qiskit-documentation/docs/guides/qiskit-addons-cutting-wires.ipynb

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   "source": [
    "# Get started with circuit cutting using wire cuts"
   ]
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   "source": [
    "This guide demonstrates a working example of wire cuts with the `qiskit-addon-cutting` package. It covers reconstructing expectation values of a seven-qubit circuit using wire cutting.\n",
    "\n",
    "A wire cut is represented in this package as a two-qubit [`Move`](/api/qiskit-addon-cutting/instructions-move) instruction, which is defined as a reset of the second qubit the instruction acts on, followed by a swap of both qubits. This operation is equivalent to transferring the state of the first qubit to the second qubit, while simultaneously discarding the incoming state of the second qubit.\n",
    "\n",
    "The package is designed to be consistent with the way you must treat wire cuts when acting on physical qubits. For example, a wire cut might take the state of physical qubit $n$ and continue it as a physical qubit $m$ after the cut. You can think of \"instruction cutting\" as a unified framework for considering both wire and gate cuts within the same formalism (since a wire cut is just a cut [`Move`](/api/qiskit-addon-cutting/instructions-move) instruction). Using this framework for wire cutting also allows for qubit re-use, which is explained in the section on [cutting wires manually](#cut-wires-using-the-low-level-move-instruction).\n",
    "\n",
    "The single-qubit [`CutWire`](/api/qiskit-addon-cutting/instructions-cut-wire) instruction acts as a more abstracted, simpler interface for working with wire cuts. It allows you to denote where in the circuit a wire should be cut at a high level and have the circuit cutting addon insert the appropriate [`Move`](/api/qiskit-addon-cutting/instructions-move) instructions for you.\n",
    "\n",
    "The following example demonstrates expectation value reconstruction after wire cutting. You will create a circuit with several non-local gates and define observables to estimate."
   ]
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joCciIiIikjC52AVQ47RaLVSV1WKX0Wxye1sIgiB2GUREREStDgO9mVJVVmNjlyfFLqPZojM2wNrBTuwyiIiIiFodDrkhIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCWOgJyIiIiKSMAZ6IiIiIiIJY6AnIiIiIpIwzkNvQbwGhGDU1vkNltWWV6I0Mx8Zmw8ibd0v0Ko1otVHRERERIbHQG+BMrcmICc+GRAE2Hu6ouukweg7fxraBHbE0blrxC6PiIiIiAyIgd4CFaVkIXNLQv3P6ev34JGEZQh6YjiSF2xCdVGpqPURERERkeFwDH0roKqsRmHyJQgyGVw6tRe7HCIiIiIyIAb6VsK5c12Qr75+U+xSiIiIiMiAWkWgVyqViImJQdeuXWFnZwdfX1/Mnj0b5eXleOaZZyAIAlauXCl2mQYjt7eBrZszbN1d4NrdD/0+ehbuoQEoTL6E0sx8scsjIiIiIgOy+DH0p0+fxujRo6FQKODo6IgePXogLy8Py5cvR0ZGBoqLiwEAvXr1ErtUg+kdMwW9Y6Y0WJYddwzH3/hCtJpIPFqtFsfOFmB17AWc+6MEVTVquLexxYQRnTFtXCDautiKXSIRERnZ5bwy/HdzOvYfy0NZRS0c7eW4r3d7vPRYMII6txG7PGohiw70SqUSY8eOhUKhwJw5czBv3jw4OzsDAD755BP83//9H+RyOQRBQFhYmNjlGkz6t3uR/fNRyKzlaNvdDz1njIejtzvU1TX128hs5Bi7dxGytiXg7LKt9cvvWzoDdp6u2B/9oUjVkyFdzL6Bx//vAJLTim5bd+jUNby1Iglzp4Zh3ku9IZMJotRIRETGU15RixfeP4xNuzKh0WgbrEtKVWLphlSMHeyHrz8cxA4eCbPoITezZs1CTk4OZs6cicWLF9eHeQCIiYlBeHg4VCoVOnfuDBcXF1FrNaTSTAXyE1KQG38K51Ztx69TF8CjVxcMWPhC/TaaGhUOzVqB0FkT0LZHJwCA36hI+IyMwOFXV4lYPRnK+YwSDHjq50bD/C2VVWq8t+YUnp9/CFqttsntiIhIeioqVXjgxd3YGJdxW5j/q59/v4L7p+5ESWm1Sesjw7HYQJ+WlobY2Fh4eHjg448/bnSbPn36AADCw8Prl936AtC3b1/Y2tpCEKTfa1mYlI6MzQfhP34gPCO61S8vOpuJ1NU7cP/yf8LB2w0DFr2I429+gcprJaLWSy1XU6vGmBl7UXyjeSfnddsuYnVsmtHrIiIi05m14CiOnC5o1rapGdfx9Ju/G70mMg6LDfSbNm2CRqNBdHQ0nJycGt3G3t4e+Fug/+OPP7BlyxZ4eXkhMjLSZPUa25klm6FRqdF77uSGy5dugUatRtS+RVAcPoes7YdFq5EMZ+v+bGTn6Taj0WffnrtjDw4REUnHtaJKfPPzHzq12XnwKi5kXTdaTWQ8Fhvo4+PjAQBDhw5tcpucnBzgb4F+0KBByM/Px44dOzBixAgTVGoaZdkKZG0/jA6DwtCuX3D9cq1KjcLEdNi5t8EfsQdErZEM5z/f697bnnG1DHuP5BqlHiIiMq11W9NRq9Lo3I5Xa6XJYm+KvXz5MgCgU6dOja5XqVQ4fLiuN/qvgV4mM/x3nIiICCgUCp3aWGtlmIe+Bq3j7LIt8B8/EL3nTsaeR98FALTrF4yuk4cibd0v6PvedOwYORfqqpq77uvvggKDUCvofuIwtXzXVwFZG+Qr8uHj4yN2OUahhYC8tu8Agu6/y5Omv4U2lb8apS4iInPQGj4HAEDp9CRgE6hzu9Xf7MeWlZOMUhPdmZeXF5KSkvRqa7GBvry8HABQWVnZ6PrY2FgolUo4OzvD39/fqLUoFArk5urW82kjWAE6PtRVcTQV670fbXL9jUu5+Mbnf0Nu5A52uG/pDJz8cCMufL0Ho7e9h3veeAKJ89brdmAAefl5qNGqdW5ncs5qQAZo1Gqd/04kQ2YLuOn3xfRmeQ1u5lvo+0JEhFbyOQAAAVrARvdmtWqZZb8vFspiA72XlxdKSkqQnJyMAQMGNFiXn5+PuXPnAgDCwsKMfuOrl5eXzm2stTLAyB3eke8+jZtXCnBh/W4AwKHZKxG1fzGu7DqOa8d0u+TWwbuDNHroraygASCzsoJ3x45il2MUWgjI02r06qF3drSGi4W+L0REaCWfAwCgtAb0mbPG2kqNdhb8vpgzffLiLRYb6EeMGIG0tDQsXLgQI0eORFBQEAAgMTERTz31FJRKJWCiB0rpc/mktqIKG7s8aZR6AKDjsN7wjxqI7cPn1C8ru3wNJz/ciIFLZmDHsDlQVTb/VHDx0kVYO9gZqVrD8RmxCbkFFfD28kbOuRyxyzGaEc/twq/H83Rut33jAgzt28EoNRERmYPW8jnw6dcpeO3TEzq3e+W5UVj4yjtGqYmMx2Jvio2JiYG7uzuuXr2KkJAQhIaGIjAwEH379kVAQACGDRsG/G38fGuSG38K33WfivJcZYPlF9bvxtYBM3UK82R+Xp4c3IytGuru3wZDIr2NUg8REZnWtHGBsLO10qmNIAAvTOputJrIeCw20Pv4+CAhIQFjxoyBnZ0dsrOz4ebmhjVr1iAuLg4XL14EWnGgJ8sWNcQP3f11e5T3//3D+MPPiIjINNxd7fDcxG7N2PJ/Jj3gjwAfy3nQZmtisUNuACA4OBg7d+68bfnNmzeRnZ0NmUyGnj17ilIbkTHJ5TLE/ecB3D8tDnkFFXfdfs7TPTFtXJBJaiMiItNYPKcv0rNvNGtK4r49PbFu/v0mqYsMz2J76O8kNTUVWq0WgYGBcHBwuG395s2bsXnzZpw/f77Bz/pOJUQkhgAfFxzbMBbD+zU9Jt6tjS0+m9sPi+YYdopUIiISn421FX5eMRIzH+8BW5vGh9/IrQQ8PbYr4r8YDScHa5PXSIZh0T30TUlJSQHuMNxm0qRJjf48depUrF+v+5SORGLx9XLC/rWjcT6jBGt+vIA1P15Ada0GdjZWWP32vZj8YADs7VrlaYCIqFWwsbbCijcG4N2XeuOrny5h/7FcHDiRjxqVBs6O1riwfSI6tHMUu0xqoVbZQ3+3QK/Vahv9j2GepKpHl7ZY9voAeLStm4nI3dUW08YFMcwTEbUS7q52eG1aKHZ/PgqebnWfBS6O1gzzFoKBvpXpNKY/+i94rsGyrpOHYlr+ZviNihStLiIiIiLST6vsnouPjxe7BNH4PdQPGT/+Vv+zk48ngqJHoCApXdS6iIiIiEg/rTLQWzIbFweMO7AEVnY2qMhTQmZrDWe/9sjY/DuOvr4W7SO74dDslXUbCwLu/fQlHP/3OkTOmyp26URERESkBwZ6C1NTWoHMbQmoLa/C2SWb0WFIOMJmTcCR1z5Hh8HhKEhMh1alBgCEvDAWBYkXUHQ2U+yyiYiIiEhPrXIMvaVz6+mP4pQsAIB7WBcUn6v7s9+oSFzeVfcYaNduvug0ph/OLN0iaq1ERERE1DLsobdAbiGd60O8e1gAru5JBAB0GNILSe9vAAC07xcMJ992mHhkBQDA3tMVAxa9CPt2bZH+zV4RqyciIiIiXTDQWxgHLzdAq0WFohgA4BbcCWeXbYFH70DcuJQLVUUVACD9m70NgvuoLfNxfu1OXNmdKFrtRERERKQ7BnoL49bTv753HgBqSsvRfeqDqC4uw5XdJ0StjYiIiIgMj4HewuTsP4mc/Sfrf945+nUAwLjflmDPxHlNttt9h3VEREREZL4Y6FuJ7UNeEbsEIiIiIjICznJDRERERCRhDPRERERERBLGQE9EREREJGEcQ2+m5Pa2iM7YIHYZzSa3txW7BCIiIqJWiYHeTAmCAGsHO7HLICIiIiIzxyE3REREREQSxkBPRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYXKxC6DGabVaqCqrxS6j2eT2thAEQewyiIiIiFodBnozpaqsxsYuT4pdRrNFZ2yAtYOd2GUQERERtTocckNEREