{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b04b8bc7",
   "metadata": {},
   "source": [
    "# How to place wire cuts using a single-qubit `CutWire` instruction\n",
    "\n",
    "This how-to guide is intended to demonstrate how to place wire cuts using single-qubit `CutWire` instructions, which may at times be more convenient than specifying them as two-qubit `Move` instructions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1aa871cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "from qiskit_aer.primitives import EstimatorV2, SamplerV2\n",
    "\n",
    "from qiskit_addon_cutting import (\n",
    "    partition_problem,\n",
    "    generate_cutting_experiments,\n",
    "    reconstruct_expectation_values,\n",
    ")\n",
    "\n",
    "from qiskit_addon_cutting.instructions import CutWire\n",
    "from qiskit_addon_cutting import cut_wires, expand_observables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06ae4c39",
   "metadata": {},
   "source": [
    "### Prepare a circuit for cutting\n",
    "\n",
    "As in the [tutorial for wire cutting](../tutorials/03_wire_cutting_via_move_instruction.ipynb), we have used a circuit inspired by Fig. 1(a) of [arXiv:2302.03366v1](https://arxiv.org/abs/2302.03366v1).  The cut locations are marked manually here with `CutWire` instructions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0ae22516",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1290.83x618.722 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_0 = QuantumCircuit(7)\n",
    "for i in range(7):\n",
    "    qc_0.rx(np.pi / 4, i)\n",
    "qc_0.cx(0, 3)\n",
    "qc_0.cx(1, 3)\n",
    "qc_0.cx(2, 3)\n",
    "qc_0.append(CutWire(), [3])\n",
    "qc_0.cx(3, 4)\n",
    "qc_0.cx(3, 5)\n",
    "qc_0.cx(3, 6)\n",
    "qc_0.append(CutWire(), [3])\n",
    "qc_0.cx(0, 3)\n",
    "qc_0.cx(1, 3)\n",
    "qc_0.cx(2, 3)\n",
    "qc_0.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ee07a81",
   "metadata": {},
   "source": [
    "### Recover the uncut circuit\n",
    "\n",
    "`CutWire` instructions decompose to nothing (they are equivalent to the identity), so the uncut circuit can be recovered as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "631286a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IJIyBnoiIiIhIwuRiF0CN02q1UFVWi11Gs8ntbSEIgthlEBEREbU4DPRmSlVZjQ2dnha7jGaLzlgPawc7scsgIiIianE45IaIiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMI4D70F8eoXghFb5jVYVlteidLMfGRsOoC0tb9Cq9aIVB0RERERGQMDvQXK3JKAnPhkQBBg7+mKzhMGove8KWgV2B5H5qwWuzwiIiIiMiAGegtUlJKFzM0J9T+nr9uNxxKWIuipoUievxHVRaUiVkdEREREhsQx9C2AqrIahckXIchkcOnQVuxyiIiIiMiAGOhbCOeOdUG++toNkSshIiIiIkNqEYFeqVQiJiYGnTt3hp2dHXx9fTFr1iyUl5fjueeegyAIWLFihdhlGozc3ga2bs6wdXeBa1c/9Pn4ebiHBqAw+SJKM/PFLo+IiIiIDMjix9CfOnUKI0eOhEKhgKOjI7p164a8vDwsW7YMGRkZKC4uBgD06NFD3EINqGfMJPSMmdRgWXbcURx780uRKiIxabVaHD1TgFWx53H2zxJU1ajh3soW44Z1xJQxgWjtYit2iUREZGSX8srw303p2Hc0D2UVtXC0l+OBnm3x8hPBCOrYSuzy6B5ZdKBXKpUYPXo0FAoFZs+ejblz58LZ2RkA8Omnn+L//u//IJfLIQgCwsLCRK7WcNK/24PsX45AZi1H665+6D59LBy93aGurqnfRmYjx+g9C5G1NQFnlm6pX/7Akumw83TFvuiPxCidDOxC9nU8+X/7kZxWdNu6gyev4u3lSZgzOQxzX+4JmUwQoUIiIjKm8opavPjBIWzcmQmNRttgXVKqEkvWp2L0QD9889EAdvBImEUPuZk5cyZycnIwY8YMLFq0qD7MA0BMTAzCw8OhUqnQsWNHuLi4iFipYZVmKpCfkILc+JM4u3Ibfps8Hx49OqHfghfrt9HUqHBw5nKEzhyH1t06AAD8RkTCZ3gEDr22UqzSyYDOZZSg3zO/NBrmb6qsUuP91Scxbd5BaLXaJrcjIiLpqahU4aGXdmFDXMZtYf5Wv/xxGQ9O3oGS0moTVkeGZLGBPi0tDbGxsfDw8MAnn3zS6Da9evUCAISHh9cvu/kFoHfv3rC1tYUgSL/XsjApHRmbDsB/bH94RnSpX150JhOpq7bjwWX/hIO3G/otfAnH3voSlVdLRKyWDKGmVo1R0/eg+HrzTs5rt17Aqtg0I1dFRESmNHP+ERw+VdCsbVMzruHZt/4wckVkLBYb6Ddu3AiNRoPo6Gg4OTk1uo29vT2AhoH+zz//xObNm+Hl5YXIyEiT1GoKpxdvgkalRs85ExsuX7IZGrUaUXsXQnHoLLK2HRKpQjKkLfuykZ2n24xGn3939o49OEREJB1Xiyrx7S9/6tRmx4ErOJ91zTgFkVFZbKCPj48HAAwePLjJbXJycgA0DPQDBgxAfn4+tm/fjmHDhhm3SBMqy1Yga9shtBsQhjZ9guuXa1VqFCamw869Ff6M3S9ihWRI//lB9972jCtl2HM41wjVEBGRqa3dko5alUbndrxaK00We1PspUuXAAAdOnRodL1KpcKhQ3W90bcGepnM8N9xIiIioFAodGpjrZVhLnobtI4zSzfDf2x/9JwzEbsffw8A0KZPMDpPHIy0tb+i9/tTsX34HKirau68o0YEBQahVtD9xGFq+a6vAbJWyFfkw8fHR+xyjEILAXmt3wUE3X+XJ0x9G60qfzNCVURE5qElfA4AgNLpacAmUOd2q77dh80rJhihIrobLy8vJCUl6dXWYgN9eXk5AKCysrLR9bGxsVAqlXB2doa/v79Ra1EoFMjN1a3n00awAnR8qKviSCrWeT/e5PrrF3Pxrc//htzIHezwwJLpOPHRBpz/ZjdGbn0f9735FBLnrtPtwADy8vNQo1Xr3M7knNWADNCo1Tr/nUiGzBZw0++L6Y3yGtzIt9D3hYgIaBmfAwAQoAVsdG9Wq5ZZ9vtioSw20Ht5eaGkpATJycno169fg3X5+fmYM2cOACAsLMzoN756eXnp3MZaKwOM3OEd+d6zuHG5AOfX7QIAHJy1AlH7FuHyzmO4elS3S27tvNtJo4feygoaADIrK3i3by92OUahhYA8rUavHnpnR2u4WOj7QkQEtIzPAQBQWgP6zFljbaVGGwt+X8yZPnnxJosN9MOGDUNaWhoWLFiA4cOHIygoCACQmJiIZ555BkqlEoBpHiilz+WT2ooqbOj0tBGqqdN+SE/4R/XHtqGz65eVXbqKEx9tQP/F07F9yGyoKpt/Krhw8QKsHeyMUapB+QzbiNyCCnh7eSPnbI7Y5RjNsBd24rdjeTq327ZhPgb3bmeEioiIzENL+Rz47JsUvP7ZcZ3bvfrCCCx49V0jVETGZLE3xcbExMDd3R1XrlxBSEgIQkNDERgYiN69eyMgIABDhgwB0HD8fEuSG38S33edjPJcZYPl59ftwpZ+M3QK82R+XpkYfPeN/qarfysMivQ2QjVERGRqU8YEws7WSqc2ggC8OKGrkSoiY7LYQO/j44OEhASMGjUKdnZ2yM7OhpubG1avXo24uDhcuHABQMsN9GTZogb5oau/bo/y/r9/GH/4GRERmYa7qx1eGN/l7hveYsJD/gjwsZwHbbYkFjvkBgCCg4OxY8eO25bfuHED2dnZkMlk6N69uwiVERmXXC5D3H8ewoNT4pBXUHHX7Wc/2x1TxgSZoDIiIjKVRbN7Iz37erOmJO7d3RNr5z1ogqrIGCy2h/5OUlNTodVqERgYCAcHh9vWb9q0CZs2bcK5c+ca/KzvVEJEYgjwccHR9aMxtE/TY+LdWtni8zl9sHC2YadIJSIi8dlYW+GX5cMx48lusLVpfPiN3ErAs6M7I/7LkXBysDZxhWQoFt1D35SUlBQATQ+3mTBhQqM/T548GevWrTNqbUSG5OvlhH1rRuJcRglW/3Qeq386j+paDexsrLDqnfsx8eEA2Nu1yNMAEVGLYGNtheVv9sN7L/fE1z9fxL6judh/PB81Kg2cHa1xftt4tGvjKHaZdI9aZA/93QK9Vqtt9D+GeZKqbp1aY+kb/eDRum4mIndXW0wZE8QwT0TUQri72uH1KaHY9cUIeLrVfRa4OFozzFsIBvoWpsOovug7/4UGyzpPHIwp+ZvgNyJSpKqIiIiISF8tsnsuPj5e7BJE4/dIH2T89Hv9z04+ngiKHoaCpHTxiiIiIiIivbXIQG/JbFwcMGb/YljZ2aAiTwmZrTWc/doiY9MfOPLGGrSN7IKDs1bUbSwIuP+zl3Hs32sROXeyuIUTERERkV4Y6C1MTWkFMrcmoLa8CmcWb0K7QeEImzkOh1//Au0GhqMgMR1alRoAEPLiaBQknkfRmUyRqyYiIiIifbXIMfSWzq27P4pTsgAA7mGdUHy27s9+IyJxaWfdY6Bdu/iiw6g+OL1ks2h1EhEREdG9Yw+9BXIL6Vgf4t3DAnBldyIAoN2gHkj6YD0AoG2fYDj5tsH4w8sBAPaerui38CXYt2mN9G/3iFM4EREREemMgd7COHi5AVotKhTFAAC34A44s3QzPHoG4vrFXKgqqgAA6d/uaRDcR2yeh3NrduDyrkRR6iYiIiIi/TDQWxi37v71vfMAUFNajq6TH0Z1cRku7zouYmVEREREZAwM9BYmZ98J5Ow7Uf/zjpFvAADG/L4Yu8fPbbLdrjusIyIiIiLzxUDfQmwb9KrYJRARERGREXCWGyIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJ4xh6MyW3t0V0xnqxy2g2ub2t2CUQERERtUgM9GZKEARYO9iJXQYRERERmTkOuSEiIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgmTi10ANU6r1UJVWS12Gc0mt7eFIAhil0FERETU4jDQmylVZTU2dHpa7DKaLTpjPawd7MQug4iIiKjF4ZAbIiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJ4zz0FsSrXwhGbJnXYFlteSVKM/ORsekA0tb+Cq1aI1J1RERERGQMDPQWKHNLAnLikwFBgL2nKzpPGIje86agVWB7HJmzWuzyiIiIiMiAGOgtUFFKFjI3J9T/nL5uNx5LWIqgp4Yief5GVBeVilgdERERERkSx9C3AKrKahQmX4Qgk8GlQ1uxyyEiIiIiA2KgbyGcO9YF+eprN0SuhIiIiIgMiUNuLJDc3ga2bs71Y+i7PPsQ3EMDUJh8EaWZ+WKXR0REREQG1CICvVKpxKeffootW7YgJycHnp6eGDduHD7++GPMnDkTX331FZYvX44ZM2aIXapB9IyZhJ4xkxosy447imNvfilSRUTiu5x/A7sP5eBaWQ0c7OWI6OaB3qGeEARB7NKIiMgEyitq8csfl5FXWAGZICDAxxkjH/CFtbX0B6xYfKA/deoURo4cCYVCAUdHR3Tr1g15eXlYtmwZMjIyUFxcDADo0aOHuIUaUPp3e5D9yxHIrOVo3dUP3aePhaO3O9TVNfXbyGzkGL1nIbK2JuDM0i31yx9YMh12nq7YF/2RGKUTGdzR0wWY/9Vp/PLHFWg02gbrenZ1x6zoEDwb1ZnBnojIQuUVlGP+V2fwzfaLKL1R22Cdl4c9XhjfBXOmhMLZ0UakCu+d9L+S3IFSqcTo0aOhUCgwe/Zs5OfnIzk5GQqFAgsWLEBcXBwSExMhCALCwsLELtdgSjMVyE9IQW78SZxduQ2/TZ4Pjx6d0G/Bi/XbaGpUODhzOUJnjkPrbh0AAH4jIuEzPAKHXlspVulEBvV9XAYenLID2/Zfvi3MA8DJ80WY8s4BTJt3sNH1REQkbWmZ19An+hcs//7cbWEeABTKSnyw+hQGTI1DQVGlCBUahkUH+pkzZyInJwczZszAokWL4OzsXL8uJiYG4eHhUKlU6NixI1xcXESs1LgKk9KRsekA/Mf2h2dEl/rlRWcykbpqOx5c9k84eLuh38KXcOytL1F5tUTEaokMY++RXDz77z+gUt89qH+55QLeXJpogqqIiMhUrhZVYsTLu5Bztfyu2546X4xH/7kHVdUqE1RmeBYb6NPS0hAbGwsPDw988sknjW7Tq1cvAEB4eHj9sk2bNmH8+PHo0KEDHBwc0LVrV7z99tu4cUPas8OcXrwJGpUaPedMbLh8yWZo1GpE7V0IxaGzyNp2SKQKiQxHq9UiZvFxqJsR5m/67NuzyFHc/aRPRETSsHR9Ki7nN/+8nnhWidhdWUasyHgsNtBv3LgRGo0G0dHRcHJyanQbe3t7AA0D/aJFi2BlZYWPP/4YO3fuxMsvv4xVq1ZhxIgR0Gg0JqndGMqyFcjadgjtBoShTZ/g+uValRqFiemwc2+FP2P3i1ghkeEcPVOAU+eLdWqjVmuxZnO6kSoiIiJTqq5R48stup/TV8amGaEa47PYQB8fHw8AGDx4cJPb5OTkAGgY6H/55Rf8+OOPiI6OxsCBAzFr1iysWLEChw4dwsGDB41btJGdWVrXG39rL32bPsHoPHEw0tb+it7vT4WVnXRvCCG6aePOTP3a7cowcCVERCSG+GN5KCyp0rnd8bOFyMwpNUJFxmWxs9xcunQJANChQ4dG16tUKhw6VDe85NZA7+npedu2ERERAIDc3Fy9aomIiIBCodCpjbVWhrnorVMbxZFUrPN+vMn11y/m4luf/4V5uYMdHlgyHSc+2oDz3+zGyK3v4743n0Li3HU6HRcAggKDUCuY/xWMfNfXAFkr5Cvy4ePjI3Y5JtdSXn+x4+OAbajO7f7MKrDo94WIWs558E5awntQbhMOOI3Tq22fBx6CrSrHwBXdnZeXF5KSkvRqa7GBvry8bsxUZWXjdyzHxsZCqVTC2dkZ/v7+d9zX/v11Q1GCg4PvuF1TFAqFzl8GbAQroK1eh2u2yPeexY3LBTi/bhcA4OCsFYjatwiXdx7D1aO6XXLKy89DjVZtjDINy1kNyACNWq33FzRJaymv36ccsNW9mVZTa9nvCxG1nPPgnbSE98DVB2h8xPVdKQsUQKW03heLDfReXl4oKSlBcnIy+vXr12Bdfn4+5syZAwAICwu74/zTubm5eOeddzBixAi956r38vLSuY21VgYYscO7/ZCe8I/qj21DZ9cvK7t0FSc+2oD+i6dj+5DZUFVWN3t/7bzbSaOH3soKGgAyKyt4t28vdjkm11Jef6ltJcr0aGejLYGnBb8vRNRyzoN30hLegxorLQoBQKsFdHnOiFYNL3cbWGlN/77okxdvErRarUVOvjxz5kwsX74cvr6+2LdvH4KCggAAiYmJeOaZZ5CZmYna2lpMnz4dK1asaHQfN27cwKBBg6BQKJCYmAhvb2+T1V9bUYUNnZ422fHuVXTGelg72Ildxl35DNuI3IIKtG/jgJx9T4pdjsm1lNd/RXEDHUf8qPPc8l+9/yCmjg0yUlVEZA5aynnwTlrCe6DVatHziZ9xOl23CRKeeNgfsQuHGKkq47HYm2JjYmLg7u6OK1euICQkBKGhoQgMDETv3r0REBCAIUPq/rJuHT9/q8rKSowePRpZWVnYs2ePScM8Ed0bXy8nRA3y06lNaxcbTHw4wEgVERGRKQmCgFcm6j5UWp825sBiA72Pjw8SEhIwatQo2NnZITs7G25ubli9ejXi4uJw4cIFAI0H+traWjz++ONISkrCzp070a1bN1OXT0T3aPkb/dC+jUOztpXJBHz70UA42FvsKEQiohbnH2ODMGqAb7O3nxUdgoER0uzAtehPr+DgYOzYseO25Tdu3EB2djZkMhm6d+/eYN3Nuet/++03/Prrr+jdW7eZZojIPPh4OeL3r0Zh5Cu78eflpqcgs7O1wvfzB+HRgbr16BMRkXmTy2X4adEQRL/5O7b+dumO2772bHcsfE26mc+iA31TUlNTodVqERQUBAeHhj1406dPx08//YQ33ngDDg4OOHr0aP26Tp06NTqtJRGZp85+Ljj902P4YVcm/vPDOSSnFdWvk8kEvDOtB14Y3wXt2zqKWCURERmLvZ0cmz4bivjjeVgZm4Zt+y83uL9q6thAvPxEMCK7SzvftchAn5KSAqDx4TY7d+4EAMyfPx/z589vsO7rr7/GlClTjF4fERmOg70c/3gsCFPHBqKguAph47egoLgKXu52eO+V+8Quj4iIjEwmEzCsb3sM69se18tq0GX0T7haXAVvT3t89f4AscszCIsdQ38ndwr02dnZ0Gq1jf5nCWG+w6i+6Dv/hQbLOk8cjCn5m+A3IlKkqoiMTxAEtHW3h7VcVv8zERG1LK2cbSD/63NAZkGfAwz0LYzfI31wedfx+p+dfDwRFD0MBUnpIlZFRERERPpqkUNu4uPjxS7BaGxcHDBm/2JY2dmgIk8Jma01nP3aImPTHzjyxhq0jeyCg7P+mndfEHD/Zy/j2L/XInLuZHELJyIiIiK9tMhAb8lqSiuQuTUBteVVOLN4E9oNCkfYzHE4/PoXaDcwHAWJ6dCq1ACAkBdHoyDxPIrOZIpcNRERERHpq0UOubF0bt39UZySBQBwD+uE4rN1f/YbEYlLO+uG27h28UWHUX1weslm0eokIiIionvHHnoL5BbSsT7Eu4cF4MruRABAu0E9kPTBegBA2z7BcPJtg/GHlwMA7D1d0W/hS7Bv0xrp3+4Rp3AiIiIi0hkDvYVx8HIDtFpUKIoBAG7BHXBm6WZ49AzE9Yu5UFVUAQDSv93TILiP2DwP59bswOVdiaLUTURERET6YaC3MG7d/et75wGgprQcXSc/jOrisgaz2xARERGRZWCgtzA5+04gZ9+J+p93jHwDADDm98XYPX5uk+123WEdEREREZkvBvoWYtugV8UugYiIiIiMgLPcEBERERFJGAM9EREREZGEMdATEREREUkYAz0RERERkYTxplgzJbe3RXTGerHLaDa5va3YJRARERG1SAz0ZkoQBFg72IldBhERERGZOQ65ISIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjC52AVQ47RaLVSV1WKX0Wxye1sIgiB2GUREREQtDgO9mVJVVmNDp6fFLqPZojPWw9rBTuwyiIiIiFocDrkhIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMM5yQxZLq9UiOa0ISalKnDinxPmsaygorgIAKEuq8NrCo+jVzQN9w9qgk6+LyNUaR15BOQ6fKsCJNCVOnS+uf/2FJVV49q0/EBHigV7dPNAn1BNyueV9v6+qVuHomUKcOKdEUqoSlxU3UFBcCQBQXqvCu/85gV7dPHB/eBt4utmLXC0RGUN2bhmOnC7AiXNKnL7Q8Dz43NwERHTzqD8XymSWN/3yjYra+teflKpEXmFF/Xmw6Fo1Plh9sv486OpiK3K1hqfVanE6vRiJZwtxIq0IaZnXGvwOzJp/BBEhdVkgsEMrkavVn6DVarViF0G3q62o4rSVerpWWo1vtl/EytjzuHDperPaDIzwwisTg/HYkI6wtpZ2sNVotNh7JBcrY9Ow48AVaDR3/yfevo0Dpj3eFS+M7wJvTwcTVGlcWTll+OKnNKzdegFF1+7+PAdruQzjh3XE9EnB6N+zLZ+pQCRxKpUGv/xxGStj07DvaF6z2nTydcZLE4IxdWwg3F3N4/PsXpzLKMGqH8/jm+0XUVZee9ft7e2s8NTITnhlYjDu6+ZhggqNq/RGDb7b8SdWxqbhXMa1ZrXp37MtXnkiGOOHd4StjZVxCzQwBnozpU+g9+oXghFb5jXcT3klSjPzkbHpANLW/gqtWmPIMuuZQ6DXarX476Z0zPn8eLNOXo0J8HHGV+8/iIER3gauzjRSLhRj6rsJOHFOqVd7a7kMb78Qjree7yHJLzYVlSq8vTwJSzekQt8z2+BIb6yd9yD8fZwNWxwRmcSR01cx9Z0EpGc3r0Pn7xzs5PhkVgRmPNlNkj32JaXVePXTY/hm+0W99/HY0A5Y+fb98PKQXgePVqvFt9v/xL8+PYprZTV67cPP2xFr5j6Ah+73MXB1xsNAb6buJdBnbklATnwyIAiw93RF5wkD0Tq4A9LX78WROauNUq/Ygf6K4gb+8W5Cs3ti7mbGk93w6auRsLeTxqg0jUaL+WtP471VJ1GruvcvbT26uuG7jwaie6CbAaozjcOnrmLyvw/gz8ul97wvR3s5Fr7WGy890ZW99UQSUV2jxr+Xn8Dn351t1pXJu3nwvrb45sOBkvpyvzPhCp6fdxB5BRX3vC+3VrZY+fb9mDgiwACVmYZCWYHn3zuIuANXDLK/F8Z3wedz+sDJwdog+zMmBnozdS+BPnHet0j9Ynv9crm9LR5LWAoHbzf8EPY8qovuPfD8nZiB/nzWNQyftgs5V8sNut+BEV7Yvmw4XJxsDLpfQ6ut1WDKOwfw/a8ZBt2vs6M1diwfjgESuFrxc3w2Js7Zj5paw16B+tfTIfh8Th+GeiIzV15Ri3Gv/YY9h3MNut+27vbY/cXDCO/ibtD9GsOXm9Mx7f2Del+dbMonsyLwxnPhht2pEWTmlGLYC7uQlVtm0P32CfXErysfhlsr876/QHrX1ElnqspqFCZfhCCTwaVDW7HLMaiMK6UY8vxOg4d5APgjSYFHZ+xBRaXK4Ps2FLVag8n//sPgYR4Ayspr8cj0PThy+qrB921IcQcuY8Lr8QYP8wCwZH0qZi86BvZ7EJmv6ho1Hnt1n8HDPABcLarEsGm7kJZ5zeD7NqR12y7ghXmGD/MA8ObSJCz8+ozhd2xAVxQ3MPi5Xw0e5gHgWEohRry8C2Xl+g3fMRUG+hbCuWNdkK++dkPkSgynukaNsbP2Ib/w3i8tNiUh+Sr+Of+I0fZ/rz79OgUbd2Yabf/llSqMmbkPhX/NiGBuMq6U4onX90OlMl7gXvxdKr7d/qfR9k9E92bO58ex94hhhls2RllShaiZe822cycptRDPv3fQqMeIWZyI3YdyjHoMfalUGox79Tdczjd8x95NiWeVeGGecd/je8VAb4Hk9jawdXOGrbsLXLv6oc/Hz8M9NACFyRdRmpkvdnkG8/4XJ3H2zxKd2iRujMKVvZOQuDGq2W2+2noBuw6a34ks9c8SvLcqWac2+rz+wpIqs/xSo9Fo8Y93E1BRpduHrD7vwaxPjyLXCFeBiOje/JGUj+Xfn9OpjT7ngD8vl+Lt5Um6lmd01TVqTPn3AajVunVq6PMePP/eQVzX8yZTY1q4LgVJqbpNBKHP64/dlYXNe7N0Lc9kWkSgVyqViImJQefOnWFnZwdfX1/MmjUL5eXleO655yAIAlasWCF2mQbTM2YSnkz9Gk+e/Qpj93+O4KkjkB13FPFTFohdmsGcOl+EBXpcAvTycIBPW0ed79x/Yd5B3KjQb+YcY9Bq68KsrsNM9H39sbuy8HN8tk5tjG31T+dx4IRC53b6vAfXy2rw8oeHdT6WudFotLheVoNrpdUGuWlQiiqrVCi6VoVaIwzRkgK1WoPi69W4UVEr+aFk1TVq/OPdBJ3b6XseXLoh1eyGIH605hRSmzkl4630eQ9yrpYjZvFxnY9lTOlZ13Tu2AL0/x14+cPDKCm9+1TIYpDGFB734NSpUxg5ciQUCgUcHR3RrVs35OXlYdmyZcjIyEBxcTEAoEePHuIWakDp3+1B9i9HILOWo3VXP3SfPhaO3u5QV//vm7XMRo7RexYia2sCzizdUr/8gSXTYefpin3RH4lRerMt+iZF5x6Je5FztRzf/5qBaY93Ndkx72T/8XwcP1to0mMu+OoMxg7paNJjNkWt1uBTE4/p/OWPyziXUYJunVqb9LiGkJ51Dat+PI912y/W97A5O1rjmUc745WJwQjpLL3XpIsbFbVY/9d81CkX/3dVb0hvb7wyMRhRgzpIcprW5tJqtThwQoGVsWnY8lt2/RA1Xy9HvPh4Vzw/vgvaukvvwWqb9mYhM8fwY6abotXW9QZvWWwe96KVV9RimY5XJ+7V1z9fxPvTe5nN78vi9alGuX+qKYUlVVi37SJefaa7yY7ZXJZ7BkNdz/zo0aOhUCgwe/Zs5OfnIzk5GQqFAgsWLEBcXBwSExMhCALCwsLELtdgSjMVyE9IQW78SZxduQ2/TZ4Pjx6d0G/Bi/XbaGpUODhzOUJnjkPrbh0AAH4jIuEzPAKHXlspVunNUlhciZ/2mP6y18rYNLPp0VoZm2byYx49U4hkPee3N7Rdh3KQnWf6+0FW/Xje5Me8F1qtFm8vS0LXMZuxdENqg8vlZeW1WBmbhu7jtuC1hUcttsf+yOmr8B/5I17+8HCDMA8A8cfz8fjsePR8Yisu51vO/UW3KiuvwajpezDoH7/ix91ZDe43uaIox79XnIDfQz/g+zjD31hvbGKcB7ftv4wchXkMv9u4M9PkQ2BqVRqs3ZJu0mM25XpZDdbvMP39Tat+TDPL86VFB/qZM2ciJycHM2bMwKJFi+Ds/L+5ZGNiYhAeHg6VSoWOHTvCxcVFxEqNqzApHRmbDsB/bH94RnSpX150JhOpq7bjwWX/hIO3G/otfAnH3voSlVd1G5duat/t+NOk38hvOp1erPM4PWMoKKrEz/sviXLsNZvN40QuVh3f/nIR1TVqUY6tjzmfHcfHX56+63aLv0vF9I8Om80XVkM5nlKIoc/vhLKk6o7bpWZcw4CpcUa9wV4MVdUqjJq+Bzvvcg9QTa0G0W/+Lko40te5jBIcPlVg8uNqNFp89fMFkx+3MV+KFKzN5XPgh12ZKBfhRuWLl0rxR5L53Y9osYE+LS0NsbGx8PDwwCeffNLoNr169QIAhIf/b37VhIQEDBs2DN7e3rC1tYWPjw8mTpyItDTT9wQY0unFm6BRqdFzzsSGy5dshkatRtTehVAcOousbYdEqrD5Dp4UbwzjIRGPfdOxlEKTDje61aFT4r9+rVYr2u9A6Y1anW/EFsu+o7n47Nuzzd7+i5/OY/vvl41YkWmp1Ro8MSceldXN+wJ2Ke8GXvrA/M9/uvjkyzNISG7+v5Xn5iZI5kuNqJ8DZnAerKxSIUmkK6bZeTeQVyD+VYqDJ3W/h8pQzOF34O8sNtBv3LgRGo0G0dHRcHJyanQbe/u6MWC3BvqSkhKEhoZi2bJl2LNnDxYsWIDU1FT069cPOTnmN9NJc5VlK5C17RDaDQhDmz7B9cu1KjUKE9Nh594Kf8buF7HC5jsh4rCPE2ni99CL+frPZV4Tfeq2y/k3UHRNvJuSxHz/dfGfH3TvhPjPD6Ydj2tMcQeu4JKOw7J2HLiCS3mmG5NtTDW1avx3s25DxGpqNaL1+upK1M+Bc0rRr2aduVAsWscOAJw4VyTasc2hBnN4/X9nsYE+Pj4eADB48OAmt7kZ0G8N9FFRUVi8eDEmTJiAgQMHIjo6Glu2bMH169exefNm4xZtZGeW1vXG39pL36ZPMDpPHIy0tb+i9/tTYWVn3k9FLb5ebdS5Zu/mZJr4/4hPnhevBrVaK3oP9an0YlGPbw6/A3eTV1CuV2/73iN5yLhi+CdJi2H1Jt3vd9BotPhyi3kMp7hXv/x+GQql7s+PWP3TebMcH/x3p86Ldx4oulZtlIcZ6kLMzwFzOH5llQrns66JdvxTIr/+xghasb9mGomvry9ycnJw8uTJRmewUalU8Pb2hlKpREZGBgICAprcV1FRETw8PLBixQpMnz5d51oiIiKgUOh2achaK8NcTW+dj6ULuYMdon5bhHOrd+D8N7sxcuv7UJ7OQOLcdTrva57sOGoF449rV8la46rrv5pcn7gx6o7TUHl52ENuJYNKrbnjh51CWYHIJ7fftlymKYX3tc90qtnQCp2nosa6Y6PrDPX6gabfA/fSb2GnEu8GunKbcFxzGtfouru9fuDefwfsq1PgVr5Jt6JNrFreEUqXqXq1dSvbAPta6YdaRat/QW2l++w9djXn4H4j1ggVmVap3UCUOQzRq613yceQac1zar