QAdder_v02.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Qiskit Libraries\n",
    "\n",
    "from qiskit import *\n",
    "from qiskit_aer import AerSimulator\n",
    "from qiskit.visualization import plot_histogram\n",
    "\n",
    "from qiskit import QuantumCircuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Circuit function for the quantum adder\n",
    "\n",
    "def quantum_adder(a, b):\n",
    "    quantum_bits = QuantumRegister(8)\n",
    "    classical_bits = ClassicalRegister(2)\n",
    "\n",
    "    circuit = QuantumCircuit(quantum_bits, classical_bits)\n",
    "\n",
    "    # Qauntum Adder Circuit\n",
    "    # 4.5.2 Making the Classical Adder a Qauntum Gate,\n",
    "    # from \"Introduction to Classical and Quantum Computing\", Thomas G. Wang (2022), p170\n",
    "\n",
    "    if a==0 and b==1:\n",
    "        circuit.x(2)\n",
    "    elif a==1 and b==0:\n",
    "        circuit.x(0)\n",
    "    elif a==1 and b==1:\n",
    "        circuit.x(2)\n",
    "        circuit.x(0)\n",
    "\n",
    "    circuit.barrier()\n",
    "\n",
    "    circuit.cx(1, 3)\n",
    "    circuit.cx(2, 3)\n",
    "    circuit.cx(3, 4)\n",
    "    circuit.cx(0, 4)\n",
    "    circuit.barrier()\n",
    "    circuit.ccx(1, 2, 5)\n",
    "    circuit.ccx(0, 3, 5)\n",
    "    circuit.barrier()\n",
    "    circuit.x(7)\n",
    "    circuit.x(5)\n",
    "    circuit.x(6)\n",
    "    circuit.ccx(5, 6, 7)\n",
    "    circuit.x(5)\n",
    "    circuit.x(6)\n",
    "\n",
    "    # Add measurements\n",
    "    circuit.measure(4, 0)  # Measure sum qubit\n",
    "    circuit.measure(7, 1)  # Measure carry-out qubit\n",
    "\n",
    "    # Simulate the circuit\n",
    "    simulator = AerSimulator()\n",
    "    result = simulator.run(circuit).result()\n",
    "    counts = result.get_counts()\n",
    "    plot_histogram(counts)\n",
    "\n",
    "    # Output\n",
    "    print(\"Measurement Results:\", counts)\n",
    "\n",
    "    return circuit, counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measurement Results: {'00': 1024}\n"
     ]
    }
   ],
   "source": [
    "# Call quantum adder function\n",
    "circuit, counts = quantum_adder(0 , 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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AwHxohgEAAAAAQYdmGAAAAAAQdGiGAQAAAABBh2YYAAAAABB0uLUSXNK2bVtt2LDB6DAAwBDUQIA8AGA+HBkGAAAAAAQdmmG4JDc3VxMmTFBubq7RoQCA31EDAfIAgPnQDMMlpaWl2rp1q0pLS40OBQD8jhoIkAcAzIdmGAAAAAAQdGiGAQAAAABBh2YYAAAAABB0aIbhkuTkZD3yyCNKTk42OhQA8DtqIEAeADAfmuGz5OTkaOHChbr77rvVvXt3hYeHy2KxaPz48UaHZqi4uDgNGTJEcXFxRocCAH5HDQTIAwDmQzN8lnnz5umOO+7QggULlJWVpfLycqNDCghHjhzRm2++qSNHjhgdCgD4HTUQIA8AmA/N8FkSEhI0dOhQPfTQQ/rggw90zz33GB1SQDhw4IDmzJmjAwcOGB0KAPgdNRAgDwCYT6jRAQSaGTNmnPF4/fr1BkWCQLB3X5Fe/3Cv8g8eV0iIRWkpsbpleLoax0cZHRoA+MXWPYf1xsfZOnj4hMLDrGrdLE63DGupBvUjjA4NAIBaMX0zbLfb9dRTT+mdd95RXl6eEhMTdcMNN+iJJ57Q5MmTtWjRIs2fP1+TJk0yOlQEkO92HdJf523UR+vyzll2/zMbdePVaXrqTz2V0jjGgOgAwPe+zLLpb/M36YtNtnOWTfufDbplWLqe/GNPNYqjKQYA