQTg4fPqzmzZs7rbv++uu1detWS9oPCgpSUlKSIiIizHXZ2dlq2LChzpw5Y8kxAABAyejZAgAAUA4GDBjgErQcPHjQsqBFuhKsfPzxx07rgoKCdO+991p2DAAAUDLCFgAAgHLgrYFx3WmTW4kAAChf3EYEAADgZTVr1tSpU6cUEhLitL558+Y6evSo5cf7+eef1bRpU6d1Vt6uBAAAikfPFgAAAC8bM2aMS9CyceNGrwQtkrRw4UKXdfRuAQCg/NCzBQAAAAAAwEL0bAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEIBdhcA31Kt46N2lwB4Xeq2mXaXAHhdZLeJdpcAeB3Xc/gCrufwBZk73yr3Y9KzBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFAuwuAGXXoEEDrV+/XpJkGIZatGhhc0UAAAAAAPguwpYqICAgQDExMZKuhC0AAAAAAMA+3EYEAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEIMkOtFjRs3LpfjNGrUqFyOAwAAAAAASkbY4kU///xzuT0dyDAMORyOcjkWAAAAAAAoGmGLl5VXAMIjnwEAAAAAqBgIW7yMEAQAAAAAAN9C2FIOyqN3C6EOAAAAAAAVA08j8qLExERzfv/+/fL39/fK1KxZM8ZrAQAAAACggiBs8aIff/zRDEFatmypkJAQrxyHXi0AAAAAAFQchC1etG3bNnPez89PXbp0sbEaAAAAAABQHghbvCg/bMnvedK1a1c7ywEAAAAAAOWAsMWLfvzxR6flbt262VQJAAAAAAAoL4QtXpSSkqLjx4+by/RsAQAAAACg6uPRz172448/qmnTppKk5s2bKzw8XOfPn7f0GBcvXtQHH3xgaZsAAAAAAKB0CFu87LHHHtNf//pXczkjI8PyY5w9e1YTJkywvF0AAAAAAOA5whYvS0xMVGJiot1lAAAAAACAcsKYLQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELTYZPXq0UlJSlJKSouTkZDVp0sTukgAAAAAAgAUIW2zStGlTRUREKCIiQidOnFB8fLzdJQEAAAAAAAsQttgkKytLkmQYho4ePWpzNQAAAAAAwCqELTZJTEw057Ozs22sBAAAAAAAWImwxSZX92Zp2LChjZUAAAAAAAArEbbYZOvWrTp58qQcDoe6deumkJAQu0sCAAAAAAAWIGyx0bx58yRJQUFBmjhxos3VAAAAAAAAKwTYXYAve/HFFzV8+HC1atVK06ZN06ZNm/TDDz/YXRYAVAoJCSd0IC5OyadPKz39kmrXrqP6DRqoQ8dOCgwMtLs8AICbuJ4DqIoIW2yUlZWl4cOHa/ny5WrWrJlWrFih6dOn65///KcuXrxod3moZGIaRqtr26bq3KaJurRtqo6tGym8xq+3px0/maLWt0yzsULAGiu//Ubz583Vrp07Cv16zZoRGnzzED0y6TFFRkaVc3VA2XE9h6/geo6qjuu5byNssdF9990nSXrrrbf0/PPPKywsTNOnT9fUqVO1Zs0a7dixQ6dPn9aFCxc8anf+/PneKBcVUN8u1+pPE36jzm2aKDoi1O5yAK9Kv3RJL0x7Vt98/WWx2507l6bFiz7Squ9WavrLf1fvPn3LqUKg9Liew5dwPUdVxvUc+QhbbDR37lwZhmEuG4Yhh8Oh0NBQ3XLLLbrllltK1S5hi+/o0KqhBvWKtbsMwOvy8vI0ZfIftP77dU7rI6Oi1Lp1G4WF1dCJEycUt3+feV1NSTmjJyY9on/Pfl+du3S1o2zAbVzP4Su4nqOq43qOfIQtFYDD4TB/mVwdvuR/zR35QU3B/eGbMrNy9EtSmpo3qW13KYAl3nxjhtMH84CAQE2e8meNGDlKgUFB5vojhw/rhWnPmF3Ss7Oz9YfHHtUnn32h2rXrlHvdQFlxPUdVw/Ucvorrue8hbLFZfpjibqhSUjvwPdk5udp35JS274vXf/fGa/u+4/rp8En17NBcK2Y/bnd5QJklnDihhQV67M1443814MaBLts2b9FC78yZq/+5f5z5AT0tLU1vz5qpZ6e9WC71AqXF9RxVHddz+Aqu55AIW2w1fvx4u0tAJbfgiy1695MflJWda3cpgNe8PWumcnNzzOXbht1R6AfzfNWqVdOLL/1NI4b9Vjk5V/b7bOkSjZ/woBo1buz1eoHS4HoOX8D1HL6A6znyEbbYaN68eXaXgEou7UKG3SUAXpWZmamVK791Wjfh/gdK3C8m5hoNuGmgVnzztSQpNzdXX335hf7n9494pU6grLieo6rjeg5fwfUc+fzsLgAAgKJs3PCDMjN+/dDSoWMnXdOsuVv7Dht2h9Pyqu9WWlobAMB9XM8B+BrCFgBAhbXhh++dlrt26+72vp26dFVAwK8dOOP271PKmTOW1QYAcB/XcwC+hrAFAFBhHT50yGn5ug4d3d63evXqanFtS+f2Dh8qYmsAgDdxPQfgawhbAAAV1rGjR52WmzRp6tH+jQsMoHj0yJEy1wQA8BzXcwC+hgFyK6DGjRurb9++at68uaKiohQWFiZJeuCBkgcRA4Cq4lxams6dS3NaV69+fY/aqFe/gdNyfPzPZawKAOAprucAfBFhSwUyZswYTZ48We3bt3da73A4ZBhGoWHLsGHDNGnSJEnS2bNnNXLkyHKpFQC87cKFC07L1UJCVL16dY/aiIqKclq+eOFimesCAHiG6zkAX0TYUgHUr19fH330kfr06SPpSrgiSYZhmPNFWb9+vT788EMFBwfLMAz17NlTmzZt8nrNAOBt6emXnJarBQd73EZwtWpOy5cuXSpiSwCAt3A9B+CLGLPFZvXr19fmzZvVp08fl2Alv0dLcVJSUvTpp5+ay6NGjfJKnQBQ3tLT052Wg0rx4bxasPOH84JtAgC8j+s5AF9E2GIjPz8/LV++XI0aNTLXJScna/r06brxxhs1aNCgEnu2SNJnn31mzg8cONAbpQKA7dy5HlqxDwDAu7ieA/AF3EZkowkTJqhjx45m75WlS5dq7NixZlLfpEkTt9pZuXKlpCu/hGJjYxUREaG0tDSv1AwA5aXg/fxZmZket5GZ5byPp2MEAADKjus5AF9E2GKjyZMnm/Pr16/XqFGjSrxtqDBpaWlKSEgwe8jExsZ6ddyW2rVrq3bt2qXa90JkDSWnMqAZgJJVrx7qtJyZleVxGwU/0PPhHADKH9dzAL6IsMUmMTExuvbaa83lxx9/vFRBS76DBw+aYUuLFi28GrY88sgjev7550u171/f/kov/fsrawsCUCXVCKvhtJyZkaH09HSPPmCfPXvWaTksPMyS2gAA7uN6DsAXMWaLTbp16ybpyhOHDh06pN27d5epvatvG4qMjCxTWwBQEURERCo8vKbTusRTpzxq49TJX5yWmzSJKWtZAAAPcT0H4IsIW2xSp04dc37fvn1lbu/qEdlDQ0OL2RIAKo9mzZo5LcfHH/do/4SEBOf2mjcvc00AAM9xPQfga7iNyCY1avzanfLSpUtlbi88PNzS9ooza9Ysffzxx6Xa90Ld31pcDYCqrPm1LbVz5w5zefeuneo/4Ea39k1PT9ehgwec1rVocW0RWwMAvInrOQBfQ9hik5SUFHM+KiqqzO1d/eSiq9v2huTkZCUnJ5dq32pBAyyuBkBV1rtPXy35eJG5/OO2rW7vu+O/Pyo3N9dcbh3bRtG1allaHwDAPVzPAfgabiOyyenTpyVdeVxzhw4dytRWaGio2rdvby4fP+5Zt0wAqKh69e6jatWqmcu7du7QsaNH3Nr3888/dVq+8aaBltYGAHAf13MAvoawxSZbtmwx5+vXr6/OnTuXuq17771X/v7+kqSsrCyntgGgMgsJCdHA3wx2WvfenNkl7vfzz8e0+ruV5nJAQICG3sJtjABgF67nAHwNYYtNkpKStGfPHnP5hRdeKFU7NWvW1NNPPy3DMGQYhtavX6+cnByrygQA2z38yCQFBASay8s+W6q1q1cVuX1WVpam/WWq07Vw2B13qvFVt1sCAMof13MAvoSwxUb/+te/zPkhQ4boL3/5i0f7h4SEaPHixWrUqJEcDock6c0337S0RlR8DetEqEn9KJepXq1wp+0C/P0K3a5J/ShFR/AEK1RcjRo31pj77nNa9+QfHtdHCxcoJzvbaf3RI0f0PxPGOg3CGBERod8/MrFcagXKgus5qjqu5/AVXM8hSQ5Jht1F+Cp/f38dOHBAMTExcjgcMgxDixYt0tSpUxUfH68mTZro2LFjkiTDMBQQ8Ot4xoMHD9aMGTMUGxtrrvvxxx/Vo0ePcn8dnqjW8VG7S6hy4r58QU0bRJepjfnLNut/pi2wqCKkbptpdwlVTl5enh579Pf6Yf33TuujoqMVG9tGoaGhSkg4of379skwfv21FhgYqHfmzFXnLl3Lu+QqL7Ibf/BYjet5xcP13HpczyserufW43pe8WTufKvcj8nTiGyUl5enUaNGad26dQoJCZHD4dBdd92lUaNGadu2bTp69KjT9lOmTFHLli01aNAgNWzY0AxoHA6H0tLSdPfdd9v0SgDAu/z9/fXaP/5Xz097Rt9+/ZW5/mxKijb8sL7QfaKio/XXl/7OB3MAqEC4ngPwFYQtNtu+fbtGjx6tjz76SNWrV5ck+fn5qXv37urevbu5ncPh0Msvv2zOSzKDlvPnz2vkyJFmLxgAqIqqh4bq1RlvaNCgwZr3wfvavWtnodvVrBmhwTcP0cMTH1NUVFT5FgkAKBHXcwC+gNuIKojY2FgtWrRIbdu2lSSnbpP58nuy5M9LUlxcnEaMGKH9+/eXX7FlwG1E8AV0Oy8fCQknFLdvn04nn1ZGeoZq1aql+g0aqFOnzgoMCrK7vCqPbufwBVzPywfXc3txPYcv4DYiH7Z//35dd911uvPOOzVp0iT16NFDgYGBLtvlBy7bt2/XzJkzNW/evEKDGQCo6ho1aqxGjRrbXQYAoIy4ngOoighbKpglS5ZoyZIlCgkJUY8ePdS4cWNFR0crKChIZ86cUVJSkjZt2qSUlBS7SwUAAAAAAIUgbKmgMjIytGbNGrvLAAAAAAAAHvKzuwAAAAAAAICqhLAFAAAAAADAQtxGVAlFR0crJiZGWVlZOnr0qNLT0+0uCQAAAAAA/H/0bLGZw+Ewp5J07dpV69atU2JiorZs2aKdO3fqzJkzmj9/vurUqVMO1QIAAAAAgJIQttjoiSeeUE5OjnJycpSYmFjoo57z9evXT2vXrlXv3r3l5+dnBjTBwcG6++67tWPHDsXExJRf8QAAAAAAoFCELTYaPny42aPl/fffV05OTqHbVatWTQsWLFBISIgkyTAM82uGYcjhcKhevXr6/PPP3eohAwAAAAAAvIewxSYBAQHq3r27GZwsW7asyG0feughNWjQwAxW0tPT9cUXX+jTTz/VxYsXzTbatm2rBx98sFzqBwAAAAAAhSNssUm7du0UFBQkh8OhzMxMbdq0qchtx40bZwYtJ0+eVLt27TRs2DCNGDFCrVu31qFDh8yvP/DAA+X4KgAAAAAAQEGELTZp1qyZpCu3AcXFxTndGnS1Jk2a6LrrrjO3nTZtmuLj482vJyYmatKkSebtQ507d2awXAAAAAAAbETYYpP69eub8ydOnChyu379+km68tSirKwsffjhhy7bfPfdd0pOTjaXO3bsaF2hAAAAAADAI4QtNgkNDTXnL1y4UOR2vXv3lnSlV8u6deuUmZlZ6Ha7du0y53kqEQAAAAAA9iFssYm/v3+h8wX17NnTnP/++++L3O7qni3h4eFlrA4AAAAAAJQWYYtNru7NEh0dXeg2ERERatu2rbm8YcMGt9oODAwsW3EAAAAAAKDUCFtskpSUJOnKWCzt2rUrdJubb77ZHPg2NzdX27ZtK7K9iIgIc/7SpUvWFQoAAAAAADxC2GKTPXv2mPP16tXT9ddf77LNvffeK+nKeC07duwocrwW6cpTi/LlBzkAAAAAAKD8EbbYJC4uTgkJCTIMQw6HQzNnznQaa2XEiBEaMmSI+Ujo5cuXF9lWcHCwWrdubS4fO3bMe4UDAAAAAIBiEbbYaN68eXI4HDIMQ506ddLhw4e1aNEirVmzRh9++KEZxOTl5Wn+/PlFttOrVy9zkN3Lly9r79695fUSAAAAAABAAYQtNnrllVd06tQpczk6Olp33nmn+vbta4YnhmFozpw5io+PL7Kd4cOHm9vu37+fMVsAAAAAALARYYuNLl68qCFDhig5Odns4XI1h8OhzZs3649//GORbQQGBmrkyJHmvqtXr/ZqzQAAAAAAoHiELTbbs2ePYmNj9corryguLk4ZGRnKyMjQ9u3bNXnyZA0YMKDYgXFHjx6tOnXqyOFwyOFw6KuvvirH6gEAAAAAQEEBdhcAKS0tTU8//bSefvppj/dds2aNOnXqZC4zXgsAAAAAAPYibKnkEhISlJCQYHcZAAAAAADg/+M2IgAAAAAAAAsRtgAAAAAAAFiIsAUAAAAAAMBChC0AAAAAAAAWYoBcLzpy5Igl7RiGofPnzys1NVWJiYnavHmzNmzYoO3bt1vSPgAAAAAAsA5hixfFxMTIMAw5HA5L2jMMQ5J01113SZJ++uknvfbaa1q4cKEl7QMAAAAAgLLjNqJyYBiGJVM+h8Mhh8Oh9u3b64MPPtCyZctUs2ZNG18hAAAAAADIR9jiZfnBiJWT9GuA43A4NHToUK1evVrBwcE2v1oAAAAAAMBtRF40YMAAS9rx9/dXWFiYIiIi1Lp1a3Xp0kX9+/dXQECAGbh06NBB77zzjsaOHWvJMQEAAAAAQOkQtnjR999/77W2a9WqpalTp2rSpEny8/OTw+HQmDFj9Prrr2vXrl1eOy4AAAAAACgetxFVUmfOnNGTTz6pe+65x2lMlyeffNLmygAAAAAA8G2ELZXcJ598onfeecccz+WWW26xuyQAAAAAAHwaYUsV8Oqrr5rzNWvWVPv27W2sBgAAAAAA30bYUgUcP35cR44cMZdjY2NtrAYAAAAAAN9G2FJFHDx40JyPioqysRIAAAAAAHwbYUsVkZqaas5HRETYVwgAAAAAAD6OsKWKqFatmjmfmZlpYyUAAAAAAPg2wpYqom7duub81b1cAAAAAABA+SJsqQICAgLUuXNnc/nUqVM2VgMAAAAAgG8jbKkCbr/9doWEhEiSDMPQ5s2bba4IAAAAAADfFWB3ASib0NBQTZ8+XYZhSJL27Nmj8+fP21wVAAAAAAC+i54tlVidOnW0bNkytWrVSg6HQ5I0e/Zsm6sCAAAAAMC30bOlkgkKClKnTp00cuRITZgwQeHh4TIMQw6HQ6dPn9acOXPsLhEAAAAAAJ9G2OJFq1atsqQdPz8/1ahRQxEREWratKn8/K50SHI4HGbQkpeXp/vuu09ZWVmWHBMAAAAAAJQOYYsX9e/f3xxLpazybxO6Wn7Qkpubq4kTJ1oW7gAAAAAAgNIjbKkkCoY2DodDDodDR44c0bhx47Rx40abKgMAAAAAAFcjbPGywnqklFVaWpo2btyouXPnaunSpZb1ngEAAAAAAGVH2OJF48ePt6QdwzB04cIFpaam6tSpUzp48KAl7QIAAAAAAOsRtnjRvHnz7C4BAAAAAACUMz+7CwAAAAAAAKhKCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFHJIMu4uA78jI4XRD1RfZbaLdJQAAALglddtMu0sAvC4k0FHux6RnCwAAAAAAgIUIWwAAAAAAACxE2AIAAAAAAGAhwhYAAAAAAAALEbYAAAAAAABYiLAFAAAAAADAQoQtAAAAAAAAFiJsAQAAAAAAsBBhCwAAAAAAgIUIWwAAAAAAACxE2AIAAAAAAGAhwhYAAAAAAAALEbYAAAAAAABYiLAFAAAAAADAQoQtAAAAAAAAFiJsAQAAAAAAsBBhCwAAAAAAgIUIWwAAAAAAACxE2AIAAAAAAGAhwhYAAAAAAAALEbYAAAAAAABYiLAFAAAAAADAQoQtAAAAAAAAFiJsAQAAAAAAsBBhCwAAAAAAgIUIWwAAAAAAACxE2AIAAAAAAGAhwhYAAAAAAAALEbYAAAAAAABYiLAFAAAAAADAQoQtAAAAAAAAFiJsAQAAAAAAsBBhCwAAAAAAgIUIWwAAAAAAACxE2AIAAAAAAGAhwhYAAAAAAAALEbYAAAAAAABYiLAFAAAAAADAQoQtAAAAAAAAFiJsAQAAAAAAsBBhCwAAAAAAgIUIWwAAAAAAACxE2AIAAAAAAGAhwhYAAAAAAAALEbYAAAAAAABYiLAFAAAAAADAQoQtAAAAAAAAFiJsAQAAAAAAsBBhCwAAAAAAgIUIWwAAAAAAACxE2AIAAAAAAGAhwhYAAAAAAAALBdhdgC/x8/NTp06d1KBBAwUFBenUqVPatWuXLl26VOo2w8PD9fjjj5vL06dPt6JUAAAAAABQSg5Jht1FVHVRUVGaPn267rrrLkVERDh9LTs7W999951mzJih77//3uO2mzRpomPHjskwrvwYAwIqdn6WkcPphqovsttEu0sAAABwS+q2mXaXAHhdSKCj3I/JbURe1qtXLx04cEAPPfSQIiMj5XA4nKbg4GANHTpUq1ev1ocffqjIyMhSHcfhKP+TBwAAAAAAuCJs8aLOnTvr22+/VVRUlBwOhwzDMCdJTvMOh0OjRo3Srl271KNHDzvLBgAAAAAAZUDY4iVBQUGaN2+eqlevboYqDodDWVlZ2r17t/773/8qLS3N7OGS//WGDRtq9erV+u1vf2v3SwAAAAAAAKVA2OIlY8eOVWxsrBmiXLp0SZMmTVJ0dLQ6d+6s7t27q1atWvrNb36jr7/+2qnnS3BwsD7++GONGjXK7pcBAAAAAAA8RNjiJQ8//LCkK7cHpaen66abbtKsWbOUmZnptN2qVat06623auTIkUpLS5N05faiwMBALViwQPfdd195lw4AAAAAAMqAsMULoqOj1aFDB7OnyrPPPqsff/yx2H2WLl2qrl27av/+/WYvF39/f7333nt64IEHyqlyAAAAAABQVoQtXtC9e3dJV3q1ZGRk6O2333Zrv59//lk9e/bU6tWrzcDFz89Pb7/9th599FFvlgwAAAAAACxC2OIFDRs2lHTldqBt27a53DpUnIsXL2rIkCH69NNPnQbOffPNN/XEE094qWIAAAAAAGAVwhYviIyMNOdPnjzp8f65ubkaOXKkFixY4BS4zJgxQ1OmTLGyVAAAAAAAYDHCFi8LDg4u1X6GYWjs2LGaPXu2U+Dy8ssv65lnnrG4SgAAAAAAYBXCFi/If6qQJNWpU6dMbT300EOaNWuWU+Dy/PPP68UXXyxjlQAAAAAAwBsC7C6gKvr5558lXRkgt3379mVub9KkScrOztYTTzxhBi5PP/20goKCNGvWrDK3DwAAAAAArEPY4gV79+4158PDw9WxY0ft3LmzTG0++eSTysnJ0Z/+9CczcJk8ebKaNWtWxmoBAAAAAICVuI3IC06ePOk0MO7w4cMtaffPf/6zXnrpJadbiu644w4ZhmFJ+wAAAAAAoOwIW7xkzZo1kq7cSjR27FjL2n3uuef0/PPPOwUuAAAAAACg4iBs8ZJvvvlG0pWnCjVq1Ei33367ZW1Pnz5dTz31lBm4AAAAAACAioOwxUu++OILZWdny+FwmE8QstKMGTP0+OOPW9omAAAAAAAoOwbI9ZILFy7oySefVExMjLmuYcOG+uWXXyw7xsyZM3Xp0iXdd999lrUJAAAAAADKxiGJ+1BQbjJyON1Q9UV2m2h3CQAAAG5J3TbT7hIArwsJLP+xTrmNCAAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG2AAAAAAAAWIiwBQAAAAAAwEKELQAAAAAAABYibAEAAAAAALAQYQsAAAAAAICFCFsAAAAAAAAsRNgCAAAAAABgIcIWAAAAAAAACxG22GD06NFKSUlRSkqKkpOT1aRJE7tLAgAAAAAAFiFssUHTpk0VERGhiIgInThxQvHx8XaXBAAAAAAALELYYoOsrCxJkmEYOnr0qM3VAAAAAAAAKxG22CAxMdGcz87OtrESAAAAAABgNcIWG1zdm6Vhw4Y2VgIAAAAAAKxG2GKDrVu36uTJk3I4HOrWrZtCQkLsLgkAAAAAAFiEsMUm8+bNkyQFBQVp4sSJNlcDAAAAAACs4pBk2F2ELwoODtaOHTvUqlUrZWRk6Oabb9YPP/xgd1lel5HD6VYeEhJO6EBcnJJPn1Z6+iXVrl1H9Rs0UIeOnRQYGGh3eVVeZDcCVAAAUDmkbptpdwk+gc/n9goJdJT7MQPK/YiQdOWJRMOHD9fy5cvVrFkzrVixQtOnT9c///lPXbx40e7yUEmt/PYbzZ83V7t27ij06zVrRmjwzUP0yKTHFBkZVc7VAWUX0zBaXds2Vec2TdSlbVN1bN1I4TV+vRXz+MkUtb5lmo0VAmXHeQ5fwHkOX8Hnc99Fzxab3HfffZKk6OhoPf/88woLC5NhGEpPT9eaNWu0Y8cOnT59WhcuXPCo3fnz53ujXMvQs8U70i9d0gvTntU3X3/p1vbR0bU0/eW/q3efvl6uzDfRs8Vafbtcqz9N+I06t2mi6IjQYrflwzkqK85z+ALO84qJni3ewefzioWeLT5k7ty5MoxfgwfDMORwOBQaGqpbbrlFt9xyS6narehhC6yXl5enKZP/oPXfr3NaHxkVpdat2ygsrIZOnDihuP37zHMuJeWMnpj0iP49+3117tLVjrIBt3Vo1VCDesXaXQbgVZzn8AWc5/AVfD6HRNhiO4fDYb7Brg5f8r/mjvygpuD+8A1vvjHD6UIeEBCoyVP+rBEjRykwKMhcf+TwYb0w7RmzC2N2drb+8Nij+uSzL1S7dp1yrxsoq8ysHP2SlKbmTWrbXQrgNZzn8AWc56hq+HwOibDFVvlhiruhSkntwPcknDihhQV6M81443814MaBLts2b9FC78yZq/+5f5x5QU9LS9Pbs2bq2Wkvlku9QGll5+Rq35FT2r4vXv/dG6/t+47rp8Mn1bNDc62Y/bjd5QGW4DyHL+A8R1XH53PkI2yxyfjx4+0uAVXA27NmKjc3x1y+bdgdhV7I81WrVk0vvvQ3jRj2W+XkXNnvs6VLNH7Cg2rUuLHX6wVKY8EXW/TuJz8oKzvX7lIAr+E8hy/gPIcv4PM58hG22GTevHl2l4BKLjMzUytXfuu0bsL9D5S4X0zMNRpw00Ct+OZrSVJubq6++vIL/c/vH/FKnUBZpV3IsLsEwOs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",
      "text/plain": [
       "<Figure size 1200x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 4), dpi=300)\n",
    "sns.heatmap(A, annot=True, cmap=\"Blues\", \n",
    "            xticklabels=itemlabels, \n",
    "            yticklabels=userlabels, \n",
    "            cbar=False)\n",
    "\n",
    "plt.title(\"User-Item Interaction Matrix\\nA\")\n",
    "plt.xlabel(\"Items\")\n",
    "plt.ylabel(\"Users\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e77056a-28f2-4835-8e70-76487f441cf9",
   "metadata": {},
   "source": [
    "## User-User Similarity Matrix\n",
    "\n",
    "The **user-user Similarity matrix** represents the relationship between users based on the items they have interacted with. The matrix captures how similar users are in terms of the items they have interacted with.\n",
    "\n",
    "The mathematical formula for the user-user interaction matrix $U$ is:\n",
    "\n",
    "$ U = A A^T $\n",
    "\n",
    "Where:\n",
    "- $A$ is the binary user-item interaction matrix.\n",
    "- $A^T$ is the transpose of the user-item interaction matrix.\n",
    "\n",
    "---\n",
    "\n",
    "### Explanation of the Matrix\n",
    "\n",
    "- The diagonal cell, $U_{ii}$, represents the total number of items with which the $i$-th user has interacted. It is the sum of interactions across all items for user $i$.\n",
    "- The off-diagonal cell, $U_{ij}$, represents the number of common items both users $i$ and $j$ have interacted with. It is the dot product of the $i$-th and $j$-th rows of the binary user-item interaction matrix.\n",
    "\n",
    "This matrix is used to measure the similarity between users based on their shared interactions with items.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "843df2e1-a727-4113-b388-7d3649d05bba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "User-User Similarity Matrix (AA'):\n",
      " [[3 1 2 1]\n",
      " [1 3 2 2]\n",
      " [2 2 4 1]\n",
      " [1 2 1 2]]\n"
     ]
    }
   ],
   "source": [
    "U = A @ A.T\n",