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhDPRERERERBLGQE9EREREJGGch96CeA0Iwait8xssqy2vRGlmPjI2H0Taul+gVWtEq4+IiIiIDI+B3gJlbk1ATnwyIAiw93RF10mD0Xf+NLQJ7Iijc9eIXR4RERERGRADvQUqSslC5paE+p/T1+/BIwnLEPTEcCQv2ITqolJR6yMiIiIiw+EY+lZAVVmNwuRLEGQyuHRqL3Y5RERERGRADPSthHPnuiBfff2m2KUQERERkQFxyI0FktvbwNbNuX4MfbenH4B7aAAKky+hNDNf7PKIiIiIyIBaRaBXKpX45JNPsHXrVuTk5MDT0xMTJkzARx99hFmzZuHLL7/EihUrMHPmTLFLNYjeMVPQO2ZKg2XZccdw/I0vRKuJSGxX8m9iz+EcXC+rgYO9HBE9PNA31BOCIIhdGhERmUB5RS1+/v0K8gorIBMEBPg4Y/R9vrC2lv6AFYsP9KdPn8bo0aOhUCjg6OiIHj16IC8vD8uXL0dGRgaKi4sBAL169RK7VINJ/3Yvsn8+Cpm1HG27+6HnjPFw9HaHurqmfhuZjRxj9y5C1rYEnF22tX75fUtnwM7TFfujPxSpeiLDOnamAAu+PIOff78KjUbbYF3v7u6YHR2Cp6O6MtgTEVmovIJyLPjyLL7ecQmlN2sbrPPysMdzE7th7rRQODvaiFZjS0n/K8kdKJVKjB07FgqFAnPmzEF+fj6Sk5OhUCiwcOFCxMXFITExEYIgICwsTOxyDaY0U4H8hBTkxp/CuVXb8evUBfDo1QUDFr5Qv42mRoVDs1YgdNYEtO3RCQDgNyoSPiMjcPjVVSJWT2Q438Vl4P5pO7H9wJXbwjwAnLpQhGlvH8Tz8w81up6IiKQtLfM6+kX/jBXfnb8tzAOAQlmJ99ecxqDpcSgoqhSlRkOw6EA/a9Ys5OTkYObMmVi8eDGcnZ3r18XExCA8PBwqlQqdO3eGi4uLqLUaU2FSOjI2H4T/+IHwjOhWv7zobCZSV+/A/cv/CQdvNwxY9CKOv/kFKq+ViFovkSHsO5qLp//9O1Tquwf1L7ZexBvLEk1SFxERmca1okqMemk3cq6V33Xb0xeK8fA/96KqWmWS2gzNYgN9WloaYmNj4eHhgY8//rjRbfr06QMACA8Pr1+2efNmTJw4EZ06dYKDgwO6d++Ot956CzdvSnt2mDNLNkOjUqP33MkNly/dAo1ajah9i6A4fA5Z2w+LViORoWi1WsQsOQF1M8L8LZ9+cw45iruf9ImISBqWbUjFlfzmn9cTzykRuzvLqDUZi8UG+k2bNkGj0SA6OhpOTk6NbmNvbw/8LdAvXrwYVlZW+Oijj7Br1y689NJLWL16NUaNGgWNRmOy+g2tLFuBrO2H0WFQGNr1C65frlWpUZiYDjv3Nvgj9oCoNRIZyrGzBTh9oVinNmq1Fmu3pButJiIiMp3qGjW+2Kr7OX1VbJpR6jE2iw308fHxAIChQ4c2uU1OTg7wt0D/888/44cffkB0dDQGDx6M2bNnY+XKlTh8+DAOHTpkgsqN5+yyut74v/bSt+sXjK6ThyJt3S/o+950WNlJ94YQols27crUr93uDIPXQkREphd/PA+FJVU6tztxrhCZOaVGqcmYLHaWm8uXLwMAOnXq1Oh6lUqFw4frhpf8NdB7enretm1ERAQAIDc3V69aIiIioFAodGpjrZVhHvrq1EZxNBXrvR9tcv2NS7n4xud/YV7uYIf7ls7AyQ834sLXezB623u4540nkDhvvU7HBYCgwCDUCuZ/BSPf9VVA1gb5inz4+PiIXY7JtZbXX+z4KGAbqnO7P7IKLPp9IaLWcx68k9bwHpTbhANOE/Rq2+++B2CryjF4TXfj5eWFpKQkvdpabKAvL68bM1VZ2fgdy7GxsVAqlXB2doa/v/8d93XgQN1QlODg4Dtu1xSFQqHzlwEbwQpor9fhmi3y3adx80oBLqzfDQA4NHslovYvxpVdx3HtmG6XnPLy81CjVRupUgNyVgMyQKNW6/0FTdJay+v3KQdsdW+m1dRa9vtCRK3nPHgnreE9cPUBGh9xfVfKAgVQKa33xWIDvZeXF0pKSpCcnIwBAwY0WJefn4+5c+cCAMLCwu44/3Rubi7efvttjBo1Su+56r28vHRuY62VAUbs8O44rDf8owZi+/A59cvKLl/DyQ83YuCSGdgxbA5UldXN3l8H7w7S6KG3soIGgMzKCt4dO4pdjsm1ltdfaluJMj3a2WhL4GnB7wsRtZ7z4J20hvegxkqLQgDQagFdnjOiVcPL3QZWWtO/L/rkxVsErVZrkZMvz5o1CytWrICvry/279+PoKAgAEBiYiKeeuopZGZmora2FjNmzMDKlSsb3cfNmzcxZMgQKBQKJCYmwtvb22T111ZUYWOXJ012vJaKztgAawc7scu4K58Rm5BbUIGO7RyQs/9xscsxudby+q8qbqLzqB90nlv+y/fux/TxQUari4jE11rOg3fSGt4DrVaL3o/9hDPpuk2Q8NiD/ohdNMxodRmLxd4UGxMTA3d3d1y9ehUhISEIDQ1FYGAg+vbti4CAAAwbVveX9dfx839VWVmJsWPHIisrC3v37jVpmCeilvH1ckLUED+d2rR1scHkBwOMVhMREZmOIAh4ebLuQ6X1aWMOLDbQ+/j4ICEhAWPGjIGdnR2ys7Ph5uaGNWvWIC4uDhcvXgSaCPS1tbV49NFHkZSUhF27dqFHjx4ivAIiaokVrw9Ax3YOzdpWJhPwzYeD4WBvsaMQiYhanX+MD8KYQb7N3n52dAgGR0izA9eiP72Cg4Oxc+fO25bfvHkT2dnZkMlk6NmzZ4N1t+au//XXX/HLL7+gb1/dZpohIvPg4+WI374cg9Ev78EfV5qegszO1grfLRiChwfr1qNPRETmTS6X4cfFwxD9xm/Y9uvlO2776tM9sehV6WY+iw70TUlNTYVWq0VQUBAcHBr24M2YMQM//vgjXn/9dTg4OODYsWP167p06dLotJZEZJ66+rngzI+P4PvdmfjP9+eRnFZUv04mE/D2873w3MRu6NjeUdQ6iYjIOOzt5Nj86XDEn8jDqtg0bD9wpcH9VdPHB+Klx4IR2VPa+a5VBvqUlBSgieE2u3btAgAsWLAACxYsaLDuq6++wrRp00xUJREZgoO9HP94JAjTxweioLgKYRO3oqC4Cl7udnj35XvELo+IiIxMJhMwon9HjOjfETfKatBt7I+4VlwFb097fPneILHLMwiLHUN/J3cK9NnZ2dBqtY3+ZwlhvtOY/ui/4LkGy7pOHopp+ZvhNypStLqIjE0QBLR3t4e1XFb/MxERtS5tnG0g//NzQGZBnwMM9K2M30P9cGX3ifqfnXw8ERQ9AgVJ6aLWRURERET6aZVDbuLj48UuwWhsXBww7sASWNnZoCJPCZmtNZz92iNj8+84+vpatI/shkOz/5x3XxBw76cv4fi/1yFy3lSxSyciIiIiPbTKQG/JakorkLktAbXlVTi7ZDM6DAlH2KwJOPLa5+gwOBwFienQqtQAgJAXxqIg8QKKzmaKXTYRERER6alVDrmxdG49/VGckgUAcA/rguJzdX/2GxWJy7vqhtu4dvNFpzH9cGbpFlFrJSIiIqKWYQ+9BXIL6Vwf4t3DAnB1TyIAoMOQXkh6fwMAoH2/YDj5tsPEIysAAPaerhiw6EXYt2uL9G/2ilg9EREREemCgd7COHi5AVotKhTFAAC34E44u2wLPHoH4salXKgqqgAA6d/sbRDcR22Zj/Nrd+LK7kTRaiciIiIi3THQWxi3nv71vfMAUFNaju5TH0R1cVmD2W2IiIiIyDIw0FuYnP0nkbP/ZP3PO0e/DgAY99sS7Jk4r8l2u++wjoiIiIjMFwN9K7F9yCtil0BERERERsBZboiIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCeFOsmZLb2yI6Y4PYZTSb3N5W7BKIiIiIWiUGejMlCAKsHezELoOIiIiIzByH3BARERERSRgDPRERERGRhDHQExERERFJGAM9EREREZGEMdATEREREUkYAz0RERERkYQx0BMRERERSRgDPRERERGRhDHQExERERFJGAM9EREREZGEMdATEREREUkYAz0RERERkYQx0BMRERERSRgDPRERERGRhDHQExERERFJGAM9EREREZGEMdATEREREUmYXOwCqHFarRaqymqxy2g2ub0tBEEQuwwiIiKiVoeB3kypKquxscuTYpfRbNEZG2DtYCd2GUREREStDofcEBERERFJGAM9EREREZGEMdATEREREUkYAz0RERERkYQx0BMRERERSRhnuSGLpdVqkZxWhKRUJU6eV+JC1nUUFFcBAJQlVXh10TH06eGB/mHt0MXXRexyjSKvoBxHThfgZJoSpy8U17/+wpIqPP3m74gI8UCfHh7oF+oJudzyvt9XVatw7GwhTp5XIilViSuKmygorgQAKK9X4Z3/nESfHh64N7wdPN3sxS6XiIwgO7cMR88U4OR5Jc5cbHgefGZeAiJ6eNSfC2Uyy5t++WZFbf3rT0pVIq+wov48WHS9Gu+vOVV/HnR1sRW7XIPTarU4k16MxHOFOJlWhLTM6w1+B2YvOIqIkLosENipjdjl6k3QarVasYug29VWVHHaSj1dL63G1zsuYVXsBVy8fKNZbQZHeOHlycF4ZFhnWFtLO9hqNFrsO5qLVbFp2HnwKjSau/8T79jOAc8/2h3PTewGb08Hk9RpTFk5Zfj8xzSs23YRRdfv/jwHa7kME0d0xowpwRjYuz2fqUAkcSqVBj//fgWrYtOw/1hes9p08XXGi5OCMX18INxdzePzrCXOZ5Rg9Q8X8PWOSygrr73r9vZ2VnhidBe8PDkY9/TwMEmNxlR6swbf7vwDq2LTcD7jerPaDOzdHi8/FoyJIzvD1sbK6DUaEgO9mdIn0HsNCMGorfMb7qe8EqWZ+cjYfBBp636BVq0xcKV1zCHQa7Va/HdzOuZ+dqJZJ6/GBPg448v37sfgCG+D12cKKReLMf2dBJw8r9SrvbVchreeC8ebz/aS5BebikoV3lqRhGUbU6HvmW1opDfWzb8f/j7Ohi6PiEzg6JlrmP52AtKzm9eh83cOdnJ8PDsCMx/vIcke+5LSarzyyXF8veOS3vt4ZHgnrHrrXnh5SK+DR6vV4psdf+BfnxzD9bIavfbh5+2ItfPuwwP3+hi8PmNhoDdTLQn0mVsTkBOfDAgC7D1d0XXSYLQN7oT0DftwdO4ao9QrdqC/qriJf7yT0OyemLuZ+XgPfPJKJOztpDEqTaPRYsG6M3h39SnUqlr+pa1Xdzd8++Fg9Ax0M0h9pnDk9DVM/fdB/HGltMX7crSXY9GrffHiY93ZW08kEdU1avx7xUl89u25Zl2ZvJv772mPrz8YLKkv97sSruLZ+YeQV1DR4n25tbHFqrfuxeRRAQapzRQUygo8++4hxB28apD9PTexGz6b2w9ODtYG2Z8xMdCbqZYE+sT53yD18x31y+X2tngkYRkcvN3wfdizqC5qeeD5OzED/YWs6xj5/G7kXCs36H4HR3hhx/KRcHGyMeh+Da22VoNpbx/Ed79kGHS/zo7W2LliJAZJ4GrFT/HZmDz3AGpqDXsF6l9PhuCzuf0Y6onMXHlFLSa8+iv2Hsk16H7bu9tjz+cPIrybu0H3awxfbEnH8+8d0vvqZFM+nh2B158JN+xOjSAzpxQjntuNrNwyg+63X6gnfln1INzamPf9BdK7pk46U1VWozD5EgSZDC6d2otdjkFlXC3FsGd3GTzMA8DvSQo8PHMvKipVBt+3oajVGkz99+8GD/MAUFZei4dm7MXRM9cMvm9Dijt4BZNeizd4mAeApRtSMWfxcbDfg8h8Vdeo8cgr+w0e5gHgWlElRjy/G2mZzRuDLZb12y/iufmGD/MA8MayJCz66qzhd2xAVxU3MfSZXwwe5gHgeEohRr20G2Xl+g3fMRUG+lbCuXNdkK++flPsUgymukaN8bP3I7+w5ZcWm5KQfA3/XHDUaPtvqU++SsGmXZlG2395pQrjZu1H4Z8zIpibjKuleOy1A1CpjBe4l3ybim92/GG0/RNRy8z97AT2HTXMcMvGKEuqEDVrn9l27iSlFuLZdw8Z9RgxSxKx53COUY+hL5VKgwmv/Ior+Ybv2Lsl8ZwSz8037nvcUgz0FkhubwNbN2