1E2mboY3b96sIUOGyGazKSYmRu3bt1d+fr6effZZ7d27V4cPH5Ykde3a1dhAEVA+zyzQiD98rOLjFdUuL69w6PUP9+qLTTateXmIWjVjIhEA5vLO6hz95r7PdLLcUe3y0hOV+ufbu7Q2y6Y1Lw9VcmK0nyMEAKD2THvNsN1u14gRI2Sz2TR16lQVFBQoKytLNptNs2fP1ooVK5SZmSmLxaLOnTsbHW7Ai46OVu/evRUdbe4PPD/8VKTrp6yusRH+pbwDJRr8u1UqKj7ph8gAGClYaqAkZW79+byN8C/tzC7U8Ekfq9yFdVH3BVMeAAgOpm2GJ0+erLy8PE2aNElz585VbGxs1bJp06apS5cuqqioUPPmzVW/fn0DI60bmjZtqvnz56tp06ZGh+JTf391iwrdaG5/zDumV5ft8WFEAAJBsNRASXr8n5tdaoRPy9pxSO9/luvDiBAogikPAAQHUzbDO3bs0NKlS5WQkKBZs2ZVu0737t0lSV26dKn1eKeb7l69eikiIkIWi6XW+ww0lZWVKi4uVmVlpdGh+ExR8UktXv6D29u9sHSHnE6nDyICECiCoQZK0k8Fxfrgv/vc3u6FpTt8EA0CTbDkAYDgYcpmOCMjQw6HQ2PHjlW9evWqXScq6tRswN5ohn/44Qe9/fbbSkpKUs+ePWu9v0C0Z88eDRw4UHv2mPco6Kff5Kuk9MKnR59tZ3ahducU+iAiAIEiGGqgJC3/709yONz/cu+zzAIVHuOSEbMLljwAEDxMOYHWmjVrJEkDBgyocZ28vFOzBHujGe7Xr58KCgokSQ8//LDWrVtX631KUo8ePWSznTuLpzeMHj3arfUPHjwoSVq5cqU2bdrk0jYjR450Oy4jlYRfItW7zqNtLx8wWBEV5848DZhFQYM/S9Y4FdgKlJqaanQ4XuFOHfSkBkp1rw4WRfaTon/l0bZtOlyiUMdR7wYUQII9B6Tg+CwAoO5JSkrSxo0bPdrWlM1wbu6pa5eaNWtW7fKKioqqhtUbzbDV6psD7DabTfv37/fJvktKStxav7S0tOq3q9v6KnafaZAqVX8iwQXZD+RLJ+rY6wXcEVspWSVHZWXdy+0auFMHPamBUh2sgwmHJA/nRjpQsE+qKPJuPIEkyHNACpLPAgCCiimb4dMF+nTRPtvSpUtlt9sVGxurtLQ0f4bmlqSkJJ/tOybGvfvjnn5Po6KiXN42JSXF7biMVB5yUgclyemU3Lju2+I8qaT4MFlVt14v4I6CkBA5JFlDQpRcx3K7Ju7UQU9qoFT36uCJ0FIdktyug1ZHkZIa15dFsRdeuY4K9hyQguOzAIC6pzY9kymb4aSkJB05ckRZWVnq06fPGcsKCgp07733SpI6d+4c0JNdeXq43xWZmZlurb9z505lZGRoyJAhatu2rUvbzJs3z4PIjHXFuOX68tsDbm1z542dtODBvT6KCAgMqYMytP/gcSUnJStvqzkuCXCnDnpSA6W6VwcdDqfaXPuWfvjJvSO8D9xzpR6+508+iiowBHsOSMHzWQBA8DDlBFqDBg2SJM2ePVu7d++uej4zM1MDBgyQ3W6XJHXt2tWI8Oqk9PR0rVq1Sunp6UaH4lN/uLm9W+tbLNI9Y9r5KBoAgSJYaqDVatGkm9yraeFhVt05qo2PIkIgCZY8ABA8TNkMT5s2TfHx8dq3b586dOigTp06qVWrVurVq5datGihgQMHSqr+euF169YpISGh6ufpp5+WJC1ZsuSM5701SVZdERoaqoYNGyo01JQnE1S58eo03XWjG0d9pl2qLm3ifRgRgEAQLDVQkib9pr2uH1j9nBtns1ikVx/rp5TG7p1ui7opmPIAQHAwZTOcmpqqtWvXatiwYYqMjFROTo4aNWqkBQsWaMWKFVVHi6trhsvLy3Xo0KGqn9PXHZeVlZ3xfHl5uV9fk9Hy8vI0derUqlm4zcpiseiFv12mqbd1PO96YaFWvTjjMk0e28FPkQEwUrDUQEkKCbFq6ZwBGn9dq/OuFx0ZqjfmDNRNQ1r6KTIYLZjyAEBwMGUzLEnt2rXT8uXLdezYMR07dkzffPONJk6cqJKSEuXk5Mhqtapjx3Mbnv79+8vpdF7wp3///v5/UQYqLi7W2rVrVVxcbHQoPme1WjT3L731w4obde/4TkpKiKpaFhJi0ROTe2jfJzfp7l9zejQQLIKpBkpSeFiI/vVoP215e6TuGdNO8Q0iqpaFhlg0b1pv7V99k0ZfHbiTUML7gi0PAJifaZvhmmzbtk1Op1OtWrVSdLSH94+oxltvvaW33npL27dvP+OxLyfBgm+1vLi+nvpzLxWsuVlNEk81xEnxUbr/ji5qHB91ga0BoO7r2KqRnv/bZbJ/cUtVHWwcH6Upt3RUg/oRF9gaAIDAFnQXfWzZskWSd+4v/Es33nhjtY/HjRunV155xatjwf8CedZxAPAH6iAAwGxohr3E6XR6dX8AAAAAAN8JutOkfdUMm11iYqKmTJmixMREo0MBAL+jBgLkAQDzCbojw2vWrDE6hDopPj5eY8eONToMADAENRAgDwCYT9AdGYZnioqKtHr1ahUVFRkdCgD4HTUQIA8AmA/NMFySn5+v6dOnKz8/3+hQAMDvqIEAeQDAfGiGAQAAAABBh2YYAAAAABB0aIYBAAAAAEGHZhguiYiIUJs2bRQREWF0KADgd9RAgDwAYD5Bd2sleCYtLU2LFy82OgwAMAQ1ECAPAJgPR4YBAAAAAEGHZhgu2bVrl/r27atdu3YZHQoA+B01ECAPAJgPzTBc4nQ6VV5eLqfTaXQoAOB31ECAPABgPjTDAAAAAICgQzMMAAAAAAg6NMMAAAAAgKDDrZXgkubNmysjI0MpKSlGhwIAfkcNBMgDAOZDMwyXREZGqmXLlkaHAQCGoAYC5AEA8+E0abikoKBAjz32mAoKCowOBQD8jhoIkAcAzIdmGC4pLCzUsmXLVFhYaHQoAOB31ECAPABgPjTDAAAAAICgQzMMAAAAAAg6NMMAAAAAgKBDMwyXWK1WdevWTVYrfzIAgg81ECAPAJgP1QwucTgc+vbbb+VwOIwOBQD8jhoIkAcAzIdmGAAAAAAQdGiGAQAAAABBh2YYAAAAABB0aIbhktjYWA0ePFixsbFGhwIAfkcNBMgDAOYTanQAqBtSUlI0c+ZMo8MAAENQAwHyAID5cGQYLikrK9O+fftUVlZmdCgA4HfUQIA8AGA+NMNwSXZ2tkaNGqXs7GyjQwEAv6MGAuQBAPOhGQYAAAAABB2aYQAAAABA0KEZBgAAAAAEHZphAAAAAEDQ4dZKcEnbtm21YcMGo8MAAENQAwHyAID5cGQYAAAAABB0aIbhktzcXE2YMEG5ublGhwIAfkcNBMgDAOZDMwyXlJaWauvWrSotLTU6FADwO2ogQB4AMB+aYQAAAABA0KEZBgAAAAAEHZphAAAAAEDQoRmGS5KTk/XII48oOTnZ6FAAwO+ogQB5AMB8aIarkZOTo4ULF+ruu+9W9+7dFR4eLovFovHjxxsdmmHi4uI0ZMgQxcXFGR0KAPgdNRAgDwCYD81wNebNm6c77rhDCxYsUFZWlsrLy40OyXBHjhzRm2++qSNHjhgdCgD4HTUQIA8AmA/NcDUSEhI0dOhQPfTQQ/rggw90zz33GB2S4Q4cOKA5c+bowIEDRocCAH5HDQTIAwDmE2p0AIFoxowZZzxev369QZEAxis+Xq69+4pUeqJS8Q0ilN60viwWi9FhAfCjnP3HdLK8UpLkcDgNjgYAAO8IiiPDdrtd06ZNU3p6uiIjI3XxxRdrypQpKikp0e233y6LxaLnnnvO6DCBgLJl92H97tF1Shrwurre+J763PqBWo94Sx1GvqP5r29TUfFJo0ME4EMnyir0yvu71evm95U25A39fKRMklRgL9Ut93+urzZzdBAAULeZ/sjw5s2bNWTIENlsNsXExKh9+/bKz8/Xs88+q7179+rw4cOSpK5duxobKBBA5r++TVNmr5ezmgNAO348qslPrte8f2/TyheuUevmTKQCmI3NflzDJ32iTdvt1S7/z4q9+s+Kvfrr7Z31xOQenC0CAKiTTH1k2G63a8SIEbLZbJo6daoKCgqUlZUlm82m2bNna8WKFcrMzJTFYlHnzp2NDjegRUdHq3fv3oqOjjY6FPjYS2/t1OQnq2+Ef+nHvGMaeMeH2n+gxD+BAQYKphpYeOykrr7roxob4V96cuH3euC5TX6ICoEgmPIAQHAwdTM8efJk5eXladKkSZo7d65iY2Orlk2bNk1dunRRRUWFmjdvrvr16xsYaeBr2rSp5s+fr6ZNmxodCnzo58Ol+sOsr11ef//B47r36Q0+jAgIDMFUA2ct/E5b9rg+W/Dj//xOW3Yf9mFECBTBlAcAgoNpm+EdO3Zo6dKlSkhI0KxZs6pdp3v37pKkLl261Hq8t956S6NGjVKzZs0UHR2ttm3b6m9/+5uKi4trve9AUFlZqeLiYlVWVhodCnxo0Xu7dbLc4dY2b32SowOHSn0UERAYgqUGniir0MJ3d7u93T/e3OmDaBBogiUPAAQP0zbDGRkZcjgcGjt2rOrVq1ftOlFRUZK80wzPnTtXISEheuKJJ7Ry5Ur97ne/04svvqjBgwfL4XCvuQhEe/bs0cCBA7Vnzx6jQ4EPefIhuLzCocUf/OCDaIDAESw18IP/7pP9yAm3t3vtgx9UdpIGyeyCJQ8ABA/TTqC1Zs0aSdKAAQNqXCcvL0+Sd5rhDz74QImJiVWPr7zySiUmJmrs2LH68ssv1a9fP7f32aNHD9lstlrHVp3Ro0e7tf7BgwclSStXrtSmTa5dHzZy5Ei34wpUBQ3+LFnjVGArUGpqqtHh+IRTUn7DByVLiNvbPvzEc5o3Y4X3g0LAMGMOuFMHPamBUt2rg8ciL5eir3J7u+Lj5WresqNCnMd8EFVgCPYckPgsACAwJSUlaePGjR5ta9pmODc3V5LUrFmzapdXVFRo3bp1krzTDP+yET6tR48ekqT9+/d7tE+bzebxthdSUuLepEelpaVVv13d1lexGyK2UrJKjspKc72uM1ikhp7NCFtSclwl+WZ9XyDJlDngTh30pAZKdbAOJh6TPJwbyXbggFTu+rXGdU6Q54DEZwEA5mPaZvh0kT5duM+2dOlS2e12xcbGKi0tzScxfPbZZ5Kkdu3aebR9UlKSN8M5Q0xMjFvrn34/o6KiXN42JSXF7bgCVUFIiBySrCEhSjbR6zpbgbNYDov7k8nFRjlV38TvC8yZA+7UQU9qoFT36mBJuEVHPdnQWanki+Jk9bSTrgOCPQckPgsACEy16ZlM2wwnJSXpyJEjysrKUp8+fc5YVlBQoHvvvVeS1LlzZ5/cH3H//v164IEHNHjwYI/vYezp4X5XZGZmurX+zp07lZGRoSFDhqht27YubTNv3jwPIgtMqYMytP/gcSUnJStva57R4fjMtKc3aM4rW9zebtOnz6tVM+43bGZmzAF36qAnNVCqe3XwaFGZmgzKUOkJ967/HTMkXUueyvZRVIEh2HNA4rMAAPMx7QRagwYNkiTNnj1bu3f//6RAmZmZGjBggOz2U/dP9LRRPZ/i4mJdd911Cg8P16JFi7y+fyOkp6dr1apVSk9PNzoU+NBdN7aVu98NXX1ZCo0wTC9YamCD+hEaO7Sl29vd82vPzoBC3RIseQAgeJi2GZ42bZri4+O1b98+dejQQZ06dVKrVq3Uq1cvtWjRQgMHDpRU/fXC69atU0JCQtXP008/LUlasmTJGc+fvub4l0pLSzVixAhlZ2fr448/VnJysm9fqJ+EhoaqYcOGCg017ckEkNTy4vr6860dXV4/JipUT07p4cOIgMAQTDXwgbu6qXF8lMvr33h1mq7o7rvLehA4gikPAAQH0zbDqampWrt2rYYNG6bIyEjl5OSoUaNGWrBggVasWFF1tLi6Zri8vFyHDh2q+jl93XFZWdkZz5eXl5+z3ejRo7Vx40atXLlS7du39/0L9ZO8vDxNnTq1agZumNdTf+6liaPbXHC9+vXCtOzZq9StXYIfogKMFUw1sGlyPa36xzVKTrzw9b/X9m+q1x7v55PLjRB4gikPAAQH0zbD0qmJq5YvX65jx47p2LFj+uabbzRx4kSVlJQoJydHVqtVHTueexSsf//+cjqdF/zp379/1Tan72n86aef6v3331evXr38+Ep9r7i4WGvXrlVxcbHRocDHrFaL/vFAXy15aoAu79b4nOXRkaGaOLqNMl+/TgN7NzEgQsD/gq0GdmkTr8zXr9XU2zqqYf3wc5Z3bt1ICx7sq3f+51eKjOAoYbAItjwAYH5B+S/Ytm3b5HQ61bp1a0VHe2fmy9///vd688039de//lXR0dFav3591bKWLVtWe+slIFBZLBaNGdxCYwa30Jbdh3XlhBU6UnRSjeqH68eVYxQXe+6HYwDmktI4RnP/0luPTuquT77er3EzvtDRYyeV2DBCm9+8nqPBAIA6z9RHhmuyZcup2XK9cX/h01auXClJevLJJ9WnT58zflasWOG1cQB/69S6kaIjT31vFhUZSiMMBJmoyFBdO6CZYqJO1YHwsBAaYQCAKQTlkWFfNMM5OTle2xcAAAAAwLc4MgyXJCYmasqUKZzuDSAoUQMB8gCA+QTlkeE1a9YYHUKdEx8fr7FjxxodBgAYghoIkAcAzCcojwzDfUVFRVq9erWKioqMDgUA/I4aCJAHAMyHZhguyc/P1/Tp05Wfn290KADgd9RAgDwAYD40wwAAAACAoEMzDAAAAAAIOjTDAAAAAICgQzMMl0RERKhNmzaKiIgwOhQA8DtqIEAeADCfoLy1EtyXlpamxYsXGx0GABiCGgiQBwDMhyPDAAAAAICgQzMMl+zatUt9+/bVrl27jA4FAPyOGgiQBwDMh2YYLnE6nSovL5fT6TQ6FADwO2ogQB4AMB+aYQAAAABA0KEZBgAAAAAEHZphAAAAAEDQ4dZKcEnz5s2VkZGhlJQUo0MBAL+jBgLkAQDzoRmGSyIjI9WyZUujwwAAQ1ADAfIAgPlwmjRcUlBQoMcee0wFBQVGhwIAfkcNBMgDAOZDMwyXFBYWatmyZSosLDQ6FADwO2ogQB4AMB+aYQAAAABA0KEZBgAAAAAEHZphAAAAAEDQoRmGS6xWq7p16yarlT8ZAMGHGgiQBwDMh2oGlzgcDn377bdyOBxGhwIAfkcNBMgDAOZDMwwAAAAACDo0wwAAAACAoEMzDAAAAAAIOjTDcElsbKwGDx6s2NhYo0MBAL+jBgLkAQDzCTU6ANQNKSkpmjlzptFhAIAhqIEAeQDAfDgyDJeUlZVp3759KisrMzoUAPA7aiBAHgAwH5phuCQ7O1ujRo1Sdna20aEAgN9RAwHyAID50AwDAAAAAIIOzTAAAAAAIOjQDAMAAAAAgg7NMAAAAAAg6HBrJbikbdu22rBhg9FhAIAhqIEAeQDAfDgyDAAAAAAIOjTDcElubq4mTJig3Nxco0MBAL+jBgLkAQDz4TRpuKS0tFRbt25VaWmp0aH4hcPh1O7cQm3abteOH4/q6LGTkqSi4pN6+5NsdW+foGZN6slisRgcqe/8fLhUm7Yf0rc7D6mw+NTrLyw+qQVv7lSPDgnqmN5QEeEhBkcJ+Eew1UCgOuQBALOhGQZ+4btdh/TiGzuVsXKviorLz1l+7HiFRk9dI0lKSojS+Ota6a7RbdU8JdbfofrEkaIyvfr+Hi14a6d2Zhees7z4eIXufnSdJCks1KqhV6Tq9ze11696N5HVat4vBgAAAGA+NMOApG0/HNHvn/hK/91oc3kbm71UTy78XrMXfa/RV6XpmfsuVXJitA+j9J3jpRV66IUsPb90u0pPVLq0TXmFQ+9/9pPe/+wntW4Wp3nTemvIFRf7OFIAAADAO7hmGEGtosKhWS9/p0vGvOdWI/xLTqf05sfZan/921r8wR45nU4vR+lb6749oK6/fldzX93iciN8tt25hRr6+491+0NrdbSozMsRAgAAAN5HMwyXJCcn65FHHlFycrLRoXjN8dIKjfjDJ5r+7EadLHfUen9Hj53UbX/7QpOe+FoOR91oiBe9u1v9frtCe3KLvLa/XmOX6aeCYq/sDwgUZqyBgLvIAwBmQzMMl8TFxWnIkCGKi4szOhSvOFFWoeGTPtZH6/K8vu8Xlu7Q3Y+uC/gjxC+/vUu3P7TW6437ntwi9fvtCuXZSry6X8BIZquBgCfIAwBmQzN8lpycHC1cuFB33323unfvrvDwcFksFo0fP97o0Ax15MgRvfnmmzpy5IjRoXjFHQ9/qc8yC3y2/3++vUuzXv7OZ/uvrU++3q+JM7/02f5z84s1+Hcf6URZhc/GAPzJbDUQ8AR5AMBsaIbPMm/ePN1xxx1asGCBsrKyVF5+7ozCwejAgQOaM2eODhw4YHQotfb2J9n6z4q9bm2TmXGt9n1ykzIzrnV5m4df/Fbf7z7sbng+V3jspCY8uFbuHLj25PVv23tUD72Q5UGEQOAxUw0EPEUeADAbmuGzJCQkaOjQoXrooYf0wQcf6J577jE6JHiR/cgJ3fP4V25vl5QQrdTGMUpKcH226PIKh8bP+ELlXrge2Zumzv1GeQfcO4XZk9cvSXNf3ar13x10axsAAADAH7i10llmzJhxxuP169cbFAl8Yf7r23Xw8Am/jfftzkN6d02Ofn1NC7+NeT579xVp0Xu7/Taew+HUwy9m6aN/DPbbmN708+FSLXpvt5Z9/pOOFJ1UVESIurWN1+/GtFP39glGhwfAx5xOp/670aYFb+7UwcOlkqSfj5zQ80u269bh6apfL9zgCAEAtWH6I8N2u13Tpk1Tenq6IiMjdfHFF2vKlCkqKSnR7bffLovFoueee87oMOEH5eUOvfT2Tr+P+8LSHX4fsyYL3tzp1unR3rDqq/364SfvzFbtLxUVDv1l7jdKvWqJ/jpvo77afFA7fjyqrB2HtPDd3epx0/vqe9sHys0/ZnSoAHzku12H1OmGdzTg9g+15KMfVV5xqnieLHdo0hNfK2VQhp5a9H3AT5YIAKiZqZvhzZs3q1OnTpozZ45sNpvat2+v8vJyPfvssxozZox27DjVpHTt2tXYQOuA6Oho9e7dW9HR7p0mG0je/yxXNnup38f970abtu81frKRspOVfj0q/Ev/eCNwvhC4kMpKh8be/7n+/trW895y66vNB9Xn1uXKzqMhDgZmqIFwXebWn3XF+BXatvdojesUH6/QffMy9Ze/b/BfYAYjDwCYjWmbYbvdrhEjRshms2nq1KkqKChQVlaWbDabZs+erRUrVigzM1MWi0WdO3c2OtyA17RpU82fP19NmzY1OhSPfbJ+v2Fjr16fb9jYp23eeUiHjpYZMvbqb4x//a566l9b9MaqbJfWLfj5uK6d/Emdua80PGeGGgjXHCs5qRF/+ETHSlybQPPp17bqPyt+8HFUgYE8AGA2pm2GJ0+erLy8PE2aNElz585VbGxs1bJp06apS5cuqqioUPPmzVW/fn0DI60bKisrVVxcrMrKSqND8dim7YcMHNtu2NiBEMO2vUfqxG2WTpZX6pn/bHNrm60/HNHHXxn3RQv8www1EK75z4q9OnDIvbOI5r66JShOlyYPAJiNKZvhHTt2aOnSpUpISNCsWbOqXad79+6SpC5dutR6vLVr12rQoEFKTk5WRESEUlNTzzgN2wz27NmjgQMHas+ePUaH4pGT5ZXasse42xxtDIRmeIdxXwZUVDj1/W7jTxW/kHdW57j9IViSnl+y3QfRIJDU9RoI1zidTo/medi887DWf2/+mfPJAwBmY8rZpDMyMuRwODR27FjVq1ev2nWioqIkeacZPnLkiDp16qS77rpLF110kfLy8jRr1iz16dNHW7duVWpqqkf77dGjh2w2W63jq87o0aPdWv/gwVP/yK9cuVKbNm1yaZuRI0e6HZevVFpidLLhtBqXZ2Zce97bBiUlRFX93vfJTTWuZ7MfV8/fLDvn+Z179nv8d+At9npjpfDW1S7z1uuXan4Phlw7RlHlxlyz7Kqj0cOkyF5ub7fi891KTZ3gg4gCR0GDP0vWOBXYCgz/W/YWd+qgJzVQCqw6WFtm/Bs4m8MSoYKG0z3advCoyYo9sc7LEflWsH0WAGBOSUlJ2rhxo0fbmrIZXrNmjSRpwIABNa6Tl5cnyTvN8LXXXqtrr732jOd69uypNm3a6O2339aUKVM82q/NZtP+/b45/bKkxL37zJaWllb9dnVbX8XukdCGUsOaF5++j+4FdxNidWm9szmcVuPfj+YVUg13AfH165ekw4eLpKIA+puoTmqFFOn+Zk5LuPH/f30ttlKySo7KStO8VnfqoCc1UAqwOlhbJvwbOEdog/P+W3E+RcfKVHSwbr0vQfdZAADOYspmODc3V5LUrFmzapdXVFRo3bpT3956oxmuTnx8vCQpNNTztzgpKclb4ZwjJsa9hub0P3pRUVEub5uSkuJ2XL5SaYnR+Y6x2+zHz7t9UkKUQkOsqqh0nHdG6pr2Y7U4lGzw+2GPCFVN02d56/Wfb1+NGtVXVGzg/E1U52hUiNz7aHiKxXlSTQLo790XCkJC5JBkDQkx/G/ZW9ypg57UQCmw6mBtmfFv4GwOhavAw23rx0YoNqxuvS/B9lkAgDnVpmcyZTN8ulif/gbzbEuXLpXdbldsbKzS0tK8Nm5lZaUcDodyc3N1//33KykpSb/+9a893p+nh/tdkZmZ6db6O3fuVEZGhoYMGaK2bdu6tM28efM8iMw3Kiociu3zmk6UVT/pR3Wn9f7Svk9uUmrjGNnspbr4qiVuj9+x7cX67q08t7fzpomPfKl/vr2r2mW+fv2S9PGKN9S9fYJH2/rLu5/m6IY/fer2djdc3U5vPW3s/19fSx2Uof0Hjys5KVl5W83xWt2pg57UQCmw6mBtmfFvoDo9f/O+Nm5zf56Hz5Y9r0sCvMadLdg+CwDA2Uw5gdbpbweysrLOWVZQUKB7771XktS5c2dZLBavjXvllVcqPDxcrVq10ubNm7VmzRolJiZ6bf9GSk9P16pVq5Senm50KB4JDbWqc6tGho3fvX28YWP/fwzGfUgLC7WqY7qH5x760YgrmyrlIvfvn3nPmHY+iAaBpK7XQLjOk3zu3SmxzjXCniAPAJiNKZvhQYMGSZJmz56t3bv/f8KezMxMDRgwQHb7qW98u3bt6tVxFy5cqPXr1ysjI0P169fX1VdfrZ9++smrYxglNDRUDRs2rNVp30YzsiENhCOiRr7+Tq0aKiI8xLDxXRUaatVfxnVya5ueHRM0oFeyjyJCoDBDDYRrxlzTQk2T3Tt9eNpvO/somsBCHgAwG1M2w9OmTVN8fLz27dunDh06qFOnTmrVqpV69eqlFi1aaODAgZKqv1543bp1SkhIqPp5+umnJUlLliw54/nT1xz/Ups2bdS7d2/ddNNN+vTTT3Xs2DE99dRTvn2xfpKXl6epU6dWTTxWFw3ua9zsp1f3Mf6aqS6t49U4PsqQsY1879015ZYOuuOG6mfdPltaSqzemzfIq2eYIDCZoQbCNdFRofrw+WsU3yDCpfVn/v4S3TCouW+DChDkAQCzMWUznJqaqrVr12rYsGGKjIxUTk6OGjVqpAULFmjFihVVR4ura4bLy8t16NChqp/T1x2XlZWd8Xx5efl5Y2jQoIHS09P1ww8/eP8FGqC4uFhr165VcXGx0aF4bFi/i93+tt8brr4sRa2axfl93LOFhVl156g2fh/XarVo4mj/j+spi8Wilx66XI9OukT164XVuN7QK1L19b9HqMlF/v+bgv+ZoQbCdR3SG+rrxSPUt1vjGtdJbBipBQ/21QN3dfNjZMYiDwCYjWnPc2nXrp2WL19+zvPFxcXKycmR1WpVx44dz1nev39/OZ3OWo9/8OBB7dq1S7179671vuAdISFW3TW6rf423/V7hHpDIF1POnF0Gz3x8ndyOGr/N+