6brrb6J1RWHo2uM8V5sM31/8Babfox/DeV2T2AUofhja4zxXnQseoIXCt26Va0AakFRyhaxzS53thZQNBUot21+boV3QxeXl5IStLveQcWO21leXndt+fKysb/omJjY6FUKuHs7Ax/f//b1qvVamg0Gly6dAlvvvkmvLy88MQTT+hVi0KhQG6ubo+kthGsACPPjBX53rO4cbkA59fV/aM8OGsFovYtwuWdx3D1qG6X6/Py81CjNcHNgjYqwLXp1Tfnlr0buZWsWdv9nUYNnf8uDS6gFrBufJWxXz8AFBWXAGUivget/YHGR9E1+/UD+r8HlVXV4v8O3I2TK6Dnff7FxdeBUjN/fc3hLABWujerqqo1/7/f5mhbCeg2xXa9/PxCQG3mQ48cNU3+/ZriPFhQoASqRPw98bzR5N+vKc6D5TcqUJ4v4uuXtwLu8H3d2L8DWq1gducJiw30Xl5eKCkpQXJyMvr169dgXX5+PubMmQMACAsLgyAIt7UfOHAgDh2qu0Gqc+fOiI+Ph6enp9616MpaKwOM2OHdfkhP+Ef1x7ahs+uXlV26ihMfbUD/xdOxfchsqCqb30PTzrudiXroXXCnW1EUyjvf0KXLt/LGWMnU8GrfvjmlGo3SRoam/mYM9frvtC8PNxfYuoj3HlTYOKGpQT93e/3Avf8O2NtZw03k34G7qbFygL5PKfBobQdbZ/N+fc1xVaiGPnd7ONhq0NrM/36b44atFa7r01CrQTuv1hD0/UZoIlettE3+/ZriPNjG0w3WGvEeTlZm54CmBseZ4jzo5GiLViL+O9EI9rjTPDPGzgIyQQ1vI7x+ffLiTRY75GbmzJlYvnw5fH19sW/fPgQFBQEAEhMT8cwzzyAzMxO1tbWYPn16o0+JTU9Px7Vr15CVlYWFCxeioKAAhw4dgp+fn0nqr62owoZOT5vkWIYQnbEe1g52Rj+OSqWBy/3forJKv6sBV/ZOgk9bR+RcLYfv8B90bj+sbzvs/e9IvY5tKC99cAirf9JvPvR7ff0AcHnPRPh6NdFFbgLHzhSg79O/6N3+Xt+Dea/ch3df6qn38U1BrdYg8NFNyMrVrZfVy8Mel3dPsoiHLM1blYz3Vp3Uud0vy4fj0YGmOc8bU3ZuGQIe+RG6fsI/NrQDtiweZpyiDGjMzL16z8p0r+cAKysBZUeehb2deH2i2/ZfwthZ+/Ruf6/vwX/f7Y8XRHzQolarhfuD61FSqt88/Pf6+vuGeeLI+ii9jm0s0j9rNyEmJgbu7u64cuUKQkJCEBoaisDAQPTu3RsBAQEYMqRubOGtN8TeqkuXLujTpw8mTZqE3377DWVlZfj0009N+RKoEXK5DD26uIt2/F7dGh+zadIagsV7/Z6t7fS+RG0oYUFusLK6/aqaqfTqJt7731xWVjK8NEH3D9tp47taRJgHgBfGd4Fcx9+TDu2cMPIBHyNVZFod2ztj1IO+Ord7ZWLw3TcyA2Kei0M6tRY1zANAr2BxP4vE/iwUBEHUGsR+/Y2xjDN3I3x8fJCQkIBRo0bBzs4O2dnZcHNzw+rVqxEXF4cLF+pu+moq0N/K1dUVnTt3xp9/SuehG5YsIqRl/yMW+/U3NkTNlOzt5OjeWfebHQ3FHH4HmuOFx7sgwMf57hv+xaetI6ZPkkaYa452bRwxKzpEpzYf/bMXrKws52Nx7ss9YWfb/BsJhvVth6F92hmxIsMR9zwo/pf69m0d0NbdXpRj21jL0D1QvHPwTWJ/FpobyzlzNSI4OBg7duxAWVkZysrKcOzYMUybNg3l5eXIzs6GTCZD9+7d77qfgoICpKeno1OnTiaomu7m8WEdRTmuk4M1Hr5f/LG14V3c0cm3+UHNkCY8dPsN5GJ4fHhHUY77QM+2d509wly0drHFzpUPw9fr7ldUvDzssXPlQ2gjUkAwlgWvRuLpR5t33l74Wm9Ej+ps5IpMKyLEEz8uHNKsUN83zBObPhsq+hf25hoc6Y3WLuJMszxhuPjnQUEQRDsPjhncATbWetxxbmCPi/T3YGtjhdFmOCzPogN9U1JTU6HVahEYGAgHh4Yfzk8//TTee+89/Pzzz/j999+xZs0aDBo0CHK5HK+++qpIFdOtHuzlhZBOriY/7jOPdoKLk/jz9MtkAl5+wvQ9qa7ONpg0ounpXU3p+XFdIJebPnhIZTjCTUEdW+Ho+tF4flwQ7O1u/wC2tbHClDGBOLYhCt0D3USo0LisrGT45sOBWP5mvya/BPcJ9cTPS4fh9SmhJq7ONEYP8sOBr0dh1ABfNJbVPVvb4a3nwxH/5SNo5Sz++a257O3k+MfYIJMf17+9Mx7ubx7DssT4HADM5zzYq5sHenfXb7KSe/HEQ/7waG38ewZ11SIDfUpKCoDGh9v07dsXv/76K6ZOnYqRI0di4cKFePDBB3Hq1Cl07mxZvTdSJQgCpk/qZvLjinXybMzUsY0HNGP6x2NBcLA3j4mxvDwc8Pgw0/bOtHW3xziRrg7di3ZtHLHmvQeRt+9JrH63P5wd6v4OWzlZI3ffJHz9wQD4eYt3k7OxyWQCZjzZDRd+mYBdqx6Gs2PdnK8ujtZI+mEMjm6IwpjBHUSu0rgiu3tix4qHkBH3BBbN7g2nv34HWrvY4MreSfhoZoToY8L18dITwZDJTPvF/pWJpj9mU0I6t8agSG+THrNbJ1cMjNB/JhZDE2OYoLkOTWSg/5sZM2bg+PHjKCkpQWVlJS5cuIDVq1ejQwfLPuFLzfPjuqBnV9ONY3xlYjBCg8ynB9OtlS0++meEyY7n7emAf0/rYbLjNceCVyPrw5kpLInpA1sb8S8z68vVxRbTHu9af5XJycEa7q7m18tkLDKZgIf7+8Dlr98ZZ0drsxwHa0z+Ps6YPTkUrf76HXCwk0v6d7qznwtmP3v3YbOGEhzgihlPmleYWxLTx6RXK//z1v1mNSwrelQn3N+jjcmONzkqEH3CTHc8XTDQtzAdRvVF3/kvNFjWeeJgTMnfBL8RkSJVpTtraxnWfTgA1nLj/wp3bOeEBa+a33sz86lu6N/TyE8f+8t/3+2P1i62JjlWc/l5O2HRbOM+TfmmcUM7YqKZDDciov+Z98p96NKxldGPI5MJWPfBANjZmteVjPAu7nhnmmmm0Z0+KdjkVwTuxspKhq/fH6DTzd/6atfGAYtj+hj9OPpqkYE+Pj4eWq0Wo0aNErsUk/N7pA8u7zpe/7OTjyeCooehICldxKr0Exbkhk91DNoKZQVyrpY368EbQN0Y4+8+HggnB9P1BDeXlZUM6z4YAHfX5gdtXV8/UHd1wlzn5X5hfBeMG9pRpza6vgcd2jlh1b/Nq1eKiOrY28mx/pOBcNBhyJA+58F5r/RE71DTj9dujjefC8eD9+nWuaPrexAa2Brz/2V+HVtA3b1CS/+vr05tdH39crmAbz4cYHYdW7cyr6+adM9sXBwwZv9iWNnZoCJPCZmtNZz92iJj0x848sYatI3sgoOz/nqQliDg/s9exrF/r0Xk3MniFq6nfz3THUXXq/Hhf081a/vIJ7c3e9821jL8tGgIHrjPfMYL/l1nPxfsWvUwhk/bhWtld3/Ahi6vHwCeeqQTlr2h24nSlARBwIb5AzFmVi32HG7eY7h1eQ/atXHAvv+OtLjZX4gsSURI3Y3NUTP3oqr67g8d1PU8+K+nQ/D2Cz30rM74rK1l+GX5Qxg2bSeSUpXNaqPLe9ClYyvsWT3CLDu2bpr2eFcUXavGW8uSmrW9Lq/fykrAhk8GYVhf8We5u5MW2UNvyWpKK5C5NQHnvozD9uFzcPzdr1GYfAGHX/8C3v27oyAxHVpV3Qkv5MXRKEg8j6IzmSJXfW8+mNELn74aadAblVydbfDL8uEYPcg8e6ZvFRHiiT++HtWs6Ql1MX1SML79aIDZz8ttZyvH9mXDMXGEYW+S7erfCgfXPYrOfi4G3S8RGd7wfu2xe9XDBp19RBCA917uic/n9DH7K3StnG3w25qRGN7PsM8R6N3dEwe+HiWJ6XrffD4cy9/sZ9B7CpwdrbHl86F44mHzH3Jp3p/UpBe37v4oTskCALiHdULx2bo/+42IxKWddcNtXLv4osOoPji9ZLNodRrSnKlhOLp+NLoZYDrLRwf4InXrODx0v3lMTdYcYUFuSNk8Ds+Pu/dp3Nq1cUDcfx7CirfuN/swf5OtjRU2LhiMDZ8Mglure7skKpMJmDMlFMmxY+Gvw4OZiEhcAyK8kbplHMYbYDaqwA4uOPD1KMx9+T6zD/M3uTjZYNeqEVjxVj843uOMZDbWMnw8MwKHvn1UUlcoZzzZDYnfj0F4l3ufxGJ4v3Y4u2UcoiQyC5Y0Pq1JJ24hHetDvHtYAIr+CvftBvVAbvxJAEDbPsFw8m2D8YeX4/HjK+F5XyD6LXwJXZ59SLS671Vkd0+c+GEMPpkVoVdvda9uHti4YBC2Lx+Odm0M29ttCq2cbbDmvQex978j9Hrao7urLWKmhiJ1yzg8oscj48UmCAKeGtUJqVvHYfqkYJ1nwBEEYPRAPxz+9lF8+lpvSU7jR9TStXG3x6bPh2LL4qHoF677bCTt2jjg/en34dSPj5n1cMumyGR10zqf2fwYpo4N1PlmUblcwKQRAUiOHYs3nw+H3AQTTxhaj67uOP59FD57vTf82+veKRPexQ3ffjQAu78YIakpfQWtVqsVuwi6XW1FFTZ0elrndg5ebhi951PEhj0PABh3aDl+f+lzyORyhL/6OH579pNG243YPA/n1uzA5V2JetUbnbEe1g7mMwWeSqVBXMIVbNyZgaRUJTKulN22jVwuIKRTa/QNa4PnHgtCpAgPqDCm81nX8OXmdBw8eRWn0otRXXP72FKfto7o1c0d44d1xISH/M1uBod7UVZeg/U7MrDjwGWcOFeEq0WVt23jaC9Hj67uGBThhefHdUFHPU7+UuMzbCNyCyrQvo0DcvY9KXY5JtfSXz/Qst6Dk2lKrN16AUdOFyDlYglqVZrbtvFv74xe3dwxaUQAogZ1gLW19EJsU4qvV2PdtgvYdSgHJ84Vofh69W3buDhZ475gDwzr0w7PjQuSxPCa5lKrNdh9OBcb4jKQmFqIi5dKb9vGykpAtwBX9An1xNSxQegX3kYyV2VuZTmf3gTgr+E2f/XOA0BNaTm6Tn4Y1cVlDWa3sXRyuQxjBneof2DMtdJqpGdfR0WVClYyAc6O1ggOcLWoAPt3Xf1dsej1uim2ams1SM++hpLSGtSqNLC3s0InHxdJXUrVlbOjDV6eGIyXJwZDq9Uir6ACl/JvoKpaDRtrGTxa2yHQz0Uyw4qISHc9gz2wIrjueQPVNWqcz7qG62U1UGu0cLCTI7BDq3sepmfO3FrZ4rVnQ/Has6HQarW4lHcDuQUVqK6pOw96eTggwMfZbB6WZWhWVjI88qBv/VXn62U19VlAEABnh7osYAlXZKX/CqiBnH0nkLPvRP3PO0a+AQAY8/ti7B4/t8l2u+6wzhK4utia7cMgTMHaWobugebzYCxTEwQB7ds6on1b6Q2lIiLDsLWxQngX0z2Q0NwIgoCO7Z1bxJXIprRytjHb6UfvFQN9C7Ft0Ktil0BERERERsBrzUREREREEsZAT0REREQkYQz0REREREQSxjH0Zkpub4vojPVil9FscnvLnSWAiIiIyJwx0JspQRDMal53IiIiIjJPHHJDRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSJhe7AGqcVquFqrJa7DKaTW5vC0EQxC6DiIiIqMVhoDdTqspqbOj0tNhlNFt0xnpYO9iJXQYRERFRi8MhN0REREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhvCmWiMjC1dSqcfZiCVIzSnCjohYAUFGpQlJqIUID3WBrYyVyhUREdC8Y6ImILFBZeQ3W78jAN9sv4uT5ItTUahqsLymrQeST22EtlyG8ixueebQznh3dGa4utiJVTERE+mKgJyKyIKU3ajB3ZTK+3HKhvjf+TmpVGiSlKpGUqsSbS5MwdWwgPpzRi8GeiEhCGOgtiFe/EIzYMq/BstrySpRm5iNj0wGkrf0VWrWmidZEJHX7jubiubkJuJxfrlf7iioV/vNDGrbGX8KauQ/gkQd9DVwhEREZAwO9BcrckoCc+GRAEGDv6YrOEwai97wpaBXYHkfmrBa7PCIyMK1Wi/e/OIn3Vp00yP7yCiowavoexEwNxfx/RfIp0EREZo6B3gIVpWQhc3NC/c/p63bjsYSlCHpqKJLnb0R1UamI1RGRob25NAkLvjpj8P1++nUKKqrUWPZGX4Z6IiIzxmkrWwBVZTUKky9CkMng0qGt2OUQkQEt/z7VKGH+phUbz2H+WuPtn4iI7h0DfQvh3LEuyFdfuyFyJURkKOezrmHO54k6tUncGIUreychcWNUs9u8u/IETp0v0rU8IiIyEQZ6CyS3t4GtmzNs3V3g2tUPfT5+Hu6hAShMvojSzHyxyyMiA1CrNZj6zgFU16h1aufl4QCfto7w8nBodhuVSosp7xxATa1uxyIiItOw+ECvVCoRExODzp07w87ODr6+vpg1axbKy8vx3HPPQRAErFixQuwyDapnzCQ8mfo1njz7Fcbu/xzBU0cgO+4o4qcsELs0IjKQTXuzcfRMocmOdzq9GOt3ZJjseERE1HwWfVPsqVOnMHLkSCgUCjg6OqJbt27Iy8vDsmXLkJGRgeLiYgBAjx49xC3UwNK/24PsX45AZi1H665+6D59LBy93aGurqnfRmYjx+g9C5G1NQFnlm6pX/7Akumw83TFvuiPxCidiJppZWyayY/5nx/OYerYQN4gS0RkZiy2h16pVGL06NFQKBSYPXs28vPzkZycDIVCgQULFiAuLg6JiYkQBAFhYWFil2tQpZkK5CekIDf+JM6u3IbfJs+HR49O6LfgxfptNDUqHJy5HKEzx6F1tw4AAL8RkfAZHoFDr60Uq3QiaoazF4tx4ITC5MdNTivC8RTTXRUgIqLmsdhAP3PmTOTk5GDGjBlYtGgRnJ2d69fFxMQgPDwcKpUKHTt2hIuLi4iVGl9hUjoyNh2A/9j+8IzoUr+86EwmUldtx4PL/gkHbzf0W/gSjr31JSqvlohYLRHdTVzClRZ5bCIiapxFBvq0tDTExsbCw8MDn3zySaPb9OrVCwAQHh7e5H5GjhwJQRDw3nvvGaNMkzq9eBM0KjV6zpnYcPmSzdCo1YjauxCKQ2eRte2QSBUSUXOdOCfejDMnzilFOzYRETXOIgP9xo0bodFoEB0dDScnp0a3sbe3B9B0oP/xxx9x6tQpY5VocmXZCmRtO4R2A8LQpk9w/XKtSo3CxHTYubfCn7H7RayQiJpLzFB94lwRtFqtaMcnIqLbWWSgj4+PBwAMHjy4yW1ycnIANB7oS0tL8a9//QuLFi0yToEiObO0rjf+1l76Nn2C0XniYKSt/RW9358KKzsbESskoua4rBDveRJXiyqhUjHQExGZE0FrgV0tvr6+yMnJwcmTJxudwUalUsHb2xtKpRIZGRkICAhosP6f//wnUlJS8Pvvv0MQBMydO/eeht1ERERAodDtBjZrrQxzNb31PmZzyB3sEPXbIpxbvQPnv9mNkVvfh/J0BhLnrtN5X/Nkx1EraAxfJBE1oIWAPLf3mlyfuDHqjnPMe3nYQ24lg0qtgUJZ2eR2CmUFIp/c3ug67+KPIENNo+vMXb7ra9DIWkGmuQ7va5+LXY4o+B4QmScvLy8kJSXp1dYip60sLy8HAFRWNv5hFRsbC6VSCWdnZ/j7+zdYl5SUhDVr1uDEiRMGq0ehUCA3N1enNjaCFdDWYCU0KvK9Z3HjcgHOr9sFADg4awWi9i3C5Z3HcPWoblPi5eXnoUbLh84QmURrNSBYNbrq5oOj7kZuJWvWdo3Jz7sCaFV6tRWdsxqQARq1WufzssXge0BkcSwy0Ht5eaGkpATJycno169fg3X5+fmYM2cOACAsLKzBfMpqtRovvvgiZsyYgZCQEIPWoytrrQwwYod3+yE94R/VH9uGzq5fVnbpKk58tAH9F0/H9iGzoaqsbvb+2nm3Yw89kYnkayugEZwbXadQVtyxrS499I0RtFXwbtcWUp2JPt/KChoAMisreLdvL3Y5ouB7QGSe9MmLN1lkoB82bBjS0tKwYMECDB8+HEFBQQCAxMREPPPMM1Aq624o+/twnBUrVuDq1asGn9VGn8sntRVV2NDpaYPWcavc+JP4vuvk25afX7ervsdeFxcuXoC1g50hSiOiuxg1fTd+TchpdF1Tw2RuurJ3EnzaOkKhrITv8B90PvaAyI74/avGjy0FPsM2IregAt5e3sg5K93XcS/4HhBZHou8KTYmJgbu7u64cuUKQkJCEBoaisDAQPTu3RsBAQEYMmQIgIY3xCqVSrzzzjt49913oVKpcO3aNVy7dg0AUFVVhWvXrkGjYQ80EYmvVzePFnlsIiJqnEUGeh8fHyQkJGDUqFGws7NDdnY23NzcsHr1asTFxeHChQsAGgb6nJwclJWV4cUXX0Tr1q3r/wOABQsWoHXr1rh8+bIor4eI6FaDI71b5LGJiKhxFjnkBgCCg4OxY8eO25bfuHED2dnZkMlk6N69e/3yzp07Y//+2+dhHzx4MCZPnowpU6bc09gmIiJDGRTpjS4dWyE9+7pJj+vn7YiRD/iY9JhERHR3Fhvom5KamgqtVougoCA4OPxvajcnJycMGjSo0TYdO3Zsch0RkakJgoBXJgZj1oKjJj3uSxOCYWVlkRd2iYgkrcWdmVNSUgA0/YRYIiIpmDo2EL5e+k07qY+27vZ4cUJXkx2PiIiaj4H+LrRarcFnvRFTh1F90Xf+Cw2WdZ44GFPyN8FvRKRIVRGRrpwdbfDlew+Y7HhfvHM/3FrZmux4RETUfAz0LYzfI31wedfx+p+dfDwRFD0MBUnpIlZFRPp46H4fnXvNFcoK5Fwtv+t89beKHtUJY4d01LE6IiIylRY3hj4+Pl7sEozKxsUBY/YvhpWdDSrylJDZWsPZry0yNv2BI2+sQdvILjg4a0XdxoKA+z97Gcf+vRaRc2+fk56IzN+yN/riUt4N7DrUvPnE7zZP/d8NjPDCmrmmuxJARES6a3E99JauprQCmVsTcO7LOGwfPgfH3/0ahckXcPj1L+DdvzsKEtOhVakBACEvjkZB4nkUnckUuWoi0peNtRW2LB6KRwf4Gnzfw/u1w44VD8HersX1/RARSQoDvQVy6+6P4pQsAIB7WCcUn637s9+ISFzaWTfcxrWLLzqM6oPTSzaLVicRGYa9nRxblwzDhzN6wVp+76d1KysB77zYAztWPAQnB2sDVEhERMbEQG+B3EI61od497AAFP0V7tsN6oHc+JMAgLZ9guHk2wbjDy/H48dXwvO+QPRb+BK6PPuQaHUTkf7kchnentYDJ34Yg75hnnrv575gdxzfEIX3p/eCjbWVASskIiJj4XVUC+Pg5QZotahQFAMA3II74MzSzfDoGYjrF3OhqqgCAKR/uwfp3+6pbzdi8zycW7MDl3clilI3ERlGaJAbDn83GsdTCrEyNg2xu7NQXaO+YxtruQwTHvLHKxODcX+PNhAEwUTVEhGRITDQWxi37v71vfMAUFNajq6TH0Z1cVmD2W2IyHIJgoA+YW3QJ6wNVr/bH2culODEOSXO/lmCGxW10GoBR3s5uge2Rq9gD4R3ceM4eSIiCeMZ3MLk7DuBnH0n6n/eMfINAMCY3xdj9/i5TbbbdYd1RCRddrZy9A71RO9Q/YfhEBGReWOgbyG2DXpV7BKIiIiIyAh4UywRERERkYQx0BMRERERSRgDPRERERGRhDHQExERERFJGG+KNVNye1tEZ6wXu4xmk9vbil0CERERUYvEQG+mBEGAtYOd2GUQERERkZnjkBsiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJk4tdADVOq9VCVVktdhnNJre3hSAIYpdBRERE1OIw0JspVWU1NnR6Wuwymi06Yz2sHezELoOIiIioxeGQGyIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiImoxtFptg/8TEVkCznJDREQWSaPRYu+RXMQfz0NSqhLJaUW4VlYDAMgrrES7oRvRK9gdESEeGDXAFxEhniJXTESkHwZ6IiKyKNdKq7FmczpW/XgeWbllTW6XX1iBHYUV2HHgCt5bdRIRIR54ZWIwokd1go21lQkrJiK6Nwz0FsSrXwhGbJnXYFlteSVKM/ORsekA0tb+Cq1aI1J1RETGF3fgMqa9fwh5BRU6t01KVeIf7yZg6YZUfPPhAIR3cTdChUREhsdAb4EytyQgJz4ZEATYe7qi84SB6D1vCloFtseROavFLo+IyOCqqlV45aPD+Prni/e8r9PpxYh4chs+mN4L//ePMD4Fm4jMHgO9BSpKyULm5oT6n9PX7cZjCUsR9NRQJM/fiOqiUhGrIyIyrIpKFaJm7sVvx/IMtk+VSos3lyYhr7ACS/+vL0M9EZk1znLTAqgqq1GYfBGCTAaXDm3FLoeIyGBqazUY/9pvBg3zt1r+/Tm8sSTRKPsmIjIUBvoWwrljXZCvvnZD5EqIiAxn/lensetQjlGP8enXKYg7cNmoxyAiuhcccmOB5PY2sHVzrh9D3+XZh+AeGoDC5IsozcwXuzwiIoM4c6EYH6w+pVObxI1R8PJwgEJZgcgntze73QvzDiF1a1u0drHVsUoiIuNrET30SqUSMTEx6Ny5M+zs7ODr64tZs2ahvLwczz33HARBwIoVK8Qu02B6xkzCk6lf48mzX2Hs/s8RPHUEsuOOIn7KArFLIyIyCK1Wi2nzDqJWpdvMXV4eDvBp6wgvDwed2uUXVuDtZUk6tSEiMhWL76E/deoURo4cCYVCAUdHR3Tr1g15eXlYtmwZMjIyUFxcDADo0aOHuIUaUPp3e5D9yxHIrOVo3dUP3aePhaO3O9TVNfXbyGzkGL1nIbK2JuDM0i31yx9YMh12nq7YF/2RGKUTETXL8ZRCHEspNOkx122/iI9nRsCVvfREZGYsuodeqVRi9OjRUCgUmD17NvLz85GcnAyFQoEFCxYgLi4OiYmJEAQBYWFhYpdrMKWZCuQnpCA3/iTOrtyG3ybPh0ePTui34MX6bTQ1KhycuRyhM8ehdbcOAAC/EZHwGR6BQ6+tFKt0IqJm+c8PaSY/ZmWVGt9sv/dpMYmIDM2iA/3MmTORk5ODGTNmYNGiRXB2dq5fFxMTg/DwcKhUKnTs2BEuLi4iVmpchUnpyNh0AP5j+8Mzokv98qIzmUhdtR0PLvsnHLzd0G/hSzj21peovFoiYrVERHdWVa3Cj3uyRDn2t7/8KcpxiYjuxGIDfVpaGmJjY+Hh4YFPPvmk0W169eoFAAgPD69f9vvvv0MQhNv+k/qQnNOLN0GjUqPnnIkNly/ZDI1ajai9C6E4dBZZ2w6JVCERUfOkXCxBdY1alGOfuViMqmqVKMcmImqKxY6h37hxIzQaDaKjo+Hk5NToNvb29gAaBvqb/vOf/+C+++6r/9nR0dE4hZpIWbYCWdsOodP4AWjTJxgFx+ouV2tVahQmpsMjrBP+jN0vcpVERHd34pxStGOrVFqcuVCC3qGeotVARPR3FttDHx8fDwAYPHhwk9vk5NTNXdxYoO/WrRv69u1b/19oaKhxCjWhM0vreuNv7aVv0ycYnScORtraX9H7/amwsrMRsUIiortLzbgm8vE5LJGIzIug1Wq1YhdhDL6+vsjJycHJkycbHS6jUqng7e0NpVKJjIwMBAQEAKgbcjN48GDs378fgwYNMkgtERERUCgUOrWx1sowV9PbIMdvitzBDlG/LcK51Ttw/pvdGLn1fShPZyBx7jqd9zVPdhy1gm7TxxER6aPEcSwqbHs2uu7mPPNN8fKwh9xKBpVaA4Wy8o7HaWqu+lblv8Kp+phuRZuRfNfXoJG1gkxzHd7XPhe7HCL6i5eXF5KS9Jse12KH3JSXlwMAKisbP2HHxsZCqVTC2dkZ/v7+t62fOHEilEol3N3dERUVhfnz58PDw0OvWhQKBXJzc3VqYyNYAW31OlyzRb73LG5cLsD5dbsAAAdnrUDUvkW4vPMYrh7VbQaJvPw81GjFGdNKRC1M+3KgiZkjb84zfzdyK1mztmvM9esluF6k2zndrDirARmgUat1/mwiIvNksYHey8sLJSUlSE5ORr9+/Rqsy8/Px5w5cwAAYWFhEAShfl2rVq0wZ84cDBgwAE5OTjhy5Ag++eQTHD16FElJSbCzs9OrFl1Za2WAETu82w/pCf+o/tg2dHb9srJLV3Hiow3ov3g6tg+ZDVVldbP31867HXvoicgkrjnIUd7EOoWy4o5tde2hb4yriwMc7do3p1SzlG9lBQ0AmZUVvNtL93UQWRp98uJNFjvkZubMmVi+fDl8fX2xb98+BAUFAQASExPxzDPPIDMzE7W1tZg+ffpdnxL7yy+/ICoqCl999RWmTp1qivJRW1GFDZ2eNsmxDCE6Yz2sHXT/skNEpKvVP53HSx/oNyPXlb2T4NPWETlXy+E7/Ae99nH8+yhEdpfuTbE+wzYit6AC7ds4IGffk2KXQ0QGYLE3xcbExMDd3R1XrlxBSEgIQkNDERgYiN69eyMgIABDhgwB0PgNsX/36KOPwtHRUe9xTUREZDi9urmLdmy5XEBoYGvRjk9E1BiLDfQ+Pj5ISEjAqFGjYGdnh+zsbLi5uWH16tWIi4vDhQsXADQv0N9069AcIiISR2igG+xsrUQ5dniQO+xsLXa0KhFJlEWflYKDg7Fjx47blt+4cQPZ2dmQyWTo3r37Xfezfft2lJeXo3dv4846Q0REd2drY4WJDwfgm+0XTX7syVGdTX5MIqK7sehA35TU1FRotVoEBQXBwaHh9GZPP/00AgICcN9999XfFPvpp5+iR48emDRpkkgVExHRrV6ZGGzyQO9gJ8ezowNNekwiouZokYE+JSUFQOPDbUJCQvD9999jyZIlqKyshI+PD1544QXMnTsXNjZ86BIRkTnoHeqJ+3u0weFTBSY75j8eC0IrZ34OEJH5sdgx9Hdyp0D/5ptvIiUlBaWlpaitrUVWVhY+//xztGrVytRlGkWHUX3Rd/4LDZZ1njgYU/I3wW9EpEhVERHpbvU7/WFjbZqPMZ+2jvhwRi+THIuISFcM9C2M3yN9cHnX8fqfnXw8ERQ9DAVJ6SJWRUSku+6Bbpj7UuNPjG2KQlmBnKvld52v/u/WzH2AvfNEZLZa5JCb+Ph4sUswGhsXB4zZvxhWdjaoyFNCZmsNZ7+2yNj0B468sQZtI7vg4Ky/5t0XBNz/2cs49u+1iJw7WdzCiYj0EDM1DEdOF2DHgSvN2j7yye06H+PtF8Ix4gEfndsREZlKi+yht2Q1pRXI3JqAc1/GYfvwOTj+7tcoTL6Aw69/Ae/+3VGQmA6tSg0ACHlxNAoSz6PoTKbIVRMR6Ucul+HHRUPw8P3GeeLpq8+E4AMOtSEiM8dAb4HcuvujOCULAOAe1gnFZ+v+7DciEpd21g23ce3iiw6j+uD0ks2i1UlEZAj2dnJsXz4c0x7vYrB9WstlWPhab3z2eh8+g4SIzB4DvQVyC+lYH+LdwwJQ9Fe4bzeoB3LjTwIA2vYJhpNvG4w/vByPH18Jz/sC0W/hS+jy7EOi1U1EpC8bayusfvcB7Fr1MHzaOt7Tvnp180By7Bi8PiWUYZ6IJKFFjqG3ZA5eboBWiwpFMQDALbgDzizdDI+egbh+MReqiioAQPq3e5D+7Z76diM2z8O5NTtweVeiKHUTERnCw/19kLp1HL7aegErf0zDxUulzW57f482ePmJYEwaEQC5nP1dRCQdDPQWxq27f33vPADUlJaj6+SHUV1c1mB2GyIiS+XiZIN/PdMdM6NDsP94PvYn5uHEuSIkpylRUFzXqSEIgJ+3E3oFe6BXN3c88qAvenR1F7lyIiL9CFqtVit2EXS72ooqbOj0tMH2N+b3xdg9fi6qiprfW6WL6Iz1sHawM8q+iYgMRavVQqXSQi4XWuxwGp9hG5FbUIH2bRyQs+9JscshIgNgD30LsW3Qq2KXQEQkOkEQYG3dMoM8EVkuDhIkIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCeNNsWZKbm+L6Iz1YpfRbHJ7W7FLICIiImqRGOjNlCAInAaSiIiIiO6KQ26IiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkTC52AdQ4rVYLVWW12GU0m9zeFoIgiF0GERERUYvDQG+mVJXV2NDpabHLaLbojPWwdrATuwwiIiKiFodDboiIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMs9wQERFZsMLiSpw4V4QT55T480opiq/XTYl8rawGazadR69uHuge2Bo21lYiV0pE+mKgJyIisjA1tWr8HH8JK2PT8EeSotFtyitVmPb+IQCAi5M1JkcF4uUnghEc4GrCSonIEAStVqsVuwi6XW1FFeehJyIinW3em4WZC44ir6BCr/ZjBvth5dv3o10bRwNXRkTGwh56C+LVLwQjtsxrsKy2vBKlmfnI2HQAaWt/hVatEak6IiIyJmVJFaZ/fBg/7s66p/1s238ZfyQpsPT/+uKZ0Z35FHAiCWCgt0CZWxKQE58MCALsPV3RecJA9J43Ba0C2+PInNVil0dERAaWlVOGYdN2IjOnzCD7u1ZWg8n/PoBT6UX47PU+DPVEZo6B3gIVpWQhc3NC/c/p63bjsYSlCHpqKJLnb0R1UamI1RERkSFdzr+Bgf+IwxVFucH3vfi7VGg0wOIYhnoic8ZpK1sAVWU1CpMvQpDJ4NKhrdjlEBGRgVTXqPHojD1GCfM3Ld2QilWxaUbbPxHdOwb6FsK5Y12Qr752Q+RKiIjIUN7/4iRSLpbo1CZxYxSu7J2ExI1RzW4z5/NEZObw6i6RubL4QK9UKhETE4POnTvDzs4Ovr6+mDVrFsrLy/Hcc89BEASsWLFC7DINSm5vA1s3Z9i6u8C1qx/6fPw83EMDUJh8EaWZ+WKXR0REBnDinBILvj6jczsvDwf4tHWEl4dDs9tUVKnw3NyD4MR4RObJosfQnzp1CiNHjoRCoYCjoyO6deuGvLw8LFu2DBkZGSguLgYA9OjRQ9xCDaxnzCT0jJnUYFl23FEce/NLkSoiIiJD