fYurvAtbsf+n30LNxDA1CYfAmlmflil2cw731+Cuf+KNGpTeKmKFzdNwWJm6Ka3ebLbRex+5D5nchS/yjBu6uTdWqjz+svLKkyyy81Go0W/3gnARVVun3I6vMezP7kGHKNcBWIiFrm96R8rPjuvE5t9DkH/HGlFG+tSNKjQuOqrlFj2r8PQq3WrVNDn/fg2XcP4YaeN5ka06L1KUhK1W0iCH1ef+zuLGzZl6VHhabRKgK9UqlETEwMunbtCjs7O/j6+mL27NkoLy/HM888A0EQsHLlSrHLNJjeMVPweOpXePzclxh/4DMETx+F7LhjiJ+2UOzSDOb0hSIs1OMSoJeHA3zaO+p85/5z8w/hZoV+M+cYg1ZbF2Z1HWai7+uP3Z2Fn+KzdazSuNb8eAEHTyp0bqfPe3CjrAYvfXBE52OZG41GixtlNbheWm2QmwalqLJKhaLrVag1whAtKVCrNSi+UY2bFbWSH0pWXaPGP95J0LmdvufBZRtTzW4I4odrTyO1mVMy/pU+70HOtXLELDmh87GMKT3rus4dW2jB78BLHxxBSendp0IWgzSm8GiB06dPY/To0VAoFHB0dESPHj2Ql5eH5cuXIyMjA8XFxQCAXr16iV2qwaR/uxfZPx+FzFqOtt390HPGeDh6u0Nd/b9v1jIbOcbuXYSsbQk4u2xr/fL7ls6Anacr9kd/KFL1zbP46xSdeyRaIudaOb77JQPPP9rdZMe8kwMn8nHiXKFJj7nwy7MYP6yzSY/ZFLVag09MPKbz59+v4HxGCXp0aWvS4xpCetZ1rP7hAtbvuFTfw+bsaI2nHu6KlycHI6Sr9F6TLm5W1GLDn/NRp1z631W9YX298fLkYEQN6STJaVqbS6vV4uBJBVbFpmHrr9n1Q9R8vRzxwqPd8ezEbmjvLr0Hq23el4XMHMOPmW6KVlvXG7x1iXnci1ZeUYvlOl6daKmvfrqE92b0MZvflyUbUo1y/1RTCkuqsH77JbzyVE+THbO5LPcM9mfP/NixY6FQKDBnzhzk5+cjOTkZCoUCCxcuRFxcHBITEyEIAsLCwsQu12BKMxXIT0hBbvwpnFu1Hb9OXQCPXl0wYOEL9dtoalQ4NGsFQmdNQNsenQAAfqMi4TMyAodfXSVi9XdXWFyJH/ea/rLXqtg0s+nRWhWbZvJjHjtbiGQ957c3tN2Hc5CdZ/r7QVb/cMHkx2wJrVaLt5Ynofu4LVi2MbXB5fKy8lqsik1Dzwlb8eqiYxbbY3/0zDX4j/4BL31wpEGYB4D4E/l4dE48ej+2DVfyLef+or8qK6/BmBl7MeQfv+CHPVkN7je5qijHv1eehN8D3+O7OMPfWG9sYpwHtx+4ghyFeQy/27Qr0+RDYGpVGqzbmm7SYzblRlkNNuw0/f1Nq39IM8vzpUUH+lmzZiEnJwczZ87E4sWL4ez8v7lkY2JiEB4eDpVKhc6dO8PFxUXUWo2pMCkdGZsPwn/8QHhGdKtfXnQ2E6mrd+D+5f+Eg7cbBix6Ecff/AKV13Qbl25q3+78w6TfyG85k16s8zg9YygoqsRPBy6Lcuy1W8zjRC5WHd/8fAnVNWpRjq2PuZ+ewEdfnLnrdku+TcWMD4+YzRdWQzmRUojhz+6CsqTqjtulZlzHoOlxRr3BXgxV1SqMmbEXu+5yD1BNrQbRb/wmSjjS1/mMEhw5XWDy42o0Wnz500WTH7cxX4gUrM3lc+D73ZkoF+FG5UuXS/F7kvndj2ixgT4tLQ2xsbHw8PDAxx9/3Og2ffr0AQCEh/9vftWEhASMGDEC3t7esLW1hY+PDyZPnoy0NNP3BBjSmSWboVGp0Xvu5IbLl26BRq1G1L5FUBw+h6zth0WrsbkOnRJvDONhEY99y/GUQpMON/qrw6fFf/1arVa034HSm7U634gtlv3HcvHpN+eavf3nP17Ajt+uGLUmU1KrNXhsbjwqq5v3Bexy3k28+L75n/908fEXZ5GQ3Px/K8/MS5DMlxpRPwfM4DxYWaVCkkhXTLPzbiKvQPyrFIdO6X4PlaGYw+/A31lsoN+0aRM0Gg2io6Ph5OTU6Db29nVjwP4a6EtKShAaGorly5dj7969WLhwIVJTUzFgwADk5JjfTCfNVZatQNb2w+gwKAzt+gXXL9eq1ChMTIedexv8EXtA1Bqb66SIwz5OponfQy/m6z+feV30qduu5N9E0XXxbkoS8/3XxX++170T4j/fm3Y8rjHFHbyKyzoOy9p58Cou55luTLYx1dSq8d8tug0Rq6nViNbrqytRPwfOK0W/mnX2YrFoHTsAcPJ8kWjHNocazOH1/53FBvr4+HgAwNChQ5vc5lZA/2ugj4qKwpIlSzBp0iQMHjwY0dHR2Lp1K27cuIEtW7aYoHLjObusrjf+r7307foFo+vkoUhb9wv6vjcdVnbm/VTU4hvVRp1r9m5OpYn/j/jUBfFqUKu1ovdQn04vFvX45vA7cDd5BeV69bbvO5qHjKuGf5K0GNZs1v1+B41Giy+2msdwipb6+bcrUCh1f37Emh8vmOX44L87fUG880DR9WqjPMxQF2J+DpjD8SurVLiQJd7Dvk6L/PobI2jF/pppJL6+vsjJycGpU6cancFGpVLB29sbSqUSGRkZCAgIaHJfRUVF8PDwwMqVKzFjxgyda4mIiIBCodulIWutDPM0fXU+li7kDnaI+nUxzq/ZiQtf78Hobe9BeSYDifPW67yv+bITqBWMP65dJWuLa67/anJ94qaoO05D5eVhD7mVDCq15o4fdgplBSIf33HbcpmmFN7XP9WjcsMpdJ6OGuvGZ5sx1OvHHd4D99JvYKcS7wa6cptwXHea0Oi6u71+GOB3wL46BW7lm/Wo3HSq5Z2hdJmuV1u3so2wr5V+qFW0+RfUVrrP3mNXcx7uN2ONUpMpldoNRpnDML3aepd8BJnWPKfmu+Vam39CZeXR6DpTnAfb3fgPrNWmH8N/S5ndfSh1GNnoOlOcBx2rjsK1YrcelRuGWnCEom1Mk+uNnQUETSU6XF+gR+V35uXlhaQk/Z53YLHTVpaX1317rqxs/C8qNjYWSqUSzs7O8Pf3v229Wq2GRqPB5cuX8cYbb8DLywuPPfaYXrUoFArk5ur2SGobwQow8sxYke8+jZtXCnBhfd0/ykOzVyJq/2Jc2XUc147pdrk+Lz8PNVoT3CxoowJcm159a27Zu5FbyZq13d9p1ND579LgAmoB68ZXGfv1A0BRcQlQJuJ70NYfaHwUXbNfP1rwHlRWVYv/O3A3Tq6Anvf5FxffAErN/PU1h7MAWOnerKqq1vz/fpujfSWg2xTb9fLzCwG1mQ89ctQ0+fdrivNgQYESqBLx98TzZpN/v6Y4D5bfrEB5voivX94GuMP3dWP/Dmi1gtmdJyw20Ht5eaGkpATJyckYMGBAg3X5+fmYO3cuACAsLAyCINzWfvDgwTh8uO4Gqa5duyI+Ph6enp5616Ira60MMGKHd8dhveEfNRDbh8+pX1Z2+RpOfrgRA5fMwI5hc6CqbH4PTQfvDibqoXfBnW5FUSjvfEOXLt/KG2MlU8OrY8dm12sMShsZmvqbMdTrv9O+PNxcYOsi3ntQYeOEpgb93O31wwC/A/Z21nAT+XfgbmqsHKDvUwo82trB1tm8X19zXBOqoc/dHg62GrQ187/f5rhpa4Ub+jTUatDBqy0Efb8Rmsg1K22Tf7+mOA+283SDtUa8h5OV2TmgqcFxpjgPOjnaoo2I/040gj3uNM+MsbOATFDD2wivX5+8eIvFDrmZNWsWVqxYAV9fX+zfvx9BQUEAgMTERDz11FPIzMxEbW0tZsyY0ehTYtPT03H9+nVkZWVh0aJFKCgowOHDh+Hn52eS+msrqrCxy5MmOZYhRGdsgLWDndGPo1Jp4HLvN6is0u9qwNV9U+DT3hE518rhO/J7nduP6N8B+/47Wq9jG8qL7x/Gmh/1mw+9pa8fAK7snQxfrya6yE3g+NkC9H/yZ73bt/Q9mP/yPXjnxd56H98U1GoNAh/ejKxc3XpZvTzscWXPFIt4yNL81cl4d/Upndv9vGIkHh5smvO8MWXnliHgoR+g6yf8I8M7YeuSEcYqy2DGzdqn96xMLT0HWFkJKDv6NOztxOsT3X7gMsbP3q93+5a+B/99ZyCeE/FBi1qtFu73b0BJqX7z8Lf09fcP88TRDVF6HdtYpH/WbkJMTAzc3d1x9epVhISEIDQ0FIGBgejbty8CAgIwbFjd2MK/3hD7V926dUO/fv0wZcoU/PrrrygrK8Mnn3xi4ldBfyeXy9Crm7tox+/To/ExmyatIVi81+/Z1k7vS9SGEhbkBiur26+qmUqfHuK9/81lZSXDi5N0/7B9fmJ3iwjzAPDcxG6Q6/h70qmDE0bf52O0mkypc0dnjLnfV+d2L08ObsZW4hPzXBzSpa2oYR4A+gSL+1kk9mehIAii1iD262+MZZy5G+Hj44OEhASMGTMGdnZ2yM7OhpubG9asWYO4uDhcvFh301dTgf6vXF1d0bVrV/zxh3QeumHJIkJa9z9isV9/Y0PUTMneTo6eXXW/2dFQzOF3oDmee7QbAnycm7FlHZ/2jpgxRRphrjk6tHPE7OgQndp8+M8+sLKynI/FeS/1hp1t828kGNG/A4b362DUmgxF3POg+F/qO7Z3QHt3e1GObWMtQ89A8c7Bt4j9WWhuLOfM1Yjg4GDs3LkTZWVlKCsrw/Hjx/H888+jvLwc2dnZkMlk6Nmz5133U1BQgPT0dHTp0sUkddOdPTqi8RlejM3JwRoP3iv+2Nrwbu7o4tv8oGZIkx64/QZyMTw6Upzfgft6t7/r7BHmoq2LLXatehC+Xne/ouLlYY9dqx5AO5ECgrEsfCUSTz7cvPP2olf7InpMV6PXZEoRIZ74YdGwZoX6/mGe2PzpcNG/sDfX0EhvtHURZ5rlSSPFPw8KgiDaeXDc0E6wsdbjjnMDe1SkvwdbGyuMNcNheRYd6JuSmpoKrVaLwMBAODg0/HB+8skn8e677+Knn37Cb7/9hrVr12LIkCGQy+V45ZVXRKuZ/uf+Pl4I6XKHqW6M5KmHu8DFSfx5+mUyAS89ZvqeVFdnG0wZ1fT0rqb07IRukMtNHzykMhzhlqDObXBsw1g8OyEI9na3fwDb2lhh2rhAHN8YhZ6BbqLUaExWVjJ8/cFgrHhjQJNfgvuFeuKnZSPw2rRQk9dnCmOH+OHgV2MwZpAvGsvqnm3t8Oaz4Yj/4iG0cRb//NZc9nZy/GN8kMmP69/RGQ8ONI9hWWJ8DsCMzoN9enigb0/9Jitpicce8IdHW+PfM6irVhnoU1JSgCaG2/Tv3x+//PILpk+fjtGjR2PRokW4//77cfr0aXTtalm9N1IlCAJmTOlh8uOKdfJszPTxjQc0Y/rHI0FwsDePibG8PBzw6AjT9s60d7fHBJGuDrVEh3aOWPvu/cjb/zjWvDMQzg51f4dtnKyRu38Kvnp/EPy8xbvJ2dhkMgEzH++Biz9Pwu7VD8LZsW7OVxdHayR9Pw7HNkZh3NBOYpdpVJE9PbFz5QPIiHsMi+f0hdOfvwNtXWxwdd8UfDgrQvQx4fp48bFgyGSm/WL/8mTTH7MpIV3bYkikt0mP2aOLKwZH6D8Ti6GJMUzQXIcmMtD/zcyZM3HixAmUlJSgsrISFy9exJo1a9Cpk2Wf8KXm2Qnd0Lu76cYxvjw5GKFB5tOD6dbGFh/+M8Jkx/P2dMC/n7/9AW1iWvhKZH04M4WlMf1gayP+ZWZ9ubrY4vlHu9dfZXJysIa7q/n1MhmLTCbgwYE+cPnzd8bZ0dosx8Eak7+PM+ZMDUWbP38HHOzkkv6d7urngjlP333YrKEEB7hi5uPmFeaWxvQz6dXK/7x5r1kNy4oe0wX39mpnsuNNjQpEvzDTHU8XDPStTKcx/dF/wXMNlnWdPBTT8jfDb1SkaHXpytpahvUfDIK13Pi/wp07OGHhK+b33sx6ogcG9jby08f+9N93BqKti61JjtVcft5OWDzHuE9TvmXC8M6YbCbDjYjof+a/fA+6dW5j9OPIZALWvz8IdrbmdSUjvJs73n7eNNPozpgSbPIrAndjZSXDV+8N0unmb311aOeAJTH9jH4cfbXKQB8fHw+tVosxY8aIXYrJ+T3UD1d2n6j/2cnHE0HRI1CQlC5qXfoIC3LDJzoGbYWyAjnXypv14A38Ocb4248Gw8nBdD3BzWVlJcP69wfB3bX5QVvX148/r06Y67zcz03shgnDdRsGo+t70KmDE1b/27x6pYiojr2dHBs+HgwHHYYM6XMenP9yb/QNNf147eZ445lw3H+Pbp07ur4HoYFtseBf5texhT/vFVr2f/11aqPr65fLBXz9wSCz69j6K/P6qkktZuPigHEHlsDKzgYVeUrIbK3h7NceGZt/x9HX16J9ZDccmv3ng7QEAfd++hKO/3sdIudNFbt0vfzrqZ4oulGND/57ulnbRz6+o9n7trGW4cfFw3DfPeYzXvDvuvq5YPfqBzHy+d24Xnb3B2zo8voB4ImHumD567qdKE1JEARsXDAY42bXYu+R5j2GW5f3oEM7B+z/72iLm/2FyJJEhNTd2Bw1ax+qqu/+0EFdz4P/ejIEbz1nXkMO/8raWoafVzyAEc/vQlKqslltdHkPunVug71rRpllx9Ytzz/aHUXXq/Hm8qRmba/L67eyErDx4yEY0V/8We7upFX20FuymtIKZG5LwPkv4rBj5FyceOcrFCZfxJHXPof3wJ4oSEyHVlV3wgt5YSwKEi+g6Gym2GW3yPsz++CTVyINeqOSq7MNfl4xEmOHmGfP9F9FhHji96/GNGt6Ql3MmBKMbz4cZPbzctvZyrFj+UhMHmXYm2S7+7fBofUPo6ufi0H3S0SGN3JAR+xZ/aBBZx8RBODdl3rjs7n9zP4KXRtnG/y6djRGDjDscwT69vTEwa/GSGK63jeeDceKNwYY9J4CZ0drbP1sOB570PyHXJr3JzXpxa2nP4pTsgAA7mFdUHyu7s9+oyJxeVfdcBvXbr7oNKYfzizdImqthjJ3ehiObRiLHgaYzvLhQb5I3TYBD9xrHlOTNUdYkBtStkzAsxNaPo1bh3YOiPvPA1j55r1mH+ZvsbWxwqaFQ7Hx4yFwa9OyS6IymYC500KRHDse/jo8mImIxDUowhupWydgogFmowrs5IKDX43BvJfuMfswf4uLkw12rx6FlW8OgGMLZySzsZbho1kROPzNw5K6Qjnz8R5I/G4cwru1fBKLkQM64NzWCYiSyCxY0vi0Jp24hXSuD/HuYQEo+jPcdxjSC7nxpwAA7fsFw8m3HSYeWYFHT6yC5z2BGLDoRXR7+gFRa2+JyJ6eOPn9OHw8O0Kv3uo+PTywaeEQ7FgxEh3aGba32xTaONtg7bv3Y99/R+n1tEd3V1vETA9F6tYJeEiPR8aLTRAEPDGmC1K3TcCMKcE6z4AjCMDYwX448s3D+OTVvpKcxo+otWvnbo/Nnw3H1iXDMSBc99lIOrRzwHsz7sHpHx4x6+GWTZHJ6qZ1PrvlEUwfH6jzzaJyuYApowKQHDsebzwbDrkJJp4wtF7d3XHiuyh8+lpf+HfUvVMmvJsbvvlwEPZ8PkpSU/oKWq1WK3YRdLvaiips7PKkzu0cvNwwdu8niA17FgAw4fAK/PbiZ5DJ5Qh/5VH8+vTHjbYbtWU+zq/diSu7E/WqNzpjA6wdzGcKPJVKg7iEq9i0KwNJqUpkXC27bRu5XEBIl7boH9YOzzwShEgRHlBhTBeyruOLLek4dOoaTqcXo7rm9rGlPu0d0aeHOyaO6IxJD/ib3QwOLVFWXoMNOzOw8+AVnDxfhGtFlbdt42gvR6/u7hgS4YVnJ3RDZz1O/lLjM2ITcgsq0LGdA3L2Py52OSbX2l8/Wtl7cCpNiXXbLuLomQKkXCpBrUpz2zb+HZ3Rp4c7powKQNSQTrC2ll6IbUrxjWqs334Ruw/n4OT5IhTfqL5tGxcna9wT7IER/TrgmQlBkhhe01xqtQZ7juRiY1wGElMLcely6W3bWFkJ6BHgin6hnpg+PggDwttJ5qrMX1nOpzcBt4bb/Nk7DwA1peXoPvVBVBeXNZjdxtLJ5TKMG9qp/oEx10urkZ59AxVVKljJBDg7WiM4wNWiAuzfdfd3xeLX6qbYqq3VID37OkpKa1Cr0sDezgpdfFwkdSlVV86ONnhpcjBemhwMrVaLvIIKXM6/iapqNWysZfBoa4dAPxfJDCsiIt31DvbAyuC65w1U16hxIes6bpTVQK3RwsFOjsBObVo8TM+cubWxxatPh+LVp0Oh1WpxOe8mcgsqUF1Tdx708nBAgI+z2Twsy9CsrGR46H7f+qvON8pq6rOAIADODnVZwBKuyEr/FVADOftPImf/yfqfd45+HQAw7rcl2DNxXpPtdt9hnSVwdbE124dBmIK1tQw9A83nwVimJggCOrZ3RMf20htKRUSGYWtjhfBupnsgobkRBAGdOzq3iiuRTWnjbGO204+2FAN9K7F9yCtil0BERERERsBrzUREREREEsZAT0REREQkYQz0REREREQSxjH0Zkpub4vojA1il9FscnvLnSWAiIiIyJwx0JspQRDMal53IiIiIjJPHHJDRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhDPRERERERBLGQE9EREREJGEM9EREREREEsZAT0REREQkYQz0REREREQSJhe7AGqcVquFqrJa7DKaTW5vC0EQxC6DiIiIqNVhoDdTqspqbOzypNhlNFt0xgZYO9iJXQYRERFRq8MhN0REREREEsZAT0REREQkYQz0REREREQSxkBPRERERCRhvCmWiMjC1dSqce5SCVIzSnCzohYAUFGpQlJqIUID3WBrYyV2iURE1AIM9EREFqisvAYbdmbg6x2XcOpCEWpqNQ3Wl5TVIPLxHbCWyxDezQ1PPdwVT4/tClcXW9FqJiIi/TDQExFZkNKbNZi3KhlfbL1Y3xt/J7UqDZJSlUhKVeKNZUmYPj4QH8zsw2BPRCQhDPQWxGtACEZtnd9gWW15JUoz85Gx+SDS1v0CrVrTZHsikrb9x3LxzLwEXMkv16t9RZUK//k+DdviL2PtvPvw0P2+Bq+RiIgMj4HeAmVuTUBOfDIgCLD3dEXXSYPRd/40tAnsiKNz14hdHhEZmFarxXufn8K7q08ZZH95BRUYM2MvYqaHYsG/IvkUaCIiM8dAb4GKUrKQuSWh/uf09XvwSMIyBD0xHMkLNqG6qFTU+ojIsN5YloSFX541+H4/+SoFFVVqLH+9P0M9EZEZ47SVrYCqshqFyZcgyGRw6dRe7HKIyIBWfJdqlDB/y8pN57FgnfH2T0RELcdA30o4d64L8tXXb4pdChEZyIWs65j7WaJObRI3ReHqvilI3BTV7DbvrDqJ0xeK9KiQiIhMgYHeAsntbWDr5gxbdxe4dvdDv4+ehXtoAAqTL6E0M1/s8ojIANRqDaa/fRDVNWqd2nl5OMCnvSO8PBya3Ual0mLa2wdRU6vbsYiIyDQsPtArlUrExMSga9eusLOzg6+vL2bPno3y8nI888wzEAQBK1euFLtMg+odMwWPp36Fx899ifEHPkPw9FHIjjuG+GkLxS6NiAxk875sHDtbaLLjnUkvxoadGSY7HhERNZ9F3xR7+vRpjB49GgqFAo6OjujRowfy8vKwfPlyZGRkoLi4GADQq1cvsUs1qPRv9yL756OQWcvRtrsfes4YD0dvd6ira+q3kdnIMXbvImRtS8DZZVvrl9+3dAbsPF2xP/pDkaonouZYFZtm8mP+5/vzmD4+kDfIEhGZGYvtoVcqlRg7diwUCgXmzJmD/Px8JCcnQ6FQYOHChYiLi0NiYiIEQUBYWJjY5RpUaaYC+QkpyI0/hXOrtuPXqQvg0asLBix8oX4bTY0Kh2atQOisCWjboxMAwG9UJHxGRuDwq6tErJ6I7ubcpWIcPKkw+XGT04pwIsV0VwWIiKh5LDbQz5o1Czk5OZg5cyYWL14MZ2fn+nUxMTEIDw+HSqVC586d4eLiImqtxlaYlI6MzQfhP34gPCO61S8vOpuJ1NU7cP/yf8LB2w0DFr2I429+gcprJaLWS0R3FpdwtVUem4iIGmeRgT4tLQ2xsbHw8PDAxx9/3Og2ffr0AQCEh4c3uZ/Ro0dDEAS8++67RqvVVM4s2QyNSo3ecyc3XL50CzRqNaL2LYLi8DlkbT8sWo1E1Dwnz4s348zJ80rRjk1ERI2zyEC/adMmaDQaREdHw8nJqdFt7O3tgTsE+h9++AGnT582ap2mVJatQNb2w+gwKAzt+gXXL9eq1ChMTIedexv8EXtA1BqJqHnEDNUnzxdBq9WKdnwiIrqdRQb6+Ph4AMDQoUOb3CYnJwdoItCXlpbiX//6FxYvXmzEKk3v7LK63vi/9tK36xeMrpOHIm3dL+j73nRY2dmIWiMR3d0VhXjPk7hWVAmVioGeiMicCFoL7Grx9fVFTk4OTp061egMNiqVCt7e3lAqlcjIyEBAQECD9f/85z+RkpKC3377DYIgYN68eS0adhMREQGFQrcb2Ky1MszT9NX7mM0hd7BD1K+LcX7NTlz4eg9Gb3sPyjMZSJy3Xud9zZedQK2gMUqdRPQ/WgjIc2v6fJS4KeqOc8x7edhDbiWDSq2BQlnZ5HYKZQUiH9/R6Drv4g8hQ02j68xdvuur0MjaQKa5Ae/rn4ldjij4HhCZJy8vLyQlJenV1iKnrSwvLwcAVFY2/mEVGxsLpVIJZ2dn+Pv7N1iXlJSEtWvX4uTJkwarR6FQIDc3V6c2NoIV0N5gJTQq8t2ncfNKAS6s3w0AODR7JaL2L8aVXcdx7ZhuU+Ll5eehRsuHzhCZRFs1IFg1uurWg6PuRm4la9Z2jcnPuwpoVXq1FZ2zGpABGrVa5/OyxeB7QGRxLDLQe3l5oaSkBMnJyRgwYECDdfn5+Zg7dy4AICwsrMF8ymq1Gi+88AJmzpyJkJAQg9ajK2utDDBih3fHYb3hHzUQ24fPqV9WdvkaTn64EQOXzMCOYXOgqqxu9v46eHdgDz2RieRrK6ARnBtdp1BW3LGtLj30jRG0VfDu0B5SnYk+38oKGgAyKyt4d+wodjmi4HtAZJ70yYu3WGSgHzFiBNLS0rBw4UKMHDkSQUFBAIDExEQ89dRTUCrrbij7+3CclStX4tq1awaf1Uafyye1FVXY2OVJg9bxV7nxp/Bd96m3Lb+wfnd9j70uLl66CGsHOwNVR0R3MmbGHvySkNPouqaGydxydd8U+LR3hEJZCd+R3+t87EGRnfHbl40fWwp8RmxCbkEFvL28kXNOuq+jJfgeEFkei7wpNiYmBu7u7rh69SpCQkIQGhqKwMBA9O3bFwEBARg2bBjwtxtilUol3n77bbzzzjtQqVS4fv06rl+/DgCoqqrC9evXodGwB5qIxNenh0erPDYRETXOIgO9j48PEhISMGbMGNjZ2SE7Oxtubm5Ys2YN4uLicPHiReBvgT4nJwdlZWV44YUX0LZt2/r/AGDhwoVo27Ytrly5ItprIiK6ZWikd6s8NhERNc4ih9wAQHBwMHbu3Hnb8ps3byI7OxsymQw9e/asX961a1ccOHD7POxDhw7F1KlTMW3atBaNbSIiMpQhkd7o1rkN0rNvmPS4ft6OGH2fj0mPSUREd2exgb4pqamp0Gq1CAoKgoPD/6Z2c3JywpAhQxpt07lz5ybXERGZmiAIeHlyMGYvPGbS4744KRhWVhZ5YZeISNJa3Zk5JSUFuMMTYomIpGD6+ED4euk37aQ+2rvb44VJ3U12PCIiaj4G+rvQarUGn/VGTJ3G9Ef/Bc81WNZ18lBMy98Mv1GRotVFRLpxdrTBF+/eZ7Ljff72vXBrY2uy4xERUfMx0Lcyfg/1w5XdJ+p/dvLxRFD0CBQkpYtaFxHp7oF7fXTuNVcoK5Bzrfyu89X/VfSYLhg/rLMeFRIRkSm0ujH08fHxYpdgVDYuDhh3YAms7GxQkaeEzNYazn7tkbH5dxx9fS3aR3bDodkr6zYWBNz76Us4/u91iJx3+5z0RGT+lr/eH5fzbmL34ebNJ363eer/bnCEF9bOM92VACIi0l2r66G3dDWlFcjcloDzX8Rhx8i5OPHOVyhMvogjr30O74E9UZCYDq1KDQAIeWEsChIvoOhspthlE5GebKytsHXJcDw8yNfg+x45oAN2rnwA9natru+HiEhSGOgtkFtPfxSnZAEA3MO6oPhc3Z/9RkXi8q664Tau3XzRaUw/nFm6RdRaiajl7O3k2LZ0BD6Y2QfW8paf1q2sBLz9Qi/sXPkAnBysDVIjEREZDwO9BXIL6Vwf4t3DAlD0Z7jvMKQXcuNPAQDa9wuGk287TDyyAo+eWAXPewIxYNGL6Pb0A6LWTkT6kctleOv5Xjj5/Tj0D/PUez/3BLvjxMYovDejD2ysrQxaIxERGQevo1oYBy83QKtFhaIYAOAW3Alnl22BR+9A3LiUC1VFFQAg/Zu9SP9mb327UVvm4/zanbiyO1G02omo5UKD3HDk27E4kVKIVbFpiN2Theoa9R3bWMtlmPSAP16eHIx7e7WDIAgmq5eIiFqOgd7CuPX0r++dB4Ca0nJ0n/ogqovLGsxuQ0SWSxAE9Atrh35h7bDmnYE4e7EEJ88rce6PEtysqIVWCzjay9EzsC36BHsgvJsbx8kTEUkYz+AWJmf/SeTsP1n/887RrwMAxv22BHsmzmuy3e47rCMi6bKzlaNvqCf6huo/DIeIiMwbA30rsX3IK2KXQERERERGwJtiiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMJ4U6yZktvbIjpjg9hlNJvc3lbsEoiIiIhaJQZ6MyUIAqwd7MQug4iIiIjMHIfcEBERERFJGAM9EREREZGEMdATEREREUkYAz0RERERkYQx0BMRERERSRgDPRERERGRhDHQExERERFJGAM9EREREZGEMdATEREREUkYAz0RERERkYQx0BMRERERSRgDPRERERGRhDHQExERERFJGAM9EREREZGEMdATEREREUkYAz0RERERkYQx0BMRERERSZhc7AKocVqtFqrKarHLaDa5vS0EQRC7DCIiIqJWh4HeTKkqq7Gxy5Nil9Fs0RkbYO1gJ3YZRERERK0Oh9wQEREREUkYAz0RERERkYQx0BMRERERSRgDPRERERGRhDHQExFRq6HVahv8n4jIEnCWGyIiskgajRb7juYi/kQeklKVSE4rwvWyGgBAXmElOgzfhD7B7ogI8cCYQb6ICPEUu2QiIr0w0BMRkUW5XlqNtVvSsfqHC8jKLWtyu/zCCuwsrMDOg1fx7upTiAjxwMuTgxE9pgtsrK1MWjMRUUsw0FsQrwEhGLV1foNlteWVKM3MR8bmg0hb9wu0ao1o9RERGVvcwSt4/r3DyCuo0LltUqoS/3gnAcs2puLrDwYhvJu7UWokIjI0BnoLlLk1ATnxyYAgwN7TFV0nDUbf+dPQJrAjjs5dI3Z5REQGV1WtwssfHsFXP11q8b7OpBcj4vHteH9GH/zfP8L4FGwiMnsM9BaoKCULmVsS6n9OX78HjyQsQ9ATw5G8YBOqi0pFrY+IyJAqKlWImrUPvx7PM9g+VSot3liWhLzCCiz7v/4M9URk1jjLTSugqqxGYfIlCDIZXDq1F7scIiKDqa3VYOKrvxo0zP/Viu/O4/WliUbZNxGRoTDQtxLOneuCfPX1m2KXQkRkMAu+PIPdh3OMeoxPvkpB3MErRj0GEVFLcMiNBZLb28DWzbl+DH23px+Ae2gACpMvoTQzX+zyiIgM4uzFYry/5rRObRI3RcHLwwEKZQUiH9/R7HbPzT+M1G3t0dbFVo9KiYiMq1X00CuVSsTExKBr166ws7ODr68vZs+ejfLycjzzzDMQBAErV64Uu0yD6R0zBY+nfoXHz32J8Qc+Q/D0UciOO4b4aQvFLo2IyCC0Wi2en38ItSrdZu7y8nCAT3tHeHk46NQuv7ACby1P0rFKIiLTsPge+tOnT2P06NFQKBRwdHREjx49kJeXh+XLlyMjIwPFxcUAgF69eoldqsGkf7sX2T8fhcxajrbd/dBzxng4ertDXV1Tv43MRo6xexcha1sCzi7bWr/8vqUzYOfpiv3RH4pUPRHR3Z1IKcTxlEKTHnP9jkv4aFYEXNlLT0RmxqJ76JVKJcaOHQuFQoE5c+YgPz8fycnJUCgUWLhwIeLi4pCYmAhBEBAWFiZ2uQZTmqlAfkIKcuNP4dyq7fh16gJ49OqCAQtfqN9GU6PCoVkrEDprAtr26AQA8BsVCZ+RETj86ioRqyciurv/fJ9m8mNWVqnx9Y6WT4tJRGRoFh3oZ82ahZycHMycOROLFy+Gs7Nz/bqYmBiEh4dDpVKhc+fOcHFxEbVWYypMSkfG5oPwHz8QnhHd6pcXnc1E6uoduH/5P+Hg7YYBi17E8Te/QOW1ElHrJSK6k6pqFX7YmyXKsb/5+Q9RjktEdCcWG+jT0tIQGxsLDw8PfPzxx41u06dPHwBAeHh4/bLffvsNgiDc9p/Uh+ScWbIZGpUavedObrh86RZo1GpE7VsExeFzyNp+WLQaiYiaI+VSCapr1KIc++ylYlRVq0Q5NhFRUyx2DP2mTZug0WgQHR0NJyenRrext7cH/hbob/nPf/6De+65p/5nR0dHI1ZrfGXZCmRtP4wuEwehXb9gFByvu1ytValRmJgOj7Au+CP2gNhlEhHd1cnzStGOrVJpcfZiCfqGeopWAxHR31lsD318fDwAYOjQoU1uk5NTN3dxY4G+R48e6N+/f/1/oaGhRqzWNM4uq+uN/2svfbt+weg6eSjS1v2Cvu9Nh5Wdjag1EhHdTWrGdZGPz2GJRGReBK1WqxW7CGPw9fVFTk4OTp061ehwGZVKBW9vbyiVSmRkZCAgIAD4c8jN0KFDceDAAQwZMsQgtUREREChUOjUxlorwzxNX4McvylyBztE/boY59fsxIWv92D0tvegPJOBxHnrdd7XfNkJ1Aq6TR9HRKSPEsfxqLDt3ei6W/PMN8XLwx5yKxlUag0Uyso7HqepuerblP8Cp+rjelRuHvJdX4VG1gYyzQ14X/9M7HKI6E9eXl5IStJvelyLHXJTXl4OAKisbPyEHRsbC6VSCWdnZ/j7+9+2fvLkyVAqlXB3d0dUVBQWLFgADw8PvWpRKBTIzc3VqY2NYAW01+twzRb57tO4eaUAF9bvBgAcmr0SUfsX48qu47h2TLcZJPLy81CjFWdMKxG1Mh3LgSZmjrw1z/zdyK1kzdquMTdulOBGkW7ndLPirAZkgEat1vmziYjMk8UGei8vL5SUlCA5ORkDBgxosC4/Px9z584FAISFhUEQhPp1bdq0wdy5czFo0CA4OTnh6NGj+Pjjj3Hs2DEkJSXBzs5Or1p0Za2VAUbs8O44rDf8owZi+/A59cvKLl/DyQ83YuCSGdgxbA5UldXN3l8H7w7soScik7juIEd5E+sUyoo7ttW1h74xri4OcLTr2Ox6zU2+lRU0AGRWVvDuKN3XQWRp9MmLt1jskJtZs2ZhxYoV8PX1xf79+xEUFAQASExMxFNPPYXMzEzU1tZixowZd31K7M8//4yoqCh8+eWXmD59uknqr62owsYuT5rkWIYQnbEB1g66f9khItLVmh8v4MX39ZuR6+q+KfBp74ica+XwHfm9Xvs48V0UIntK96ZYnxGbkFtQgY7tHJCz/3GxyyEiA7DYm2JjYmLg7u6Oq1evIiQkBKGhoQgMDETfvn0REBCAYcOGAU3cEPt3Dz/8MBwdHfUe10RERIbTp4e7aMeWywWEBrYV7fhERI2x2EDv4+ODhIQEjBkzBnZ2dsjOzoabmxvWrFmDuLg4XLx4EWhmoL/lr0NziIhIHKGBbrCztRLl2OFB7rCztdjRqkQkURZ9VgoODsbOnTtvW37z5k1kZ2dDJpOhZ8+ed93Pjh07UF5ejr59jTvrDBER3Z2tjRUmPxiAr3dcMvmxp0Z1NfkxiYjuxqIDfVNSU1Oh1WoRFBQEB4eG05s9+eSTCAgIwD333FN/U+wnn3yCXr16YcqUKaLVTERE//Py5GCTB3oHOzmeHhto0mMSETVHqwz0KSkpQBPDbUJCQvDdd99h6dKlqKyshI+PD5577jnMmzcPNjZ86BIRkTnoG+qJe3u1w5HTBSY75j8eCUIbZ34OEJH5sdgx9Hdyp0D/xhtvICUlBaWlpaitrUVWVhY+++wztGnTRoRKDa/TmP7ov+C5Bsu6Th6Kafmb4TcqUrS6iIh0tebtgbCxNs3HmE97R3wws49JjkVEpCsG+lbG76F+uLL7RP3PTj6eCIoegYKkdFHrIiLSVc9AN8x7sfEnxjZFoaxAzrXyu85X/3dr593H3nkiMlutcshNfHy82CUYjY2LA8YdWAIrOxtU5Ckhs7WGs197ZGz+HUdfX4v2kd1waPaf8+4LAu799CUc//c6RM6bKnbpREQ6i5kehqNnCrDz4NVmbR/5+A6dj/HWc+EYdZ+PHtUREZlGq+yht2Q1pRXI3JaA81/EYcfIuTjxzlcoTL6II699Du+BPVGQmA6tSg0ACHlhLAoSL6DobKbYZRMR6UUul+GHxcPw4L3GeeLpK0+F4H0OtSEiM8dAb4HcevqjOCULAOAe1gXF5+r+7DcqEpd31Q23ce3mi05j+uHM0i2i1kpE1FL2dnLsWDESzz/azWD7tJbLsOjVvvj0tX58BgkRmT0GegvkFtK5PsS7hwWg6M9w32FIL+TGnwIAtO8XDCffdph4ZAUePbEKnvcEYsCiF9Ht6QdErZ2ISB821lZY88592L36Qfi0d2zRvvr08EBy7Di8Ni2UYZ6IJKFVjqG3ZA5eboBWiwpFMQDALbgTzi7bAo/egbhxKReqiioAQPo3e5H+zd76dqO2zMf5tTtxZXeiaLUTEbXUgwN9kLptAr7cdhGrfkjDpculzW57b692eOmxYEwZFQC5nP1dRCQdDPQWxq2nf33vPADUlJaj+9QHUV1c1mB2GyIiS+XiZIN/PdUTs6JDcOBEPg4k5uHk+SIkpylRUFzXqSEIgJ+3E/oEe6BPD3c8dL8venV3F7t0IiK9CFqtVit2EXS72ooqbOzypMH2N+63JdgzcR6qiprfW6WL6IwNsHawM8q+iYgMRavVQqXSQi4XWu1wGp8Rm5BbUIGO7RyQs/9xscshIgNgD30rsX3IK2KXQEQkOkEQYG3dOoM8EVkuDhIkIiIiIpIwBnoiIiIiIgljoCciIiIikjAGeiIiIiIiCeNNsWZKbm+L6IwNYpfRbHJ7W7FLICIiImqVGOjNlCAInAaSiIiIiO6KQ26IiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkTC52AdQ4rVYLVWW12GU0m9zeFoIgiF0GERERUavDQG+mVJXV2NjlSbHLaLbojA2wdrATuwwiIiKiVodDboiIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMs9wQERFZsMLiSpw8X4ST55X442opim/UTYl8vawGazdfQJ8eHugZ2BY21lZil0pEemKgJyIisjA1tWr8FH8Zq2LT8HuSotFtyitVeP69wwAAFydrTI0KxEuPBSM4wNXE1RJRSwlarVYrdhF0u9qKKs5DT0REOtuyLwuzFh5DXkGFXu3HDfXDqrfuRYd2jgavjYiMgz30FsRrQAhGbZ3fYFlteSVKM/ORsfkg0tb9Aq1aI1p9RERkPMqSKsz46Ah+2JPVov1sP3AFvycpsOz/+uOpsV35FHAiCWCgt0CZWxOQE58MCALsPV3RddJg9J0/DW0CO+Lo3DVil0dERAaWlVOGEc/vQmZOmUH2d72sBlP/fRCn04vw6Wv9GOqJzBwDvQUqSslC5paE+p/T1+/BIwnLEPTEcCQv2ITqolJR6yMiIsO5kn8Tg/8Rh6uKcoPve8m3qdBogCUxDPVE5ozTVrYCqspqFCZfgiCTwaVTe7HLISIiA6muUePhmXuNEuZvWbYxFatj04y2fyJqOQb6VsK5c12Qr75+U+xSiIjIQN77/BRSLpXo1CZxUxSu7puCxE1RzW4z97NEZObw6i6RubL4QK9UKhETE4OuXbvCzs4Ovr6+mD17NsrLy/HMM89AEASsXLlS7DINSm5vA1s3Z9i6u8C1ux/6ffQs3EMDUJh8CaWZ+WKXR0REBnDyvBILvzqrczsvDwf4tHeEl4dDs9tUVKnwzLxD4MR4RObJosfQnz59GqNHj4ZCoYCjoyN69OiBvLw8LF++HBkZGSguLgYA9OrVS+xSDap3zBT0jpnSYFl23DEcf+ML0WoiIiLD+nDtaajVpgvYvyXmI+GkAoMivE12TCJqHovtoVcqlRg7diwUCgXmzJmD/Px8JCcnQ6FQYOHChYiLi0NiYiIEQUBYWJjY5RpU+rd7seex+dgX/SGS3v8WVcVlcPR2h7q6pn4bmY0c435bgrDZExq0vW/pDIzY+JYIVRMRUXPlKMqx/cAVkx931Q8cS09kjiw20M+aNQs5OTmYOXMmFi9eDGdn5/p1MTExCA8Ph0qlQufOneHi4iJqrYZWmqlAfkIKcuNP4dyq7fh16gJ49OqCAQtfqN9GU6PCoVkrEDprAtr26AQA8BsVCZ+RETj86ioRqyciortZty0dGo3ph79s2Z+NgqJKkx+XiO7MIgN9WloaYmNj4eHhgY8//rjRbfr06QMACA8Pv23dtm3bcO+998LR0RFt2rTBwIEDkZqaavS6jaUwKR0Zmw/Cf/xAeEZ0q19edDYTqat34P7l/4SDtxsGLHoRx9/8ApXXdLvBioiITOtAojj3Q6lUWhw+fU2UYxNR0ywy0G/atAkajQbR0dFwcnJqdBt7e3ugkUC/fPlyPPbYY7jvvvuwY8cObNq0CSNGjEBlpbR7JM4s2QyNSo3ecyc3XL50CzRqNaL2LYLi8DlkbT8sWo1ERHR3Go0WyWlFoh3/5HmlaMcmosZZ5E2x8fHxAIChQ4c2uU1OTg7wt0CfkZGBuXPnYsmSJZg5c2b98oceesio9ZpCWbYCWdsPo8vEQWjXLxgFx+vGQWpVahQmpsMjrAv+iD0gdplERHQXGVdLUVZeK9rxxfwyQUSNs8hAf/nyZQBAp06dGl2vUqlw+HBdT/RfA/2XX34Ja2trPPfccwatJyIiAgqFQqc21loZ5qGvQes4u2wL/McPRO+5k7Hn0XcBAO36BaPr5KFIW/cL+r43HTtGzoW6quau+/q7oMAg1Aoag9ZLRES3q5b7Ai7PNroucVPUXaej9PKwr///1X1TmtxOoaxA5OM7blu+/7dj8PF5Rue6iejOvLy8kJSUpFdbiwz05eV1T8xraphMbGwslEolnJ2d4e/vX7/8yJEj6NatGzZs2IAPPvgAV69eRWBgIN555x08/vjjetejUCiQm5urUxsbwQrQ8aGuiqOpWO/9aJPrb1zKxTc+/xtyI3eww31LZ+Dkhxtx4es9GL3tPdzzxhNInLdetwMDyMvPQ41WrXM7IiLSkaMj0MRcDrfmmG8OuZWs2dv+VW2tRufPNCIyLosM9F5eXigpKUFycjIGDBjQYF1+fj7mzp0LAAgLC4MgCA3W5ebm4o033sDChQvh6+uLdevW4YknnoCnpydGjBihdz26stbKACN3eEe++zRuXinAhfW7AQCHZq9E1P7FuLLrOK4d021qsg7eHdhDT0RkAjVWbVHYxDqFsuKu7b087CG3kkGl1kChbPr+sKb2ZW0toF3Hjs2ul4iaR5+8eIugtcDHvs2aNQsrVqyAr68v9u/fj6CgIABAYmIinnrqKWRmZqK2thYzZsxo8JTYoKAgXLp0Cdu2bcP48eMBAFqtFr169YKrqyt+//13k72G2ooqbOzypNH233FYbwxe9S9sHz4H5bn/u8Gp+7RR6PHCw9gxbA5UldXN3l90xgZYO9gZqVoiIrolr6AcHUd8r3f7q/umwKe9I3KulcN3pO77mfSAP35YPEzv4xOR4VnkLDcxMTFwd3fH1atXERISgtDQUAQGBqJv374ICAjAsGF1J6K/z3Dj5uYGAA164gVBwIgRI3Du3DkTvwrjyo0/he+6T20Q5gHgwvrd2Dpgpk5hnoiITKdDO0d4e955nLwx9enhLtqxiahxFhnofXx8kJCQgDFjxsDOzg7Z2dlwc3PDmjVrEBcXh4sXLwKNBPqQkJAm91lVVWX0uomIiJqjT7B4obpPDw/Rjk1EjbPIQA8AwcHB2LlzJ8rKylBWVobjx4/j+eefR3l5ObKzsyGTydCzZ88GbcaNGwcA2Lt3b/0yjUaDffv2ITIy0uSvgYiIqDFjh/iJcty2Lja4N1zHGRuIyOgs8qbYO0lNTYVWq0VQUBAcHBpeshw7dizuv/9+PP/88ygqKoKfnx+++OILpKamYt++faLVTERE9FdPPNQFr316wuTz0U8fHwQH+1YXHYjMnsX20DclJSUFaGS4Df4cL79jxw5MnDgRb775JqKionD58mX88ssv9ePuiYiIxObkYI2pUYEmP+6Lk7qb/JhEdHcM9H/j6uqKNWvWoLCwENXV1Thx4gQefPBBE1dJRER0Z289Fw63NrYmO97Lk4MR2KmNyY5HRM3HQN/KdBrTH/0XNHwSbtfJQzEtfzP8RvE+ASIiqfDycMCK1wc0Y8uW69zBCQtf4WcEkblqdQPh4uPjxS5BVH4P9UPGj7/V/+zk44mg6BEoSEoXtS4iItLd4w8F4Offr+D73ZnNbnPrgVHNeQgVAFjLZVj/wSA4OVjrXScRGVerC/SWzsbFAeMOLIGVnQ0q8pSQ2VrD2a89Mjb/jqOvr0X7yG44NPvPh2kJAu799CUc//c6RM6bKnbpRESkI0EQsP6DQSgurcbeI7nNahP5+I5m79/KSsDGBUMwOMK7BVUSkbG1uiE3lq6mtAKZ2xJw/os47Bg5Fyfe+QqFyRdx5LXP4T2wJwoS06FVqQEAIS+MRUHiBRSdbX7PDhERmRdbGytsXzYCjwzvZND92tlaYctnwzHpAX+D7peIDI+B3gK59fRHcUoWAMA9rAuKz9X92W9UJC7vOgEAcO3mi05j+uHM0i2i1kpERC1nZyvHls+GY807Aw0yNGZg7/Y4u/kRjBtq2C8JRGQcDPQWyC2kc32Idw8LQNGf4b7DkF7IjT8FAGjfLxhOvu0w8cgKPHpiFTzvCcSARS+i29MPiFo7ERHpRxAEPP9od5zb+gimjAqAXC7ovA9fL0csf70/fv/yIc5oQyQhHENvYRy83ACtFhWKYgCAW3AnnF22BR69A3HjUi5UFVUAgPRv9iL9m/89EXfUlvk4v3YnruxOFK12IiJquU4dnLHpk6H4rLAfvtiajh/3ZuF85nWo1dpGt3d1tsHA3u3x3MRuGHO/L+Ry9vURSQ0DvYVx6+lf3zsPADWl5eg+9UFUF5fhyu4TotZGRESm4+3pgLdf6I23X+iNikoVzlwswh9XSlFZrYbcSgZXZxv06u4G/47OEATde/OJyHwIWq228a/sJKraiips7PKkwfY37rcl2DNxHqqKSg22z7+KztgAawc7o+ybiIiIiJrGHvpWYvuQV8QugYiIiIiMgAPliIiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMN8WaKa1WC1VltdhlNJvc3pazJBARERGJgIGeiIiIiEjCOOSGiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjCGOiJiIiIiCSMgZ6IiIiISMIY6ImIiIiIJIyBnoiIiIhIwhjoiYiIiIgkjIGeiIiIiEjC/h9hHPxzwKy+RwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 956.385x618.722 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.transpiler import generate_preset_pass_manager\n",
    "from qiskit.quantum_info import SparsePauliOp\n",
    "from qiskit_ibm_runtime.fake_provider import FakeManilaV2\n",
    "from qiskit_ibm_runtime import SamplerV2, Batch\n",
    "from qiskit_aer.primitives import EstimatorV2\n",
    "\n",
    "from qiskit_addon_cutting.instructions import Move, CutWire\n",
    "from qiskit_addon_cutting import (\n",
    "    partition_problem,\n",
    "    generate_cutting_experiments,\n",
    "    cut_wires,\n",
    "    expand_observables,\n",
    "    reconstruct_expectation_values,\n",
    ")\n",
    "\n",
    "\n",
    "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.cx(3, 4)\n",
    "qc_0.cx(3, 5)\n",
    "qc_0.cx(3, 6)\n",
    "qc_0.cx(0, 3)\n",
    "qc_0.cx(1, 3)\n",
    "qc_0.cx(2, 3)\n",
    "\n",
    "# Define observable\n",
    "observable = SparsePauliOp([\"ZIIIIII\", \"IIIZIII\", \"IIIIIIZ\"])\n",
    "\n",
    "# Draw circuit\n",
    "qc_0.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d332ed5a-63e9-4862-9498-f86b0147607b",
   "metadata": {},
   "source": [
    "## Cut wires using the high-level `CutWire` instruction\n",
    "\n",
    "Next, make wire cuts using the single-qubit [`CutWire`](/api/qiskit-addon-cutting/instructions-cut-wire) instruction on qubit $q_3$. Once the subexperiments are prepared to be executed, use the [`cut_wires()`](/api/qiskit-addon-cutting/qiskit-addon-cutting#cut_wires) function to transform `CutWire` to [`Move`](/api/qiskit-addon-cutting/instructions-move) instructions on newly allocated qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9bac1915-316b-49d0-a1a1-145047679530",
   "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_1 = QuantumCircuit(7)\n",
    "for i in range(7):\n",
    "    qc_1.rx(np.pi / 4, i)\n",
    "qc_1.cx(0, 3)\n",
    "qc_1.cx(1, 3)\n",
    "qc_1.cx(2, 3)\n",
    "qc_1.append(CutWire(), [3])\n",
    "qc_1.cx(3, 4)\n",
    "qc_1.cx(3, 5)\n",
    "qc_1.cx(3, 6)\n",
    "qc_1.append(CutWire(), [3])\n",
    "qc_1.cx(0, 3)\n",
    "qc_1.cx(1, 3)\n",
    "qc_1.cx(2, 3)\n",
    "\n",
    "qc_1.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcddcde7-9ed3-4718-a17f-1b555c4c2662",
   "metadata": {},
   "source": [
    "<Admonition type=\"info\" title=\"Note about expanding observables\">\n",
    "    When a circuit is expanded through one or more wire cuts, the observable needs to be updated to account for the extra qubits that are introduced. The `qiskit-addon-cutting` package has a convenience function [`expand_observables()`](/api/qiskit-addon-cutting/qiskit-addon-cutting#expand_observables), which takes `PauliList`s and the original and expanded circuits as arguments, and returns a new `PauliList`.\n",
    "\n",
    "    This returned `PauliList` will not contain any information about the original observable's coefficients, but these can be ignored until reconstruction of the final expectation value.\n",