6q4f0uVrMmsX4bzxssFotmTOymP97SUa9/uFfvf5ar1evzdbLcoXpRofr2zZFKb1rf6DAB+FCrZnH68tXh2rzzkF56a6cWvrtbJ8sdigwP0cJHrtCoq5rXics/AAA1M+WR4fPZtm2bnE6nWrVqpeho9yfKqc4tt9yihx9+WO+9954+//xz/fOf/1T//v0VGhqqP/3pT14ZA97x+5vae3yfXE9c1vUiDe93sd/Gu5CLk+pp0k3+a85DQy165J5L/Daet9WLDtPE0W214vlrlNjw1A2I42LDaYSBINK1bbxemNG3qgbEN4jQzcNa0ggDgAkEXTO8ZcsWSd69v/Cll16qDz/8UL/97W81ZMgQzZkzR1dccYU2b97MjIsBJi42XC892NcvY0VGhOhfM/spJCSw0uyJyT3U8mL/HKmdcWdXdW1r/EzaAAAAwNlMe5p0TXzRDE+aNEmTJk3y2v4CUWJioqZMmWKKW0UNueJi3XVjWy14c6fL29jsx8/47YrZf+yp1s2Nv1b4bDHRYXrl0X4acMeHqqhw7XRpT15/z44Jmn5HV09CBAKOmWog4CnyAIDZ0AzDJfHx8Ro7dqzRYXjN/L/2Uf7B4/rgv67d+qrnb5a5tf+/jOukP9zc3pPQ/OLyS5L07yf66+a/fu7S9cPuvv62aXFa8dzVCgsLrKPigKfMVgMBT5AHAMwm6D6prlmzRk6nU8OGDTM6lDqlqKhIq1evVlFRkdGheEVYmFVvPT1Qv74mzev7nn5HFz31554Bf7udMYNbaOlTAxQW6t0y0LVtI32+aJgSGxlzGyfAF8xWAwFPkAcAzCbommF4Jj8/X9OnT1d+fr7RoXhNeFiIljw1QC/OuEz1omu+hY6rkhOjtezZq/T45B4B3wifNvrqNG1ccp26eeG6XotF+vNtHfXVayMMu58x4CtmrIGAu8gDAGZDM4ygZrFYdPev22nL2yN13YCm8qSHDf+/+/due/cGjejf1PtB+ljn1o30zX+u1eN/6K5GcREe7aNnxwR9+epw/f0vvRUVGXRXXwAAAKAO4lMrIKl5Sqzee+YqZecd00tv79S/l+9V3oGS827TNi1Ov72utSaMbK2E/7vlRl0VFmbV9Du76k+3dtQbq7K14K2d2rD1Z1VW1nw9cYPYcF0/sJnuGdNOPTsymQoAAADqFpph4BfSUmM1a0pPzZrSUzb7cW3abteOHwt1/ESFrFapXlSYOrdupEvaxatBfc+OogayqMhQjbuulcZd10qlJyr0/e7D+nbnIR0uLFN5hUORESFKS4lVjw4JSkuJrTOngwMAAABnoxmGSyIiItSmTRtFRJivAaxJUkK0hvVrqmH9jI7EGFGRoerd+SL17nyR0aEAhgvGGgicjTwAYDY0w3BJWlqaFi9ebHQYAGAIaiBAHgAwHybQAgAAAAAEHZphuGTXrl3q27evdu3aZXQoAOB31ECAPABgPjTDcInT6VR5ebmczppnFwYAs6IGAuQBAPOhGQYAAAAABB2aYQAAAABA0KEZBgAAAAAEHW6tBJc0b95cGRkZSklJMToUAPA7aiBAHgAwH5phuCQyMlItW7Y0OgwAMAQ1ECAPAJgPp0nDJQUFBXrsscdUUFBgdCgA4HfUQIA8AGA+NMNwSWFhoZYtW6bCwkKjQwEAv6MGAuQBAPOhGQYAAAAABB2aYQAAAABA0KEZBgAAAAAEHZphuKRRo0YaN26cGjVqZHQoAOB31ECAPABgPjTDcInValVYWJisVv5kAAQfaiBAHgAwH6oZXGK32/Xyyy/LbrcbHQoA+B01ECAPAJgPzTAAAAAAIOjQDAMAAAAAgg7NMAAAAAAg6NAMwyWxsbEaPHiwYmNjjQ4FAPyOGgiQBwDMJ9ToAFA3pKSkaObMmUaHAQCGoAYC5AEA8+HIMFxSVlamffv2qayszOhQAMDvqIEAeQDAfGiG4ZLs7GyNGjVK2dnZRocCAH5HDQTIAwDmw2nSAAAAgEk4nU5VVlYaHYZbQkJCZLFYjA4DQYhmGAAAADCJyspKvf3220aH4ZZRo0YpNJS2BP7HadIAAAAAgKBDMwwAAAAACDqcjwCXtG3bVhs2bDA6DAAwBDUQIA8AmA9HhgEAAAAAQYdmGC7Jzc3VhAkTlJuba3QogF8dL63QruyjKq9wSJIqHU6DI/Ivh8Op3PxjVa+/otKhykqHwVH5HzUQIA8AmA+nScMlpaWl2rp1q0pLS40OBfCpigqHln/xk97/7Cdt2m7X9h+PqrLy/xtgm71UKYMy1L1dgq7skaRx17ZSQsNIAyP2vh0/HtWry/bomy0/K2uHXUXF5VXLDhw6ofp9Fqtr20bq2SFRtwxvqR4dEg2M1j+ogQB5AMB8aIYBQFLx8XLN+/dWLXhzl/IOlJx33fyDx5V/8Cd98N+f9Lf5m3Tj1c113287q2OrRn6K1jeW//cnPf3aVn2WWXDe9Y6fqNBXmw/qq80H9cx/tqlHhwRNGdtBNw9tKauV+0QCAIC6gdOkAQS9Nd/kq9MN7+iB57Iu2Aifrexkpf69fK8uGfO+Hl3wrcrL694pxD8fLtWv/7JGI/7wyQUb4eps3GbXrdP/q6smrlTO/mM+iBAAAMD7aIYBBC2Hw6m/zP1Gv7pzpXLyi2u1r/IKhx58PkuX3rJM+91sqI302YZ8tR/5jt78OLvW+1qzoUAdb3hHb6z60QuRAQAA+BbNMFySnJysRx55RMnJyUaHAniFw+HUbx/4Qn9/batX95u145AuH7e8ThwhXbl2n4bc87HsR054bZ8lpRW6adpnWvTubq/tMxBQAwHyAID50AyfJScnRwsXLtTdd9+t7t27Kzw8XBaLRePHjzc6NEPFxcVpyJAhiouLMzoUwCsmP/m1XvvgB5/sOye/WFfd9ZF+Phy4k8x8mWXTDX/+VGUnK72+b6dTuuPhtXr7k9ofbQ4U1ECAPIDnDh48KLvdbnQYwDmYQOss8+bN0zPPPGN0GAHnyJEjWr16tQYNGqSGDRsaHQ5QK+9/lqvnl+xwa5vMjGuVlBAtm/24ev5m2QXX/+GnIk2a9bWWzhnoaZg+c6zkpMbe/7lOlLneCLv7+p1O6faHv9SlnS9SSuOY2oQbEKiBAHkQbPLy8rR9+3b9+OOPysnJUVFRkSorKxUWFqbExES1aNFCLVq0UKdOnVS/fv0a93Pw4EHNnDlTVqtVDz74oBISEvz4KoDzoxk+S0JCgoYOHaqePXuqR48eWrlypV544QWjwzLcgQMHNGfOHHXq1Il/AFGnHS4s092PrnN7u6SEaKW62dS9sSpbN16VrdFXp7k9ni/d+3Smfipw77pmT15/4bGTuvORL7Xi+atlsdTtWaapgQB5EAwqKir0zTff6OOPP9auXbtqXM9ut2vHjlNfKoeFhenSSy/V1VdfrVatWp2x3ulG+PRR4YULF+q+++7z3QsA3EQzfJYZM2ac8Xj9+vUGRQLAFx56IUs2u/9OX54062uN6N9UEeEhfhvzfDZtt2vBmzv9Nt7KL/P0/me5un5gc7+NCQBw3w8//KAXX3xR+/fvP2eZxWJRgwYNFBISorKyMh079v/zYpSXl2vt2rVau3atLrvsMo0fP17169c/pxFu0qSJJk6c6LfXA7jC9M2w3W7XU089pXfeeUd5eXlKTEzUDTfcoCeeeEKTJ0/WokWLNH/+fE2aNMnoUAH4WFHxSb3y/h6/jnngUKne+iRbY4el+3XcmjyXsd2AMXfQDANAgHI4HFq6dKmWLVsmp9NZ9Xxqaqr69++v1q1bq1mzZoqIiKhadvToUWVnZ2vLli3673//q5KSU2cbffXVV9q2bZvGjBmjd95554xG+IEHHuCMAgQcUzfDmzdv1pAhQ2Sz2RQTE6P27dsrPz9fzz77rPbu3avDhw9Lkrp27WpsoAD84t/Lf1Dx8XK/j/vC0h0B0QwfOnpCSz7y/22PPv0mXzuzj6ptWgO/jw0AqFlFRYXmz5+vb775puq5Fi1aaOzYsWrfvn2Nl7g0aNBA3bp1U7du3XTTTTfpiy++UEZGhkpKSlRYWKiXXnqpal0aYQQy084mbbfbNWLECNlsNk2dOlUFBQXKysqSzWbT7NmztWLFCmVmZspisahz585GhxvwoqOj1bt3b0VHRxsdCuAxIxpBSfpq80Hts9XuPsbe8MF/f3Jr0ixvemNV3Z5ZmhoIkAdm43A49Pzzz1c1wiEhIRozZoxmzpypDh06uDzXQ3h4uAYNGqS5c+eqY8eOZyxr2LAhjTACmmmPDE+ePFl5eXmaNGmS5s6de8ayadOm6fXXX9d3332ntLS0886Ah1OaNm2q+fPnGx0G4LHKSoeydhwybPyN2+y6OKmeYeOfjiEYx/YGaiBAHpjNihUr9PXXX0s6NQnW1KlTa3W2ZHl5uWw22xnPFRUVqbi4mGYYAcuUR4Z37NihpUuXKiEhQbNmzap2ne7du0uSunTp4vXxhwwZIovFoocfftjr+zZKZWWliouLVVlpzFEloLZ25xappLTCsPE3bTe+GTQyhk07jH/9tUENBMgDM9m/f7/eeOMNSacmx/rTn/5Uq0b47MmyTp89UFlZqRdffJG/GQQsUzbDGRkZcjgcGjt2rOrVq/5ITFRUlCTvN8NvvPGGNm/e7NV9BoI9e/Zo4MCB2rPHv5MPAd6yK+eoweMXGjq+0THkHzxuyPXa3kINBMgDs3A6nXrppZdUXn6qJg8dOlSXXHKJx/urbtboJ598UikpKZKkH3/8UR9++GHtAwd8wJSnSa9Zs0aSNGDAgBrXycvLk+TdZrioqEh//OMfNXfuXN1yyy213l+PHj3OOd3EW0aPHu3W+gcPHpQkrVy5Ups2bXJpm5EjR7odF+Arx8M7SvVurHZZZsa1Sko4/zVwSQlRVb/3fXJTjevZ7MfV8zfLznn+gxWrlLp0nBsRe9+RhjMkS1i1yy70HtT29UtSqzYdFeJ07/7GvuROHfSkBkrmqoMFDf4sWeNUYCtQamqq0eH4nRlfP58FzCk8PLzGMyOlU7dQOn0P4aSkJI0ZM8bjsaprhE9fI/y73/1ODzzwgJxOp1auXKmhQ4cqJKT62wy2bt1aJ0+e9DgOBLekpCRt3LjRo21N2Qzn5uZKkpo1a1bt8oqKCq1bt06Sd5vhv/3tb2rdurXGjh3rlWbYZrNVe683bzg9Bb6rSktLq367uq2vYgc8Epcs1XDJblJCtFIbx7i0m9AQq8vr/lLZiePG50QDh1TDfCiuvgeevn5JshXslyoDpxl2pw56UgMlk9XB2ErJKjkqK831ulxlwtfPZwFz+uUtkKrz8ccfV/33yJEjFR4e7tE452uEJSk9PV3du3fXxo0bdfjwYW3atEm9evWqdl/5+fkqKyvzKA6gNkzZDJ8u0KeL9tmWLl0qu92u2NhYpaWleWXMjRs36p///KdbRwwuJCkpyWv7OltMjHsfZk+/p1FRUS5ve/r0GCAQnAiLUU3TZ9nsxy+4fVJClEJDrKqodMhmr762nG9fURFWNTI4JwpUJoeq/5B0ofegtq9fToeaJCXIogauhutz7tRBT2qgZK46WBASIocka0iIkk30ulxlxtfPZwFzOl9ze+LEiapJs2JiYtSnTx+PxrhQI3zaVVddVXXE7rPPPquxGW7SpAlHhuGx2vRMpmyGk5KSdOTIEWVlZZ2T5AUFBbr33nslSZ07d3Z52vjzqays1F133aVJkyapQ4cOtd7faZ4e7ndFZmamW+vv3LlTGRkZGjJkiNq2bevSNvPmzfMgMsA38g+WKGXQkmqX1XRa7y/t++QmpTaOkc1eqouvqn4/5/PIX+/Qvb991u3tvGnw3R9p1VfVH6W50HtQ29ffrmUjbX8vx+3tfMmdOuhJDZTMVQdTB2Vo/8HjSk5KVt7WPKPD8Tszvn4+C5hTRUWF3n777WqXZWdnq6Li1GSSvXv39uiosKuNsCR16tRJ9evXV1FRkfbs2SOn01ntZ+/du3crNNSUbQkCnCkn0