+2jNKajVpgvYvyfmI+GEAgMivE12TCJqHovtoVcqlRg9ejQUCgVmz56N/Px8JCcnQ6FQYMGCBYiLi0NiYiIEQUBYWJjY5RpU+nd7sPuJedgb/RGSPvgOVcVlcPR2h7q6pn4bmY0cY35fjLBZ4xq0fWDJdAzb8LapSyYiIh3kKMqxbf9lkx935Y8cS09kjiw20M+cORM5OTmYMWMGFi1aBGdn5/p1MTExCA8Ph0qlQseOHeHi4iJipYZXmqlAfkIKcuNP4uzKbfht8nx49OiEfgterN9GU6PCwZnLETpzHFp36wAA8BsRCZ/hETj02kqxSiciomZYuzUdGo3ph79s3peNgqJKkx+XiO7MIgN9WloaYmNj4eHhgU8++aTRbXr16gUACA8Pv23d1q1bcf/998PR0RGtWrVC//79kZqaatSajakwKR0Zmw7Af2x/eEZ0qV9edCYTqau248Fl/4SDtxv6LXwJx976EpVXdbvBioiITGt/ojj3Q6lUWhw6dVWUYxNR0ywy0G/cuBEajQbR0dFwcnJqdBt7e3sAtwf6ZcuW4YknnsADDzyA7du3Y+PGjRg2bBgqK6XdI3F68SZoVGr0nDOx4fIlm6FRqxG1dyEUh84ia9shkSokIqLm0Gi0SE4rEu34J84pRTs2ETXOIm+KjY+PBwAMHjy4yW1ycnIANAz0GRkZmDNnDhYvXowZM2bUL3/kkUeMVKnplGUrkLXtEDqNH4A2fYJRcKxuHKRWpUZhYjo8wjrhz9j9IldJRER3k3GlFGXltaIdX8wvE0TUOIsM9JcuXQIAdOjQodH1KpUKhw7V9UTfGui/+uorWFtb44UXXjBoPREREVAoFDq1sdbKMBe9DVrHmaWb4T+2P3rOmYjdj78HAGjTJxidJw5G2tpf0fv9qdg+fA7UVTV33lEjggKDUCtoDFovERHdrlruC7g83+i6xI1Rd52O0svDvv7/V/ZOanI7hbICkU9uv235vt+PwsfnOR0qJqLm8PLyQlJSkl5tLTLQl5fXPTGvqWEysbGxUCqVcHZ2hr+/f/3yw4cPo0uXLli/fj0+/PBDXLlyBYGBgXj33Xfx5JNP6l2PQqFAbm6uTm1sBCtAx4e6Ko6kYp33402uv34xF9/6/G/IjdzBDg8smY4TH23A+W92Y+TW93Hfm08hce463Q4MIC8/DzVatc7tiIhIR46OQBNzOdycY7455FayZm97q9pajc6faURkXBYZ6L28vFBSUoLk5GT069evwbr8/HzMmTMHABAWFgZBEBqsy83NxZtvvokFCxbA19cXa9euxVNPPQVPT08MGzZM73p0Za2VAUbu8I5871ncuFyA8+t2AQAOzlqBqH2LcHnnMVw9qtvUZO2827GHnojIBGqsWqOwiXUKZcVd23t52ENuJYNKrYFC2fT9YU3ty9paQJv27ZtTKhHpQJ+8eJOgtcDHvs2cORPLly+Hr68v9u3bh6CgIABAYmIinnnmGWRmZqK2thbTp09v8JTYoKAgXLx4EVu3bsXYsWMBAFqtFj169ICrqyv++OMPk72G2ooqbOj0tNH2335ITwxc+S9sGzob5bn/u8Gp65QR6Pbio9g+ZDZUldXN3l90xnpYO9gZo1QiIrpFXkE52g/7Qe/2V/ZOgk9bR+RcLYfvcN33M+Ehf/y4aIjexyciw7PIWW5iYmLg7u6OK1euICQkBKGhoQgMDETv3r0REBCAIUPqTkR/n+HGzc0NABr0xAuCgGHDhuHs2bOmewEmkBt/Et93ndwgzAPA+XW7sKXfDJ3CPBERmU67No7w9rzzOHlj6tXNXbRjE1HjLDLQ+/j4ICEhAaNGjYKdnR2ys7Ph5uaG1atXIy4uDhcuXABwe6APCQlpcp9VVVVGrZmIiKi5egWLF6p7dfMQ7dhE1DiLDPQAEBwcjB07dqCsrAxlZWU4duwYpk2bhvLycmRnZ0Mmk6F79+4N2owZMwYAsGfPnvplGo0Ge/fuRWRkpEnrJyIiasroQX6iHLe1iw3uD9dxxgYiMjqLvCn2TlJTU6HVahEUFAQHh4aXLEePHo0HH3wQ06ZNQ1FREfz8/PDll18iNTUVe/fuFaliIiKihp56pBNe/+y4yeejnzo2CA72LS46EJk9i+2hb0pKSgqA24fbAHXj5bdv347x48fjrbfeQlRUFC5duoRff/21ftw9ERGR2JwcrDE5KtDkx31pQleTH5OI7o6B/m9cXV2xevVqFBYWorq6GsePH8fDDz9syhKJiIju6u0XwuHWytZkx3tlYjACO7Qy2fGIqPkY6FuYDqP6ou/8hk/C7TxxMKbkb4LfCN4nQEQkFV4eDlj+Rr+7b2gAHds5YcGr/IwgMlctbiBcfHy82CWIyu+RPsj46ff6n518PBEUPQwFSeniFUVERHp58pEA/PLHZfywK7PZbW4+MKo5D6ECAGu5DOs+HAAnB2u9aiQi42txgd7S2bg4YMz+xbCys0FFnhIyW2s4+7VFxqY/cOSNNWgb2QUHZ/31MC1BwP2fvYxj/16LyLmTxS2ciIh0JggC1n04AMWl1dhzOLdZbSKf3N7s/VtZCdgwfxAGRnjrWyIRmUCLG3Jj6WpKK5C5NQHnvozD9uFzcPzdr1GYfAGHX/8C3v27oyAxHVqVGgAQ8uJoFCSeR9GZ5vfsEBGRebG1scK2pcPw2NAOBt2vna0VNn8+FBMe8jfofonI8BjoLZBbd38Up2QBANzDOqH4bN2f/UZE4tLO4wAA1y6+6DCqD04v2SxanUREZBh2tnJs/nwoVr/b3yBDY/r3bIszmx7DmMGG/ZJARMbBQG+B3EI61od497AAFP0V7tsN6oHc+JMAgLZ9guHk2wbjDy/H48dXwvO+QPRb+BK6PPuQaHUTEZH+BEHAtMe74uyWxzBpRADkckHnffh6OWLZG33xx1ePcEYbIgnhGHoL4+DlBmi1qFAUAwDcgjvgzNLN8OgZiOsXc6GqqAIApH+7B+nf/u+JuCM2z8O5NTtweVeiKHUTEZFhdGjnjI2fDsbnhX3w5ZZ0/LQnC+cyr0Gt1ja6vauzDfr3bIsXxnfBqAd9IZezr49IahjoLYxbd//63nkAqCktR9fJD6O6uAyXdx0XsTIiIjIlb08HvPNiT7zzYk9UVKpw+kIR/rxcispqNeRWMrg626BHVzf4t3eGIOjem09E5kPQarWNf2UnUdVWVGFDp6cNtr8xvy/G7vFzUVVUarB93io6Yz2sHeyMsm8iIiIiahp76FuIbYNeFbsEIiIiIjICDpQjIiIiIpIwBnoiIiIiIgljoCciIiIikjDeFGumtFotVJXVYpfRbHJ7W86SQERERCQCBnoiIiIiIgnjkBsiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwBnoiIiIiIgn7f2Ec/HOg66AzAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 956.385x618.722 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_0.decompose(\"cut_wire\").draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcd8dea0",
   "metadata": {},
   "source": [
    "### Specify an observable\n",
    "\n",
    "This observable has 7 qubits, just like the original circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "847a3205",
   "metadata": {},
   "outputs": [],
   "source": [
    "observable = SparsePauliOp([\"ZIIIIII\", \"IIIZIII\", \"IIIIIIZ\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59730746",
   "metadata": {},
   "source": [
    "### Transform cuts to moves\n",
    "\n",
    "The next step is to call `cut_wires`, which transforms each `CutWire` into a `TwoQubitQPDGate` which wraps a `Move` instruction.  An additional qubit is added to the circuit for each `CutWire` in the input circuit.\n",
    "\n",
    "Notice that, unlike in the [wire cutting tutorial](../tutorials/03_wire_cutting_via_move_instruction.ipynb), where `Move` operations were placed manually, this function does not result in the _re_-use of a qubit.  Because any method for qubit re-use is based on heuristics, this function naively allocates an additional qubit for each cut.  Users wishing to re-use qubits might wish to experiment with [qiskit-qubit-reuse](https://github.com/qiskit-community/qiskit-qubit-reuse)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e4ee1559",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1290.83x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_1 = cut_wires(qc_0)\n",
    "qc_1.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c22b9572",