    "</Admonition>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d398b397-0167-4db9-97ae-6ea502dc43e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expanded Observable: ['ZIIIIIIII', 'IIIZIIIII', 'IIIIIIIIZ']\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1290.83x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Transform CutWire instructions to Move instructions\n",
    "qc_2 = cut_wires(qc_1)\n",
    "\n",
    "# Expand the observable to match the new circuit size\n",
    "expanded_observable = expand_observables(observable.paulis, qc_0, qc_2)\n",
    "print(f\"Expanded Observable: {expanded_observable}\")\n",
    "qc_2.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcdcb972-beb7-4126-9720-861359aa6ae7",
   "metadata": {},
   "source": [
    "### Partition the circuit and observable\n",
    "\n",
    "Now the problem can be separated into partitions. This is accomplished using the [`partition_problem()`](/api/qiskit-addon-cutting/qiskit-addon-cutting#partition_problem) function with an optional set of partition labels to specify how to separate the circuit. Qubits sharing a common partition label are grouped together, and any non-local gates spanning more than one partition are cut.\n",
    "\n",
    "If no partition labels are provided, then the partitioning will be automatically determined based on the connectivity of the circuit. Read the next section on [cutting wires manually](#cut-wires-using-the-low-level-move-instruction) for more information on including partition labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5fb034f2-da8a-4f4d-ab9b-c990593e04fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Subobservables to measure: \n",
      "{0: PauliList(['IIIII', 'ZIIII', 'IIIIZ']), 1: PauliList(['ZIII', 'IIII', 'IIII'])}\n",
      "\n",
      "Sampling overhead: 256.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 974.616x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partitioned_problem = partition_problem(\n",
    "    circuit=qc_2,\n",
    "    observables=expanded_observable,\n",
    ")\n",
    "subcircuits = partitioned_problem.subcircuits\n",
    "subobservables = partitioned_problem.subobservables\n",
    "bases = partitioned_problem.bases\n",
    "\n",
    "print(f\"Subobservables to measure: \\n{subobservables}\\n\")\n",
    "print(f\"Sampling overhead: {np.prod([basis.overhead for basis in bases])}\")\n",
    "subcircuits[0].draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d0e86f81-7c7e-4ccf-951c-9cd039135dc9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 723.984x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "subcircuits[1].draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97c6c48c-30e5-4f43-b44c-23384ca0beff",
   "metadata": {},
   "source": [
    "In this partitioning scheme, you have cut two wires, resulting in a sampling overhead of $4^4$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5495f3ad-f4fe-4051-b5fe-67341179a58e",
   "metadata": {},
   "source": [
    "### Generate subexperiments to execute and post-process results\n",
    "\n",
    "To estimate the expectation value of the full-sized circuit, several subexperiments are generated from the decomposed gates' joint quasi-probability distribution and then executed on one (or more) QPUs. The [`generate_cutting_experiments`](/api/qiskit-addon-cutting/qiskit-addon-cutting#generate_cutting_experiments) method does this by ingesting arguments for the `subcircuits` and `subobservables` dictionaries you created above, as well as for the number of samples to take from the distribution.\n",
    "\n",
    "<Admonition type=\"note\" title=\"Note about the number of samples\">\n",
    "    The `num_samples` argument specifies how many samples to draw from the quasi-probability distribution and determines the accuracy of the coefficients used for the reconstruction. Passing infinity (`np.inf`) ensures all coefficients are calculated exactly. Read the API docs on [generating weights](/api/qiskit-addon-cutting/qpd#generate_qpd_weights) and [generating cutting experiments](/api/qiskit-addon-cutting/qiskit-addon-cutting#generate_cutting_experiments) for more information.\n",
    "</Admonition>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "30257a7a-ad41-46d7-b4d6-c4bfa354ab28",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate subexperiments\n",
    "subexperiments, coefficients = generate_cutting_experiments(\n",
    "    circuits=subcircuits, observables=subobservables, num_samples=np.inf\n",
    ")\n",
    "\n",
    "# Set a backend to use and transpile the subexperiments\n",
    "backend = FakeManilaV2()\n",
    "pass_manager = generate_preset_pass_manager(\n",
    "    optimization_level=1, backend=backend\n",
    ")\n",
    "isa_subexperiments = {\n",
    "    label: pass_manager.run(partition_subexpts)\n",
    "    for label, partition_subexpts in subexperiments.items()\n",
    "}\n",
    "\n",
    "# Submit each partition's subexperiments to the Qiskit Runtime Sampler\n",
    "# primitive, in a single batch so that the jobs will run back-to-back.\n",
    "with Batch(backend=backend) as batch:\n",
    "    sampler = SamplerV2(mode=batch)\n",
    "    jobs = {\n",
    "        label: sampler.run(subsystem_subexpts, shots=2**12)\n",
    "        for label, subsystem_subexpts in isa_subexperiments.items()\n",
    "    }\n",
    "    # Retrieve results\n",
    "    results = {label: job.result() for label, job in jobs.items()}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "890ce542-0a74-451e-a3b2-ced3b35d62b3",
   "metadata": {},
   "source": [
    "Lastly, the expectation value of the full circuit can be reconstructed using the [`reconstruct_expectation_values()`](/api/qiskit-addon-cutting/qiskit-addon-cutting#reconstruct_expectation_values) method.\n",
    "\n",
    "\n",
    "The code block below reconstructs the results and compares them with the exact expectation value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "55ac9aef-494a-4834-b277-9fc4028137cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reconstructed expectation value: 1.55984855\n",
      "Exact expectation value: 1.59099026\n",
      "Error in estimation: -0.03114171\n",