    "print(\"\\nUser-User Similarity Matrix (AA'):\\n\", U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "66099e3d-b3ed-49ae-9a32-19ce2117412c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2SUxMNKKiojx6vnrpZXkBvHiV+FWePsjffvvtLts/8MADpTp2UFDQNbd56KGHXI731ltvleg448ePd+lj6tSp19yvMOvXrzdCQ0M5BzgHvHoOSDJeeeWVQmsyjLwPZbNnzzYefPBBo3379qUa6KMk52Fpw1y+tWvXGsHBwdfcf9SoUS77xsXFmcuvvPJKsep47733XPoZPXp0qd6Dp8NcWFhYqf+ebrnlFuPy5ctOx33ooYeKtW9BYc4wDCM7O9sYNmyYV88bd35A37hxo1Nfv/32W4n/fTz33HMufy433XRTqWsqzutaYU6SsWDBAqefv/vuu0X2+f333ztt/9e//tXp52UJc6U9bx0Oh/HBBx84HfPixYtGeHi418+VgsJcvqVLlxp+fn5u+XssyUBj06dPd9l//fr1BZ7DderUMWJjY122v/POOz16rnrxZXkBvHiV+FWePshPnjzZadtLly65/QNj/svX19flg9BXX31Vqr6u/hAXGxtrBAQEFLlPQZKSkox69epxDnAOeP0ckPK+8d2wYUOBdRUkLS3N2Lx5s/HGG28YQ4cONWrXru3W87AsYS4hIaFEI7MVNnJpTExMsUcqjYyMdPm2eu7cuaV6D94YzbIsr3/84x9Ox92yZUux9isszL366qteP2/c+QH9/vvvd3lPQ4cOLfb+Pj4+LoPsHDhwwON/j8UJc7fccovTz5OTkwu9KtaoUSOXOxWaNm3qtE1ZR7Ms7SswMNA4ceKE03EfeeQRr58rhYW5Y8eOFevLp+L+PZYkzDkcDpcQbhiG8be//c1lu9WrV7ts99prr3n8789bL3s9tQuUQ6GhoU7rFy5c8Nj8MKNGjVLjxo3N9dzcXE2ZMqVUfb300ktOD6jXrVtXvXr1KnE/r7/+us6cOVOqGioKzgHrzoHMzEzdfvvtxX54PSgoSD169NBjjz2mpUuXKjY2VjExMZowYYLT/FJW+Ne//lXgoC6FWb58eYHtzz77bLGf04qNjdXGjRud2jp37lzsGuxk7ty5TuudOnVyetazJFJSUjR9+nQ3VGWdJUuWKD4+3qmtJAOhDB482GWQnXfffdcttZXV6tWrdfz4cXO9WrVqGjp0aIHbTpgwwWmAknXr1unIkSOeLrFYMjMz9cknnzi13XDDDRZV4+qFF17QpUuXLDm2YRi67777FBsb69Q+depU3X777eb69OnTdfPNNztts2nTJj3zzDNeqdMbCHNAGSUmJjqt16lTR02bNvXIsYYNG+a0vnbt2lL/p3P69Gnt3r3bqa1v374l6iM3N9cjD4nbDeeAtefAhQsXdPfdd2vs2LE6dOhQifb18fFRv3799OGHH+rXX3/Vfffd56Eqr62kf447duxwacufULws/bRo0aJE+9vF1eeGv7+/y0ATxbV48WLLPsS6S1ZWlt5//32ntptuuknNmzcv1v4PP/yw03paWpo++ugjd5VXZlfXcvVolVLe6Ibjxo1zarP699nVrj5vSzLarSdduHDBJWh629mzZ3XfffcpOzvbbPPx8dHHH3+sBg0aqH///nruueec9klMTNTIkSOd9rE7RrMEymjLli1O6z4+Pvrvf/+rIUOGlGpksKL06dPHaf3qb9RL6tixY+rQoYO5XtIRpw4fPqzffvutTDVUBJwD5eMcmD9/vhYtWqSBAwfqvvvu0+DBg0s0lH2jRo20YMEC9e/fXw8//HCxR3Vzh4MHD5boqpwknThxwqVt/fr1JT72lVcwpLyQExwcXO7Dio+Pj3r16qWOHTuqXbt2ioyMVGhoqEJDQ+XnV7yPN1FRUaU6dkxMTKn2K2/effdd/fnPf5a/v7+kvD/Thx9+WE899VSR+zVu3FgDBgxwalu8eLE5em55MGfOHL3wwgvmVbd+/fqpcePGTud7//79ne50SElJ0dKlSz1aV0REhPr06aN27dqpdevWql69ukJDQxUcHCyHw1Hg9ldq2LChR+srri1btigjI8PqMrR27VpNnz5df/3rX822mjVratmyZWrUqJHTdCu5ubkaP368Tp06ZUWpHkOYA8po165d2r59u9OtSV27dtXBgwe1ZMkSLVmyRGvWrCnzL73WrVu7zOUybty4Ms0RdvUHmZo1a5Zo/9IMZV8RcQ6UHzk5Ofryyy/15ZdfysfHRx07djSH+u7cubNatmx5zQ/6EyZMUHBwsEaOHOmlqlWsIcOvVtAQ5e7qp1q1auU2zNWpU0fPPPOMRo0apbp165apr/Dw8FLtV97O+9L67bff9Nlnnzld8R8/fryee+65In9fFTSf5r///W+P1VkaJ0+e1Jo1a8ypPHx8fDR+/Hin22Ovvlq3ePFipaWleaSem2++WU888YQGDBiggICAUvdTXr5sKU//BmbNmqU+ffo4fcHQvXt3l+3++c9/6osvvvBmaV5BmAPc4NFHH9XatWtVpUoVsy0oKEjjxo3TuHHjlJmZqa1bt2rz5s3asmWLfvjhB509e7ZEx7hyUuB8DRs2dOu3dCWd+LMk72HGjBm66667StT/u+++q//85z8l2scqnAPlT25urrZv3+70oSP/mbmbbrpJw4cPL3CePilvMtz169d7bb66pKSkEu+TlZXlsX7yr9SUNw899JBeffXVMk0efqXS9lOez/uSeuutt5zCXEREhEaOHKmPP/64wO39/f1dQtDPP/+srVu3erTO0vjwww+d5mUcP368ZsyYIcMwFB4ernvuucdle3cLDQ3V+++/79Yvh8rDly3l6d+AYRgaM2aMduzYUeD/k1LeXSzTpk3zcmXeQZgD3GDLli264447tGjRItWqVcvl54GBgbrhhhucHlzet2+fli5dqgULFujgwYPXPEZJP2SXRkkHA0hJSSn2tlFRUerYsWOJ+i/rt+7exDlgD+np6Vq7dq3Wrl2rF198Ubfddpv++c9/ukygLUl/+ctfNHv2bKWnp3u8roIClZX9lEd/+tOf9I9//MOtfZY2tNrtvC/KunXrtGfPHqd/Aw8//HChYW7o0KGqXbu2U1t5uyqXb/ny5UpKSlL16tUl5d1Kfcstt+j777/X/fff7/Tl2/79+7V582a3Hj80NFTffvttqQaWKkp5+LKlvP0bOHfunEaPHq1169Y5DWgj/f6cnKcGJrMaA6DAlgp6cPXKX8plUdCH2eI8KLt69Wq1bNlSs2bNUkJCwjW3b9OmjV544QXt379fn3zyidN9+wXJ/8+oPLHyAWLOgfLB7g+Rr1q1St26ddNXX33l8rM6deqU+GoyPKN3794FBrmLFy9qwYIFeuSRR9S3b181bdpU4eHhCgoKksPhcHm5S0X7UPj22287rffs2bPQL9+uHvEyOTlZixYt8lRpZZKZmelS24QJEyS53mLpiatyr7/+eoFB7uDBg3r99dc1fPhwdevWTZGRkQoLC1NAQIDLOTt+/Hi31+UO5fF3f3R0tEuQk/IG+ypPVxLdjTAHWyroIeuQkBC39F1QP8W9dSkpKUnPPfecIiMjNWDAAL366qvasmWLMjMzC93Hx8dHw4YN086dO3XbbbcVul1BVwfuvvvuAj+wlPZ13XXXFet9lgecA3kq8zngLhkZGRo1alSBAfyWW26xoCJc7V//+pdL25w5c9SgQQONGTNG7777rn744QcdPXpUFy5cKPB5L6unnijP5s6d6/I7taBpCtq0aaMbb7zRqW3evHkee87MHa4OaUOGDFG/fv2cnnHOysrSvHnz3Hrc6OhoMzjmS01N1f3336+WLVvqqaee0tKlS7Vt2zbFxcUpNTW1wCvrpZ0+o7Lp2LFjgb8nJKlDhw765z//6eWKvIcwB1sq6IN1aR9kL04/JX0OJScnR6tWrdLUqVPVs2dPhYWF6YYbbtAzzzyjmJiYAn9hV6tWTcuWLSt0WOhz5865tNnpg/eECRNKHCxmzJhRaH+cA3nsdA6UZ6mpqQUOq96yZUvvFwMnTZs2Vbdu3ZzaVq5cqYkTJ+rChQvF7scbtynbVVpamsttlffdd5/LHJoFBbzyMrdcYX7++Wf98ssv5npQUJDmz5/vtM3XX3/tMudeWY0cOdJlkJhx48Zp4cKFJern6tEs4So0NFRLliwp8u6cyZMnFzrXoN0R5mBLBX2obdWqVZn7DQ0NVf369Z3acnNzdf78+TL1e/nyZW3YsEGvvPKKbr75ZtWtW1dTp051CQghISGaOXNmgX0U9B9N+/bty1SXnXEO5KnM54C7/fTTTy5tJR3dE+536623urS99NJLJe6nSZMm7iinwnr77beVm5trroeEhGjs2LHmetWqVTVmzBinfdatW6d9+/Z5rcbSmjNnjtP61b/jPXGL5dXn7Z49e7RixYoS98N5e23vv/++y5eg33//vcuXprNnz66Qf56EOdhSQUPiuuNDbUGDIOzdu7fIW+RK4/z583r11VfVs2dPl4eI77jjjgKHLf7ll19cbrMbOHCgW+uyE86BPJX5HHC3gq7ylMfnQiqbq0drTU9P188//1ziftw9CEVFc+jQIX3//fdObVdeibvvvvtc7loorwOfXG3evHmF/g6Pj4/3yHD1V5+3pZkDUuK8vZZHH33UZaTQPXv26K677tLzzz/v1F6tWjUtWbKkTFNDlEeEOdjSjh07XIblbdGihZo1a1amfguar2vDhg1l6rMoBw8e1OzZs53agoOD1bRpU5dtMzMz9eOPPzq11atXTzfffLPH6ivPOAfyVOZzwN3q1Knj0ubuW69QcldfHS3tVfIRI0a4oxxLXf3lwtW38ZXV1VNxREdHmyPwPvzww04/i4+P1/Lly916fE9JTEwsNLDNmzfPIwPauOO8jY6OVps2bUp1fE+fK+VBp06dXJ6Fu3jxooYPH6709HS98sorLoNbdenSpcI9P0eYgy3l5OQU+C3XlbeElJSPj49Gjx7t0r5mzZpS91kcBw4ccGkrbO6jzz77zKXtyglQKxPOgd9V1nPA3QoKxUeOHLGgElzp6i9tqlevXuKRKW+88UZ17drVnWVZ4uoJ3t016FO+L774QseOHXNqe/jhh9WtWzd16dLFqX327Nm2mgqjsFspPXGLpeR63pbmlu0nn3yy1Mf39LlitbCwsAKfk3v00Ued/k994IEHdOrUKadtKtrzc4Q52FZBk/n+7//+b6knUH7iiSdcBpM4depUqe5xL4nIyEiXtsKGtZ89e7ZiY2Od2vr06aOpU6d6pLbyjnMgT2U9B+64445rTudQXE2aNCnwyo0nbr9CyVx9vletWlV9+vQp9v5BQUF677333F2WJa5+xtbdAyAZhuFy6+SwYcNcblfLycmx3Z/pV199pbp16zq9ateurf3793vkeFeft/379y/RlxC33HKLxo0bV+rje/pcsdrs2bNd7sSZPXu2y6ikiYmJGjVqVIV+fo4wB9v68ssvXR68Dg0N1dKlS0s8+tOAAQMKHHTijTfeuOYzM0888YT69+9fouPlCw0NdZlDJjk5WSdPnixw+4yMDL388ssu7bNmzdIf//jHUtUg5b3/q+cZsgPOgd9VxnNg8ODBOnjwoD788MMyjToZGRmpFStWKDg42Kn97NmzLs8QwfsKugL/8ssvy8/P75r7BgYG6pNPPqkwo5Lu3r3baT08PFzXX3+9W48xe/Zsp2dzAwMDdeeddzpt88033+jEiRNuPa43xMfHO72KMx9oaV193jZt2tTlVtXCdOrUSYsWLSpwzrTi8sa5YpXJkydr2LBhTm27d+/W5MmTC9x+48aNBT4/t3jx4grx/BxhDrb20EMPuXzb0r17d23ZskX33nvvNfcPDw/XzJkztXLlSlWtWtXpZ1u3btWbb755zT769u2r7777Trt379a0adOK/aGhTZs2+v77712uLCxevLjIW1fefvttffrpp05tvr6+euutt7R8+fJiDwLSuHFjTZ06Vbt27dI333zjMneQXXAO5Kms54C/v78mTJigAwcOaNOmTfrjH/+ounXrFmvfoKAgTZo0STt27Cjwz+xPf/qT2we+Qcn99NNPOn78uFPbDTfcoOXLlxc53UDXrl21fv16DR48WFLBA9zYzcaNG13aPvzwQ/Xr189tk6KfP3/+mpOA22XgEystWbLEpe2NN94ocHqHfD4+Pnr00UcVExOjWrVqSSr9eeuNc8UKXbp00WuvvebUlv+cXEHzS+Yr6Pm5rl27Vojn5679tRZQjm3cuFF//vOf9frrrzu1N2vWTMuWLdPJkye1Zs0a7dq1S4mJiUpLS1P16tVVp04d9e7dW3369CnwPvLExEQNHz5cly9fLnYt0dHRmjVrlmbNmqVjx45px44d2rVrl+Lj45WcnKzs7GyFhYWpWbNm6tOnj3r37u3yrdu5c+f04osvXvNYY8aM0Y8//qiOHTs6tQ8ZMkRDhgzRzp07tXbtWh06dEiJiYmS8kJLzZo11b59e3Xp0qXAATbsiHOgo1N7ZTwH8vXs2VM9e/bUW2+9pWPHjmnLli3at2+fzp07p8TERBmGobCwMDVq1Ejt27fXLbfcUuhzJIsXL9bcuXO9/A5QkNzcXM2YMcNlePk777xTx48f17Jly7R582adO3dOISEhioqK0qBBg9S9e3enf1+TJ092+8TQ3vbTTz9p7969atu2rdnWsmVLxcTEKC0tTadPny5wAu/bb7/d5ba/orz11luaOHFigT87fvy4y4diuFqzZo3WrVunvn37mm3+/v5655139Pjjj2vFihXat2+f0tPTVatWLUVHR+vuu+92mjYhLi5O//znP/Xqq6+W+PjeOle8KX80ysDAQKf2Rx55RL/++us193/ggQe0Y8cOp0cxJk+erLVr12rZsmVur9ebDF687P569NFHjczMTMMd9u/fb7Rq1arYx16xYoVbjpuUlGT06dOn2McNCQkxPvnkE7cc2zAMY/fu3dc85tVefPFFy//uOQcq7znw73//223v/Upz5swxfHx8ilXDnDlznPY9duxYsfY7duyYyzFL+v4bNWrkUvu4ceNK3M+4ceNc+mnUqJHH3kNp91uwYEHJ/zL/n5kzZ5b6/H3xxRdd9ivruVva80aScdNNNxlZWVklev/F+fu8+rVx48YC+5o2bVqZ339ZXn379nWp6bnnnvPoMd9///1S/Zk2bNjQiI2NLdHfVb7k5GSjc+fOpf736c5zxV2/a67199i3b98i91m2bJnLPu+//36Jjtu7d2/j8uXLTn0kJSUZ1113naXndVle3GaJCuGdd95Rv379Cpz0t7gyMzP13nvvqXv37gWOLliYuLi4Uh8z3/r163X99deXaB6a/NsKHn74YZ0+fbpMxz9x4oTLt952wzlQ+c6BefPmaf78+S4P+pfWkSNHdNddd2nChAlOkyejfJgwYYLef//9Eu2Tnp6uKVOmuDwvY2cxMTEaMmSIW37vFKWgAaYuX77sMpUKCnfq1CndfPPNJfr/RMob4fj6668vcD7VkvDWueINjz32mMujE7/88oumTJlSon42bNjg8vsgPDzc9vPPWZ4oefFy56tfv37GokWLjN9+++2a30BlZ2cbO3fuNGbNmmVERkaW+phRUVHGI488YixZssQ4depUsb79unTpkrFkyRLjjjvuKPN79vf3N/7whz8Yq1atMi5evFis9/3zzz8br7zyyjW/CbvydbXydGWOc6DyngN+fn7GTTfdZEyfPt34/vvvjZSUlGL9+RuGYcTGxhrz5s0zBg0aZPj6+pb42FyZK/l7KOt7HzRokLF+/foi/16TkpKMf//73y7ftl/Njlfm8l+BgYHGsGHDjPfff9/YvHmzcebMGSM1NdXIyckp1d/n1a8WLVq49LNo0aIyv/eyvux0ZS7/FRwcbEybNs04c+ZM4SetYRh79+41Jk+ebPj7+5v7luXKnLvOFauvzHXt2tXIyMhw2jY1NdVo2bJlqY//5Zdfuhz/zTfftPz8Ls3L8f8WgAqpadOmatOmjSIiIhQREaGgoCBduHBB58+fV3x8vLZt26aUlBS3H7du3bpq1qyZGjdurIiICAUHBys3N1epqak6d+6c9u7dqwMHDnhkolJ/f3916dJFDRo0UM2aNVW9enVlZ2ebxz548KAOHjxY5IPCFQnnQOU8B+rXr6/mzZsrKipKYWFhCg0NlWEYSklJUWpqqmJjY7V7924mBbex2rVrq3fv3qpXr57Cw8OVmZmp+Ph47d+/Xzt27PDIv63K5OWXX9azzz7r1Na3b1/98MMPFlVUMbRr106dOnVSzZo1FRQUpNTUVJ04cUI7d+605QihsB5hDgAAACY/Pz+dPHnSaQ7Mffv2OQ2mAaB84Jk5AAAAmIYPH+4U5KS855IBlD9cmQMAAIAkyeFwaNeuXWrXrp3ZduHCBdWvX1+XLl2ysDIABeHKHAAAACRJf/zjH52CnCS99957BDmgnOLKHAAAQCUXFBSkxx57TC+99JLTEO0pKSlq0qSJEhMTLawOQGH8rC4AAAAA3jVjxgzdddddkqRq1aqpYcOG8vNz/Vj40ksvEeSAcowwBwAAUMlERUWpY8eORW4TExOj119/3TsFASgVnpkDAACAk1WrVunuu++WYfA0DlCecWUOAACgksvIyFBcXJy2bt2q+fPna+XKlVaXBKAYGAAFAAAAAGyI2ywBAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAlAMhISFKTU2VYRhOr/Pnz6tKlSper2fChAkutRiGoX//+99uO8aLL77o1PecOXPc1jcAVAaEOQAAyoFRo0YpJCTEpb169eq69957vV7PH/7whwLbR48eraCgIC9XAwAoCGEOAIByoLDwdK2feULLli3Vu3fvAn9WrVo1DRs2zKv1AAAKRpgDAMBibdq0Uc+ePQv9eb9+/XTdddd5rZ5rhUdvh0sAQMEIcwAAWOzqcJSbm+u07uPjo4kTJ3qlFj8/P40dO7bIevr27aumTZt6pR4AQOEIcwAAWMjPz09jxoxxalu9erW2bt3q1DZu3Dg5HA6P13PHHXeobt26Tm1///vfXbbzVrgEABSOMAcAgIXuvvtu1a5d26nt448/1ty5c53aGjZsqAEDBni8nquvEqakpOivf/2rfv75Z6f2cePGyceHjxEAYCV+CwMAYKGrw1NqaqqWL1+uhQsX6vLly0Vu626RkZEaOHCgU9vSpUuVnp6ujz/+2Km9fv36GjRokEfrAQAUjTAHAIBF6tevr9tuu82pbdmyZUpPT9f58+f15ZdfOv3srrvuUs2aNT1Wz/jx4+Xn5+fUln+F0IpwCQAoGmEOAACLTJgwQb6+vk5tV14Bu/pqWEBAgMvzde6u50rHjx/XunXrJEmJiYn66quvnH4+ePBg1apVy2P1AACKRpgDAMAiV4enEydOaO3ateb6l19+qYSEBKdtPHU1rG/fvmrevLlT27x585zWCwqXDzzwgEfqAQBcG2EOAAAL3HzzzWrSpIlT2/z5853Ws7OztWjRIqe26Ohode/e3e31FBQSrx6E5csvv9S5c+euuR8AwDsIcwAAWKA44amwNncHqLCwMA0dOtSpbePGjTp8+LBTW1ZWlv773/86tbVu3Vq9evVyaz0AgOIhzAEA4GXh4eEaMmSIU9vmzZt18OBBl21//vln7d2716lt1KhRCgoKcls99913n6pWrerUVlCIlFxvtZS4OgcAVjJ48eLFixcvXt57/fGPfzSu9vDDDxe6/Z/+9CeX7R944AG31bN161anvtPT043w8PBCt9+7d6/T9ikpKUZwcLDlf668ePHiVdleXJkDAMDLrr6SlZmZqcWLFxe6/fz585WdnV1kH6XVrl07de3a1ant888/V3JycqH7XH11LjQ0VCNGjHBLPQCA4iPMAQDgRR07dlSnTp2c2r744gslJSUVuk9sbKy+//57p7Ybb7zRZfTJ0njwwQdd2gq7xTLf/PnzlZOT49TGrZYA4H2EOQAAvKig8FTQc2hXKyhgTZw4sUy1BAQE6P7773dqO3v2rL7++usi9ztz5oxWr17t1Na7d2+1bNmyTPUAAEqGMAcAgJcEBgbqvvvuc2pLSEi4ZniSpBUrVujChQtObQ888IDLpOMlMWTIENWoUcOpbeHChS5X3QpSUAAta7gEAJQMYQ4AAC8ZOnSoqlev7tS2aNEil+fhCpKRkaFPPvnEqa1evXoaNGhQqesp7vQIBVmxYoVSUlKc2soaLgEAJUOYAwDASwoKT8W5xbKobUv7rFpUVJRuueUWp7bdu3drx44dxdo/PT3dJVzWrVtXd9xxR6nqAQCUHGEOAAAvuO6669SvXz+ntr1792r79u3F7uPHH3/UkSNHnNoGDx6sOnXqlLieiRMnysfH+WNAca/K5WPOOQCwFmEOAAAvcEd4Kmgff39/PfDAAyXqw+FwaPz48U5t2dnZWrBgQYn6Wb9+vY4ePerUNmjQINWtW7dE/QAASsehvAnnAACAh/j4+Oj48eNq2LChR/o/cOCAWrduXeztb7vtNn377bceqUWSnnnmGb3yyise6x8AkIcrcwAAeNiAAQM8FuQkqVWrVrr++uuLvb2nb4VkVEsA8A7CHAAAHuaN58iKe4yIiAjdfffdHq2lRYsW6tOnj0ePAQDgNksAADyqZs2a+u233xQQEGC2paamugxkUlJNmzZVaGiouX7x4kXVrVtXly5dKnK/xx9/XP/3f//n1HbixAklJSWVuhZ/f3+1bdvWqe3jjz92eS4PAOB+Bi9evHjx4sXLM68nn3zSuNrf/va3Mvf797//3aXfiRMnXnO/Xbt2uezXsmXLMtXicDiM06dPO/V58eJFIzQ01PI/f168ePGqyC9uswQAwIMKen5s/vz5Ze533rx5Lm3XutWyW7duat++vVPbtm3b9Ouvv5apFsMw9N///tepLTg4WKNGjSpTvwCAohHmAADwkJ49e7rcfrhjxw7t3bu3zH3v3btXO3fudGq7/vrr1apVq0L3KSjsFRQKS6M04RIAUDaEOQAAPKSgMOOOq3JF9VVYgAoKCnK5Upadne1yRa20du3apd27dzu19ejRwyXMAgDchzAHAIAHVK1aVSNHjnRqy8nJ0aJFi9x2jIULFyonJ8epbezYsfLz83PZdvjw4apWrZpT23fffaezZ8+6rZ6CJh3n6hwAeA5hDgAADxg5cqTTaJOStHr1asXGxrrtGLGxsVqzZo1TW506dXTHHXe4bOvJWyzzLViwQLm5uU5tY8aMkb+/v1uPAwDIQ5gDAMADPH2LZVF9Xn3sZs2a6cYbb3RqS01N1aeffurWWk6fPq1169Y5tdWqVUt33XWXW48DAMhDmAMAwM1atmyp3r17O7VdunRJy5cvd/uxli1b5jK33MCBAxUZGWmuFxQsV6xYofT0dLfXU5Ln+AAAZUOYAwDAzQoKL5999tk1J/QujUuXLumzzz5zavPz8zMn7Pbx8dEDDzzgsp8nrhJK0tKlS11C4m233aYGDRp45HgAUJk5lDfhHAAAAADARrgyBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANiQn9UFoHLp8dFwq0sASmztmI+sLgEola9PrrS6BKDEBkXdZXUJQIkF+QVbclyuzAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABvys7oAlF29evW0fv16SZJhGGrWrJnFFQEAAADwNMJcBeDn56fGjRtLygtzAAAAACo+brMEAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEMMgOJBDRs29MpxGjRo4JXjAAAAACg/CHMedPz4ca+NLmkYhhwOh1eOBQAAAMB6hDkP81bAYkoCAAAAoHIhzHkYIQsAAACAJxDmvMAbV+cIjQAAAEDlwmiWHhQXF2cu79+/X76+vh55NWnShOflAAAAgEqGMOdB27ZtM0NWixYtFBQU5JHjcFUOAAAAqHwIcx60detWc9nHx0ddunSxsBoAAAAAFQlhzoPyw1z+lbOuXbtaWQ4AAACACoQw50Hbtm1zWu/WrZtFlQAAAACoaAhzHpSYmKgTJ06Y61yZAwAAAOAuTE3gYdu2bVOjRo0kSU2bNlVYWJhSUlLceoyLFy/q448/dmufAAAAAMo3wpyHPfbYY/rrX/9qrqenp7v9GOfPn9fEiRPd3i8AAACA8osw52FxcXFO880BAAAAgDvwzBwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwpxFRo0apcTERCUmJiohIUFRUVFWlwQAAADARghzFmnUqJHCw8MVHh6uU6dO6eTJk1aXBAAAAMBGCHMWyczMlCQZhqGjR49aXA0AAAAAuyHMWSQuLs5cvnz5soWVAAAAALAjwpxFrrwaV79+fQsrAQAAAGBHhDmL/PTTTzpz5owcDoe6deumoKAgq0sCAAAAYCN+VhdQmc2dO1fPPPOMAgICNHnyZL366qtWlwQbCPT1V6Nq9VU3uJZqVa2uqv5B8vPx1aXL6bqQmaojyad0LPmUcoxcq0sFANvLzclV4pnzij+ZoNTEFGWkZcrX31dBIUGqERmhBi3qKaBKgNVlAqikCHMWeumllzRkyBC1bNlSL774ojZt2qQff/zR6rJQDg1u1k9d60arbc1mqh9aV74+RV9Uv5SVrtXHN+mT/V/rUNIJL1UJFO30qdPas2ev9u3Zp7179mr/vgO6dOmS+fN69SL19fdfWVghkCf5bLL2bNivwzuO6tieE8pMyyx0Wx8fHzXr3ETX39lDrXq08GKVQOH4fVt5EOYslJmZqSFDhuiLL75QkyZNtGrVKs2cOVNvvvmmLl68aHV5KEcmdRyp2sE1ir19sH+Q7mp+s25v2lefHPhGb22bx5U6WGLrT9s0+/0PtW/PPl24cMHqcoBrWvT3pdq1dnext8/NzdXBbYd1cNthterRQkOfuFuh1UM8WCFQMH7fVk6EOQuNHTtWkvT2229r+vTpCg0N1cyZMzVt2jTFxMRox44dOnv2rFJTU0vU77x58zxRLsqR9KwM/ZYar7hL53QpK10+DofCAkPUNDxKNatWN7fz8/HV6DaDFRlSS8+u/adyDcPCqlEZ/XrgV23asMnqMoBiO/dbYoHtYTXDVLNehEKqhyg3J1fnY5MUeyxORu7vv1cPbDmo/zz9oSa9OkGhEaHeKhmQxO/byoowZ6GPPvpIxhUfrg3DkMPhUHBwsAYPHqzBgweXql/CXMWTnp2pH05u1abfdmp3wq86knRKhgoOZm1rNtfDnUaqW732Zlu/qO4a3eYOLdj7ubdKBooUEBCgOnXq6NSpU1aXAhSqXtNIdR3QSS27NleNehEuP79wLkWrF6zVT1//bLad+y1RC15eokmvTZTD4fBmuUCB+H1bsRHmygGHw2GGOuOqKyfF/Y8gPwhevT8qhvs+e0o5Rk6xtt177pAe++5lvXDDHzWo6Y1m+/j292rJ/q+VlZvtqTKBAvn5+alps6ZqG91GbaPbqm10GzVr3kw7d+zSg+Mfsro8wIlDUqvuLdR/TD81aFH01EHVaobp3sfvUmSTuvrs7S/N9uN7T+qXdXvUoV87D1cLOOP3beVDmLNYflgr67d3fPtXsRU3yOUzZOjVLbPVN6q7qvpXkSSFBgSrS9222nxmlydKBAp01913avjIYQoMDLS6FKBY7ntuhCLqVr/2hlfodWd3Hdl1THt+3Ge2bV+9izAHr+L3beVEmLPQhAkTrC4BFVhaVrp2nT2gXvU7mm0NwupKhDl4UVi1MKtLAEqkpEEuX687uzuFuaO/HHdTRUDx8Pu2ciLMWWju3LlWl4AKLiXTeVTUqn5MTg8AnlCvaV2n9azMLKVfTFdQCL93AXhO0ZNVAbC1yJCaTuvn0pMsqgQAKjYfX9ePVDnZJbtFHgBKijAHVFANwyLVpmZzcz3XyNWOuH1F7AEAKK3EM+ed1n18fVQ1rKpF1QCoLAhzQAVUIyhcs/r+r/x8fM22NSe2KPZSgoVVAUDFtXu985dlDZrXk48PH7MAeBbPzAEVgK/DR6EBwWoc3kA3NOise1rcqpCA378RPp0ap39umW1hhQBQcWWmZ2rbt9ud2tr2bm1RNQAqE8JcOdSwYUP16dNHTZs2VUREhEJDQyVJDz74oMWVobx4ots4jWpTvEnlt8Xu0Ywf31RSRoqHqwKAyumbOd8rNen3AaeqhFRRt4GdLawIQGVBmCtH7r//fj399NNq1855Xpr8ycALCnP33HOPpkyZIkk6f/68hg8f7pVaUf79cHKrlv76rX4684vVpQBAhbVnw35tWvmTU9uAcbeoaijPywHwPMJcORAZGalFixbphhtukPT7BOCGYVxzMvD169dr4cKFCgwMlGEY6tWrlzZt2uTxmlH+9arfST4OH13OydLO+P1WlwMAFc6Zo3Fa8tpyp7bmnZuq5x3dLKoIQGVDmLNYZGSkNm/erPr165tX4PLlrxcV6BITE7VixQqNGjVKkjRixAjCXCXw4a6lWrzvK3M90C9A1QJD1DyisfpGdVe3yHby9/XTDQ276IaGXfTJgW/0r5/mKPeK8wsAUHrJZ5P10QsLdDn9stkWXjtcI6cOveYXsQDgLoQ5C/n4+OiLL75QgwYNzBCXkJCg//znP4qJiZGvr6++++67a/bz6aefmmGuf//+Hq0Z5UPK5UtKuXzJpX3X2V+19MC36lC7pab3maLIkNqSpOGtBirQN0CzNr7r7VIBoMK5mHxRH0ybq5Rzvz+LHFo9RA/+7QGFhAdbWBmAyoYwZ6GJEyeqY8eOZpBbvny5xo0bp7S0NElSVFRUsfrJD3wOh0OtW7dWeHi4kpOTPVKzJNWqVUu1atUq1b7Vq4QxEIcX7Dr7qx79dobmDP6bwquESZLuan6z1p/apvWntllcHQDYV1pqmj54Zq7O/ZZotgVXq6oH/zZONevXsLAyAJURYc5CTz/9tLm8fv16jRgxwuk2y+JKTk7W6dOn1aBBA0lS69atPXqr5aOPPqrp06eXat8Pdn6iD3Z94t6CUKDYiwn6cNcyPdljgtk2NvouwhwAlFLGpQzNfnae4o7Hm21BIUH6w6wHVKdxbQsrA1BZMZulRRo3bqzmzZub648//nipgly+gwcPmsvNmjUrU22oOL47vsFpvW3NFgrxZ4Q1ACipzLRMffjcPP126IzZFlg1UBNfHqN6TSMtrAxAZUaYs0i3bnkjXRmGoUOHDumXX8o2fPyVt1VWr169TH2h4kjKSNGFzN/nPvL18VG9UL49BoCSuJxxWXOen6+TB06bbQFBAZr41zFq2LKBhZUBqOy4zdIitWv//oF63759Ze4v/zk7SQoO9uzD1++8844++aR0t0pGvdDLzdXgWnJys53W/X38LaoEAOwnKzNLH72wQMf3njTb/AP9Nf6l+9WoTfGebQcATyHMWSQkJMRcvnTJdVTCkgoLC3Nrf0VJSEhQQkJCqfYNzWjr5mpQlAAff1ULDHNqO5+RbE0xAGAzWZez9PH0hTr6y3GzzS/AT+Om36cm7RpbVhcA5OM2S4skJv4+ClZERESZ+7ty5Msr+0bl1jUyWr4+v/8zT8/KUELaeQsrAgB7yM7K1vyZi3V4x1Gzzc/fTw+8MFrNOjWxsDIA+B1hziJnz56VlDedQIcOHcrUV3BwsNq1a2eunzhxokz9oWJwyKGJHYY6tW0+s0vZuTkWVQQA9pCTk6OFsz7Rr1sPmW2+fr66/y8j1KIrg4wBKD8IcxbZsmWLuRwZGanOnTuXuq8xY8bI19dXkpSZmenUN+xveKuBqhEUXqJ9fB2+eq73w4qu1cKpfemBb9xYGQBUPLk5uVr8yjLt23TAbPPx9dHoacPVukdLCysDAFc8M2eR+Ph47d6927yiNmPGDN15550l7qdatWp69tlnzWkN1q9fr6ysLLfWCmvd2fxm/bHL/Vp74id9f3yjtsftVVp2RoHbBvr668ao7hrfboiaVnd+MP+rI+v0c9xeb5QMOImPi1d2jusV4XPnzjmtZ+fk6LffzrhsJ0lVqwYxUi+8Yum/PtUvPzj/rhww/hbVa1pX5+OSStRXaESI/AMYdArew+/byocwZ6F///vfeueddyRJgwYN0nPPPaeXX3652PsHBQVpyZIl5mThhmHojTfe8EitsFYVv0ANbNpHA5v2Ua6Rq9MpcYq9lKDUy2nKzslWVf8qqhtSS9dVayB/X9d/1j+e+ll/2/gfCyoHpPFjJujMmdhrbnc2/qxuv3VwgT+76547NXPWS+4uDXCx/ftdLm1fz/5OX8/+rsR9PfTKeDXtcJ07ygKKhd+3lQ9hzkIffPCB/vSnP6lx48ZyOByaMWOG2rRpo2nTpunkyZNF7jtgwAC99tprat26tXlVbtu2bfr666+9UTos5OPwUVS1eoqqVu+a22ZkZ2rOL8s1f89K5Rg8KwcAAFCREOYslJOToxEjRmjdunUKCgqSw+HQyJEjNWLECG3dulVHjx512n7q1Klq0aKFbr31VtWvX18Oh0OGYcjhcCg5OVmjR4+26J3Ak/628T/q07CrukZGq2WN6xToG3DNfY4nn9a3x37UF4fXMnolAABABeWQZFhdRGU3ePBgLVq0SFWrVpUkM6TlL+e7ui0/yKWkpGjo0KFas2aNlysvuR4fDbe6BFvzdfjquvD6qhdSR7WqRqiqfxX5+fgqLStDl7LSFXvxrA6eP67Uy56da7CyWTvmI6tLAErl65MrrS4BKLFBUXdZXQJQYkF+wZYclytz5cCXX36pHj16aPHixWrb1nlS7fwAJ/0e8vJDnMPh0IEDBzRs2DDt37/f22XDAjlGjg4nndThpKJvwwUAAEDFx9QE5cT+/fvVvn17jRgxQuvXr1d2drYZ2PJf0u9X5bZv366JEycqOjqaIAcAAABUQlyZK2eWLVumZcuWKSgoSD179lTDhg1Vo0YNBQQE6Ny5c4qPj9emTZuUmJhodakAAAAALESYK6fS09MVExNjdRkAAAAAyiluswQAAAAAGyLMAQAAAIANcZulDdWoUUONGzdWZmamjh49qrS0NKtLAgAAAOBlXJmz2NWjVRala9euWrduneLi4rRlyxbt3LlT586d07x581S7dm0vVAsAAACgvCDMWeiJJ55QVlaWsrKyFBcXJ39//0K37du3r9auXavevXvLx8fHDICBgYEaPXq0duzYocaNG3uveAAAAACWIsxZaMiQIeYVuTlz5igrK6vA7apUqaL58+crKChIkvNE4vkTiNetW1efffZZsa7wAQAAALA/wpxF/Pz81L17dzOYrVy5stBtJ02apHr16pnBLS0tTZ9//rlWrFihixcvmn20bdtWDz30kFfqBwAAAGAtwpxFoqOjFRAQIIfDoYyMDG3atKnQbcePH28GuTNnzig6Olr33HOPhg0bplatWunQoUPmzx988EEvvgsAAAAAViHMWaRJkyaS8m6TPHDggNOtk1eKiopS+/btzW1ffPFFnTx50vx5XFycpkyZYt5e2blzZwZDAQAAACoBwpxFIiMjzeVTp04Vul3fvn0l5Y16mZmZqYULF7ps8/333yshIcFc79ixo/sKBQAAAFAuEeYsEhwcbC6npqYWul3v3r0l5V2VW7dunTIyMgrcbteuXeYyo1oCAAAAFR9hziK+vr4FLl+tV69e5vIPP/xQ6HZXXpkLCwsrY3UAAAAAyjvCnEWuvBpXo0aNArcJDw9X27ZtzfUNGzYUq++i5qsDAAAAUDEQ5iwSHx8vKe9ZuOjo6AK3GThwoDmwSXZ2trZu3Vpof+Hh4ebypUuX3FcoAAAAgHKJMGeR3bt3m8t169ZVjx49XLYZM2aMpLzn5Xbs2FHo83JS3qiX+fKDIgAAAICKizBnkQMHDuj06dPm/HBvvfWW07Nuw4YN06BBg8wpC7744otC+woMDFSrVq3M9WPHjnmucAAAAADlAmHOQnPnzpXD4ZBhGOrUqZMOHz6sxYsXKyYmRgsXLjSDXk5OjubNm1doP9dff705iEpubq727t3rrbcAAAAAwCKEOQu98sorio2NNddr1KihoUOHqk+fPmY4MwxDs2fPdpoo/GpDhgwxt92/fz/PzAEAAACVAGHOQhcvXtSgQYOUkJBgXqG7ksPh0ObNm/Xkk08W2oe/v7+GDx9u7rtmzRqP1gwAAACgfCDMWWz37t1q3bq1XnnlFR04cEDp6elKT0/X9u3b9fTTT+umm24qcuCTUaNGqXbt2nI4HHI4HPrqq6+8WD0AAAAAqzgkGdfcCuVWgwYNFBERYa7v3btXOTk5FlZUtB4fDbe6BKDE1o75yOoSgFL5+uRKq0sASmxQ1F1WlwCUWJBfsCXH9bPkqHCb06dP6/Tp01aXAQAAAMDLuM0SAAAAAGyIMAcAAAAANkSYAwAAAAAbIswBAAAAgA0xAIoHHTlyxC39GIahlJQUJSUlKS4uTps3b9aGDRu0fft2t/QPAAAAwH4Icx7UuHFjGYYhh8Phlv7yJwYfOXKkJGnPnj169dVXtWDBArf0DwAAAMA+uM3SCwzDcMsrX/4E4e3atdPHH3+slStXqlq1aha+QwAAAADeRpjzsPzg5c6X9HtAdDgcuv3227VmzRoFBgZa/G4BAAAAeAu3WXrQTTfd5JZ+fH19FRoaqvDwcLVq1UpdunRRv3795OfnZwa6Dh066L333tO4cePcckwAAAAA5RthzoN++OEHj/Vds2ZNTZs2TVOmTJGPj48cDofuv/9+vf7669q1a5fHjgsAAACgfOA2S5s6d+6cnnrqKd13331Oz9Q99dRTFlcGAAAAwBsIcza3dOlSvffee+bzdIMHD7a6JAAAAABeQJirAP7xj3+Yy9WqVVO7du0srAYAAACANxDmKoATJ044TVDeunVrC6sBAAAA4A2EuQri4MGD5nJERISFlQAAAADwBsJcBZGUlGQuh4eHW1cIAAAAAK8gzFUQVapUMZczMjIsrAQAAACANxDmKog6deqYy1depQMAAABQMRHmKgA/Pz917tzZXI+NjbWwGgAAAADeQJirAO6++24FBQVJkgzD0ObNmy2uCAAAAICn+VldAMomODhYM2fOlGEYkqTdu3crJSXF4qoAAAAAeBpX5mysdu3aWrlypVq2bCmHwyFJ+uCDDyyuCgAAAIA3cGXOZgICAtSpUycNHz5cEydOVFhYmAzDkMPh0NmzZzV79myrSwQAAADgBYQ5D1q9erVb+vHx8VFISIjCw8PVqFEj+fjkXVB1OBxmkMvJydHYsWOVmZnplmMCAAAAKN8Icx7Ur18/81m2ssq/jfJK+UEuOztbkydPdlt4BAAAAFD+EeZs4upQ6HA45HA4dOTIEY0fP14bN260qDIAAAAAViDMeVhBV9TKKjk5WRs3btRHH32k5cuXu+3qHwAAAAD7IMx50IQJE9zSj2EYSk1NVVJSkmJjY3Xw4EG39AsAAADAvghzHjR37lyrSwAAAABQQTHPHAAAAADYEGEOAAAAAGyIMAcAAAAANkSYAwAAAAAbIswBAAAAgA0R5gAAAADAhghzAAAAAGBDhDkAAAAAsCHCHAAAAADYEGEOAAAAAGyIMAcAAAAANkSYAwAAAAAbIswBAAAAgA0R5gAAAADAhghzAAAAAGBDhDkAAAAAsCHCHAAAAADYEGEOAAAAAGyIMAcAAAAANuSQZFhdBCqP9OxLVpcAlFi/+eOtLgEolT/feK/VJQBApXBvk9GWHJcrcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIb8rC6gMvHx8VGnTp1Ur149BQQEKDY2Vrt27dKlS5dK3WdYWJgef/xxc33mzJnuKBUAAABAOUeY84KIiAjNnDlTI0eOVHh4uNPPLl++rO+//16vvfaafvjhhxL3HR4erunTp8swDEmEOQAAAKCy4DZLD7v++uv166+/atKkSapevbocDofTKzAwULfffrvWrFmjhQsXqnr16qU6jsPhcHPlAAAAAMozwpwHde7cWd9++60iIiLkcDhkGIb5kuS07HA4NGLECO3atUs9e/a0smwAAAAANkCY85CAgADNnTtXVatWNUObw+FQZmamfvnlF/38889KTk42r9Dl/7x+/fpas2aN7rzzTqvfAgAAAIByjDDnIePGjVPr1q3NkHbp0iVNmTJFNWrUUOfOndW9e3fVrFlTt912m77++munK3eBgYH65JNPNGLECKvfBgAAAIByijDnIY888oikvNsn09LSdMstt+idd95RRkaG03arV6/WHXfcoeHDhys5OVlS3u2X/v7+mj9/vsaOHevt0gEAAADYAGHOA2rUqKEOHTqYV9qef/55bdu2rch9li9frq5du2r//v3mVTpfX199+OGHevDBB71UOQAAAAC7IMx5QPfu3SXlXZVLT0/Xu+++W6z9jh8/rl69emnNmjVmoPPx8dG7776rP/7xj54sGQAAAIDNEOY8oH79+pLybpfcunWry62VRbl48aIGDRqkFStWOA2M8sYbb+iJJ57wUMUAAAAA7IYw5wFXzhV35syZEu+fnZ2t4cOHa/78+U6B7rXXXtPUqVPdWSoAAAAAmyLMeVhgYGCp9jMMQ+PGjdMHH3zgFOhmzZqlv/zlL26uEgAAAIDdEOY8IH9USkmqXbt2mfqaNGmS3nnnHadAN336dL300ktlrBIAAACAnflZXUBFdPz4cUl5A6C0a9euzP1NmTJFly9f1hNPPGEGumeffVYBAQF65513ytw/AAAAAPshzHnA3r17zeWwsDB17NhRO3fuLFOfTz31lLKysvSnP/3JDHRPP/20mjRpUsZqAQAAANgRt1l6wJkzZ5wGPhkyZIhb+n3mmWf08ssvO91yee+998owDLf0DwAAAMA+CHMeEhMTIynvVstx48a5rd8XXnhB06dPdwp0AAAAACofwpyHfPPNN5LyRqVs0KCB7r77brf1PXPmTP35z382Ax0AAACAyocw5yGff/65Ll++LIfDYY5A6U6vvfaaHn/8cbf2CQAAAMA+GADFQ1JTU/XUU0+pcePGZlv9+vX122+/ue0Yb731li5duqSxY8e6rU8AAAAA9uCQxH168Jr07EtWlwCUWL/5460uASiVP994r9UlAEClcG+T0ZYcl9ssAQAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizFlg1KhRSkxMVGJiohISEhQVFWV1SQAAAABshjBngUaNGik8PFzh4eE6deqUTp48aXVJAAAAAGyGMGeBzMxMSZJhGDp69KjF1QAAAACwI8KcBeLi4szly5cvW1gJAAAAALsizFngyqtx9evXt7ASAAAAAHZFmLPATz/9pDNnzsjhcKhbt24KCgqyuiQAAAAANuNndQGV1dy5c/XMM88oICBAkydP1quvvmp1SQDgMYG+/mpUrb7qBtdSrarVVdU/SH4+vrp0OV0XMlN1JPmUjiWfUo6Ra3WpgJPcnFwlnjmv+JMJSk1MUUZapnz9fRUUEqQakRFq0KKeAqoEWF0m4ITztvJwSDKsLqIyCgwM1I4dO9SyZUulp6dr4MCB+vHHH60uy+PSsy9ZXYLtnT51Wnv27NW+Pfu0d89e7d93QJcu/f7nWq9epL7+/isLK6x4+s0fb3UJtjS4WT91rRuttjWbqX5oXfn6FH0zyKWsdK0+vkmf7P9ah5JOeKnKiu3PN95rdQm2lHw2WXs27NfhHUd1bM8JZaZlFrqtj4+PmnVuouvv7KFWPVp4sUrAGeette5tMtqS4xLmLNSyZUt98cUXatKkiTIzMzVz5ky9+eabunjxotWleQxhrnS2/rRNs9//UPv27NOFCxeK3JYw536EudJZOezfqh1co8T7Zefm6JMD3+itbfO4UldGhLmSW/T3pdq1dnep9m3Vo4WGPnG3QquHuLkqoGict9azKsxxm6VFxo4dK0l6++23NX36dIWGhmrmzJmaNm2aYmJitGPHDp09e1apqakl6nfevHmeKBcW+/XAr9q0YZPVZQBlkp6Vod9S4xV36ZwuZaXLx+FQWGCImoZHqWbV6uZ2fj6+Gt1msCJDaunZtf9UrsF3jvCec78lFtgeVjNMNetFKKR6iHJzcnU+Nkmxx+Jk5P5+fh7YclD/efpDTXp1gkIjQr1VMsB5W4kR5izy0UcfybjiA4phGHI4HAoODtbgwYM1ePDgUvVLmKtcAgICVKdOHZ06dcrqUgAX6dmZ+uHkVm36bad2J/yqI0mnZBRyM0jbms31cKeR6lavvdnWL6q7Rre5Qwv2fu6tkgEn9ZpGquuATmrZtblq1Itw+fmFcylavWCtfvr6Z7Pt3G+JWvDyEk16baIcDoc3ywUkcd5WNoQ5izkcDjPUGVd9+1zcf0z5QfDq/VGx+Pn5qWmzpmob3UZto9uqbXQbNWveTDt37NKD4x+yujzAxX2fPaUcI6dY2+49d0iPffeyXrjhjxrU9EazfXz7e7Vk/9fKys32VJmAE4ekVt1bqP+YfmrQoujpg6rVDNO9j9+lyCZ19dnbX5rtx/ee1C/r9qhDv3YerhbIw3lbeRHmLJQf1sr6DQjfoFR8d919p4aPHKbAwECrSwGKrbhBLp8hQ69uma2+Ud1V1b+KJCk0IFhd6rbV5jO7PFEi4OK+50Yoom71a294hV53dteRXce058d9Ztv21bv4UAyv4bytvAhzFpkwYYLVJcBGwqqFWV0C4BVpWenadfaAetXvaLY1CKsrEebgJSX9QJyv153dnT4UH/3luJsqAq6N87byIsxZZO7cuVaXAADlUkqm84i+Vf2CLKoEKL56Tes6rWdlZin9YrqCQjh/UX5x3tpf0ZP+AADgZZEhNZ3Wz6UnWVQJUHw+vq4fqXKyS3arMeBtnLf2R5gDAJQbDcMi1aZmc3M918jVjrh9RewBlA+JZ847rfv4+qhqWFWLqgGKh/PW/ghzAIByoUZQuGb1/V/5+fiabWtObFHspQQLqwKKZ/d65y8dGjSvJx8fPmahfOO8tT+emQMAWMLX4aPQgGA1Dm+gGxp01j0tblVIwO/fCJ9OjdM/t8y2sEKgeDLTM7Xt2+1ObW17t7aoGqB4OG8rBsJcOdOwYUP16dNHTZs2VUREhEJDQyVJDz74oMWVAUDZPNFtnEa1GVysbbfF7tGMH99UUkaKh6sCyu6bOd8rNen3gXuqhFRRt4GdLawIuDbO24qBMFdO3H///Xr66afVrp3z3B75k4EXFObuueceTZkyRZJ0/vx5DR8+3Cu1AoCn/HByq5b++q1+OvOL1aUAxbJnw35tWvmTU9uAcbeoaijPHaH84rytOAhzFouMjNSiRYt0ww03SPp9AnDDMK45Gfj69eu1cOFCBQYGyjAM9erVS5s2bfJ4zQDgKb3qd5KPw0eXc7K0M36/1eUARTpzNE5LXlvu1Na8c1P1vKObRRUB18Z5W7EQ5iwUGRmpzZs3q379+uYVuHz560UFusTERK1YsUKjRo2SJI0YMYIwB6Dc+nDXUi3e95W5HugXoGqBIWoe0Vh9o7qrW2Q7+fv66YaGXXRDwy765MA3+tdPc5R7xe9GoLxIPpusj15YoMvpl8228NrhGjl16DW/jAWswnlb8RDmLOLj46MvvvhCDRo0MENcQkKC/vOf/ygmJka+vr767rvvrtnPp59+aoa5/v37e7RmACiLlMuXlHL5kkv7rrO/aumBb9WhdktN7zNFkSG1JUnDWw1UoG+AZm1819ulAkW6mHxRH0ybq5Rzvz/TGVo9RA/+7QGFhAdbWBlQOM7biokwZ5GJEyeqY8eOZpBbvny5xo0bp7S0NElSVFRUsfrJD3wOh0OtW7dWeHi4kpOTPVJzvlq1aqlWrVoePQaAymfX2V/16LczNGfw3xReJUySdFfzm7X+1DatP7XN4uqAPGmpafrgmbk691ui2RZcraoe/Ns41axfw8LKgMJx3lZchDmLPP300+by+vXrNWLECKfbLIsrOTlZp0+fVoMGDSRJrVu39vitlo8++qimT59eqn2zc7OUbWS5tyAAFUbsxQR9uGuZnuwxwWwbG30XYQ7lQsalDM1+dp7ijsebbUEhQfrDrAdUp3FtCysDCsd5W7ExK6AFGjdurObNm5vrjz/+eKmCXL6DBw+ay82aNStTbQBgte+Ob3Bab1uzhUL8GWEN1spMy9SHz83Tb4fOmG2BVQM18eUxqtc00sLKgMJx3lZ8hDkLdOuWN1qQYRg6dOiQfvmlbENwX3lbZfXq1cvUFwBYLSkjRRcyf5/7yNfHR/VC+fYY1rmccVlznp+vkwdOm20BQQGa+NcxatiygYWVAYXjvK0cuM3SArVr//6hZN++fWXuL/85O0kKDvb8A6zvvPOOPvnkk1Lt+/MvW91cDYCKKCc322nd38ffokpQ2WVlZumjFxbo+N6TZpt/oL/Gv3S/GrUp3vPtgLdx3lYehDkLhISEmMuXLrmO7FZSYWFhbu3vWhISEpSQkODx4wConAJ8/FUtMMyp7XxGsjXFoFLLupylj6cv1NFfjpttfgF+Gjf9PjVp19iyuoCicN5WLtxmaYHExN9HEoqIiChzf1eOfHll3wBgR10jo+Xr8/t/T+lZGUpIO29hRaiMsrOyNX/mYh3ecdRs8/P30wMvjFazTk0srAwoHOdt5UOYs8DZs2cl5U0n0KFDhzL1FRwcrHbt2pnrJ06cKFN/AGAlhxya2GGoU9vmM7uUnZtjUUWojHJycrRw1if6deshs83Xz1f3/2WEWnRloDGUT5y3lRNhzgJbtmwxlyMjI9W5c+dS9zVmzBj5+vpKkjIzM536BgCrDG81UDWCwku0j6/DV8/1fljRtVo4tS898I0bKwOKlpuTq8WvLNO+TQfMNh9fH42eNlyte7S0sDKgcJy3lRfPzFkgPj5eu3fvNq+ozZgxQ3feeWeJ+6lWrZqeffZZc1qD9evXKyuLOdwqqvi4eGXnuF6dOHfunNN6dk6OfvvtjMt2klS1ahAjnsIr7mx+s/7Y5X6tPfGTvj++Udvj9iotO6PAbQN9/XVjVHeNbzdETas7P5j/1ZF1+jlurzdKBiRJS//1qX75wfmcGzD+FtVrWlfn45JK1FdoRIj8Axi8B57HeVt5OSSVfoIzlNqkSZP0zjvvmEHsxRdf1Msvv2z+PCoqSseOHZOUN4WBn59z7g4KCtKnn36q/v37m9vceeed+vrrr730DkonPdvzA7RUVIP6364zZ2LL1Mdd99ypmbNeclNFlUe/+eOtLsF25t75D7WIaGyu5xq5Op0Sp9hLCUq9nKbsnGxV9a+iuiG1dF21BvL3df1u8cdTP2va2n8q66qRLVF8f77xXqtLsJ1nBr7otr4eemW8mna4zm39AYXhvLXevU1GW3JcrsxZ5IMPPtCf/vQnNW7cWA6HQzNmzFCbNm00bdo0nTx5ssh9BwwYoNdee02tW7c2w+C2bdvKfZADUHn5OHwUVa2eoqrVu+a2GdmZmvPLcs3fs1I5Bs/KAQBQGMKcRXJycjRixAitW7dOQUFBcjgcGjlypEaMGKGtW7fq6NGjTttPnTpVLVq00K233qr69evL4XDIMAw5HA4lJydr9Ghrvg0AgIL8beN/1KdhV3WNjFbLGtcp0DfgmvscTz6tb4/9qC8Or2X0SgAAioHbLC02ePBgLVq0SFWrVpUkM6TlL+e7ui0/yKWkpGjo0KFas2aNlysvHW6zhB1xm2XZ+Dp8dV14fdULqaNaVSNU1b+K/Hx8lZaVoUtZ6Yq9eFYHzx9X6mV+P7gbt1kCgHdwm2Ul9eWXX6pHjx5avHix2rZt6/Sz/AAn/R7y8kOcw+HQgQMHNGzYMO3fv9/bZQNAseUYOTqcdFKHk4q+hRwAAJQMUxOUA/v371f79u01YsQIrV+/XtnZ2WZgy39Jv1+V2759uyZOnKjo6GiCHAAAAFBJcWWuHFm2bJmWLVumoKAg9ezZUw0bNlSNGjUUEBCgc+fOKT4+Xps2bVJiYqLVpQIAAACwGGGuHEpPT1dMTIzVZQAAAAAox7jNEgAAAABsiDAHAAAAADbEbZY2U6NGDTVu3FiZmZk6evSo0tLSrC4JAAAAgAW4Mmehq0erLErXrl21bt06xcXFacuWLdq5c6fOnTunefPmqXbt2l6oFgAAAEB5QpizyBNPPKGsrCxlZWUpLi5O/v7+hW7bt29frV27Vr1795aPj48ZAAMDAzV69Gjt2LFDjRs39l7xAAAAACxHmLPIkCFDzCtyc+bMUVZWVoHbValSRfPnz1dQUJAk54nE8ycQr1u3rj777LNiXeEDAAAAUDEQ5izg5+en7t27m8Fs5cqVhW47adIk1atXzwxuaWlp+vzzz7VixQpdvHjR7KNt27Z66KGHvFI/AAAAAOsR5iwQHR2tgIAAORwOZWRkaNOmTYVuO378eDPInTlzRtHR0brnnns0bNgwtWrVSocOHTJ//uCDD3rxXQAAAACwEmHOAk2aNJGUd5vkgQMHnG6dvFJUVJTat29vbvviiy/q5MmT5s/j4uI0ZcoU8/bKzp07MxgKAAAAUEkQ5iwQGRlpLp86darQ7fr27Sspb9TLzMxMLVy40GWb77//XgkJCeZ6x44d3VcoAAAAgHKLMGeB4OBgczk1NbXQ7Xr37i0p76rcunXrlJGRUeB2u3btMpcZ1RIAAACoHAhzFvD19S1w+Wq9evUyl3/44YdCt7vyylxYWFgZqwMAAABgB4Q5C1x5Na5GjRoFbhMeHq62bdua6xs2bChW30XNVwcAAACg4iDMWSA+Pl5S3rNw0dHRBW4zcOBAc2CT7Oxsbd26tdD+wsPDzeVLly65r1AAAAAA5RZhzgK7d+82l+vWrasePXq4bDNmzBhJec/L7dixo9Dn5aS8US/z5QdFAAAAABUbYc4CBw4c0OnTp8354d566y2nZ92GDRumQYMGmVMWfPHFF4X2FRgYqFatWpnrx44d81zhAAAAAMoNwpxF5s6dK4fDIcMw1KlTJx0+fFiLFy9WTEyMFi5caAa9nJwczZs3r9B+rr/+enMQldzcXO3du9dbbwEAAACAhQhzFnnllVcUGxtrrteoUUNDhw5Vnz59zHBmGIZmz57tNFH41YYMGWJuu3//fp6ZAwAAACoJwpxFLl68qEGDBikhIcG8Qnclh8OhzZs368knnyy0D39/fw0fPtzcd82aNR6tGQAAAED54Wd1AZ500003aciQIbruuuuUmZmp/fv3a/78+fr111+tLk1S3kAorVu31tSpU3XXXXepUaNGkvKeqVu4cKHeeustZWVlFbr/qFGjVLt2bXP9q6++8njNAAAAAMoHhyTjmluVA9HR0Ro+fLikvFsKZ82apcuXLxe4bWBgoObPn2/egnil3Nxcvfzyy5oxY4ZH6/WGBg0aKCIiwlzfu3evcnJyLKzo2tKzuQ0U9tNv/nirSwBK5c833mt1CQBQKdzbZLQlx7XNlbkpU6boD3/4gyRp7dq1hQY5SXr77bd1772//wd25S2Mvr6+ev7555WVlaVZs2Z5rmAvOH36tE6fPm11GQAAAAAsYJtn5gYNGmROoj137txCt+vSpYsmTJggwzDMEOdwOMxX/iiRL7zwglq0aOGV2gEAAADA3WwR5iIjI1W/fn1z/Ztvvil02yeeeEKSzOD3zjvvqEuXLurQoYNef/11SXlX6vz8/DR16lTPFQ0AAAAAHmSLMNe6dWtJeSHszJkzOnv2bIHbBQQE6K677jKvyi1atEhTpkzRzp07tWfPHv3pT3/Sv/71L/Mq3b333mtOAwAAAAAAdmKLMJc/yqOUN9JjYXr27KmQkBDzqtw//vEPl23+/ve/m4OEhIWFKTo62s3VAgAAAIDn2WIAlPDwcHM5KSmp0O369OkjKe8K3tGjR7V7926XbRITE7V792517NhRktS2bVvt2rXLrfVK0pEjR9zSj2EYSklJUVJSkuLi4rR582Zt2LBB27dvd0v/AAAAAOzJFmEuKCjIXE5PTy90u169epnL3333XaHbHT161AxzNWrUKHuBBWjcuLE52Io75A/mMnLkSEnSnj179Oqrr2rBggVu6R8AAACAvdjiNsvMzExzOTg4uNDtrgxzGzZsKHS7tLQ0czkkJKSM1RUt//m9sr7y5T/v165dO3388cdauXKlqlWr5tH3AAAAAKD8sUWYu3Dhgrl85fNzV+rUqZPT7ZibNm0qtL8rA2FWVlbZCyzElVMiuOsl/R4QHQ6Hbr/9dq1Zs0aBgYEeex8AAAAAyh9b3GZ56NAhSXnhqH379goNDVVqaqrTNkOGDDGX4+PjdezYsUL7u/LWyiuDojvddNNNbunH19dXoaGhCg8PV6tWrdSlSxf169dPfn5+ZqDr0KGD3nvvPY0bN84txwQAAABQ/tkizO3cuVM5OTny8fGRn5+fHnvsMb388svmz6tWrao//OEP5u2IMTExRfbXtm1bc/nkyZMeqfmHH37wSL+SVLNmTU2bNk1TpkyRj4+PHA6H7r//fr3++useGcwFAAAAQPljm9ss16xZY95q+MILL+gvf/mLWrdurb59+2rVqlWqW7eueRvikiVLCu0rKirK6cpc/lU/Ozl37pyeeuop3XfffU7P1D311FMWVwYAAADAW2wR5qS8+eGkvOfF/Pz8NH36dO3evVurV69Wz549zVBz+PBhff7554X2M3jwYHM5KSlJR48e9XjtnrJ06VK99957Zsi98r0BAAAAqNhsE+bWrl2rN998Uw6Hw7wSdeWgIA6HQ7m5uXr00UedRn+82rBhwyTlhcKiBkmxiysnRq9WrZratWtnYTUAAAAAvMU2YU6SnnjiCT3//PPKzMx0mr/N4XDo7NmzGj58uNasWVPo/i1btlTfvn3N9W+++caj9XrDiRMnnCYob926tYXVAAAAAPAWWwyAcqVZs2bpzTff1IABA8xpCg4cOKDVq1crIyOjyH07d+6slStXmutXLtvZwYMH1bRpU0lSRESExdUAAAAA8AbbhTlJSk1N1dKlS0u836JFi7Ro0SIPVGStpKQkc/nKufYAAAAAVFy2us0SBatSpYq5fK2rkwAAAAAqBluEuVGjRikxMVGJiYlKSEhQVFSU1SWVK3Xq1DGXr7xKBwAAAKDiskWYa9SokcLDwxUeHq5Tp055bKJvO/Lz81Pnzp3N9djYWAurAQAAAOAttghzmZmZkvKmE7DzvHCecPfddysoKEhS3p/P5s2bLa4IAAAAgDfYYgCUuLg4c/ny5csWVlK+BAcHa+bMmea8ert371ZKSorFVQEAAADwBltcmbvyalz9+vUtrKT8qF27tlauXKmWLVuac+598MEHFlcFAAAAwFtsEeZ++uknnTlzRg6HQ926dTNvK6xsAgIC1KNHD7322ms6cOCA+vbta16VO3v2rGbPnm1xhQAAAAC8xRa3WUrS3Llz9cwzzyggIECTJ0/Wq6++anVJRVq9erVb+vHx8VFISIjCw8PVqFEj+fjk5W+HwyHDMORwOJSTk6OxY8eazxYCAAAAqPgckgyriyiOwMBA7dixQy1btlR6eroGDhyoH3/80eqyCpWTk2NeNSur/Nsor5Qf5LKzszV58mS9//77bjmWp6VnX7K6BKDE+s0fb3UJQKn8+cZ7rS4BACqFe5uMtuS4trjNUsob0XLIkCE6evSogoKCtGrVKk2bNk0hISFWl+ZxhmE4vaS8gHfkyBHddNNNtglyAAAAANzHNlfmxo4dK0mqUaOGpk+frtDQUBmGobS0NMXExGjHjh06e/asUlNTS9TvvHnzPFGucnJyPNJvcnKyNm7cqI8++kjLly9329U/b+HKHOyIK3OwK67MAYB3WHVlzjZhrqDbFvNvPyxLoPHz88xjgw888IBb+jEMQ6mpqUpKSlJsbKwOHjzoln6tQpiDHRHmYFeEOQDwDqvCnG0GQMmXP/CH5BriCnq2rCD5z5t58qrW3LlzPdY3AAAAANgqzOWHteKGtmv1AwAAAAB2ZZswN2HCBKtLAAAAAIBywzZhjtsWAQAAAOB3tpmaAAAAAADwO8IcAAAAANgQYQ4AAAAAbIgwBwAAAAA2ZJsBUArTsGFD9enTR02bNlVERIRCQ0MlSQ8++KDFlQEAAACA59g2zN1///16+umn1a5dO6f2/MnACwpz99xzj6ZMmSJJOn/+vIYPH+6VWgEAAADA3WwX5iIjI7Vo0SLdcMMNkn6fANwwjGtOBr5+/XotXLhQgYGBMgxDvXr10qZNmzxeMwAAAAC4m62emYuMjNTmzZt1ww03uAS3/CtyRUlMTNSKFSvM9REjRnikTgAAAADwNNuEOR8fH33xxRdq0KCB2ZaQkKCZM2fq5ptv1q233nrNK3OS9Omnn5rL/fv390SpAAAAAOBxtrnNcuLEierYsaN59W358uUaN26c0tLSJElRUVHF6ue7776TlHclr3Xr1goPD1dycrJHagYAAAAAT7HNlbmnn37aXF6/fr1GjBhhBrmSSE5O1unTp8311q1bu6U+AAAAAPAmW4S5xo0bq3nz5ub6448/fs3n44py8OBBc7lZs2Zlqg0AAAAArGCLMNetWzdJeSNWHjp0SL/88kuZ+rvytsrq1auXqS8AAAAAsIItwlzt2rXN5X379pW5vytvzwwODi5zfwAAAADgbbYIcyEhIebypUuXytxfWFiYW/sDAAAAAG+zRZhLTEw0lyMiIsrc35UjX17ZNwAAAADYhS3C3NmzZyXlTSfQoUOHMvUVHBysdu3amesnTpwoU38AAAAAYAVbzDO3ZcsWczkyMlKdO3fW9u3bS9XXmDFj5OvrK0nKzMx06hue9/XJlVaXAJTYn2+81+oSgFK593+evvZGQDmT/s3Ba28EQJJNrszFx8dr9+7d5vqMGTNK1U+1atX07LPPyjAMGYah9evXKysry11lAgAAAIDX2CLMSdK///1vc3nQoEF67rnnSrR/UFCQlixZogYNGsjhcEiS3njjDbfWCAAAAADeYpsw98EHH+jYsWOS8p6dmzFjhhYsWOA0mElhBgwYoJ9++km33HKLeVVu27Zt+vrrrz1dNgAAAAB4hC2emZOknJwcjRgxQuvWrVNQUJAcDodGjhypESNGaOvWrTp69KjT9lOnTlWLFi106623qn79+nI4HDIMQw6HQ8nJyRo9erRF7wQAAAAAys4hybC6iJIYPHiwFi1apKpVq0qSGdLyl/Nd3ZYf5FJSUjR06FCtWbPGy5VDkpYfXWR1CQBQaTAACuyIAVBgR0F+wZYc1za3Web78ssv1aNHD+3bt88pvEkyb6HMD275bVJeqDtw4ICuv/56ghwAAAAA27NdmJOk/fv3q3379hoxYoTWr1+v7OxsORwOp5f0+1W57du3a+LEiYqOjtb+/futLB0AAAAA3MI2z8wVZNmyZVq2bJmCgoLUs2dPNWzYUDVq1FBAQIDOnTun+Ph4bdq0SYmJiVaXCgAAAABuZeswly89PV0xMTFWlwEAAAAAXmPL2ywBAAAAoLIjzAEAAACADVWI2yyLUqNGDTVu3FiZmZk6evSo0tLSrC4JAAAAAMrMVlfmrh6tsihdu3bVunXrFBcXpy1btmjnzp06d+6c5s2bp9q1a3uhWgAAAADwHNuEuSeeeEJZWVnKyspSXFyc/P39C922b9++Wrt2rXr37i0fHx8zAAYGBmr06NHasWOHGjdu7L3iAQAAAMDNbBPmhgwZYl6RmzNnjrKysgrcrkqVKpo/f76CgoIk/T5peP6yw+FQ3bp19dlnnxXrCh8AAAAAlEe2CHN+fn7q3r27GcxWrlxZ6LaTJk1SvXr1zOCWlpamzz//XCtWrNDFixfNPtq2bauHHnrIK/UDAAAAgLvZIsxFR0crICBADodDGRkZ2rRpU6Hbjh8/3gxyZ86cUXR0tO655x4NGzZMrVq10qFDh8yfP/jgg158FwAAAADgPrYIc02aNJGUd5vkgQMHnG6dvFJUVJTat29vbvviiy/q5MmT5s/j4uI0ZcoU8/bKzp07MxgKAAAAAFuyRZiLjIw0l0+dOlXodn379pWUN+plZmamFi5c6LLN999/r4SEBHO9Y8eO7isUAAAAALzEFmEuODjYXE5NTS10u969e0vKuyq3bt06ZWRkFLjdrl27zGVGtQQAAABgR7YIc76+vgUuX61Xr17m8g8//FDodldemQsLCytjdQAAAADgfbYIc1dejatRo0aB24SHh6tt27bm+oYNG4rVd1Hz1QEAAABAeeVndQHFER8fLynvWbjo6OgCtxk4cKA5sEl2dra2bt1aaH/h4eHm8qVLl9xXqAeEhIToxhtvVLNmzRQYGKj4+HgdOnSoyBE9AQAAAFR8tghzu3fvNpfr1q2rHj16aMuWLU7bjBkzRlLe83I7duwo9Hk5KW/Uy3z5QdHTunbtqiFDhqhZs2YKDQ3VmTNnFBMToyVLlhQ4AXpgYKBefvllTZo0yZwA/UoJCQl655139Pe//73QCdQBAAAAVFwOSQWP81/OnDhxQvXr15fD4dD27dt1yy23KCUlRZI0bNgwLV682Jyy4MUXX9TLL79cYD+BgYFKTU2Vr6+vDMPQ9ddfr59++sljddeuXVsffPCBbr/99gJ/fvLkSd1///1OV9oiIiK0evVqtWvXzrzaWBDDMPTrr7+qf//+io2NdXvtnrD86CKrSwCASuPe/3na6hKAEkv/5qDVJQAlFuQXfO2NPMAWz8xJ0ty5c+VwOGQYhjp16qTDhw9r8eLFiomJ0cKFC82JwHNycjRv3rxC+7n++uvNQVRyc3O1d+9ej9Vcq1YtrV27VrfffrscDodLMHM4HGrUqJFWrVql7t27m+3Lly93mi/v6nn18tscDodatWqlmJgYVa9e3WPvAwAAAED5Y5sw98orrzhdfapRo4aGDh2qPn36mOHMMAzNnj3baaLwqw0ZMsTcdv/+/R59Zu7jjz9Wy5YtzeNJMkNdfjA1DENVq1bV/Pnz5evrq7Fjx6pPnz5mWHM4HNq/f79WrFihJUuWaOPGjcrOzjb3l6RmzZrpn//8p8feBwAAAIDyxxbPzEnSxYsXNWjQIK1atUq1a9d2uVrlcDi0adMmPfnkk4X24e/vr+HDh5v7rlmzxmP13nHHHRowYIBTiFu/fr2++uornT9/Xo0aNdLIkSPVtGlTSVKTJk10//33a/LkyWYfGzdu1COPPKI9e/Y49R0WFqa//OUvevLJJ83Q98ADD+iNN95wmkMPAAAAQMVlmytzUt5AKK1bt9Yrr7yiAwcOKD09Xenp6dq+fbuefvpp3XTTTUUOfDJq1CjVrl3bvOL11VdfeazWSZMmSZJ5Be1//ud/1K9fP/3jH//QBx98oOeff15t2rTRwoULzX0ee+wxdenSRYZhaO3atbrllltcgpwkpaSkaOrUqXrkkUecrtBNmDDBY+8HAAAAQPlimwFQ3KFBgwaKiIgw1/fu3aucnBy3HycoKEgXLlyQj09eVn7nnXf02GOPFbitn5+f9u3bpyZNmkjKC38ZGRlq0aKFfvvtt2se6/PPPzcHV4mLi1P9+vXd9C48gwFQAMB7GAAFdsQAKLAjBkDxgtOnT+uXX34xX54IcpLUsWNH+fr6mgOevPbaa4Vum52drXfffdfc1jAMLV26tFhBTpJef/11c7lOnTrlPswBAAAAcI9KFea85cpBTw4dOlTkgCyS67N73333XbGPFRMTo9TUVHO9Q4cOJagUAAAAgF0R5jwgPDzcXP7111+vuf2RI0ckybw6t2/fvhId7+pJ1QEAAABUfIQ5D6hataq5fOHChWtuf+WVNUlKSkoq0fHi4+PN5bCwsBLtCwAAAMCeys3UBPlXp8rKMAylpKQoKSlJcXFx2rx5szZs2KDt27e7pf/iuHJEzYCAgBLvn52dXaLtr5wr78ogCQAAAKDiKjdhrnHjxuacae6QP1z/yJEjJUl79uzRq6++qgULFril/6JceTWuWrVqxd7v6rnziis4+PfRc9LT00vVBwAAAAB7KXe3WRqG4ZZXvvw55dq1a6ePP/5YK1euLFHAKo3Tp0+by/lTDhRHaYNs9erVzeXi3NYJAAAAwP7KzZU5qfRh5lryw53D4dDtt9+uNWvW6Prrr1dmZqZHjnfs2DHzeI0bN5a/v7+ysrKK3GfIkCHm8tmzZ0t0vFatWpnLp06dKtG+AAAAAOyp3IS5m266yS39+Pr6KjQ0VOHh4WrVqpW6dOmifv36yc/Pz7yNs0OHDnrvvfc0btw4txzzaocOHVJmZqYCAwPl5+enrl27atOmTUXus3LlylIdq06dOk4jWB46dKhU/QAAAACwl3IT5n744QeP9V2zZk1NmzZNU6ZMkY+PjxwOh+6//369/vrr2rVrl9uPZxiG9u7dq86dO0uS+vTpc80wV1q33367uZycnKzjx4975DgAAAAAypdy98ycJ5w7d05PPfWU7rvvPqdn6p566imPHTM/vDkcDt1xxx0eO07+AC+GYWjz5s0eOw4AAACA8qXcXJnzhqVLl+qmm27Sww8/LEkaPHiwx461bNkyc/LwnJwc+fj4KDc3163H6NChg/r372+ur1q1yq39AwAAACi/HJJKNx6+TTVq1EhHjx6VlHc1q1OnTtq9e7fFVZXOvffeqxtuuMFcf/31151G0iyPlh9dZHUJAFBp3Ps/T1tdAlBi6d8ctLoEoMSC/IKvvZEHVKorc5J04sQJHTlyRE2bNpUktW7d2rZhbvny5Vq+fLnVZQAAAACwQKV4Zu5qBw/+/o1PRESEhZUAAAAAQOlUyjCXlJRkLuc/1wYAAAAAdlIpw1yVKlXM5YyMDAsrAQAAAIDSqZRhrk6dOubylVfpAAAAAMAuKl2Y8/PzMyfzlqTY2FgLqwEAAACA0ql0Ye7uu+9WUFCQJCbaBgAAAGBflWpqguDgYM2cOVOGkTe13u7du5WSkmJxVQAAAABQcpXmylzt2rW1cuVKtWzZUg6HQ5L0wQcfWFwVAAAAAJROhb4yFxAQoE6dOmn48OGaOHGiwsLCZBiGHA6Hzp49q9mzZ1tdIgAAAACUSrkJc6tXr3ZLPz4+PgoJCVF4eLgaNWokH5+8i48Oh8MMcjk5ORo7dqwyMzPdckwAAAAA8LZyE+b69etnPstWVvm3UV4pP8hlZ2dr8uTJbguPAAAAAGCFchPm3OnqUOhwOORwOHTkyBGNHz9eGzdutKgyAAAAAHCPchXmCrqiVlbJycnauHGjPvroIy1fvtxtV/8AAAAAwErlJsxNmDDBLf0YhqHU1FQlJSUpNjZWBw8edEu/AAAAAFCelJswN3fuXKtLAAAAAADbqDTzzJUno0aNUmJiohITE5WQkKCoqCirSwIAAABgM4Q5CzRq1Ejh4eEKDw/XqVOndPLkSatLAgAAAGAzhDkL5M9vZxiGjh49anE1AAAAAOyIMGeBuLg4c/ny5csWVgIAAADArghzFrjyalz9+vUtrAQAAACAXRHmLPDTTz/pzJkzcjgc6tatm4KCgqwuCQAAAIDNEOYskj8VQ0BAgCZPnmxxNQAAAADsxiHJsLqIyigwMFA7duxQy5YtlZ6eroEDB+rHH3+0uiyPW350kdUl2F5uTq4Sz5xX/MkEpSamKCMtU77+vgoKCVKNyAg1aFFPAVUCrC4TcMJ5a417/+dpq0sASiz9m4NWlwCUWJBfsCXHLTeThlc2mZmZGjJkiL744gs1adJEq1at0syZM/Xmm2/q4sWLVpeHcib5bLL2bNivwzuO6tieE8pMyyx0Wx8fHzXr3ETX39lDrXq08GKVgDPOW1R0i559W6Nuutup7XjcKV03tpdFFQF5Tp86rT179mrfnn3au2ev9u87oEuXLpk/r1cvUl9//5WFFcJduDJnkbFjx0qSatSooenTpys0NFSGYSgtLU0xMTHasWOHzp49q9TU1BL1O2/ePE+U6zZcmSu5RX9fql1rd5dq31Y9WmjoE3crtHqIm6sCisZ5Wz5wZc5z7ux1q1a+NMelnTBXdlyZK52tP23T7Pc/1L49+3ThwoUityXMuR9X5iqZjz76SIbxe442DEMOh0PBwcEaPHiwBg8eXKp+y3uYQ8md+y2xwPawmmGqWS9CIdVDlJuTq/OxSYo9Ficj9/fz6sCWg/rP0x9q0qsTFBoR6q2SAc5bVGjVgsP078f+ZnUZgJNfD/yqTRs2WV0GvIwwZzGHw2GGuivDXf7PiiM/CF69Pyqeek0j1XVAJ7Xs2lw16kW4/PzCuRStXrBWP339s9l27rdELXh5iSa9NrHY5xTgTpy3qGj+OekF1a9ZV5KUcilVYcF86YDyKyAgQHXq1NGpU6esLgUeQJizUP4HlLJ+UOGDTsXmkNSqewv1H9NPDVoUPS9htZphuvfxuxTZpK4+e/tLs/343pP6Zd0edejXzsPVAnk4b1FR3dLpBv1h0ChJUlZ2ll74+DX936MzLK4KyOPn56emzZqqbXQbtY1uq7bRbdSseTPt3LFLD45/yOry4AGEOYtMmDDB6hJgE/c9N0IRdauXaJ9ed3bXkV3HtOfHfWbb9tW7+FAMr+G8RUVUtUqQ3v/ff5jrry97XzuP7CtiD8B77rr7Tg0fOUyBgYFWlwIvIsxZJH+eOeBaSvqBOF+vO7s7fSg++stxN1UEXBvnLSqiv02cpusioyRJR84c1/S5r6tHq04WVwXkCasWZnUJsACThgMVVL2mdZ3WszKzlH4x3aJqgOLhvEV51atNF/3xrnHm+qT/e0YZlzMsrAgACHNAheXj6/rPOyc7x4JKgOLjvEV5FOAfoA+f+qd8fX0lSR+tWqLVO360uCoAIMwBFVbimfNO6z6+PqoaVtWiaoDi4bxFeTR97JNqFdVMknQ26ZyeevcliysCgDyEOaCC2r3e+aH8Bs3ryceHf/Io3zhvUd50ahatp4dPMtef+Pd0nU9Ntq4gALgCA6CUMw0bNlSfPn3UtGlTRUREKDQ0b+6aBx980OLKYCeZ6Zna9u12p7a2vVtbVA1QPJy3KG98fXz14dP/lL+fvyTp659itCjmU2uLAoArEObKifvvv19PP/202rVzHoI7fzLwgsLcPffcoylTpkiSzp8/r+HDh3ulVpR/38z5XqlJF831KiFV1G1gZwsrAq6N8xblzTOj/qiOTdtKki6mX9Ij/980iysCAGeEOYtFRkZq0aJFuuGGGyT9PgG4YRjXnAx8/fr1WrhwoQIDA2UYhnr16qVNmzZ5vGaUb3s27NemlT85tQ0Yd4uqhvLcEcovzluUN62jmusv9z9mrj//0as6EX/awooAwBUPIlgoMjJSmzdv1g033OAS3PKvyBUlMTFRK1asMNdHjBjhkTphH2eOxmnJa8ud2pp3bqqed3SzqCLg2jhvUd44HA7Nfuo1VQmoIknadnCX/r9PP7S4KgBwRZiziI+Pj7744gs1aNDAbEtISNDMmTN1880369Zbb73mlTlJ+vTTT83l/v37e6JU2ETy2WR99MICXU6/bLaF1w7XyKlDi3UuAVbgvEV59PiQP6hXmy6SpKzsLD34+p+Um5trcVUA4IrbLC0yceJEdezY0bz6tnz5co0bN05paWmSpKioqGL1891330nK+xaxdevWCg8PV3JyskdqzlerVi3VqlWrVPsG+ATqcm6mmyvCxeSL+mDaXKWcSzHbQquH6MG/PaCQ8GALKwMKx3mL8ui6ulH66/ip5vrry97XriP7itgDAKxDmLPI008/bS6vX79eI0aMuOZtlQVJTk7W6dOnzSt8rVu39vhzc48++qimT59eqn33J+3RgeQ97i2okktLTdMHz8zVud8SzbbgalX14N/GqWb9GhZWBhSO8xbl1ftP/kPBQXnPah45c1zT575ucUUAUDhus7RA48aN1bx5c3P98ccfL1WQy3fw4EFzuVmzZmWqDfaScSlDs5+dp7jj8WZbUEiQ/jDrAdVpXNvCyoDCcd6ivHro9vt1S6cbzPVJ//eMMi5nWFgRABSNK3MW6NYt76F+wzB06NAh/fLLL2Xq78rbKqtXr16mvmAfmWmZ+vC5efrt0BmzLbBqoCa+PEb1mkZaWBlQOM5blGczHnjSXP5yy2odPnNcjeo0KGIPqW6E82MHfr5+LvucSYxXVnaW+woFgP+HMGeB2rV//+Z5376y34ef/5ydJAUHe/45k3feeUeffPJJqfb9x1d/dXM1ldPljMua8/x8nTzw+zDZAUEBmvjXMWrYsugPHoBVOG9R3gUFVjGXB/e4RYN73FLiPhrUitTx+Zud2jo+fBvP3QHwCMKcBUJCQszlS5culbm/sLAwt/Z3LQkJCUpISCjVvgx+UnZZmVn66IUFOr73pNnmH+iv8S/dr0ZtijdwDuBtnLcAALgfz8xZIDHx9wf+IyIiytzflSNfXtk3Kp6sy1n6ePpCHf3luNnmF+CncdPvU5N2jS2rCygK5y0AAJ7BlTkLnD17VlLedAIdOnQoU1/BwcFq166duX7ixIky9YfyKzsrW/NnLtbhHUfNNj9/Pz3wwmg169TEwsqAwnHewk6qD2lb4n36tu+ltf/8/dGD43GndN3YXu4sCwAKxZU5C2zZssVcjoyMVOfOnUvd15gxY+Tr6ytJyszMdOobFUdOTo4WzvpEv249ZLb5+vnq/r+MUIuujGCK8onzFgAAzyLMWSA+Pl67d+8212fMmFGqfqpVq6Znn31WhmHIMAytX79eWVmMllXR5ObkavEry7Rv0wGzzcfXR6OnDVfrHi0trAwoHOctAACex22WFvn3v/+td955R5I0aNAgPffcc3r55ZeLvX9QUJCWLFliThZuGIbeeOMNj9QKay3916f65Ye9Tm0Dxt+iek3r6nxcUon6Co0IkX+AvzvLAwrEeQsA3hcfF6/snByX9nPnzjmtZ+fk6LffzrhsJ0lVqwYx1ZWNOCSVfrZqlJqvr69+/fVXNW7cWA6HQ4ZhaPHixZo2bZpOnjypqKgoHTt2TFJeUPPz+z13DxgwQK+99ppat25ttm3btk09e/b0+vsoqeVHF1ldgu08M/BFt/X10Cvj1bTDdW7rDygM5235cO//PG11CRUez8y5X/o3B60uwbYG9b9dZ87ElqmPu+65UzNnveSmiiqPID/PTw9WEK7MWSQnJ0cjRozQunXrFBQUJIfDoZEjR2rEiBHaunWrjh496rT91KlT1aJFC916662qX7++GQAdDoeSk5M1evRoi94JAAAAACsQ5iy0fft2jRo1SosWLVLVqlUlST4+Purevbu6d+9ubudwODRr1ixzWZIZ5FJSUjR8+HDzKh4AAACAyoHbLMuB1q1ba/HixWrbNm9IZMNw/SvJvxKXvyxJBw4c0LBhw7R//37vFVtG3GYJAN7DbZawI26zhB1ZdZslo1mWA/v371f79u01YsQIrV+/XtnZ2XI4HE4v6fcQt337dk2cOFHR0dG2CnIAAAAA3IfbLMuRZcuWadmyZQoKClLPnj3VsGFD1ahRQwEBATp37pzi4+O1adMmJSYmWl0qAAAAAIsR5sqh9PR0xcTEWF0GAAAAgHKM2ywBAAAAwIYIcwAAAABgQ9xmaTM1atRQ48aNlZmZqaNHjyotLc3qkgAAAABYgCtzFrp6tMqidO3aVevWrVNcXJy2bNminTt36ty5c5o3b55q167thWoBAAAAlCeEOYs88cQTysrKUlZWluLi4uTv71/otn379tXatWvVu3dv+fj4mAEwMDBQo0eP1o4dO9S4cWPvFQ8AAADAcoQ5iwwZMsS8IjdnzhxlZWUVuF2VKlU0f/58BQUFSXKeUNwwDDkcDtWtW1efffZZsa7wAQAAAKgYCHMW8PPzU/fu3c1gtnLlykK3nTRpkurVq2cGt7S0NH3++edasWKFLl68aPbRtm1bPfTQQ16pHwAAAID1CHMWiI6OVkBAgBwOhzIyMrRp06ZCtx0/frwZ5M6cOaPo6Gjdc889GjZsmFq1aqVDhw6ZP3/wwQe9+C4AAAAAWIkwZ4EmTZpIyrtN8sCBA063Tl4pKipK7du3N7d98cUXdfLkSfPncXFxmjJlinl7ZefOnRkMBQAAAKgkCHMWiIyMNJdPnTpV6HZ9+/aVlDfqZWZmphYuXOiyzffff6+EhARzvWPHju4rFAAAAEC5RZizQHBwsLmcmppa6Ha9e/eWlHdVbt26dcrIyChwu127dpnLjGoJAAAAVA6EOQv4+voWuHy1Xr16mcs//PBDodtdeWUuLCysjNUBAAAAsAPCnAWuvBpXo0aNArcJDw9X27ZtzfUNGzYUq++i5qsDAAAAUHEQ5iwQHx8vKe9ZuOjo6AK3GThwoDmwSXZ2trZu3Vpof+Hh4ebypUuX3FcoAAAAgHKLMGeB3bt3m8t169ZVjx49XLYZM2aMpLzn5Xbs2FHo83JS3qiX+fKDIgAAAICKjTBngQMHDuj06dPm/HBvvfWW07Nuw4YN06BBg8wpC7744otC+woMDFSrVq3M9WPHjnmucAAAAADlBmHOInPnzpXD4ZBhGOrUqZMOHz6sxYsXKyYmRgsXLjSDXk5OjubNm1doP9dff705iEpubq727t3rrbcAAAAAwEKEOYu88sorio2NNddr1KihoUOHqk+fPmY4MwxDs2fPdpoo/GpDhgwxt92/fz/PzAEAAACVBGHOIhcvXtSgQYOUkJBgXqG7ksPh0ObNm/Xkk08W2oe/v7+GDx9u7rtmzRqP1gwAAACg/CDMWWj37t1q3bq1XnnlFR04cEDp6elKT0/X9u3b9fTTT+umm24qcuCTUaNGqXbt2nI4HHI4HPrqq6+8WD0AAAAAKzkkGdfcCuVSgwYNFBERYa7v3btXOTk5FlZ0bcuPLrK6BACoNO79n6etLgEosfRvDlpdAlBiQX7BlhzXz5Kjwi1Onz6t06dPW10GAAAAAAtwmyUAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAD+//buPL6K+t7/+PskIQshJCEsYU1kTcCwKbsWULyytCoKKKIGUFQsVlv5tYpVEaq9KmoRtYULCshSLIuliJarREAMAgUChH0JIBAgkBAgISTh+/uDmyMnG1lOMpmT1/Px+DweZyZzvvM5YRjmzcyZAWyIG6BUkIMHD7plHGOM0tPTlZqaquTkZG3YsEHr16/Xli1b3DI+AAAAAHsizFWQyMhIGWPkcDjcMl7eg8EffPBBSdLOnTv1zjvvaP78+W4ZHwAAAIC9cJllBTPGuKXy5D0gPCYmRnPmzNHy5csVHBxs4ScEAAAAYAXCXAXKC17uLOnngOhwODRw4ECtXr1afn5+Fn9aAAAAAJWJyywrSN++fd0yjre3t4KCghQSEqKoqCjdcsst6tOnj3x8fJyBrkOHDpoxY4ZiY2Pdsk4AAAAAVR9hroKsXbu2wsauW7euXnrpJT377LPy8vKSw+HQiBEj9N577ykhIaHC1gsAAACg6uAySxtKSUnRCy+8oIcfftjlO3UvvPCCxZ0BAAAAqCyEORtbvHixZsyY4fw+3aBBg6xuCQAAAEAlIczZ3Ntvv+18HRwcrJiYGAu7AQAAAFBZCHM2d+TIEZcHlEdHR1vYDQAAAIDKQpjzAPv27XO+rlOnjoWdAAAAAKgshDkPkJqa6nwdEhJiXSMAAAAAKg1hzgP4+/s7X1++fNnCTgAAAABUFsKcB2jQoIHz9fVn6QAAAAB4LsKczfn4+Khz587O6ZMnT1rYDQAAAIDKQpizuXvvvVcBAQGSJGOMNmzYYHFHAAAAACqDj9UNoOwCAwM1efJkGWMkSTt27FB6errFXQEAAACoDJyZs6n69etr+fLlatOmjRwOhyRp5syZFncFAAAAoLJwZs5GfH191alTJw0dOlSjR49W7dq1ZYyRw+HQ6dOnNWvWLKtbBAAAAFBJCHMV5Ntvv3XLOF5eXqpVq5ZCQkIUEREhL69rJ1MdDoczyOXm5urRRx9VVlaWW9YJAAAAoOojzFWQPn36OL/LVl55l1FeLy/I5eTkaNy4cW4LjwAAAADsgTBnA/lDocPhkMPh0MGDBzVy5Ej98MMPFnUGAAAAwCqEuQpU2Bm18kpLS9MPP/yg2bNna+nSpW47+wcAAADAXghzFWTUqFFuGccYowsXLig1NVUnT57Uvn373DIuAAAAAHsjzFWQuXPnWt0CAAAAAA/Gc+YAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2JCP1Q2gehnQ7B6rWwBK7aujy61uASiTzK/3Wd0CUGrsc4GS48wcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADflY3QBKplatWho1apRzetq0aRZ2AwAAAMBqhDmbqFOnjv7yl7/IGCOJMAcAAABUd1xmaTMOh8PqFgAAAABUAYQ5AAAAALAhLrOsQE2bNnXbWE2aNCkwXdRZumPHjrltvQAAAACqJsJcBUpKSnJ+x82dHA6HkpKSCv2ZMUY1atRw+zoBAAAAVC2EuQpWUd9x47tzAAAAQPVGmKtg7jwzd32AK2xcAh4AAABQfRDmKkFFhCyCGwAAAFC9cTfLSpKenq5f//rX8vb2LlM1b97cOZYxpsjlfHzI5wAAAEB1QJirQM8884wuXLggSQoKCtKHH36odevWKSoqqtRjVcSNVAAAAADYF2GuAk2fPl0333yzvvrqKzkcDjkcDvXs2VNbt27Va6+9xlk0AAAAAGVGmKtgx48f1y9/+UvFxsbq3LlzkiRfX1+98sorSkhIUK9evSzuEAAAAIAdEeYqybx58xQdHa0lS5Y450VFRem7777Txx9/rKCgIAu7AwAAAGA3hLlKlJKSomHDhmnIkCE6deqUJMnLy0tPPvmkdu/erfvuu8/aBgEAAADYBmHOAsuWLVPbtm01d+5c57yGDRtq8eLFWrp0qRo2bGhhdwAAAADsgDBnkfPnz2vUqFEaMGCAjh075px/zz33aNeuXXr66act7A4AAABAVUeYs9iqVavUrl07/fWvf3XOq127drkeYwAAAADA8xHmqoCMjAyNGzdOffr00YEDB5zzr3+Mga+vr4UdAgAAAKhqCHNVyPfff6/27dtrypQpunr1qowxzscYxMXFWd0eAAAAgCqEMFfFXLlyRX/4wx/Uo0cPJSYmOuc3atRIxhgLOwMAAABQlRDmqqj//Oc/6ty5s15//XVlZ2dLkhwOh8VdAQAAAKgqfKxuAEXLzc3VpEmTtGTJEk2YMEEBAQFWtwQAAACgiiDM2UBiYqJGjBhhdRsAAAAAqhAuswQAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhziIPPfSQzp49q7Nnz+rMmTNq1qyZ1S0BAAAAsBHCnEUiIiIUEhKikJAQHTt2TEePHrW6JQAAAAA2QpizSFZWliTJGKNDhw5Z3A0AAAAAuyHMWSQ5Odn5+sqVKxZ2AgAAAMCOCHMWuf5sXOPGjS3sBAAAAIAdEeYssnHjRp04cUIOh0NdunRRQECA1S0BAAAAsBHCnIXmzp0rSfL19dW4ceMs7gYAAACAnfhY3UB1NmnSJA0ePFht2rTRa6+9pvj4eH3//fdWtwUAbnc196rOnjinU0fP6MLZdF3OyJJ3DW8F1ApQWMM6atK6kXz9fa1uEwA8Avvc6oMwZ6GsrCwNHjxYK1asUPPmzbVq1SpNnjxZ06ZN08WLF61uD1XUT8d+0s6didq1c5cSdyZq9649unTpkvPnjRo11FffrLSwQ+CatNNp2rl+tw5sPaTDO48oKyOryGW9vLzUsnNz9fxVN0V1a12JXQLFY58Lu2CfWz05JBmrm6iuHn30UUlSWFiYJk6cqKCgIBljlJGRobi4OG3dulWnT5/WhQsXSjXuZ599VhHtukVmzqUbL4QCNm3crFn/84l27dyl8+fPF7ssBxbu99XR5Va3YDsL/3uxEr7bUab3RnVrrQeev1dBobXc3FX1M6DZPVa3YEvsc63FPrf02Oda7/7mwy1ZL2fmLDR79mwZ83OWNsbI4XAoMDBQgwYN0qBBg8o0blUOcyibvXv2Kn59vNVtACWWcvxsofNr162tuo3qqFZoLV3NvapzJ1N18nCyzNWf94V7ftyn6eM/0VPvjFJQnaDKahlwYp8Lu2GfW30R5qoAh8PhDHXXh7u8n5VEXhDM/354Nl9fXzVo0EDHjh2zuhWgSI1aNNStd3dSm1tbKaxRnQI/P5+Srm/nf6eNX/3HOS/l+FnNf+NzPTVldIn3g0BFY58LO2CfW70Q5iyW9xemvH9x+Ivn+Xx8fNSiZQu1u7mt2t3cTu1ubquWrVpq29YEPTFyjNXtAS4ckqK6tla/R/qoSevin6UZXLe27n/uHjVsHq5/fvSlc35S4lFtX7NTHfrEVHC3QEHsc2En7HOrL8KchUaNGmV1C7CJe+79lYY+OER+fn5WtwKUyMMvD1Od8NBSvafHr7rqYMJh7fx+l3Pelm8TOLBApWOfC7thn1t9EeYslPecOeBGagfXtroFoFRKe1CRp8evurocWBzanuSmjoCSY58Lu2GfW33x0HAAQJXRqEW4y3R2VrYyL2Za1A0AeDb2ufZHmAMAVBle3gX/WcrNybWgEwDwfOxz7Y8wBwCoMs6eOOcy7eXtpZq1a1rUDQB4Nva59keYAwBUGTvW7XKZbtKqkby8+KcKACoC+1z74wYoVVDTpk11++23q0WLFqpTp46Cgq49wPGJJ56wuDMAqDhZmVna/O8tLvPa9Yq2qBsA8Gzscz0DYa4KGTFihMaPH6+YGNdbwuY9DLywMHfffffp2WeflSSdO3dOQ4cOrZReAcDdvv70G11Iveic9q/lry79O1vYEQB4Lva5noEwVwU0bNhQCxcu1G233Sbp5weAG2Nu+DDwdevWacGCBfLz85MxRj169FB8fHyF9wwA7rRz/W7FL9/oMu/u2DtVM4jvbgCAu7HP9RxcFGuxhg0basOGDbrtttsKBLe8M3LFOXv2rJYtW+acHjZsWIX0CQAV5cShZH0+ZanLvFadW6j7L7tY1BEAeC72uZ6FMGchLy8vrVixQk2aNHHOO3PmjCZPnqw77rhDd9111w3PzEnSF1984Xzdr1+/imgVACpE2uk0zX51vq5kXnHOC6kfogd//0CJ9n8AgJJjn+t5uMzSQqNHj1bHjh2dZ9+WLl2q2NhYZWRkSJKaNWtWonH+93//V9K1M3nR0dEKCQlRWlpahfQMAO5yMe2iZr40V+kp6c55QaG19MSfH1OtkEALOwMAz8M+1zMR5iw0fvx45+t169Zp2LBhN7yssjBpaWn66aefnGf4oqOjK/R7c/Xq1VO9evUqbHwAni/jQoZmvjhXKcfPOucFBtfUE3+OVd3GYRZ2BgCeh32u5yLMWSQyMlKtWrVyTj/33HNlCnJ59u3b5wxzLVu2rNAw98wzz2jixIllem/O1WzlmGz3NgTAVi5fuqxZEz5TctIp57yAWgF6/M3H1CCyvoWdAYDnYZ/r2fjOnEW6dLn2JVNjjPbv36/t27eXa7zrL6sMDQ0t11gAUFGyMrL0ycuf6fj+E855fjX9NPqNR9SoRUMLOwMAz8M+1/MR5ixSv/7P/xOya9euco+X9z07SQoM5LpnAFXPlctX9Okr83R0z0/Oeb4Bvhr9p0fUtE2TYt4JACgt9rnVA5dZWqRWrVrO15cuXSr3eLVr13breMX5+OOP9Y9//KNM7/3P9k1u7gaAHWRnZWv2q/OVlHjUOa+GXw2NnDRCEW1LdrMnAEDJsM+tPghzFjl79ucvoNapU6fc411/58vrx64IZ86c0ZkzZyp0HQA8R/aVbM2ZuECHtic55/n4+ih24sNqHhNpWV8A4InY51YvXGZpkdOnT0u69jiBDh06lGuswMBAxcTEOKePHDlSrvEAwF1ysnM0b/IiHdh6yDnPp4aPHnt1uFp2am5hZwDgedjnVj+EOYv8+OOPztcNGzZU586dyzzWI488Im9vb0lSVlaWy9gAYJXc3FwtePMf2rtpv3Oet4+3RvxxmFrf2tLCzgDA87DPrZ4IcxY5deqUduzY4Zx+/fXXyzROcHCwJkyYIGOMjDFat26dsrO59T8Aa13NvapFby3Rrvg9znle3l4a/tJQRXdrY2FnAOB52OdWX3xnzkJ//etf9fHHH0uSBgwYoJdffllvvPFGid8fEBCgzz//3Pl8OWOMpk6dWiG9wnqnkk8pJze3wPyUlBSX6ZzcXB0/fqLAcpJUs2YAj65ApVj8/hfavjbRZd7dI+9UoxbhOpecWqqxgurUUg3fGu5sD7gh9rmwE/a51ZdDUtmfVI1y8fb21t69exUZGSmHwyFjjBYtWqSXXnpJR48eVbNmzXT48GFJ14Kaj8/P2fvuu+/WlClTFB0d7Zy3efNmde/evdI/R2lk5lTsnTY92YB+A3XixMlyjXHPfb/S5Dcnuamj6uOro8utbsF2Xuz/mtvGGvPWSLXocJPbxqtOBjS7x+oWbIt9rnXY55Ye+1zr3d98uCXr5cychXJzczVs2DCtWbNGAQEBcjgcevDBBzVs2DBt2rRJhw4dcln+97//vVq3bq277rpLjRs3dgZAh8OhtLQ0DR9uzUYEAAAAoPIR5iy2ZcsWPfTQQ1q4cKFq1qwpSfLy8lLXrl3VtWtX53IOh0Nvvvmm87UkZ5BLT0/X0KFDnWfxAAAAAHg+LrOsIqKjo7Vo0SK1a9dO0rWgll/embi815K0Z88eDRkyRLt37668ZsuByyxhR1zyA7viMkvYEftc2JFVl1lyN8sqYvfu3Wrfvr2GDRumdevWKScnRw6Hw6Wkn0Pcli1bNHr0aN188822CXIAAAAA3IfLLKuYJUuWaMmSJQoICFD37t3VtGlThYWFydfXVykpKTp16pTi4+N19uxZq1sFAAAAYCHCXBWVmZmpuLg4q9sAAAAAUEVxmSUAAAAA2BBhDgAAAABsiMssbSgsLEyRkZHKysrSoUOHlJGRYXVLAAAAACoZZ+Yslv9ulcW59dZbtWbNGiUnJ+vHH3/Utm3blJKSos8++0z169evhG4BAAAAVBWEOQs9//zzys7OVnZ2tpKTk1WjRo0il+3du7e+++479erVS15eXs4A6Ofnp+HDh2vr1q2KjIysvOYBAAAAWIowZ6HBgwc7z8h9+umnys7OLnQ5f39/zZs3TwEBAZJcHyhujJHD4VB4eLj++c9/lugMHwAAAAD7I8xZxMfHR127dnUGs+XLlxe57FNPPaVGjRo5g1tGRob+9a9/admyZbp48aJzjHbt2mnMmDGV0j8AAAAAaxHmLHLzzTfL19dXDodDly9fVnx8fJHLjhw50hnkTpw4oZtvvln33XefhgwZoqioKO3fv9/58yeeeKISPwUAAAAAqxDmLNK8eXNJ1y6T3LNnj8ulk9dr1qyZ2rdv71z2tdde09GjR50/T05O1rPPPuu8vLJz587cDAUAAACoBghzFmnYsKHz9bFjx4pcrnfv3pKu3fUyKytLCxYsKLDMN998ozNnzjinO3bs6L5GAQAAAFRJhDmLBAYGOl9fuHChyOV69eol6dpZuTVr1ujy5cuFLpeQkOB8zV0tAQAAAM9HmLOIt7d3oa/z69Gjh/P12rVri1zu+jNztWvXLmd3AAAAAKo6wpxFrj8bFxYWVugyISEhateunXN6/fr1JRq7uOfVAQAAAPAMhDmLnDp1StK178LdfPPNhS7Tv39/541NcnJytGnTpiLHCwkJcb6+dOmS+xoFAAAAUCUR5iyyY8cO5+vw8HB169atwDKPPPKIpGvfl9u6dWuR35eTrt31Mk9eUAQAAADguQhzFtmzZ49++ukn5/PhPvzwQ5fvug0ZMkQDBgxwPrJgxYoVRY7l5+enqKgo5/Thw4crrnEAAAAAVQJhzkJz586Vw+GQMUadOnXSgQMHtGjRIsXFxWnBggXOoJebm6vPPvusyHF69uzpvInK1atXlZiYWFkfAQAAAIBFCHMWeuutt3Ty5EnndFhYmB544AHdfvvtznBmjNGsWbNcHhSe3+DBg53L7t69m+/MAQAAANUAYc5CFy9e1IABA3TmzBnnGbrrORwObdiwQb/73e+KHKNGjRoaOnSo872rV6+u0J4BAAAAVA2EOYvt2LFD0dHReuutt7Rnzx5lZmYqMzNTW7Zs0fjx49W3b99ib3zy0EMPqX79+nI4HHI4HFq5cmUldg8AAADAKg5J5oZLocpq0qSJ6tSp45xOTExUbm6uhR0VLzOHS0BhP18dXW51C0CZDGh2j9UtAKXGPhd2dH/z4Zas18eStcJtfvrpJ/30009WtwEAAACgknGZJQAAAADYEGEOAAAAAGyIMAcAAAAANkSYAwAAAAAb4gYoFejgwYNuGccYo/T0dKWmpio5OVkbNmzQ+vXrtWXLFreMDwAAAMB+CHMVKDIyUsYYORwOt4yX92DwBx98UJK0c+dOvfPOO5o/f75bxgcAAABgH1xmWQmMMW6pPHkPCI+JidGcOXO0fPlyBQcHW/gJAQAAAFQ2wlwFywte7izp54DocDg0cOBArV69Wn5+fhZ/WgAAAACVhcssK1Dfvn3dMo63t7eCgoIUEhKiqKgo3XLLLerTp498fHycga5Dhw6aMWOGYmNj3bJOAAAAAFUbYa4CrV27tsLGrlu3rl566SU9++yz8vLyksPh0IgRI/Tee+8pISGhwtYLAAAAoGrgMkubSklJ0QsvvKCHH37Y5Tt1L7zwgsWdAQAAAKgMhDmbW7x4sWbMmOH8Pt2gQYOsbgkAAABAJSDMeYC3337b+To4OFgxMTEWdgMAAACgMhDmPMCRI0dcHlAeHR1tYTcAAAAAKgNhzkPs27fP+bpOnToWdgIAAACgMhDmPERqaqrzdUhIiHWNAAAAAKgUhDkP4e/v73x9+fJlCzsBAAAAUBkIcx6iQYMGztfXn6UDAAAA4JkIcx7Ax8dHnTt3dk6fPHnSwm4AAAAAVAbCnAe49957FRAQIEkyxmjDhg0WdwQAAACgovlY3QDKJzAwUJMnT5YxRpK0Y8cOpaenW9wVAAAAgIrGmTkbq1+/vpYvX642bdrI4XBIkmbOnGlxVwAAAAAqA2fmbMbX11edOnXS0KFDNXr0aNWuXVvGGDkcDp0+fVqzZs2yukUAAAAAlYAwV4G+/fZbt4zj5eWlWrVqKSQkRBEREfLyunZC1eFwOINcbm6uHn30UWVlZbllnQAAAACqNsJcBerTp4/zu2zllXcZ5fXyglxOTo7GjRvntvAIAAAAoOojzNlE/lDocDjkcDh08OBBjRw5Uj/88INFnQEAAACwAmGughV2Rq280tLS9MMPP2j27NlaunSp287+AQAAALAPwlwFGjVqlFvGMcbowoULSk1N1cmTJ7Vv3z63jAsAAADAvghzFWju3LlWtwAAAADAQ/GcOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA25JBkrG4CQNnVq1dPzzzzjHP6448/1pkzZyzsCLgxtlvYFdsu7Ijt1rMZiqLsW23btjXXa9u2reU9UdSNiu2Wsmux7VJ2LLZbzy0uswQAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhH6sbAFA+Z86c0cSJE12mgaqO7RZ2xbYLO2K79VwOScbqJgAAAAAApcNllgAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsyMfqBgAAsLPGjRurXbt2ioyMVEhIiCQpNTVVx48f18aNG5WSkmJtg0A+Xl5eatWqlW666SY1adJEwcHB8vf3V0ZGhtLS0rR3715t27ZNGRkZVrcKoAQMRVEUZU3Fxsaa68XFxZV5rN69e7uMdfjwYcs/nydW7dq1zYgRI8xnn31mfvrpJ3MjW7duNU8++aTx8/OzvHd3Fdut/apPnz5m2rRpZvPmzSYzM/OG2212drZZsWKF+dWvfmV57xRFFV1cZgmPERsbK2OMs+Li4so8Vu/evV3GOnz4sBs7RWHq1q2r/v3765VXXtHy5ct14sQJlz8DY4wiIiKsbhPV3K9//WudPn1a8+bN0yOPPKLGjRvf8D0dO3bU9OnTtWXLFt1yyy2V0CVQ0OOPP65x48bplltukb+//w2X9/Hx0aBBg7R8+XJ99dVXql+/fiV0WfE4VvBcTz31VIHjhupw7MBllgAs07BhQ02dOlVdunRRZGSk1e0ANxQZGSk/P78C88+fP68dO3bo9OnTysrKUqNGjdSlSxfVrFnTuUzbtm21Zs0a9e/fX99//31ltg0UkJ2draSkJB06dEjnz5/XlStXFBwcrDZt2qh169Yuy/bv319r165Vnz59lJycbFHHQNGaNGmit956y+o2LEGYA2CZ+vXra+jQoVa3AZTJsWPHNHfuXC1dulTbtm3T1atXXX5es2ZNPf3005o8ebIz1AUGBuqf//yn2rRpw3fpUKlyc3O1fv16rVixQuvWrdPmzZuVlZVV6LKRkZEaP368xo4dKy+vaxdxtWnTRjNnztQvf/nLymwbKJG//e1vCg4OtroNSxDmAFQ5ubm52rdvn6Kjo61uBShg+/btev3117Vs2TIZY4pcLiMjQ++9957WrVunb7/9VkFBQZKkOnXqaPLkyRo7dmxltQzoiSeeUE5OTomWTUpK0rhx47Rt2zb9z//8j3P+oEGD1LVrV23cuLGi2gRK7ZFHHtGgQYMkSenp6apdu7bFHVUuvjMHwHIHDhzQ3//+d73wwgvq3bu3goOD1bZtW6vbAgr44IMP1KFDBy1durTYIHe9TZs26aWXXnKZ9+CDD8rHh/9PReUpaZC73syZM7V27VqXeYMHD3ZXS0C51atXT3/5y1+c0/n3tdUBYQ6AZfbs2aPQ0FC1atVKw4cP13vvvae1a9fq0qVLVrcGFOrYsWNlet8nn3yizMxM53RoaKg6derkrraACrNy5UqX6ZYtW1rUCVDQRx99pLCwMElSfHy8/vrXv1rcUeXjvwUBWCYrK6vI72yg8kVHRysmJkYNGjRQUFCQcnNzdenSJZ08eVKHDh3Szp07lZ2dXebxw8PD1a1bN9WvX19hYWG6ePGiTp8+rU2bNrn9LnAOh0Ndu3ZV8+bNFR4eLj8/Px05ckQLFy5063pKKjMzU3v37lXHjh2d8xo1amRJL56G7bZinTt3zmU673JhwGqDBw92fu/+ypUrGjNmTImvmPAkhDmgAnBwAbsICgrS73//e8XGxqpp06bFLpuVlaWNGzdq2bJlev/990s0vo+Pjx5//HE988wzat++fZHL7du3T1OmTNEnn3yi3NzcG44bGxur2bNnO6dHjhypOXPmyN/fX6+88opiY2MLPDYgLS3N0u02/2Vuvr6+FnVif2y3lSf/bd1PnDhhUSeeh2OFsgsJCdFHH33knH7rrbeUmJhYIeuyA8sfdkdR7iirH2IbFBRkJk+ebI4ePXrDh7FevnzZrF271vz2t78tcU8+Pj7mqaeeMgkJCcWOvXfvXjNmzBjj7e1dpt9bbGyskWT8/f3NG2+8UehDkVNTUyvlzzS/iIgIy7czT9puY2JiSvTQ68KUZPvq3LmzOXDgQKnG3bJli2nUqFGZttuoqCiza9euIseurO22qDp79qxLP7fddpvl2x/bLdttcVWjRg2zf/9+l34effRRy7c/u267EscK7qpPP/3UuZ49e/YYX19f58/y88RjB5c/cwEot5iYGH311VcleoCwJPn5+en222/X7bffrg8++OCG/6PbuXNnff7552rRosUNx27durVmzJihsWPH6pe//GWZ/hc1KipKS5cu5W6SHiw0NFSrVq1SeHi4y/yTJ09q586dOnv2rHJzcxUUFKSmTZsqKipKAQEBJR5/0KBBWrRokQIDA13mnzhxQgkJCTp37pwCAwPVtm1bl2daderUST/++KO6d++u48ePl3h9derU0YoVK5x/R7KysrRp0yYdP35cvr6+at68uZo1a1bi8dztzjvvVJ06dZzTWVlZSkhIsKwfu2K7rTw1atTQJ5984vIduaNHj+rzzz+3pB9PwLGCe/zXf/2XRo4cKUm6evWqnnzySV25cqVSe6hKCHNAOXFwATv6f//v/7lss1u3btW4ceP0ww8/FLq8t7e3evTooXvuuUejRo0qduzo6Gj9/e9/d9lmv/rqK7322mvatGlTgeU7duyoqVOn6he/+IWkaw9/Xbhwofr06VPg2W1FmThxomrXrq3MzExNmjRJ06ZNK3AjHSsfTP/b3/7WZfrbb7/VhQsXLOrGvthuK47D4VBQUJBatGihvn37auzYsS5BLiMjQyNGjOB7zmXEsYJ7BAYGasaMGc7pwu64Wh1ZfnqQotxRVl068eabb7osu2XLFtOzZ88il/f29ja33Xabefvtt82ZM2eKvcQhOjraXLhwwWX8lStXmi5duhS6fMeOHc2aNWtcll+7dq3x8vIq8e/t/PnzxhhjMjIyzIsvvmgCAwMLvCcyMrJS/kyrw6USVm23iYmJzuVSUlJMaGhoidfj5+dX5M8cDofZvn27Sx+vvvrqDcf09vY2ixcvdnlfcZdz5f+9GXPtkqTevXtb/meav+6///4Cvfbt29fyvspTbLf2327vvffeAr0U5eDBg6ZHjx6Wb3d23nY5VnBPffjhh84eTpw4YYKDgwssk58nHjvkK8sboCi3FAcX18rOBxf5qzrskK3abi9evOhc7h//+IfbPs8DDzzg0sPf//73Er83MDDQJCcnO9+bkJBQ4t+bMcb88Y9/tPzPM39FRkYW+K7cokWLLO+rvMV2+3PZdbstSZjbsmWLGTlypKlRo4bl25y7imOFa2XHY4XbbrvN5ObmOtf/wAMPFLpcfp547HB98Zw5oJyuv9NXXFycUlNTS/ze4i5Xuf/++xUTE+OcXrRokSZNmnTDMXNzcxUbG6tTp045540fP77EPUnSn/70J61Zs6ZU74F91a9f321j/eY3v3G+vnr1ql588cUSv/fSpUuaPn26c7p9+/YF7qRX3Hs/+OCDkjdaCYKCgvSvf/3L5btyJ06c0DPPPGNhV56D7bbiderUSb/+9a81fPhwORwOq9uxNY4VysfPz08zZ86Ul9e16LJ8+XItWbKkUtZd1RHmADfi4AJ2sWfPHufrXr16OZ/VUx41a9ZU9+7dndObNm1SUlJSqcaIi4tzmb799ttL/L709PRSrasi1ahRQ0uXLtXNN9/snJeVlaVhw4bp7NmzFnZmb2y37rNq1SpFRkY6q2XLlurSpYtiY2M1b948Xb58WZJ06623as6cOfruu++cD2dG+XCsUHqTJk1SmzZtJEnp6en8p9h1CHNAOXFwATtasGCB87W3t7c+//xzffnllxo+fLhCQ0PLNGb37t1dnp126NAhRURElKry/tc1T0nuyiZduxFGVeHl5aWFCxeqX79+znnZ2dl66KGHtH79egs7sz+2W/fJzMzUkSNHnHXw4EFt3rxZc+fO1aOPPqrWrVu7/Dvyi1/8QqtXry7VTTnwM44Vyu6WW27R7373O+f0hAkTSnWzFk/H3SyBclqwYIFuueUWST8fXKxcuVLz5s3T119/XapLKfIUdXBRGnY8uEDl+fDDDzVkyBD16NHDOW/gwIEaOHCgrl69qsTERMXHx2v9+vVas2aNjhw5csMx8z+8efjw4Ro+fHi5+rz+EsXinD59ulzrcReHw6FPP/1UDzzwgHNe3uVMX3zxhXWNeQi228pz7NgxDRgwQN9++6169eol6dqZmzfeeMPlwBolw7FC2fj4+OiTTz6Rj8+1yBIfH6+PP/64UtZtF4Q5oJw4uEB5GGNcpvP/w1oa3t7exY59vStXrqhfv35677339Pjjjzv/oczrISYmRjExMXryySclSQkJCZo9e7amT5+uzMzMQsesiEuwgoKCSrRcVbnN/9/+9jc99thjzumrV6/qiSee0MKFCy3syv3Ybotnt+22KFlZWRo7dqy2b9/unPfUU09p4sSJXMFRShwrlM2ECRPUvn17Sdf+/o8ZM6bYfUR1xGWW8BhWH1xMnz5dOTk5BXrIO7CYM2eOkpKStG3bNj3//PPFXqrCwUX1kf/3XatWrTKPlf/P+EYHWxkZGXr66afVqlUrvfrqq9q4caOys7MLXbZDhw56//33tX//fvXp06fQZa7/H2J3sdNNF6ZNm+YMEXmeeeYZzZ4925qGKhDbbfHstN3eyI4dO5SYmOicrlmzpvPZenbEsULxqtKxQrt27TRhwgTn9FtvveWyLeIawhw8BgcXxfOkgwtPkv/SmpCQkDKPlf+9Jb1sJykpSZMnT1a3bt0UEhKiPn366OWXX9a///1v500Q8jRu3FgrV65U165dC4yTkpLiMv3SSy/J4XCUq270oOeq4t1339W4ceNc5j333HMuNxfwJGy3nrHdltTevXtdpq9/mLjdcKxQvKp0rPDyyy/Lz89P0rU7Ac+bN69E32HNr0mTJi4/L2lgtQvCHDwGBxfV6+DCU5w8edJlOiIiQv7+/mUaKyoqymU6OTm51GNkZGRozZo1evPNN9W/f3+FhYVpzJgxOnHihHOZgIAAvfvuuwXee/0triWpdevWpV6/Hf33f/93ge8QjR8/3qPvCst2W73kDxx5B9h2xLGCfY4Vrj8r2ahRI+3du1dJSUk3rPy+//57l5+PHj26Ej9FxSPMwWNwcAE72rt3r8sBgLe3tzp16lSmsfK+XJ9nw4YN5epNurYdz5w5Uz179tTFixed83v27Kl69eq5LBsfH6+rV686p++6665yr7+qmzRpkv7whz+4zJswYUKhf689Cdtt9dKkSROX6fz/RtkJxwrwNIQ5eAwOLmBXP/zwg8t0WW5ZXa9evQKX4rjzNvhHjhzR6tWrndNeXl6KjIx0WSYlJcXlDmdNmjTRgAED3NZDVfPKK6/olVdecZk3ceJE/fnPf7aoo8rFdls9BAcHq0uXLi7z9u/fb1E35cexAjwNYQ4ehYML2FH+G2SMHj1a4eHhpRrjxRdfVI0aNZzTO3bs0ObNm93RnlP+L+1nZWUVWObDDz90mZ4yZYoCAwPd2kdVMH78eE2aNMll3ptvvqnXX3/doo4qH9tt9fDyyy+7fDfr9OnTio+Pt7Cj8uNYwR4GDx5cpktF84uMjHT5+dSpUy34NBXLUJSn1JAhQ8z10tLSTHh4eKnGePfdd13G2L59u9v7XLJkics62rdvX2CZkSNHuiyTmJhoAgMD3d5LbGysy3piY2Mt/3PMq/wiIiIs76kiysvLy+zfv9/ls8bFxZlatWqV6P1Dhgwx2dnZLu9/7LHHily+adOm5rHHHjO+vr4l7jE8PNycP3/eOf7ly5cL7c/Ly8vs2rXLpZdVq1aZkJCQUv1O6tatawYPHlzkz63cbseNG1dg23znnXcs344qu9hu7bPdPvDAA6Zjx46lft+YMWNMbm6uS88TJ060fNsrb3GsUPqqyscK+Ss/Tz12uK4sb4Ci3FYcXBSsqnpwUZKqTjvkXr16mStXrrh83t27d5shQ4aYGjVqFPqeyMhI89FHH5mcnByX93355ZfFrqtDhw7GGGOSk5PNtGnTzB133GH8/f2LXL5fv35mz549LutYsGBBkcu3bdvWpKWluSx/9OhR8/TTTxf7dzE0NNQMGzbMLFiwwGRmZpq4uLgqt92OGjWqwMHt4sWLTURERKkrODjY8u2O7bZ6bLfvv/++yc3NNf/+97/N6NGjiw0uDofD9O3b1/zrX/8y+e3Zs8f4+flZvt2VtzhWKFh2PlbIX/l58rHD/5XlDVCUW4uDC3scXORVWFhYkQe7+fXq1avQ5Ro3bmz5dueOevLJJwtsg8YYc+nSJbNu3TqzePFiM2/ePPPll18WOBDJs23bNhMaGlqi7fZ62dnZZseOHebLL7808+fPN/PnzzerVq0yp06dKrBscnLyDf8X+8477zSpqamFrmfLli3miy++MHPnzjWLFy8233zzjTl69GiBZavidhsXF1fo770sXnvtNcu3Obbb6rHdvv/++wX6PHHihFm9erVZsmSJmTt3rlmyZIn5/vvvXQLE9fbv32+aNGli+fbmruJYwV7HCqWp/AhzFGXD4uDCVVXeQX/66aeF/v5L4/Dhw5Zvc+6qu+66yyQnJ5fp9zBv3jwTEBBww3UUtt2W1M6dO02LFi1K9FlatGhhNm7cWOZ1LV26tMptt4Q5ttsbqYrbbWFhrjTmzJljwsLCLN/O3F0cK7iqyscKpan8CHMUZdPi4OJnVfHgIq8IcwUrICDAjBs3zmzbtq3AJX35paammvnz55tOnTqVeHwfHx9z9913m6lTp5odO3YUejCT3+bNm83YsWONt7d3qT/PoEGDzKpVq0xmZuYN15OYmGimTp1qevXqVeyYhLmqV2y3VXe7bdasmXn++efNypUrzblz5274eYwx5uTJk2batGml+jOyY3Gs8LOqfKxQmsrP08Oc4/9eAB4pICBAjz/+uJ544gnFxMTIy6voG7impaVp5cqVmjJlisvdoYrj4+OjO++8UwMHDtQdd9yh6OhoeXt7F/ue//znP5o1a5ZmzJih3NzcUn2eQYMG6bnnntPtt99+w+fi7Nq1S998840+//zzYu+wFRsb63JXupEjR2rOnDml6qs8Pv30U40cObJcYyQlJemmm25yT0NVTEhIiLp3766GDRsqNDRU/v7+SktL07lz57R7925t375dxpRvNx4UFKR27drppptuUoMGDRQYGKjs7Gylp6crKSlJ27ZtK9Pzk/Lz8/NTt27dFBERobCwMAUGBurSpUtKTU3VgQMHtHv3bp07d67c64H12G6rtubNm6tVq1Zq2rSpgoODFRAQoIyMDKWnpys5OVkJCQk6duyY1W1WGo4Vqv6xQmnk37dERkbqyJEjFnVT8QhzqDY4uAAAAMXhWAF2Q5gDAAAAABvioeEAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQAAAACwIcIcAAAAANgQYQ4AAAAAbIgwBwAAAAA2RJgDAAAAABsizAEAAACADRHmAAAAAMCGCHMAAAAAYEOEOQBAtRYbGytjjLPi4uLKPFbv3r1dxjp8+LAbOwUAwBVhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQz5WNwAAAKTo6GjFxMSoQYMGCgoKUm5uri5duqSTJ0/q0KFD2rlzp7Kzs8s8fnh4uLp166b69esrLCxMFy9e1OnTp7Vp0ya3P0LB4XCoa9euat68ucLDw+Xn56cjR45o4cKFRb4nJCREHTt2VKtWrRQcHCw/Pz9lZmYqLS1NR44c0e7du3XixAm39gkAnsBQFEVRVHWt2NhYc724uLgyj9W7d2+XsQ4fPlzs8kFBQWby5Mnm6NGj5kYuX75s1q5da37729+WuB8fHx/z1FNPmYSEhGLH3rt3rxkzZozx9vYu0+8sNjbWSDL+/v7mjTfeMD/99FOBdaSmphY6Vp8+fczXX39tsrOzb/g7OHbsmJkxY4Zp37695dsNRVFUFSnLG6AoiqIoy8qqMBcTE1No6CmJkoSuzp07mwMHDpRq3C1btphGjRqV+ncWGxtroqKizK5du4ocu7Aw95e//KUsH99MnjzZ8u2GoiiqKhSXWQIAUMlCQ0O1atUqhYeHu8w/efKkdu7cqbNnzyo3N1dBQUFq2rSpoqKiFBAQUOLxBw0apEWLFikwMNBl/okTJ5SQkKBz584pMDBQbdu2VevWrZ0/79Spk3788Ud1795dx48fL/H66tSpoxUrVqhFixaSpKysLG3atEnHjx+Xr6+vmjdvrmbNmrm8Z8KECXruuedc5mVnZ2v79u06cuSILl26pICAAIWGhioqKkqNGzcucT8AUJ1YnigpiqIoyqqy4szcm2++WeCMWM+ePYsc19vb29x2223m7bffNmfOnCn2zFx0dLS5cOGCy/grV640Xbp0KXT5jh07mjVr1rgsv3btWuPl5VXi39n58+eNMcZkZGSYF1980QQGBhZ4T2RkpPN17dq1TUZGhvP92dnZ5tVXXzXBwcFFrjM8PNyMHDnSrF692kyaNMny7YaiKKqKlOUNUBRFUZRlZUWYS0xMdC6TkpJiQkNDS7wOPz+/In/mcDjM9u3bXXp49dVXbzimt7e3Wbx4scv7Hn300RL/zoy59p2+3r17l+gzDB061OW9r732Wql+z/7+/pZvNxRFUVWheDQBAACVLCIiwvk6Li5OqampJX5vVlZWkT+7//77FRMT45xetGiRJk2adMMxc3NzFRsbq1OnTjnnjR8/vsQ9SdKf/vQnrVmzpkTLXv/5JWnx4sWlWtfly5dLtTwAeCrCHAAAFqpfv77bxvrNb37jfH316lW9+OKLJX7vpUuXNH36dOd0+/btC4Su4t77wQcflLzRfNz5OwCA6oQwBwBAJduzZ4/zda9evTR06NByj1mzZk11797dOb1p0yYlJSWVaoy4uDiX6dtvv73E70tPTy/xeq7//JL0xhtvFLhZCwDgxribJQAAlWzBggW65ZZbJEne3t76/PPPtXLlSs2bN09ff/11qS67zNO9e3f5+vo6pw8dOlTiM2t5vLxc/4837+6UN7J169ZSrefbb7/VqVOn1KBBA0lSjx49tH//fs2aNUvLli3T1q1bZYwp1ZgAUB0R5gAAqGQffvihhgwZoh49ejjnDRw4UAMHDtTVq1eVmJio+Ph4rV+/XmvWrNGRI0duOGbTpk1dpocPH67hw4eXq886deqUaLnTp0+XatzMzEw9/fTTWrx4sby9vSVJDRs21B//+Ef98Y9/VGpqquLj4xUfH69169Zpw4YNxX5XEACqKy6zBABUa/nPAOU/O1UaecGkqLHzXLlyRf369dP06dOVk5NTYP0xMTF68sknNWfOHCUlJWnbtm16/vnni33WXFhYWJn7LkpQUFCJlrtw4UKpx/7iiy/Uv39/7d+/v8DPQkNDNXDgQE2ePFnfffedzpw5o3nz5unWW28t9XoAwJMR5gAA1Vr+IFKrVq0yj5U//BT3PbKMjAw9/fTTatWqlV599VVt3LhR2dnZhS7boUMHvf/++9q/f7/69OlT6DLXX2LpLg6Hw+1jXu+bb75RdHS0Bg8erIULFyo5ObnQ5YKCgjRixAht2rRJs2bNkr+/f4X2BQB2QZgDAFRr+b+fFhISUuax8r+3JN99S0pK0uTJk9WtWzeFhISoT58+evnll/Xvf/+7wC34GzdurJUrV6pr164FxklJSXGZfumll+RwOMpVo0aNKv0voZRyc3P1xRdf6OGHH1bDhg3VsmVLPfroo/rb3/6mgwcPFlh+9OjRmj9/foX3BQB2QJgDAFRrJ0+edJmOiIgo85mfqKgol+mizjQVJSMjQ2vWrNGbb76p/v37KywsTGPGjNGJEyecywQEBOjdd98t8N7rnxEnSa1bty7VuquKgwcPat68eRo7dqxatmypjh07asGCBS7L3H///brzzjst6hAAqg7CHACgWtu7d6/LGTRvb2916tSpTGPl3aEyz4YNG8rVW0ZGhmbOnKmePXvq4sWLzvk9e/ZUvXr1XJaNj4/X1atXndN33XVXudZdVSQkJGjEiBH66KOPXOYPHjzYoo4AoOogzAEAqr0ffvjBZbosz32rV69ege+zrV+/vjxtOR05ckSrV692Tnt5eSkyMtJlmZSUFJdHBDRp0kQDBgxwy/qrglmzZrlM33TTTRZ1AgBVB2EOAFDtzZ4922V69OjRCg8PL9UYL774omrUqOGc3rFjhzZv3uyO9iSpwF0vC7tV/4cffugyPWXKFI95GHdJPj8AVDeEOQBAtbd06VIdOHDAOR0cHKyFCxeW+M6WQ4YM0W9+8xuXeVOmTCl02aZNm+qxxx4r1d0nw8PD1a9fP+d0VlaWDh06VGC5uXPnavfu3c7ptm3batmyZaW+qUvdunUr9DLGhx9+uMD3C2/ksccec5m+/nMCQHVmKIqiKKq6V69evcyVK1fM9Xbv3m2GDBliatSoUeh7IiMjzUcffWRycnJc3vfll18WuZ4OHToYY4xJTk4206ZNM3fccYfx9/cvcvl+/fqZPXv2uIy/YMGCIpdv27atSUtLc1n+6NGj5umnnza1atUq8n2hoaFm2LBhZsGCBSYzM9PExcUVuWxsbKzL+LGxsaX6XS9btszk5uaa1atXm2eeecZEREQUuWzdunXNO++8Y3Jzc53ry8nJMdHR0ZZvMxRFUVaX4/9eAABQ7T355JP6+OOPCzz8OyMjQ1u2bNGpU6d0+fJlhYaGqnXr1mrZsmWBMRISEtS3b98iH0vQoUMHbdu2zWVeTk6O9uzZo6NHjyotLU3Ste/gdejQQfXr13dZ9tSpU+rYsWOxd8q88847tXjx4gJn5HJycrRjxw4dPXpU6enpqlmzpkJCQtS6dWs1bdrUZdnvvvtOffv2LXT82NhYl0tTR44cqTlz5hTZT37Lli3Tfffd5zIvJSVFiYmJOnv2rC5duqSaNWuqefPmiomJkY+Pj8uykydP1quvvlri9QGAJ7M8UVIURVFUVam77rrLJCcnm7KYN2+eCQgIKHb8vDNzZbFz507TokWLEn2OFi1amI0bN5Z5XUuXLi1ybHecmSuLK1eumFdeecXybYSiKKoKleUNUBRFUVSVqoCAADNu3Dizbds2l8v7CpOammrmz59vOnXqVKKxfXx8zN13322mTp1qduzYUeASzcJs3rzZjB071nh7e5f6swwaNMisWrXKZGZm3nA9iYmJZurUqaZXr17FjlneMNesWTMzbtw4s2LFCnP27Nkb9pWWlmY+/fRTExUVZfm2QVEUVZWKyywBAChGSEiIunfvroYNGyo0NFT+/v5KS0vTuXPntHv3bm3fvl3GlP2f0qCgILVr10433XSTGjRooMDAQGVnZys9PV1JSUnatm1bqR8+Xhg/Pz9169ZNERERCgsLU2BgoC5duqTU1FQdOHBAu3fv1rlz58q9nrJo2bKlWrVqpWbNmik4OFg1atTQxYsXdfbsWSUmJmrnzp3Kzs62pDcAqMoIcwAAAABgQzyaAAAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIANEeYAAAAAwIYIcwAAAABgQ4Q5AAAAALAhwhwAAAAA2BBhDgAAAABsiDAHAAAAADZEmAMAAAAAGyLMAQAAAIAN/X+XM8BZn4BHNAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 900x900 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3, 3), dpi=300)\n",
    "sns.heatmap(U, annot=True, cmap=\"Greens\", xticklabels=userlabels, \n",
    "            yticklabels=userlabels, cbar=False)\n",
    "plt.title(\"User-User Similarity Matrix\\n AA'\")\n",
    "plt.xlabel(\"Users\")\n",
    "plt.ylabel(\"Users\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b86ba446-6f61-40e3-88c6-416e0ce461a7",
   "metadata": {},
   "source": [
    "## Item-Item Co-occurrence Matrix\n",
    "\n",
    "The **item-item co-occurrence matrix** is used to capture how often pairs of items are interacted with together. This matrix is typically derived from a binary user-item interaction matrix, where each element represents the number of times items have co-occurred in the same user's interaction history.\n",
    "\n",
    "The mathematical formula for the item-item co-occurrence matrix $I$ is:\n",
    "\n",
    "$$ I = A^T A $$\n",
    "\n",
    "Where:\n",
    "- $A$ is the binary user-item interaction matrix.\n",
    "- $A^T$ is the transpose of the user-item interaction matrix.\n",
    "\n",
    "---\n",
    "\n",
    "### Explanation of the Matrix\n",
    "\n",
    "- The diagonal cell, $I_{ii}$, represents the total number of times the $i$-th item has been interacted with. It is the sum of interactions across all users for item $i$.\n",
    "- The off-diagonal cell, $I_{ij}$, represents the number of common users who have interacted with both items $i$ and $j$. It is the dot product of the $i$-th and $j$-th rows of the binary user-item interaction matrix.\n",
    "\n",
    "This matrix helps identify which items are frequently interacted with together by users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2eb885d2-4437-4b6e-aab6-13baac2c6fad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Item-Item Co-occurrence Matrix (A'A):\n",
      " [[2 1 1 1 2]\n",
      " [1 2 1 2 1]\n",
      " [1 1 3 2 1]\n",
      " [1 2 2 3 1]\n",
      " [2 1 1 1 2]]\n"
     ]
    }
   ],
   "source": [
    "I = A.T @ A\n",
    "print(\"\\nItem-Item Co-occurrence Matrix (A'A):\\n\", I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "42615c33-8fae-41bb-b7b2-f3f000c480cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yRSkpKUpPT1eBH5PDGWM0ZsyYIFbsrSrNPwNn1ald2+kSgKDjOAeKd+Ko5/wVEdG1HKoEKIWfQcsZZvEc6eywpfV5dlUEBAWfW3BGpQtbpNMTzLZt21YhISGyLEuS1KpVKyUnJ/vVj2VZjoQtUtWZfwYAADgntpnnCNlj+4qY/wKoxMzurR7PrfBIKaqmdOpEMVsAQMXgcroAf/Xr10/r1q3TiBEjFB4eLmOMe6lM3n33XX322WeyLEsPP/ywhgwZ4nRJAACgEolvlayki7q4nxcUFGjzoiUOVgQEQUG+d1tIpfy+GEA1U6nClg4dOuiTTz5R7dq13SNaLMsKeHHasGHDNHv2bIWEhGjq1Kl688031bx5c6fLAgAAFVzthg10x0fvKiT01z86f5zxqY7s3OVgVUAQxCV4PDX5edIJLr8HUPFVqlj4jTfeUFRUlIwxsixLWVlZmjZtmubNm6fNmzfr2LFjleruPlVh/hkAABB8rpAQ1agbo4bnnqPzr/6tevxupKLq1HH/PHXrdv337ocdrBAIDlenSzwbdm6WKtmIdgDVU6UJW9q0aaPu3bu7LxdKSUnRlVdeqV27Kvc3OFVh/hkAAGCvG175qy67/67SV5S04ZtFmnzLHcpMPRzkqoByFhEpq3t/j6aCn793qBgA8E+lCVu6desm6XSoUFBQoCFDhlT6oKVfv3768MMPFR0dLUmVbt4ZAADgnJ8/m6OF/5yolHnfOF0KEBSugbfJqlPP/dycPC7zHfc2B1A5VJqwJT4+XtLpQOLHH3/U+vXrHa6obM7MPxMVFSVJ7kujAAAAfNHuin6yQkKUm5WlLd8udbocwFZWh25y9b7Go61g1nvSyeMOVQQA/qk0YUtmZqb78ebNmx2sxB5Vbf4ZAABgnznPvqhv/jHB/TwsKlI1Y+spseP56jjoarW5rLdCw8N1/tW/1flX/1YL3/i3pt/3qIwfc70BFVbj5nKNeNCjqWD9DzKL5zhUEAD4r9KELXv37nU/Dg8Pd7CSsquq888AAAB7nExL08m0NK/2rd8t08J//lstL7lYo96fqNikZpKk3nffobCoSE0Zc3d5lwrYq26cQu4aKyuyhrvJHDmogsnjHSwKAPxXacKWVatWqaCgQJZlqVWrVk6XUyaVff6ZuLg4xcXFBbi1JYm5aQAAKIut3y3Ty32u1p9WLlSt+rGSpEtG36o1s77Qz7O+cLg6IEC16ijk3udl1a3vbjLHjir/tSel49zuGUDlUmnClr1792rhwoXq27ev2rdvrxYtWmjbtm1OlxWQyj7/zF133aWxY8cGtnFulpSbbWs9AABUR0d27NScZ1/U0Nf+5m7r/+j9hC2onGrUUsh942Q1aOJuMpnHlP/aE1LqPgcLA4DAuJwuwB8vvPCC+/FLL73kYCVlU9XmnwEAAM5Y9d8ZHs+bX9xVUXXqOFQNEKDIGgq553lZjZu7m8yJTOW//qS0v/KM/gaAs1WqsGXBggV66qmnZFmWrrnmGk2YMEGhoZVmcI5bVZp/BgAAOCcz9bBOHP11bhdXSIjqN2/mYEWAnyKiFHL3s7Ka/TpNgDl1QvlvPCXtqZyj2AFAqkSXEZ0xbtw4HTt2TH//+991xx13qFevXho/frz+97//af/+/U6X55PKPv/MhAkT9NFHHwW07bqV39tcDQAA1Vt+bq7H89CICIcqAfwUHqGQP4yV1eJcd5PJOqn8fz4t7dzkYGEAUHaVKmzZunWr+3Fubq7Cw8PVpk0bTZw4UZJ0/PhxpaWlqcCP2x4aY5ScnGx7rSWp7PPPpKamKjU1NcCtmRwXAAC7hEZEuCfIPSPj4CGHqgH8EBYu111jZSW3dzeZ7CzlTxgrbUtxri4AsEmlCluSkpJkjJFlWTLGuG+dbFmWJCk6OlrR0dF+9Xmmj/L2wgsvqG/fvpJOzz8zaNAgR+oAAACVV5vLessVEuJ+nn3ihNL3MpkoKrjQMLnufEqu1ue7m0xOtgrefFbass7BwgDAPpVqzpYzCgckZ4IXfxcnVZX5ZwAAgDMsy9KVf37Uo23d/772uqwIqFBCQuW64wm5zu3kbjK5OSp463mZjT87WBgA2KtS/XW/a9cux0MSO1WF+WcAAEDZ9L77d1o941NlHDjo8zau0FDd/O/X1OLirh7ti/450e7yAPu4XHKNeUyu9r8etyYvVwUTX5BJWe1gYQBgv0oVtjRv3rz0lSqJqjL/DAAAKJtLRt+i6158Rj/O/Fyrpn+sTQuXKPv48SLXDYuMVIdrr9YVTzysxu3bevxs2XvTtHHB4vIoGfCf5ZJr5CNydejmbjL5eSqY9KLMLysdLAwAgqNShS1VSVWafwbOOnDwoPLy873aDx8+4vE8Lz9fe/YVfR1/jagaqlc3JhjlAbbgOEdVF16jhi66eaguunmoCgoKlLplm47s2KVT6enKy8lVZHQt1WuWqEZt2yg0PNxr+zWfz9X7t9/jQOWAb1y33CdX554ebQWfvSuze6tUL96/zjLSpDwul0PFxecWSJIlbg/jiPz8fFvDkTOhTUWf98WcSHe6hCqn75UDtbeMl50NuuYq/fXZp22qCLAfx3nFc2fNRKdLqDKe+HGJEjueX/qKRcg5eVJfPP93ffX3V1WQl2dzZXjj9z2cLqHKCJ0wx7a+8l95TGbzWtv6q+5Cx091uoQqh88tFY9VM6bc91mx/zKvwqra/DMAACAw799+r84fcKXaXNZLTS/ooLDIyFK32Z+yUSs++FDfT/6Auw8BAFABEbY4pCrNPwMAAAK3c9Vq7Vy1Wp8/9bxcoaFqdO45qt8iSTGNExRRq6ZCwsKUffyEsjIydGTHLu3+cY1Opqc7XTYAAChBlbuMqE6dOoqOjpZlWdq9e7fT5aAQLiMCgKqBy4hQHXAZEaoDLiNCdcBlRAEYOHCgBgwYoB49eigpKUkul0vS6cliw8LCvNZv1qyZmjZtKkk6ceKEVq/mNnMAAAAAAMA+lTZs6d+/v1577TX3rY7P3MWnNC1bttS8efNkjFFOTo4SEhKUzlBcAAAAAABgE5fTBQTiz3/+s+bMmaPk5GSvkKW0SWe/+eYbpaSkyLIshYeHa+jQocEsFQAAAAAAVDOVLmy55557NHbsWPflQpKUnZ2txYsXa/bs2T6NcJk+fbr78VVXXRWUOu1Qp04dNWnSRImJXBcPAAAAAEBlUanCluTkZI0fP17GGBljlJ2drUcffVSxsbHq06eP7rnnHp/6mTVrlqTTlx716FFxJj4bOHCgJk2apE2bNiknJ0dHjhzRjh07tG3btiLXb9asmXr06KEePXroggsuKOdqAQAAAABAUSrVnC3PPvusQkNPl3zq1CldfvnlWrZsmd/9rFmzRllZWYqMjFR0dLRatWqlzZs3212uz5h/BgAAAACAqqPSjGwJDw/XgAED3KNannzyyYCCFun0vC4pKSnu523atLGrTL8x/wwAAAAAAFVLpQlbLrnkEkVFRcmyLJ08eVITJkwoU3/79u1zP05ISChreQGpTvPPAAAAAABQXVSasCUpKUnS6dEeK1asUE5OTpn6y8jIcD+Ojo4uU1+BqOrzzwAAAAAAUF1Vmjlb4uLi3I8PHDhQ5v7OHk1y9uPyUlXnnwEAAAAAoLqrNCNbsrOz3Y8jIiLK3F9sbKz7cVpaWpn780dVnX8GAAAAAABUorAlNTXV/bhJkyZl7q9Dhw5F9l0equL8MwAAAAAA4LRKE7Zs27ZN0um5STp27KgaNWoE3FenTp08LktavXp1mevzR1WbfwYAAAAAAPyq0oQtK1asUEZGhowxCgsL06hRowLu68EHH3Q/3rlzp3bt2mVHiT6ravPPAAAAAACAX1Wav8wLCgo0Z84cWZYly7L0zDPPBHQ50bXXXqubbrrJPV/KtGnTglBtyarS/DMAAAAAAMBTpQlbJOm5555TQUGBjDGKiYnRwoUL1bZtW5+3HzFihKZOnSpjjCzLUlZWll599dUgVly0qjT/DAAAAAAA8FSpwpaNGzfq9ddfl2VZMsaoefPmWr16td5++231799f8fHxXts0adJEo0aN0tKlSzVp0iRFRES4t3/66acdCSeq0vwzAAAAAADAU6jTBfjroYceUtu2bdWvXz/3/C233XabbrvtNklyj1qRpOPHjysyMtK97ZmQxbIsffLJJ3rppZeceAnu+Weio6Pd88+88cYbAfXl9PwzAAAAAADAU6Ua2SKdDlMGDhyoyZMnu8MTSe65XM6sI8l9e+Uz7WfWe+eddzRs2LDyL/7/VaX5ZwAAAAAAgKdKF7ZIpyeYHT16tIYOHap169Z5hClnOxNCSKdDlq1bt2r48OG6/fbblZ+fX54le6kq88/g/9q78zivyrpv4N8zMwwgsoWAbLIIqbiRuaSJQgV5l2J6q0jeZqZ2l2n0mHZXmqJZ3qZtZlqZlqYiRpYLmQ8p3Lij6a0mY4KyqKRA7MMyzMx5/uDhJyMgs5yZM8v7/Xpdr9c553fOdb4/5lKu+XAWAAAAqKnF3Ua0talTp8bUqVNj1KhRMWbMmDjyyCNjwIAB0aNHjygtLY1ly5bFO++8E0888UQ89NBD8eCDD0Z1dXXeZUfEu8+fmThxYo3nz9x+++1x9913x/Lly7c5pn///jF27Ng4++yz49BDD61xJU9ez58BAAAAakoiIs27iLYqSZJ48MEHC8+f2fq2qK33SdM0NmzYsMPnz9xzzz1x8sknN3X59ZKWr8y7BAAy8KVOA/IuARrd9V8emXcJ0OhKrr0z7xKg0SWdujX5OVvkbUStRWt4/gwAAABQk7AlZ63h+TMAAADAu1rUM1sefvjhiNgcPEyYMKHezyjp1atX4c09aZrGJz7xicxqrK+W/PwZAAAA4F0tKmwZNWpU4eqOrZ9fUlcdOnSIUaNGRURs84yUvM2cOTNmzpyZdxkAAABAPbW424h2dJsNAAAAQHPQ4sIWAAAAgOasRd1GlJWSkne/dmVlZS41tObnzwAAAEBb1ibDlt12262wXF5enksNbeH5MwAAANAWtcnbiI466qiI2BxOLF68OLc6PH8GAAAAWp8We2VLXa/iKCkpiT59+sTYsWPj4osvLmx/6aWXsi4NAAAAaMOaXdhSm2eoJEkSCxYsqPc5tr6i5L777qt3P81Bc3j+DAAAAPCuZhe21PbWmobcgpOmaSRJEq+88kpMnTq13v00B83h+TMAAADAu5rlM1sa+0GvSZLEs88+G8cee2yLvxqkuTx/BgAAANis2V3ZMmvWrB2GLUcffXREbA4WZs+eHRs2bKhVn2maxsaNG2PlypVRVlYWM2bMiMceeyyzmhvK82cAAACg9Wh2Ycvo0aN3+FlVVVUhmBg/fny88cYbTVVWvXj+DAAAALQ9zS5s2ZkkSRr9NqOseP4MAAAAtD0tKmy5/PLLC8srV67Mr5A62BKGNJYtz58ZP358i3/+DAAAALQGLSpsueKKK/IuoU7a4vNnAAAAoK1rUWFLS9Oanj8DAAAA1E6zfPVzW9GYtxcBAAAA+WhWV7aMHDkyl/M++uijTX7Olvj8GQAAAGDnmlXYMnPmzCZ/01CaptGuXbsmPWdEy3v+DAAAAFA7zSps2cLtNQAAAEBL1SzDlqa6ukWoAwAAAGStWYUtixYtavLbiAAAAACy1KzClsGDB+ddQmba0sN+AQAAgHc1q7ClNWlLD/sFAAAA3iVsaWSeCwMAAABti7ClkXnYLwAAALQtwpZG4mG/AAAA0DYJWxpJa3rYLwAAAFB7RXkXAAAAANCaCFsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMhQEhFp3kXQdqTlK/MuARpd5YWfzbsEADJw3o2P5l0CNLpflL+RdwnQ6JJO3Zr8nK5sAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAyV5F0AtdOhQ4cYM2ZMYf3+++/PsRoAAABgR4QtLUSvXr3iT3/6U6RpGmmaRrt27fIuCQAAANgOYUsLkyRJ3iUAAAAA78MzWwAAAAAyJGwBAAAAyJDbiBpRZWVlo/SbJMkO+/Y8FwAAAMiXsKURNebzVTy7BQAAAJonYUsjS9M0s762Dli2168ABgAAAPInbGkCjRGCCFYAAACgeRK2NJHVq1fHt7/97Zg2bVq9jh8wYEDMmjUrIjZf1TJkyJAsywMAAAAyImxpRD/4wQ/iggsuiOLi4ujcuXP87Gc/iyOPPDImTpwYy5Yta1DfixYtyqhKAAAAIEte/dyIvvWtb8VHPvKReOmllyJJkkiSJMaPHx9lZWVxxhln5F0eAAAA0AiELY3s+eefj4MPPjguu+yyqKioiCRJ4gMf+EDcfPPNMX36dLcDAQAAQCsjbGkCVVVVceWVV8ZBBx0Us2fPLmwfPXp0vPjii/GNb3wjior8KAAAAKA18Bt+EyorK4vDDz88Lrzwwli/fn0kSRIdO3aM73//+/Hss8/Ghz/84bxLBAAAABpI2JKDH//4x3HggQfGzJkzC9sOPPDAePLJJ+OHP/xhdOzYMb/iAAAAgAYRtuTk9ddfj49//OPx5S9/OdasWRMREcXFxTFx4sSYM2dOHHPMMTlXCAAAANSHsCVnv/rVr2LfffeNP//5z4Vte+yxRzzwwANxxx13xG677ZZjdQAAAEBdCVuagcWLF8dxxx0Xn/vc52L58uUREdu8JjpJkpyrBAAAAGpD2NKM3HHHHTF8+PCYOnVqYduW10T/8Y9/zLEyAAAAoLaELc3MsmXLYvz48XHiiSfG22+/Xdh+wAEHRJqmOVYGAAAA1IawpZm69957Y999941bb73VLUQAAADQgpTkXQA7tmrVqvjCF74QkydPjkmTJnklNAAAALQAwpYWYPr06TF9+vS8ywAAAABqwW1EAAAAABkStgAAAABkSNgCAAAAkCFhCwAAAECGhC0AAAAAGRK2AAAAAGRI2AIAAACQIWELAAAAQIaELQAAAAAZErYAAAAAZEjYAgAAAJAhYQsAAABAhoQtAAAAABkStgAAAABkSNgCAAAAkCFhCwAAAECGhC0AAAAAGSrJuwBqKi0tjf333z969+4dXbp0iXbt2tW5j9/97neNUBkAAABQG8KWZuL000+Ps846Kw4//PAoLi5uUF/CFgAAAMiPsCVngwYNiilTpsSHP/zhiIhIkqRe/aRpGkmSRJqmWZYHAAAA1JGwJUe77757zJw5M/r3718ISraEJnVV35AGoEVJiiJ69omkzx4RXT8Q0bFTROWmiHVrI132z4iFcyMqNuZdJTSMcU4b0K5Dh9h97w/GBwYOiG59+0T7zrtGcbt2sWH1mij/1/J46+9z4p8vl0V1VVXepQLUi7AlRz/+8Y9jwIABNUKW119/PaZPnx5z586NVatWRWVlZd5l0kK88eZb8dLLc+KlOWXx95fnxMuv/CPKy8sLn/fr0yce+fO9OVYI9dS9ZyQjjohk7xGRDN03ko6ddrhrWlUV6SvPR/o/D0T692easEhoIOOcNuDwz58We33s6Bh82MHRc8/BUbSTW+c3rFkTf7v7jzHjZ7+MN194qYmqhOyYn7dtwpac9OzZM0466aRCyLJ27do466yzYurUqXmXRgvy9LN/i1/d8tv4+5yyWLlqdd7lQOaKzrwoig4ZVev9k+LiSPY9OGLfg6P6paej+vbrItasbLT6IAvGOW3FuO9eEt3796v1/h06d46PnvW5+MgZn42ZP/tl/OGiS1zpQrNnfs4WwpacjB49OoqKNr95O03TOO200+KBBx7IuSpamrJ/vBqPPfl03mVAo0l6bX9Snq5YFunSxRGrV0QUFUey2+4R/QdHUvTuv5IW7X9YJBdcHVU//ubm/aCZMs5pqzaWl8fS1+bH8kVvxobVayIpKopOH+ge/fYfHl377F7Yr7ikJD7+f74SPQbtEb886fRIq6tzrBren/k5WwhbctK3b9+I2By0zJs3T9BCpkpLS2P33r1i0Rtv5l0KZCZdNC+qn5we6cvPRix7e9sduvaIok9NiKKR/1bYlPTuH8VnfzOqfvRfTVgp1J9xTmu2sXxdvHDvtPj7g9Pj9SeejsV/n7PDlzsMPuyQGHflJbHPJ0YXto044bj4xAXnxfRrr2uqkiEz5udtj7AlJ6WlpYXlF198McdKaOnalZTE0D2HxH7D94n99x0e+w3fJz44dGg898IL8blzvpx3edBAaVS/NDuqp90RsWje+++66l9RPfn6SN+aH8WnnlvYnAzdL5IPHxXp32Y1cq1QX8Y5bcMV+x0W1bV8HuH8p5+J68Z+Js649ZfxkdNPLWz/t4svjBnX/SIqKyoaq0xoMPNzIoQtuVmyZElh2UNwqa8Tjvt0TDjpxGjfvn3epUCjqLrpqojlS3a+41bSWdOi+oMHRNFBRxa2JYd9zC+hNFvGOW1FbYOWLdI0jbu+8vUYccKx0WHXXSMiYpdu3eKDo4+KOQ/9tTFKhAYzP2eLorwLaKuee+65wvKAAQNyrISWrGuXLv5HTutWx19At0hnTauxnnxw/yyqgcZhnMMObVizJl577Kka23oNHZJTNbBz5udsIWzJyYsvvhivvfZaJEkShxxySHTp0iXvkgBajfSN12qsJ6UdIt7nVbrQEhnntBXly2s+/Ll9511zqgSg9oQtOfre974XERElJSXxzW9+M+dqAFqR6u28GrTYnbO0MsY5bUSPgTWvAl+1eDsPjwZoZoQtObr11lvj3nvvjSRJ4sILL4xTTjkl75IAWoeefWusplWVEeWrcyoGGolxThvQa9jQGHTYwYX16urqmPs/j+VYEUDtCFtyduqpp8YDDzwQxcXFceedd8YvfvGLGDx4cN5lAbRoRR/6aM0NC+dG7OD1otBSGee0dl127x1f/P2tUVzy7hVbz0/9U/xr4aIcqwKoHdea5qyioiKOP/74+PrXvx6TJk2Ks88+O84+++yYN29elJWVxcqVK6O6urrW/aVpGmeffXYjVgzQzLXvEMkRY2tsqn7hyZyKgUZinNMKFRUXxy7du8Xu++wVBxx7TIz8zzOjY9euhc+XvjY/7jrvwhwrBKg9YUsz0Ldv3xg+fHgUFxdHkiQRETFs2LAYOnRonfpJkkTYArR5Rcd/PpKuHyisp+vWRvr4QzlWBNkzzmkNTv7xf8fHv3ZurfZ95ZH/id+e/sVYs3RZI1cFkA1hS87GjBkTd999d3Tu3DkiNl+ZAkD9JAceHkWjjquxrfq+2yLWrc2pIsiecU5b8sK902Lmz2+KsumP5F0KQJ0IW3J04IEHxh//+Mfo2LFjRGwOWrZc2QJAHfUbHEVnXFBjU/Wcv0U6a1pOBUEjMM5pY/b9tzGRFBfHpg0bYt6jT+RdDkCtCVtydP3110fHjh0LIcuGDRti8uTJMX369Jg7d26sWrUqKisr8y4ToPnr3jOKz50USYddCpvSf70T1b+9NseiIGPGOa3MtCuujkd+ckNhvV3HDtGpxwdiwIgDYsQJx8beHx8VJaWlccCxx8QBxx4TM6//VUyZ+I1I6/A8Q4C8CFtysvfee8cRRxxRuG2orKwsPvWpT8WiRZ6uDlAnu3aN4q9eGUn33Qqb0lXLo+q6SyLWeg0urYRxTiu0bsWKWLdixTbbX3v8qZj581/Fnh/9SHzh9puix6CBEREx6rwvRruOHeJ3Z5/X1KUC1JmwJSeHH354RGx+qG11dXWccsopLSZo6dmzZ/Ts2bOeRycR4bk0QEZ22TWKJ34vkt79C5vSNaui6rqLI5YuzrEwyJBxThv12uNPxY9GHxvfemZm7Lpbj4iI+OhZn4sX7/tzvHDfn3OuDuD9CVty0qtXr4jY/JyW559/PubMmZNzRbV37rnnxqRJk+p38KYNEZs2ZloP0EZ12CWKz78ykn6DC5vS8jVR9bNLIv7ZMsJr2CnjnDbuXwsWxrQrro7x1/2gsG3sN74mbAGavaK8C2ir1qxZU1ieO3dujpUAtEDtO0bxeVdEMnBYYVO6vjyqrr804s3XcywMMmScQ0REPHvX1Brrgz9ySHTs2jWnagBqR9iSk7feequwXFpammMlAC1Mafso/sqkSIbsU9iUblgXVT+/LGLhqzkWBhkyzqFgzdJlUb783We7FBUXx26DB+ZYEcDOuY0oJ88++2xUV1dHkiQxbNiwnR/QjNxwww3x+9//vl7HvvzMkxlXA7Qp7Uqj6NxJkQzdr7Ap3bghqm6YFPF6WX51QZaMc9hG1aZNNdZL2rfPqRKA2hG25OStt96KmTNnxsc+9rHYb7/9YsiQIfH66y3jkuClS5fG0qVL63m0h+MC9VTSLoq+dGkUffCAwqa0YmNU/+KKiHkv51gYZMg4h22UtG9feEDuFqvfWZJTNQC14zaiHH3/+98vLP/whz/MsRKAZq64JIq+eHEU7fOhwqZ0U0VU//LKSP/xQo6FQYaMc9iuvT8+KoqKiwvrG8vLY+Vb3sQFNG/ClhzNmDEjLr300kiSJI477ri44YYboqTExUYANRQVRdHZ34yi/Q4pbEorN0X1Td+PtOy5HAuDDBnnsF1JksSnvvONGtte/stft7mtCKC5Ebbk7Hvf+15MnDgxNm3aFF/84hfjhRdeiDPPPDP69OmTd2kA+UuKoujMi6LowMMLm9Kqyqi++epI//5MjoVBhoxz2oBR5/1ndNm9d52OKSopidNv/nkM+cghNbb/z89vyrI0gEbhMoocvfbaa4XlTZs2RWlpaey9995x002b/wJZu3ZtrFixIqqrq2vdZ5qmMXTo0Mxrpfl6+513orKqapvty5b9q8Z6ZVVVvLl4+5fc7tJxl/hA926NUR40SNHpE6Pow0fV2FZ9762RvvFaxAd61a2z1SsiKv1LKM2PcU5b8NGzTo8Tr748nr/n/nh2yh/i1ZmPxca1a7e7b7sOHeLAzxwb/3bxhdFvv+E1PnvqtsnxjxmzmqJkqDfzcyIikvDE0txUVVVFmqaRJEmk6bs/hiRJ6t1nmqbN+laktHxl3iW0Oh/71PHx1j//2aA+Tjju0/HfV1yWUUVUXvjZvEtoNUpumJZZX1U//makc1/KrD/IinHefJ1346N5l9BqXPz8YzFgxLsPfq6uro6l816Pfy1YFOtXrozKik3RofOu8YGBA6LP8L2jpLR0mz5evP/B+NVJp0dlRUVTlt7q/aL8jbxLaHXMz5ufpFO3Jj9n8/2tvA3ZOmjZ3nptNSSkAQCAplJUVBS9Pzg0en9w51dkV6xbF3++8pr4v9f8NKorK5ugOoCGE7bkaNGiRfUOVgAAoKW4/ZyvxgHjPhV7f/zo2OOgA6Ndhw47PeafZf+I2XfcHU/+9g5vHwJaHLcR0aTcRkRb4DYigNbBbUSNo6ikJPrss1fsNmRQdOvXN9rv2imK27WLjWvLY8Pq1fGvBYvijedfjHUrV+ZdapvgNiLaArcRAQAArVp1ZWW89dLL8dZLL+ddCkCj8epnAAAAgAwJWwAAAAAyJGwBAAAAyJBntjRzXbt2jc6dO0eSJPHGGx5eBQAAAM2dsKWZOf7442PcuHExcuTIGDRoUBQVbb74KE3TaNeu3Tb7Dxw4MPbYY4+IiCgvL4/nnnuuSesFAAAAahK2NBNjx46N6667LoYOHRoREUmS1Oq4PffcM6ZPnx5pmkZFRUX07ds3VnpNHgAAAOTGM1uage985zsxbdq0GDp06DYhS5qm73vsI488EmVlZZEkSZSWlsb48eMbs1QAAABgJ4QtOTv//PNj0qRJhduFIiI2btwYs2bNigceeKBWV7hMmTKlsPzpT3+6UeoEAAAAakfYkqOhQ4fGtddeG2maRpqmsXHjxvjGN74RPXr0iNGjR8f5559fq37uu+++iNh869HIkSMbs2QAAABgJzyzJUdXXHFFlJRs/hGsX78+PvGJT8RTTz1V535efPHF2LBhQ3To0CE6d+4cw4YNi7lz52ZdLgAAAFALrmzJSWlpaYwbN65wVcsll1xSr6AlYvNzXcrKygrre++9d1ZlAgAAAHUkbMnJRz/60ejYsWMkSRLr1q2LG264oUH9LV68uLDct2/fhpYHAAAA1JOwJSeDBg2KiM1XpcyePTsqKioa1N/q1asLy507d25QXwAAAED9CVty0rNnz8Ly22+/3eD+tn6b0dbLAAAAQNPyW3lONm7cWFhu3759g/vr0aNHYXnFihUN7g8AAACoH2FLTpYuXVpY7t+/f4P7O/DAA7fbNwAAANC0hC05ef311yMiIkmSGDFiROyyyy717utDH/pQjduSnnvuuQbXBwAAANSPsCUns2fPjtWrV0eaptGuXbv4whe+UO++LrjggsLywoULY9GiRVmUCAAAANSDsCUn1dXVMW3atEiSJJIkicsvv7xetxN95jOfic9+9rORpmmkaRqTJ09uhGoBAACA2hK25Oi73/1uVFdXR5qm0a1bt5g5c2YMHz681sefccYZceedd0aappEkSWzYsCF++tOfNmLFAAAAwM4IW3L0j3/8I372s59FkiSRpmkMHjw4nnvuufj1r38dY8eOjV69em1zTP/+/eMLX/hCPPHEE3HzzTdH+/btC8dfdtllHo4LAAAAOUsiIs27iLYsSZJ48MEHY8yYMYUrVNI03WafNE1jw4YN0aFDh222J0kS99xzT5x88slNXX6dpeUr8y4BGl3lhZ/NuwQAMnDejY/mXQI0ul+Uv5F3CdDokk7dmvycrmzJWZqmcfzxx8dvf/vbGkHLlme5bNknIqJjx441tm/Z75ZbbolTTz216YsHAAAAtiFsaQY2btwYZ511VowfPz5efvnlGmHK1rY8BDdic8jy2muvxWmnnRbnnHNOVFVVNWXJAAAAwA6U5F0A75o6dWpMnTo1Ro0aFWPGjIkjjzwyBgwYED169IjS0tJYtmxZvPPOO/HEE0/EQw89FA8++GBUV1fnXTYAAACwFWFLMzRz5syYOXNm3mUAAAAA9eA2IgAAAIAMCVsAAAAAMuQ2ohw9/PDDEbH5wbcTJkyIpUuX1qufXr16xeTJkwt9feITn8isRgAAAKBuhC05GjVqVOHtQh06dKh3Px06dIhRo0ZFxLuviQYAAADy4TainO3oNc8AAABAyyRsAQAAAMiQsKUVKCl5926wysrKHCsBAAAAhC2twG677VZYLi8vz7ESAAAAQNjSChx11FERsfnhuIsXL865GgAAAGjbvI2omajrW4RKSkqiT58+MXbs2Lj44osL21966aWsSwMAAADqQNjSyGrzDJUkSWLBggX1PsfWbzS677776t0PAAAA0HDClkZW21c7N+QV0GmaRpIk8corr8TUqVPr3Q8AAADQcJ7Z0gTqeotQXSVJEs8++2wce+yx3kYEAAAAOXNlSyObNWvWDsOWo48+OiI2hzGzZ8+ODRs21KrPNE1j48aNsXLlyigrK4sZM2bEY489llnNAAAAQP0JWxrZ6NGjd/hZVVVVIYgZP358vPHGG01VFgAAANBI3EaUs4Y8qwUAAABoflzZkqPLL7+8sLxy5cr8CgEAAAAyI2zJ0RVXXJF3CQAAAEDG3EYEAAAAkCFhCwAAAECGhC0AAAAAGfLMlkY0cuTIXM776KOP5nJeAAAAQNjSqGbOnBlpmjbpOdM0jXbt2jXpOQEAAIB3CVuaQJIkeZcAAAAANBFhSxNoqqtbhDoAAACQP2FLI1q0aFGT30YEAAAA5EvY0ogGDx6cdwkAAABAE/PqZwAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMpRERJp3EbQdm778qbxLgEZXcu2deZcAAFArlRd+Nu8SoNG1u/HPTX5OV7YAAAAAZEjYAgAAAJAhYQsAAABAhoQtAAAAABkStgAAAABkSNgCAAAAkCFhCwAAAECGhC0AAAAAGRK2AAAAAGRI2AIAAACQIWELAAAAQIaELQAAAAAZErYAAAAAZEjYAgAAAJAhYQsAAABAhoQtAAAAABkStgAAAABkSNgCAAAAkCFhCwAAAECGhC0AAAAAGRK2AAAAAGRI2AIAAACQIWELAAAAQIaELQAAAAAZErYAAAAAZEjYAgAAAJAhYQsAAABAhoQtAAAAABkStgAAAABkSNgCAAAAkKGSvAtg+zp16hSnnHJKHHPMMXHAAQdEz549o2PHjrFs2bJYvHhxzJw5M+6999546qmn8i4VAAAA2IqwpRn6yle+Epdeemn06NEjIiKSJCl81r9//+jXr18ccsghcdFFF8Vf//rX+NrXvhavvPJKXuUCAAAAWxG2NKKHH344IiLSNI0JEybE0qVL33f/du3axS233BITJkwoBCxpmkaaptvsu+XzMWPGxBNPPBGf+cxnYtasWRl/AwAAAKCuhC2NaNSoUYWgpEOHDjvd/8Ybb4zPfvazERGF47a+quW9tuzTtWvXmDZtWnz4wx+OV199taFlAwAAAA0gbGlkSZJs98qU9zr55JPjzDPPrBGyrF+/Pm677bb4y1/+EgsWLIj169fHbrvtFocddlhMmDAhDj744MKVL7vsskvcfvvtceihhzb2VwIAAADeh7Clmbj88ssLy0mSxOOPPx6nnHJKvP322zX2mzt3bjz55JPxk5/8JD73uc/FL37xiygtLY2IiIMOOiiOO+64uP/++5u0dgAAAOBdXv3cDIwdOzb22muvwlUts2fPjo997GPbBC3vddttt8XJJ58cEe/eUnTuuec2brEAAADA+xK2NANjxoyJiM1XtFRVVcVpp50WlZWVtTp22rRp8Zvf/CaSJIkkSeKoo46K4uLixiwXAAAAeB/ClmbgiCOOiIjNV6f88Y9/jNdff71Ox19zzTWF5fbt28dBBx2UaX0AAABA7QlbmoF+/foVlh966KE6H//qq6/GokWLCuvDhg3LpC4AAACg7oQtzUCPHj0Kyy+99FK9+nj55ZcLy927d29wTQAAAED9CFuagSRJCsvLly+vVx8rVqwoLHfp0qXBNQEAAAD1I2xpBpYuXVpY3vIa57ra+rjaPlwXAAAAyJ6wpRn4+9//Xljebbfd6tVH165dC8vl5eUNrgkAAACon5K8C2jt0jSNiIiTTjopli1btt19qqurC8vDhw+Pxx57rM7nGTp0aGH57bffrvPxAAAAQDaELU0gSZIar2d+P0cccUT86le/qlP/nTt3jsGDBxfWFy5cWKfjAQAAgOwIW5pAmqY1HoK7vc+37HPMMcdEkiSFK2Jq45Of/GSNvubMmdOgegEAAID688yWRpYkyfsGLe/dZ7fddovjjz++Tuc45ZRTImJz0DJ37txYv359/YoFAAAAGsyVLY3ozDPPrNdxdXnmyqBBgwrhTJIk9XreCwAAAJAdYUsjuu222xr9HCNGjIg77rijsH777bc3+jkBAACAHRO2tHB/+tOf4k9/+lPeZQAAAAD/n2e2AAAAAGRI2AIAAACQIWELAAAAQIaELQAAAAAZErYAAAAAZEjYAgAAAJAhYQsAAABAhoQtAAAAABkStgAAAABkSNgCAAAAkCFhCwAAAECGhC0AAAAAGRK2AAAAAGRI2AIAAACQIWELAAAAQIaELQAAAAAZErYAAAAAZEjYAgAAAJChkrwLoKbS0tLYf//9o3fv3tGlS5do165dnfv43e9+1wiVAQAAALUhbGkmTj/99DjrrLPi8MMPj+Li4gb1JWwBAACA/AhbcjZo0KCYMmVKfPjDH46IiCRJ6tVPmqaRJEmkaZpleQAAAEAdCVtytPvuu8fMmTOjf//+haBkS2hSV/UNaWhFkqKInn0i6bNHRNcPRHTsFFG5KWLd2kiX/TNi4dyIio15VwkAAG2D+XmbJmzJ0Y9//OMYMGBAjZDl9ddfj+nTp8fcuXNj1apVUVlZmXeZNGfde0Yy4ohI9h4RydB9I+nYaYe7plVVkb7yfKT/80Ckf3+mCYuE7Lzx5lvx0stz4qU5ZfH3l+fEy6/8I8rLywuf9+vTJx758705VggNZ5zTFhjntFrm5/x/wpac9OzZM0466aRCyLJ27do466yzYurUqXmXRgtRdOZFUXTIqFrvnxQXR7LvwRH7HhzVLz0d1bdfF7FmZaPVB1l5+tm/xa9u+W38fU5ZrFy1Ou9yoFEY57QFxjmtnfk5WxO25GT06NFRVLT5zdtpmsZpp50WDzzwQM5V0ZIkvfptd3u6YlmkSxdHrF4RUVQcyW67R/QfHEnRuw9eLtr/sEguuDqqfvzNzftBM1b2j1fjsSefzrsMaFTGOW2BcU5rZ37O1oQtOenbt29EbA5a5s2bJ2ihQdJF86L6yemRvvxsxLK3t92ha48o+tSEKBr5b4VNSe/+UXz2N6PqR//VhJVCdkpLS2P33r1i0Rtv5l0KNBrjnLbAOKc1Mj9H2JKT0tLSwvKLL76YYyW0XGlUvzQ7qqfdEbFo3vvvuupfUT35+kjfmh/Fp55b2JwM3S+SDx8V6d9mNXKt0DDtSkpi6J5DYr/h+8T++w6P/YbvEx8cOjSee+GF+Nw5X867PMiEcU5bYJzTupmf8y5hS06WLFlSWPYQXOqj6qarIpYv2fmOW0lnTYvqDx4QRQcdWdiWHPYx/zOnWTvhuE/HhJNOjPbt2+ddCjQa45y2wDintTM/Z2tFeRfQVj333HOF5QEDBuRYCS1WHf9HvkU6a1qN9eSD+2dRDTSarl26mJjT6hnntAXGOa2e+TlbEbbk5MUXX4zXXnstkiSJQw45JLp06ZJ3SbQR6Ruv1VhPSjtEvM8r6QAAgMZjft46CVty9L3vfS8iIkpKSuKb3/xmztXQZlRXbbut2B2FAACQC/PzVknYkqNbb7017r333kiSJC688MI45ZRT8i6JtqBn3xqraVVlRPnqnIoBAIA2zvy8VRK25OzUU0+NBx54IIqLi+POO++MX/ziFzF48OC8y6IVK/rQR2tuWDg3Ik3zKQYAANo48/PWybVJOauoqIjjjz8+vv71r8ekSZPi7LPPjrPPPjvmzZsXZWVlsXLlyqiurq51f2maxtlnn92IFdOite8QyRFja2yqfuHJnIoBAIA2zvy81RK2NAN9+/aN4cOHR3FxcSRJEhERw4YNi6FDh9apnyRJhC28r6LjPx9J1w8U1tN1ayN9/KEcKwIAgLbL/Lz1ErbkbMyYMXH33XdH586dI2LzlSnQGJIDD4+iUcfV2FZ9320R69bmVBEAALRd5uetm7AlRwceeGD88Y9/jI4dO0bE5qBly5UtkKl+g6PojAtqbKqe87dIZ03LqSAAAGjDzM9bPWFLjq6//vro2LFjIWTZsGFDTJ48OaZPnx5z586NVatWRWVlZd5l0tJ17xnF506KpMMuhU3pv96J6t9em2NRAADQRpmftwnClpzsvffeccQRRxRuGyorK4tPfepTsWjRopwro1XZtWsUf/XKSLrvVtiUrloeVdddErHW6+QAAKBJmZ+3GcKWnBx++OERsfmhttXV1XHKKae0mKClZ8+e0bNnz/odvGvXiLWrsi2I7dtl1yie+L1IevcvbErXrIqq6y6OWLo4x8IAAKANMj9vU4QtOenVq1dEbH5Oy/PPPx9z5szJuaLaO/fcc2PSpEn1OrZ62h1RPe3ObAtiWx12ieLzr4yk3+DCprR8TVT97JKIf7aMUA8AAFoN8/M2pyjvAtqqNWvWFJbnzp2bYyW0Ou07RvF5V0QycFhhU7q+PKquvzTizddzLAwAANog8/M2SdiSk7feequwXFpammMltCql7aP4K5MiGbJPYVO6YV1U/fyyiIWv5lgYAAC0QebnbZbbiHLy7LPPRnV1dSRJEsOGDdv5Ac3IDTfcEL///e/rdewLnz4w42ooaFcaRedOimTofoVN6cYNUXXDpIjXy/KrCwAA2iLz8zZN2JKTt956K2bOnBkf+9jHYr/99oshQ4bE66+3jEvIli5dGkuXLq3fwUcPyrQW/r+SdlH0pUuj6IMHFDalFRuj+hdXRMx7OcfCAACgDTI/b/PcRpSj73//+4XlH/7whzlWQotWXBJFX7w4ivb5UGFTuqkiqn95ZaT/eCHHwgAAoA0yPyeELbmaMWNGXHrppZEkSRx33HFxww03REmJi42og6KiKDr7m1G03yGFTWnlpqi+6fuRlj2XY2EAANAGmZ/z/wlbcva9730vJk6cGJs2bYovfvGL8cILL8SZZ54Zffr0ybs0mrukKIrOvCiKDjy8sCmtqozqm6+O9O/P5FgYAAC0QebnbMVlFDl67bXXCsubNm2K0tLS2HvvveOmm26KiIi1a9fGihUrorq6utZ9pmkaQ4cOzbxWmp+i0ydG0YePqrGt+t5bI33jtYgP9KpbZ6tXRFRuyrA6yNbb77wTlVVV22xftuxfNdYrq6rizcWLt9vHLh13iQ9079YY5UEmjHPaAuOc1sz8nK0lEZHmXURbVVVVFWmaRpIkkabv/hiSJKl3n2maNutbkTZ9+VN5l9BqlNwwLbO+qn78zUjnvpRZf21dybV35l1Cq/OxTx0fb/3znw3q44TjPh3/fcVlGVUE2TPOaQuM8+an8sLP5l1Cq2F+3ny1u/HPTX7O5vtbeRuyddCyvfXaakhIAwAAAGRD2JKjRYsW1TtYAQAAAJontxHRpNxGRFvgNiIAoKVwGxFtQR63EXkbEQAAAECGhC0AAAAAGRK2AAAAAGRI2AIAAACQIW8jaua6du0anTt3jiRJ4o033si7HAAAAGAnhC3NzPHHHx/jxo2LkSNHxqBBg6KoaPPFR2maRrt27bbZf+DAgbHHHntERER5eXk899xzTVovAAAAUJOwpZkYO3ZsXHfddTF06NCIiEiSpFbH7bnnnjF9+vRI0zQqKiqib9++sXLlykasFAAAAHg/ntnSDHznO9+JadOmxdChQ7cJWdI0fd9jH3nkkSgrK4skSaK0tDTGjx/fmKUCAAAAOyFsydn5558fkyZNKtwuFBGxcePGmDVrVjzwwAO1usJlypQpheVPf/rTjVInAAAAUDvClhwNHTo0rr322kjTNNI0jY0bN8Y3vvGN6NGjR4wePTrOP//8WvVz3333RcTmW49GjhzZmCUDAAAAO+GZLTm64ooroqRk849g/fr18YlPfCKeeuqpOvfz4osvxoYNG6JDhw7RuXPnGDZsWMydOzfrcgEAAIBacGVLTkpLS2PcuHGFq1ouueSSegUtEZuf61JWVlZY33vvvbMqEwAAAKgjYUtOPvrRj0bHjh0jSZJYt25d3HDDDQ3qb/HixYXlvn37NrQ8AAAAoJ6ELTkZNGhQRGy+KmX27NlRUVHRoP5Wr15dWO7cuXOD+gIAAADqT9iSk549exaW33777Qb3t/XbjLZeBgAAAJqW38pzsnHjxsJy+/btG9xfjx49CssrVqxocH8AAABA/QhbcrJ06dLCcv/+/Rvc34EHHrjdvgEAAICmJWzJyeuvvx4REUmSxIgRI2KXXXapd18f+tCHatyW9NxzzzW4PgAAAKB+hC05mT17dqxevTrSNI127drFF77whXr3dcEFFxSWFy5cGIsWLcqiRAAAAKAehC05qa6ujmnTpkWSJJEkSVx++eX1up3oM5/5THz2s5+NNE0jTdOYPHlyI1QLAAAA1JawJUff/e53o7q6OtI0jW7dusXMmTNj+PDhtT7+jDPOiDvvvDPSNI0kSWLDhg3x05/+tBErBgAAAHZG2JKjf/zjH/Gzn/0skiSJNE1j8ODB8dxzz8Wvf/3rGDt2bPTq1WubY/r37x9f+MIX4oknnoibb7452rdvXzj+sssu83BcAAAAyFkSEWneRbRlSZLEgw8+GGPGjClcoZKm6Tb7pGkaGzZsiA4dOmyzPUmSuOeee+Lkk09u6vLrbNOXP5V3CdDoSq69M+8SAABqpfLCz+ZdAjS6djf+ucnP6cqWnKVpGscff3z89re/rRG0bHmWy5Z9IiI6duxYY/uW/W655ZY49dRTm754AAAAYBvClmZg48aNcdZZZ8X48ePj5ZdfrhGmbG3LQ3AjNocsr732Wpx22mlxzjnnRFVVVVOWDAAAAOxASd4F8K6pU6fG1KlTY9SoUTFmzJg48sgjY8CAAdGjR48oLS2NZcuWxTvvvBNPPPFEPPTQQ/Hggw9GdXV13mUDAAAAWxG2NEMzZ86MmTNn5l0GAAAAUA9uIwIAAADIkLAFAAAAIENuI8rRww8/HBGbH3w7YcKEWLp0ab366dWrV0yePLnQ1yc+8YnMagQAAADqRtiSo1GjRhXeLtShQ4d699OhQ4cYNWpURLz7mmgAAAAgH24jytmOXvMMAAAAtEzCFgAAAIAMCVtagZKSd+8Gq6yszLESAAAAQNjSCuy2226F5fLy8hwrAQAAAIQtrcBRRx0VEZsfjrt48eKcqwEAAIC2zduImom6vkWopKQk+vTpE2PHjo2LL764sP2ll17KujQAAACgDoQtjaw2z1BJkiQWLFhQ73Ns/Uaj++67r979AAAAAA0nbGlktX21c0NeAZ2maSRJEq+88kpMnTq13v0AAAAADeeZLU2grrcI1VWSJPHss8/Gscce621EAAAAkDNXtjSyWbNm7TBsOfrooyNicxgze/bs2LBhQ636TNM0Nm7cGCtXroyysrKYMWNGPPbYY5nVDAAAANSfsKWRjR49eoefVVVVFYKY8ePHxxtvvNFUZQEAAACNxG1EOWvIs1oAAACA5seVLTm6/PLLC8srV67MrxAAAAAgM8KWHF1xxRV5lwAAAABkzG1EAAAAABkStgAAAABkSNgCAAAAkCHPbGlEI0eOzOW8jz76aC7nBQAAAIQtjWrmzJmRpmmTnjNN02jXrl2TnhMAAAB4l7ClCSRJkncJAAAAQBMRtjSBprq6RagDAAAA+RO2NKJFixY1+W1EAAAAQL6ELY1o8ODBeZcAAAAANDGvfgYAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIENJRKR5FwFkr2fPnnHuuecW1m+44YZYunRpjhVB9oxz2gLjnLbAOKctMM7bnlTTtNbXhg8fnm5t+PDhudekaVk341xrC80419pCM861ttCM87bV3EYEAAAAkCFhCwAAAECGhC0AAAAAGRK2AAAAAGRI2AIAAACQIWELAAAAQIaELQAAAAAZErYAAAAAZEjYAgAAAJAhYQsAAABAhoQtAAAAABkStgAAAABkSNgCAAAAkKGSvAsAGsfSpUtj0qRJNdahtTHOaQuMc9oC45y2wDhvW5KISPMuAgAAAKC1cBsRAAAAQIaELQAAAAAZErYAAAAAZEjYAgAAAJAhYQsAAABAhoQtAAAAABkStgAAAABkSNgCAAAAkCFhCwAAAECGhC0AAAAAGRK2AAAAAGRI2AIAAACQoZK8CwAAIgYPHhzDhw+PAQMGRLdu3aKysjJWrFgRixYtitmzZ8eqVavyLhEapF27drHXXnvFwIEDo3///tG5c+do3759rF27NlasWBFz5syJF198MSoqKvIuFQAykWqapmktv82fPz/d2tFHH517TdqOW8+ePdNzzjkn/f3vf58uXbo0fT9VVVXpo48+mk6YMCFNkiT32vNsxnnLascff3x60003pS+++GJaUVHxvuM8TdN0/fr16V133ZWOHDky99o1TdM0rYEt9wI0rdGbyXnLbX379k2PP/749Morr0z/8pe/pMuWLdtmcp53jc2l1XWcz5gxw59jTu2///u/002bNu30F8/tefzxx9M999wz9++QVzPOW1Z79NFH6zXO0zRNf/e736WdOnXK/Tvk0cxbWme76qqrtjvW864rr2act6x2xhln1Pv/52mapjNmzMj9OzR1cxsRbMeMGTNi1KhRhfUkSfIrpg3ab7/94nvf+14ccsgh0adPn7zLgcztueeeUVKy7V/BS5cujTlz5sTSpUujuro6BgwYEB/+8IejtLS0sM8RRxwRjz/+eBx99NHxj3/8oynLhgbbsGFDvP7667FgwYJYvXp1VFVVRffu3WP48OExaNCgGvv+x3/8RwwZMiTGjh0b5eXl+RTcQpi3NH8f+tCH4utf/3reZbRoxjktjbAFaHb23HPPGDduXN5lQJP4xz/+Eb/5zW/i/vvvjzlz5mzzeffu3ePCCy+Mb3zjG4WApnfv3vHAAw/EfvvtFxs3bmzqkqHWNm7cGNOnT48///nP8dhjj8Xzzz8fVVVV2913+PDhcemll8b48eML24444oi4+uqr47zzzmuqkiFzJSUlccstt0S7du3yLgVoQsIWoMXYtGlTvPbaa7H33nvnXQo02KOPPhqTJk2KRx555H33W7FiRVx88cXx1FNPxT333FMIXIYOHRpf+9rX4uqrr26KcqFejjnmmKisrKzVvnPmzIlTTz015s2bFxdffHFh+5e+9KW48sor4+23326sMqFRffOb34wRI0ZERMTq1aujS5cu+RYEGbjwwgtj6tSptd5/w4YNjVhN8+TVz0CzVFVVFXPmzIlbb701zj///Dj88MOjc+fOccwxx+RdGjTYhRdeGEcdddROg5at3X///fGTn/ykxrbTTz8948ogW7UNWrZ26aWXxuuvv15YLy4ujuOPPz7LsqDJ7LPPPnHJJZcU1r/97W/nWA1kZ9myZbFw4cJat3feeSfvkpucsAVodh5++OHo2rVr7LvvvvH5z38+rr/++njqqafcLkGrsXDhwnod9/Of/7zG+r777hs9e/bMoiRoNqqrq+P//t//W2Pb0KFDc6oG6i9Jkrjllluiffv2ERExZcqUeOCBB3KuCmgqbiMCmp21a9fmXQINUFxcHIceemgMGTIkevbsGe3bt4+lS5fGggUL4vHHH888NOvfv38cfPDB0a9fv+jcuXMsWbIknnzyySgrK9vpsQceeGAcdNBB0atXr6ioqIjFixfHjBkzYsmSJZnWmJUFCxbEypUro1u3boVtffv2jaVLl+ZXVBtlnDeu5cuX11jv3LlzTpVA/X3ta1+Lj3zkIxGxeUx/9atfjY4dO+ZcFdBUhC3QhEzOydtll10WkyZN2u5nm98+uX0zZ86M0aNHv2/fe++9d1xyySVx7LHHRteuXbe7z7p16+K+++6LSy+9NObOnVurmufPn194S8mCBQti8ODBERExevTo+Pa3vx2jR4+O4uLibY57/PHH47zzzov//d//3eazM844Iy655JLt/mt5VVVVTJ06Nf7P//k/8c9//rNWNTal996WsfWbitjMON+sJY/zgQMH1lhfvHhxTpW0beYt9TdkyJD47ne/W1i/6KKLYsmSJduMbfJnnNOYcn//tKY1dps/f36N97wfffTR2+xz2WWXNdo74/fee+/09ttvT1euXLnDfsrLy9PJkyenw4YNq9f3mj9/fmH76NGj0+nTp6eVlZXbPddjjz2WjhgxYrt9nnHGGencuXO3e1xlZWV61113pX369MntZzlw4MBt6sp7fDWXltc4LyoqSn/0ox/tcLxtT0VFRfrVr3613uP84osvrtV5ysvL009+8pOFvtq3b5/ec889tTp24cKF6ZAhQ3L/uW7dunbtuk2d/fv3z70u43z7jPP6tQ984APp8uXLa9Q5cuTI3OtqC+N8SzNvaXh7+OGHC3U88sgjhe3mMcZ5Sx3nZ5xxRo3znnHGGbmPoRbQci9A0xq9mZxvq6VOzk1Smtc479ChQ/qXv/xlm/03btyYPv300+kf/vCH9M4770wfeeSRdO3atdvsd9lll9V5nJ9//vk1+njxxRfTP/zhD+nkyZPTZ599Nq2qqqrx+apVqwqBxL333lvYXlFRkT7++OPpXXfdlU6dOjV99dVXt6nvmWeeSYuKinL/2W5pZ511Vo363nrrrdxrMs6N8yxb586d0+nTp9eo7+mnn869rrYwziPMW7JqX/ziFwvnXrduXY1f1M1jjPP305zHubClXi33AjSt0ZvJeeuZnJukNGycd+3aNR04cGA6cODA9Mknn6yx/5bt22u9e/fe7jlvvvnmGn2sWLEinThxYrrrrrtu97+JCy64IF23bl1h/6qqqvSYY46p9fdas2ZNumHDhjRN0/S+++7b7r807bfffumcOXNq1HXLLbekF154YZqmm/8F6Oqrr067deu2zbHjxo1LV69eXePY5jKZSJIk/d///d8atf385z/PvS7j3DhvSCsqKkq7deuWHnbYYel3vvOddPHixTXqWrp0abrXXnvlPu6a4zg3b2me85Z+/frVuFLiW9/6Vo3PzWOM85Y6zt8bttx3333pAw88kC5YsCAtLy9P165dmy5cuDB94okn0muvvbZGaNSGW+4FaFqjN5Pzza01TM5NUho2zrduM2bMaNCf40knnVTj+Pnz56cDBw7c6XGHH354jbH+6quvpkmS1Pp7pWma/vKXv9zpOCkvLy/sv379+sKkacKECe977Mknn1zjXLNmzcr9ZxsR6QUXXFCjroqKijpd1txamnH+bmuJ43zixInbfM8def7559O999479zGXRzNv2dxa4rzl/vvvL5zvhRdeSEtKSmp8bh5jnLfUcf7esKU2ysrK0lNOOSX3sZZjy70ATWv0ZnL+bmuJk/P31v9eeY+v5tKaepy/+OKLhWMrKirS/fffv9bHbplAbHHCCSfU+nuVlZWlpaWlOz3Hr3/9623Gyk033VSr+ubNm1c4ZtOmTWmHDh1y/dkecsghhcnaFldffXXuYy6PZpzXbC1tnNcmbJk5c2Z64oknvu/ff629mbe821rSvOW0004rnKuysjI99NBDt/t93ivv8ZZXM85b1jivT9iyxc0331yrv9NaYcu9AE1r9GZyXrO1tMn51s0kZcetKcf56NGjaxz7m9/8pk7Hd+zYscbE5f2Of+/3Ovvss2t1jvHjx28zVvbcc89aHXvjjTfWOO6QQw7J7efar1+/9M0336xRzwsvvJC2b98+9zGXRzPOa7aWNs5rE7ZUVlamM2fOTMeNG5f7eMurmbfUbC1h3tKzZ8906dKlhXP95Cc/2e5+5jE7Hg/GefMe51vCliVLlqS33XZb+qUvfSk96qij0uHDh6dDhw5NDz300PSss85K77777nTTpk3bfJc77rgj9zGXQ8u9AE1r9GZyXrO1tMn51s0kZcetKcf597///RrH7uyS2u21mTNnFo6fN29erb9Xv379atX/QQcdVOO4V199tda1vfeWnWOPPTaXn2nXrl3TF154oUYty5cvb5O3D+1oPBjnLWucd+7cucal/sOGDUsPO+yw9Jxzzkn/+Mc/bjNB//3vf5/7lWV5NPOWmq0lzFumTJlSOMfChQvTTp06bXc/85gdjwfjvHmP88MPPzw98cQT0+Li4p3uO3To0PTpp5/e5vucf/75uY+7pmwlAWRqzJgxNdanTJlSp+PXr18fs2fPjqOPPjoiIkaOHFnrYx988MFa7Td37txt1l977bV6Hdu7d+/aFUercuSRR9ZYX758eQwcOLBOfaxevbqwPGjQoEiSJDbPnXZszZo18dZbb9Wq/1WrVtVYLysrq3Vt7z22S5cutT42K7vssktMmzYtDjjggMK2tWvXxqc+9alt/jukcRjn2VuzZk2sWbNmm+1PP/103HTTTbHvvvvGHXfcEQceeGBERJx00knRpUuXOOaYY3b650b9mLc03PHHHx+nnHJKYf3cc8+N8vLyzM9D/RnnDffkk0/Wet958+bFyJEj4+GHH67xd+mll14av/3tb7f790BrJGyBjJmc0xYMGDCgxvrTTz/doP6Ki4ujW7dusWLFivfdb2efb62ysrLG+sqVK+t9bLt27Wp9bBbat28f9957b3z0ox8tbFu3bl0cd9xx8dRTTzVpLW2Zcd70Xn755Rg9enQ8/fTTMWzYsIiIGDt2bJx//vlx3XXX5Vxd62Te0jDdunWLG264obA+ZcqUmDZtWqbnoOGM86ZXUVERp5xySsybNy922WWXiIjYbbfd4pRTTombb7455+qahrAFMmZyTlvQo0ePzPvs3LnzTsdxdXV1vftvyLFNqV27dvGHP/whPvGJTxS2bdiwIT7zmc/EzJkz8yusDTLO87FixYr4+te/Hvfdd19h20UXXSRsaSTmLQ3zox/9KPr27RsRm3+B/+pXv5pp/2TDOM/HP//5z7jtttviS1/6UmHbMccc02bClqK8C4DWprEm5zvT1ifnNK3S0tLM+0ySJPM+W5ri4uK4++6749Of/nRhW0VFRZx88skxffr0HCtrm4zz/Pz5z3+u8S+1/fv3j/322y/Hilov85b6GzNmTJx55pmF9YsuuiiWLFmSY0XsiHGen7/85S811re+Pbq1c2ULZMzknLZg2bJl0a9fv4jYfB/zlstDqb+ioqKYPHlyfOYznyls27RpU5x66qnxwAMP5FdYG2ac56eqqipee+21OOiggwrbhg4dGn//+99zrKp1Mm+pv8svv7yw/MILL8Qjjzyy01tT+vfvv8229x6zZMmSWL9+fTZFEhHGeZ4WLFhQY71nz575FJIDYQtkzOSctuCdd94pjPOOHTvGHnvsEYsWLcq5qpYrSZL43e9+FyeffHJhW2VlZfzHf/xH/PGPf8yxsrbNOM/Xpk2baqy3b98+p0paN/OW+uvYsWNh+cADD4z58+fXq5/3/jL6mc98Ju69996GlMZ7GOf5eW9wuPV/N62d24ggY++8805hecvkHJqjhrzZ44knnqixPnbs2IaW02YlSRK/+c1v4rOf/WxhW1VVVXz+85+Pu+++O8fKWgfjvOV67xUAW//9SnbMW2gLjPP87LbbbjXWly1bllMlTU/YAtthck5bsHHjxhrrdbnE9qGHHqqxfvbZZ2dSU1v0y1/+Ms4444zCenV1dZxzzjlxxx135FhV62Gct0zDhw8v/Cv0Fl55vmPmLbQFxnnLdNhhh9VYX7x4cU6VND1hC2yHyTltwXufct+nT59aH/vggw/GvHnzCuuHHXZYjYcEUjvXX399nHPOOTW2ffnLX47f/OY3OVXU+hjnLdOkSZNqrP/tb3+r9etT2yLzlnx86EMfiiRJ6tQGDRq0TT/v3cctRNtnnLdMEyZMqLHelt6sKGyB7TA5py0oKyursV6Xf+WpqqqKSy+9tMa2G2+8MU444YQ61/Hxj388Bg8eXOfjWrprr702vvKVr9TYdt5558WvfvWrnCpqnYzz/Jx55pmx55571vm4K664osbziyI2B5PsmHkLbYFx3vJ87nOfi0MOOaTGtrYUJgpbYDtMzmkLZsyYUWP9mmuuiYsuuigOO+yw2HPPPWPgwIGF1rt3722Onzx5ctx8882F9fbt28c999wTt99+e403iLxXUVFRjBgxIi699NJ4+eWX469//Wubu3d60qRJ8fWvf73Gtp/+9KfxwAMP1Phzr03r1KlTTt+iZTDO8zNu3LgoKyuLe+65J8aPHx/du3ff4b4lJSVx7LHHxmOPPRbf+c53anz2P//zP/Hb3/62katt2cxbaAuM8/yccMIJdf7On/70p+OXv/xljW1//etft7mlqzXzNiLYjhkzZtR4nd8111wT3bp1i1mzZsWyZcuisrKy8NmGDRu2eWjf5MmT4+Mf/3icddZZEfHu5PyOO+6IH/3oR/Hcc89t97xFRUVxwAEHxLhx42L8+PExfPjwGDVqVL2fbt+S9e7dOzp06LDN9tq8MnGL7f1seNejjz4azzzzTOFfHLp27Ro/+MEPtrvvzJkzY/To0dts/9KXvhTdu3ePE088sbDttNNOi9NOOy2WLFkSL7zwQvzrX/+K6urq6NKlS/Tt2zf22WefNvUk+u3Z+hktW0ycODEmTpxY574+//nPx6233ppFWa2ScZ6vdu3axQknnFD4hWbhwoUxd+7cWLlyZaxfvz46d+4cffv2jf3222+7bweZPXt2HH/88U1ddotj3kJbYJznZ9y4cTFlypS499574+67746HHnooVq9evd1999prr7jwwgvjC1/4QhQVvXttx6pVq+o1z2nJhC2wHSbn+bvrrrti1KhRtdr3va9M3GJHPxveNX78+Jg2bVrss88+9Tq+srIy/v3f/z0uuuiiuPzyy2uM3169esWYMWN22kdFRUWUl5fX6/xQG8Z587HlKqKdqaysjOuuuy6+853vxLp165qgspbNvIW2wDjPV7t27eKkk06Kk046KSIiXn/99Zg3b16sWrUqKioqonv37rHvvvtu9//x69atixNOOCHmzJnT1GXnStgCO2ByTlswf/78GDFiRJx00kkxbty42H///aNv377RqVOnaNeuXa37ueaaa+K2226LiRMnxoQJE7b7AMCtrV69Oh599NGYNm1aTJkyJZYvX97AbwI7Zpzn41vf+lbMnj07xowZEwcffHB07tx5p8csWLAg7rrrrrjlllu8faiOzFtoC4zz5mPIkCExZMiQne733HPPxX/8x39scxtYWyBsgR0wOaelqe/9wxUVFXHnnXfGnXfe2aDzv/POO/Htb387vv3tb8egQYPioIMOip49e0b37t2juro61qxZE4sXL45XXnkl5s6dG9XV1bXqt77fa+HChZEkSb2OvfXWWxv11py2dq93lozzmprzOH/llVfiqquuiquuuiqSJIm99tor9txzz+jfv3906dIl2rdvH+Xl5bF69ep488034/nnn48lS5Y0Wj2tnXkLbYFxno9bb701qqqq4sgjj4xhw4bVuD1oezZs2BCzZs2KG2+8Me67775a/13Y2iQRUf8XlgN1luXkHACgMZm30BYY57XXqVOnGD58eAwcODB233336NSpU5SUlMTq1atjxYoVMXfu3Hjuuedi06ZNeZeaO2ELAAAAQIa8+hkAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAKBVmT9/fqRpWmhHH3103iUBAG2MsAUAaLNmzJhRI5gBAMiCsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDJXkXAADQ2hQXF8ehhx4aQ4YMiZ49e0b79u1j6dKlsWDBgnj88cdj48aNmZ6vf//+cfDBB0e/fv2ic+fOsWTJknjyySejrKxsp8ceeOCBcdBBB0WvXr2ioqIiFi9eHDNmzIglS5bUu55evXrFiBEjYsiQIdGlS5coKSmJ9evXx7/+9a9YuHBhvPzyy7Fs2bJ69w8ALUGqaZqmaZrWWtr8+fPTrR199NE1Pr/sssvS+pgxY8ZOz7333nunt99+e7py5cod9lNeXp5Onjw5HTZsWL2+0/z58wvbR48enU6fPj2trKzc7rkee+yxdMSIEdvt84wzzkjnzp273eMqKyvTu+66K+3Tp0+d/uxPPPHE9NFHH02rqqp2+uc5d+7c9Cc/+Uk6ePDg3MeMpmmapjVCy70ATdM0TdO0zFoeYUtRUVH6ox/9aIehx/ZUVFSkX/3qV+v8nbaELRdffHGtzlNeXp5+8pOfLPTVvn379J577qnVsQsXLkyHDBmy0/pKS0vT3//+97X+7ls766yzch8zmqZpmpZ1cxsRAEADdOjQIf70pz/FJz/5yRrbKyoq4n//93/jzTffjI0bN8buu+8ehx56aHTq1CkiItq1axc//elPo3v37nH55ZfX6Zznn39+XHnllYX1l156KebOnRsVFRUxbNiw+NCHPhRFRZsfzbfLLrvE3XffHfvuu2+8+eabcffdd8e4ceMiImLTpk3xzDPPxBtvvBElJSVxwAEHxLBhwwr97rHHHjFlypQ47LDDorq6eof1XH/99XHSSSfV2LZ+/fp44YUX4s0334z169dHp06dokePHrHPPvtEr1696vR9AaAlyj3x0TRN0zRNy6rt7MqWrl27pgMHDkwHDhyYPvnkkzX23bJ9e613797bPd/NN99co48VK1akEydOTHfddddt9u3QoUN6wQUXpOvWrSvsX1VVlR5zzDG1/k5r1qxJN2zYkKZpmt53333bvR1pv/32S+fMmVOjrltuuSW98MIL0zTdfJvQ1VdfnXbr1m2bY8eNG5euXr26xrFnnHHGDmvba6+9auy7du3a9Lzzzks7duy4w2MGDRqUnnvuuekzzzzjyhZN0zSttbbcC9A0TdM0Tcus7Sxs2brNmDGjxr51PddJJ51U4/j58+enAwcO3Olxhx9+eI3A5dVXX02TJKn1d0rTNP3lL3/5vucYOHBgWl5eXth//fr16dq1a9M0TdMJEya877Enn3xyjXPNmjVrh/tedNFFtQ5mttfat2+f+5jRNE3TtEZouRegaZqmaZqWWWvKsOXFF18sHFtRUZHuv//+tT52y1UmW5xwwgm1/k5lZWVpaWnpTs/x61//epuQ5qabbqpVffPmzSscs2nTprRDhw7b3e/666+v0X+nTp1yHwOapmmalnfbfDMvAAB1Mnr06Nh///0L63fccUe89NJLtT7+5z//eaxfv76wvuU5KrXxwx/+MCoqKna63/Tp07fZ9t///d+1OsfWx5aUlNT4ru/H81gAIELYAgBQD2PGjKmxPmXKlDodv379+pg9e3ZhfeTIkbU+9sEHH6zVfnPnzt1m/bXXXqvXsb17997ufq+88kqN9WuvvTZKSryDAYC2zd+EAAD1cOSRR9ZYX758eQwcOLBOfaxevbqwPGjQoEiSJDbfzbRja9asibfeeqtW/a9atarGellZWa1re++xXbp02e5+99xzT1xzzTXRoUOHiIg48cQT45VXXolf//rXce+999bpnADQWghbAADqYcCAATXWn3766Qb1V1xcHN26dYsVK1a87347+3xrlZWVNdZXrlxZ72PbtWu33f0WL14c//Vf/xU//elPC9v23HPPuOqqq+Kqq66Kd955J5544ol44okn4tFHH41nn302qqqqal0HALREbiMCAKiHHj16ZN5n586dd7pPdXV1vftvyLHv57rrrosJEybE4sWLt/msd+/eccIJJ8Q111wTTz31VLz99tvxi1/8Ij74wQ82Si0A0BwIWwAA6qG0tDTzPpMkybzPpnLXXXfFnnvuGaeffnrce++9sXz58u3ut9tuu8V//ud/xpw5c+Kqq65q0d8ZAHbEbUQAAPWwbNmy6NevX0RsftjtLrvsknNF+duwYUPcfvvtcfvtt0eSJLHPPvvE4YcfHkceeWSMHTs2+vbtW9i3uLg4vvnNb0ZpaWl8/etfz7FqAMieK1sAAOrhnXfeKSx37Ngx9thjjxyraX7SNI05c+bEzTffHGeeeWb069cvRo4cGQ899FCN/SZOnOiWIgBaHWELANBm7ezNP+/niSeeqLE+duzYhpbT6j322GNxzDHHxP3331/YVlxcHOPGjcuxKgDInrAFAGizNm7cWGO9Ls9hee8VGmeffXYmNbUFv/nNb2qsDx48OKdKAKBxCFsAgDbrva9C7tOnT62PffDBB2PevHmF9cMOOyzOPPPMrEpr1d77Wun3hl4A0NIJWwCANqusrKzGel1uBaqqqopLL720xrYbb7wxTjjhhDrX8fGPf7zFXt3xxS9+MQYMGFCnYz73uc/VWH/vzwEAWjphCwDQZs2YMaPG+jXXXBMXXXRRHHbYYbHnnnvGwIEDC613797bHD958uS4+eabC+vt27ePe+65J26//fY46KCDdnjeoqKiGDFiRFx66aXx8ssvx1//+tcW+4DdL3/5y/H666/HfffdF5///Odj99133+G+AwYMiFtvvTVOOumkwra1a9fGH/7wh6YoFQCajFc/AwBt1qOPPhrPPPNMHHLIIRER0bVr1/jBD36w3X1nzpwZo0eP3mb7l770pejevXuceOKJhW2nnXZanHbaabFkyZJ44YUX4l//+ldUV1dHly5dom/fvrHPPvtEx44dG+dL5aCkpCSOO+64OO644yIiYvHixfHKK6/E8uXLY/369bHrrrvGBz/4wdhnn32iqKjmv/VNnDgxli9fnkfZANBohC0AQJs2fvz4mDZtWuyzzz71Or6ysjL+/d//PS666KK4/PLLa4QovXr1ijFjxuy0j4qKiigvL6/X+Zujvn37Rt++fd93n3Xr1sVXv/rVuOWWW5qoKgBoOm4jAgDatPnz58eIESPitNNOiylTpsScOXNi5cqVsWnTpjr1c80118TgwYPjqquuigULFux0/9WrV8e0adPi3HPPjT59+sSzzz5bz2+QrwkTJsQ3vvGNePjhh2PNmjU73f+dd96J66+/Pvbaa68at2ABQGuSRESadxEAAK3NoEGD4qCDDoqePXtG9+7do7q6OtasWVO4xWbu3LlRXV2dd5mZKioqir322iuGDRsW/fv3j86dO0dxcXGsXbs23nnnnfj73/8eZWVlre57A8B7CVsAAAAAMuQ2IgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEPCFgAAAIAMCVsAAAAAMiRsAQAAAMiQsAUAAAAgQ8IWAAAAgAwJWwAAAAAyJGwBAAAAyJCwBQAAACBDwhYAAACADAlbAAAAADIkbAEAAADIkLAFAAAAIEP/D0tD+wVzM5o+AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1200x1200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 4), dpi=300)\n",
    "sns.heatmap(I, annot=True, cmap=\"Reds\", \n",
    "            xticklabels=itemlabels, \n",
    "            yticklabels=itemlabels, \n",
    "            cbar=False)\n",
    "\n",
    "plt.title(\"Item-Item Co-occurrence Matrix\\nA'A\")\n",
    "plt.xlabel(\"Items\")\n",
    "plt.ylabel(\"Items\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "26d1cbf8-a592-4b11-ba75-d9f64a33477e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}