   "metadata": {},
   "source": [
    "### Update the observable terms to account for the extra qubit\n",
    "\n",
    "The transformed circuit contains additional qubits (one for each `CutWire` instruction), so the observables must be updated for the new circuit.  This can be done using the `expand_observables` function. Since the observable coefficients are ignored until reconstruction of the final expectation value, the input and output types of the observables for ``expand_observables`` are ``PauliList``s.\n",
    "\n",
    "The resulting observables have 9 qubits, just like the transformed circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "95fbeda0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PauliList(['ZIIIIIIII', 'IIIZIIIII', 'IIIIIIIIZ'])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observable_expanded_paulis = expand_observables(observable.paulis, qc_0, qc_1)\n",
    "observable_expanded_paulis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f64acd6",
   "metadata": {},
   "source": [
    "### Separate the circuit and observables\n",
    "\n",
    "In this case, `partition_labels` need not be passed to `partition_problem`, as the labels can be determined automatically from the connectivity of the circuit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "99bef123",
   "metadata": {},
   "outputs": [],
   "source": [
    "partitioned_problem = partition_problem(\n",
    "    circuit=qc_1, observables=observable_expanded_paulis\n",
    ")\n",
    "subcircuits = partitioned_problem.subcircuits\n",
    "subobservables = partitioned_problem.subobservables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce2bf0cd",
   "metadata": {},
   "source": [
    "From here forward, the cutting workflow is the same as usual, but the remaining steps are spelled out here explicitly so one can follow along with the results."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bae9ac63",
   "metadata": {},
   "source": [
    "### Visualize the decomposed problem\n",
    "\n",
    "Notice that once the circuits have been cut, some of the instructions are able to commute past each other.  For instance, in subcircuit \"A\", half of the second `Move` operation is actually the _first_ operation on the final qubit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "abeee650",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: PauliList(['IIIII', 'ZIIII', 'IIIIZ']),\n",
       " 1: PauliList(['ZIII', 'IIII', 'IIII'])}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subobservables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aaef5b3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 974.616x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subcircuits[0].draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "975a3ca9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 723.984x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subcircuits[1].draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e02632b",
   "metadata": {},
   "source": [
    "### Generate and run the cutting experiments; reconstruct and compare against uncut expectation values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "459dcee8",
   "metadata": {},
   "outputs": [],
   "source": [
    "subexperiments, coefficients = generate_cutting_experiments(\n",
    "    circuits=subcircuits,\n",
    "    observables=subobservables,\n",
    "    num_samples=np.inf,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "dc9fe287",
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = SamplerV2()\n",
    "results = {\n",
    "    label: sampler.run(subexperiment, shots=2**12).result()\n",
    "    for label, subexperiment in subexperiments.items()\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e317a998",
   "metadata": {},
   "outputs": [],
   "source": [
    "reconstructed_expval_terms = reconstruct_expectation_values(\n",
    "    results,\n",
    "    coefficients,\n",
    "    subobservables,\n",
    ")\n",
    "reconstructed_expval = np.dot(reconstructed_expval_terms, observable.coeffs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5ae568ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstructed expectation value: 1.56514591\n",
      "Exact expectation value: 1.59099026\n",
      "Error in estimation: -0.02584435\n",
      "Relative error in estimation: -0.01624419\n"
     ]
    }
   ],
   "source": [
    "estimator = EstimatorV2()\n",
    "exact_expval = (\n",
    "    estimator.run([(qc_0.decompose(\"cut_wire\"), observable)]).result()[0].data.evs\n",
    ")\n",
    "print(f\"Reconstructed expectation value: {np.real(np.round(reconstructed_expval, 8))}\")\n",
    "print(f\"Exact expectation value: {np.round(exact_expval, 8)}\")\n",
    "print(f\"Error in estimation: {np.real(np.round(reconstructed_expval-exact_expval, 8))}\")\n",
    "print(\n",
    "    f\"Relative error in estimation: {np.real(np.round((reconstructed_expval-exact_expval) / exact_expval, 8))}\"\n",
    ")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  }
 },
 "nbformat": 4,
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}