      "Relative error in estimation: -0.01957379\n"
     ]
    }
   ],
   "source": [
    "reconstructed_expval_terms = reconstruct_expectation_values(\n",
    "    results,\n",
    "    coefficients,\n",
    "    subobservables,\n",
    ")\n",
    "# Apply the coefficients of the original observable\n",
    "reconstructed_expval = np.dot(reconstructed_expval_terms, observable.coeffs)\n",
    "\n",
    "\n",
    "# Compute the exact expectation value using the `qiskit_aer` package.\n",
    "estimator = EstimatorV2()\n",
    "exact_expval = estimator.run([(qc_0, observable)]).result()[0].data.evs\n",
    "print(\n",
    "    f\"Reconstructed expectation value: {np.real(np.round(reconstructed_expval, 8))}\"\n",
    ")\n",
    "print(f\"Exact expectation value: {np.round(exact_expval, 8)}\")\n",
    "print(\n",
    "    f\"Error in estimation: {np.real(np.round(reconstructed_expval-exact_expval, 8))}\"\n",
    ")\n",
    "print(\n",
    "    f\"Relative error in estimation: {np.real(np.round((reconstructed_expval-exact_expval) / exact_expval, 8))}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a27ea20-4064-4864-8a92-cd6c6cb84fa2",
   "metadata": {},
   "source": [
    "<Admonition type=\"caution\" title=\"Note about observable coefficients\">\n",
    "    To accurately reconstruct the expectation value, the coefficients of the original observable (which are different from the output of `generate_cutting_experiments()`) must be applied to the output of the reconstruction, since this information was lost when the cutting experiments were generated or when the observable was expanded.\n",
    "\n",
    "    Typically these coefficients can be applied through `numpy.dot()` as shown previously.\n",
    "</Admonition>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34609068-25a7-4aae-b786-836984d305d2",
   "metadata": {},
   "source": [
    "## Cut wires using the low-level `Move` instruction\n",
    "\n",
    "One limitation of using the higher-level `CutWire` instruction is that it does not allow for qubit re-use. If this is desired for a cutting experiment, you can instead manually place [`Move`](/api/qiskit-addon-cutting/instructions-move) instructions. However, because the `Move` instruction discards the state of the destination qubit, it is important that this qubit does not share any entanglement with the remainder of the system. Otherwise, the reset operation will cause the state of the circuit to partially collapse after the wire cut.\n",
    "\n",
    "The code block below performs a wire cut on qubit $q_3$ for the same example circuit as previously shown. The difference here is that you can reuse a qubit by reversing the `Move` operation where the second wire cut was made (however, this is not always possible and depends on the circuit being cut)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "15461a2c-85a9-4cb2-a632-b9597ccbc4bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1290.83x702.333 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc_1 = QuantumCircuit(8)\n",
    "for i in [*range(4), *range(5, 8)]:\n",
    "    qc_1.rx(np.pi / 4, i)\n",
    "qc_1.cx(0, 3)\n",
    "qc_1.cx(1, 3)\n",
    "qc_1.cx(2, 3)\n",
    "qc_1.append(Move(), [3, 4])\n",
    "qc_1.cx(4, 5)\n",
    "qc_1.cx(4, 6)\n",
    "qc_1.cx(4, 7)\n",
    "qc_1.append(Move(), [4, 3])\n",
    "qc_1.cx(0, 3)\n",
    "qc_1.cx(1, 3)\n",
    "qc_1.cx(2, 3)\n",
    "\n",
    "# Expand observable\n",
    "observable_expanded = SparsePauliOp([\"ZIIIIIII\", \"IIIIZIII\", \"IIIIIIIZ\"])\n",
    "qc_1.draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b4f8998-4f30-4e93-84fe-957c658df678",
   "metadata": {},
   "source": [
    "The circuit above can now be partitioned and cutting experiments generated. To explicitly specify how the circuit should be partitioned, you can add partition labels to the `partition_problem()` function. Qubits that share a common partition label are grouped together, and any non-local gates spanning more than one partition are cut. The keys of the dictionary output by `partition_problem()` will match those specified in the label string."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2139745a-bdc3-40bd-bd6f-d26d2a5b5b14",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Subobservables to measure: \n",
      "{'A': PauliList(['IIII', 'ZIII', 'IIIZ']), 'B': PauliList(['ZIII', 'IIII', 'IIII'])}\n",
      "\n",
      "Sampling overhead: 256.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1058.43x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "partitioned_problem = partition_problem(\n",
    "    circuit=qc_1,\n",
    "    partition_labels=\"AAAABBBB\",\n",
    "    observables=observable_expanded.paulis,\n",
    ")\n",
    "subcircuits = partitioned_problem.subcircuits\n",
    "subobservables = partitioned_problem.subobservables\n",
    "bases = partitioned_problem.bases\n",
    "\n",
    "print(f\"Subobservables to measure: \\n{subobservables}\\n\")\n",
    "print(f\"Sampling overhead: {np.prod([basis.overhead for basis in bases])}\")\n",
    "subcircuits[\"A\"].draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4aeb3f1f-a55e-49c4-a7bd-837132429ee1",
   "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[\"B\"].draw(\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb356463-966f-409f-af7b-eed6506e410f",
   "metadata": {},
   "source": [
    "Now the cutting experiments can be generated and the expectation value reconstructed in the same way as the previous section.\n",
    "\n",
    "## Next steps\n",
    "\n",
    "<Admonition type=\"tip\" title=\"Recommendations\">\n",
    "    - Read the [Get started with circuit cutting using gate cuts](/guides/qiskit-addons-cutting-gates) guide.\n",
    "    - Read the arXiv paper on [optimal wire cutting](https://arxiv.org/abs/2302.03366) to better understand the equivalence between wire cutting and gate cutting.\n",
    "</Admonition>"
   ]
  }
 ],
 "metadata": {
  "description": "A worked example of wire cutting using the circuit cutting addon to get started with the package",
  "kernelspec": {
   "display_name": "Python 3",
   "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"
  },
  "title": "Get started with wire cuts"
 },
 "nbformat": 4,
 "nbformat_minor": 2
}