Bo0aJAkafbs2dq9e3fV85mZmRowYEBV8tZm1rxfeu6553TgwAFTzR59tvT0dK1atUrp6elGhwJ4pMlFMUpONO7emD06JBg29mnd2xsXQw8Dx/YGaiBAHpjBjz/+WPXfLVu2dHt7dxphSbJarWrRooUkqbi4WD///LMHUQO+Y8pmeNq0aYqPj9e+ffvUoUMHderUSa1atVKvXr3UokULDRw4UFL11wuvW7dOCQkJVT9PP/20JGnJkiVnPH/6mmO73a4HHnhADz74oCoqKnT06FEdPXpU0qlTUY4ePSqHw+GfF+5DoaGhatiwId/aoU7r0/kiQ8YNC7XqknbGN4N9uhjz+o0e2xuogQB5YAY//fRT1X+7e6mgu41wdeP8cnwgEJiyGU5NTdXatWs1bNgwRUZGKicnR40aNdKCBQu0YsWKqqPF1TXD5eXlOnToUNXP6euOy8rKznj+9HT0eXl5OnbsmO666y41bNiw6kc6dWS6YcOGpkj8vLw8TZ06tWoWbqAuuv2G1oaMe+PVaYqL9WyCEm+65rJUNbnI/0fHoyJDdNOQFn4f15uogQB5YAa/nE+nQYMGLm/naSMsSXFxcdWODwQC0361165dOy1fvvyc54uLi5WTkyOr1aqOHTues7x///5yOp0uj5Oenq7PPvvsnOcHDBigcePGafz48T6dCMtfiouLtXbtWt15551GhwJ47JrLUpSWEqvs/cf8Ou49Y9r5dbyahIVZNXFUGz384rd+HffmIS3VsP75ZzcNdNRAgDwwg4kTJ+rWW29VeXn5GU3qhRw4cECFhafuVe9OIyxJl19+ubp27aqwsDDFxsZ6FDfgK6Zthmuybds2OZ1OtW7dWtHRtT9CUq9ePfXv37/aZc2bN69xGQD/Cwmxauq4jpr0xNd+G7NPl4t0WdfAOUX4rhvb6u+vbdWxknK/jBcSYtGUsd6bWBAA4Ll69eqpXr0a7jN4Hp06ddLUqVO1ZMkS3XfffS43wrUZE/AHU54mfT5btmyR5N37CwOoO+6+sa36dmvsl7EiwkO08JErvDJrvbckJUTr71Orv7WFL0y/o4s6tW7kt/EAAL7RtWtXPfHEE241wkCgC7ojw/5qht051RqA/4SEWPWvmVeoy43vqvREpcvbnb5/riv3JD5t5j2XqF2LBu6G6HN3jGqjt1bn6OMabrNUHU9ef6dWDTVjYld3wwMABCirNeiOo8HkaIbhksTERE2ZMkWJiYlGhwLUWqtmcfr3E/1141/WyOFw7YsrV+5F/Es3DW6hqePOnZcgEFgsFi1+/Er1++0K7copdGkbd19/UkKU3vmfQQoPC/EkxIBDDQTIAwDmE3Rf76xZs0ZOp1PDhg0zOpQ6JT4+XmPHjlV8fLzRoQBeccOg5vr3E1cqNNT7pzDfeHWaXn28n0JCArfEXhQfpU//OURt01yfQMVVyYnRWv3SEKU3re/1fRuFGgiQBwDMJ3A/qSGgFBUVafXq1SoqKjI6FMBrfjO0pT56YbBSG8d4ZX8hIRbNmNhVGbP714kjoimNY7T2leG6tn9Tr+2zb7fG+uq14eqQbq5ryqiBAHkAwHxohuGS/Px8TZ8+Xfn5+UaHAnjVry5toq3v3KAJI2t3D+IOLRto/b9H6NFJ3QP6iPDZEhpG6r1nBmnxE1eqYX3P74UcFRmi/7m3t/67aKiap5jv1hnUQIA8AGA+QXfNMACcLS42XAsfuUKTb26vF9/YqX8v/0ElpRUubTugZ7LuGdNO1w1oprCwutME/5LFYtEtw9M1rN/FevX9PXrhjR3ak+vakZ/UxjGaOLqN7rihjZITa3+7OgAAAH+hGQaA/9OlTbz+8UBfzf5jT63ZkK9N2+3auM2u7P3FOnGyQmGhVsXHReqSdvHq3j5B/bonqXVz719za5SG9SP0x1s7avLYDlr//UF9s+Vnbdpu15Y9R3SspFxOp1MxUaFq37KhurePV88OierXPUmhoXXzSwAAABDcaIYB4CxxseEa+avmGvmr5kaHYgir1aLLujbWZV39cz9mAAAAI/B1PlwSERGhNm3aKCIiwuhQAMDvqIEAeQDAfDgyDJekpaVp8eLFRocBAIagBgLkAQDz4cgwAAAAACDo0AzDJbt27VLfvn21a9cuo0MBAL+jBgLkAQDzoRmGS5xOp8rLT80mCwDBhhoIkAcAzIdrhgEAAACTCAkJ0ahRo7y2vzkLlupYSYliY2J0711jznnsDSEhIV7ZD+AummEAAADAJCwWi0JDvfcR3ynJ4Tz1OzQ09JzHQF3GadIAAAAAgKDD1zlwSfPmzZWRkaGUlBSjQwEAv6MGAuQBAPOhGYZLIiMj1bJlS6PDAABDUAMB8gCA+XCaNFxSUFCgxx57TAUFBUaHAgB+Rw0EyAMA5kMzDJcUFhZq2bJlKiwsNDoUAPA7aiBAHgAwH5phAAAAAEDQoRkGAAAAAAQdmmEAAAAAQNChGYZLrFarunXrJquVPxkAwYcaCJAHAMyHagaXOBwOffvtt3I4HEaHAgB+Rw0EyAMA5kMzDAAAAAAIOjTDAAAAAICgQzMMAAAAAAg6NMNwSWxsrAYPHqzY2FijQwEAv6MGAuQBAPMJNToA1A0pKSmaOXOm0WEAgCGogQB5AMB8ODIMl5SVlWnfvn0qKyszOhQA8DtqIEAeADAfmmG4JDs7W6NGjVJ2drbRoQCA31EDAfIAgPlwmjQAAABMw+l06nhphdFhuCU6KlQWi8XoMGAS5IDraIYBAABgGsdLK1Tv0teMDsMtxetvU0x0mNFhwCTIAddxmjQAAAAAIOjQDAMAAAAAgg6nScMlbdu21YYNG4wOAwAMQQ0EyAMA5sORYQAAAABA0KEZhktyc3M1YcIE5ebmGh0KAPgdNRAgDwCYD6dJwyWlpaXaunWrSktLjQ4FAPwu2GpgZaVDm7Yf0sZtP2vTjkPanVOog4dPSJLsR07o3r9vUPf28erT5SI1axJrcLS+8VNBsb7+7qA2bbfru92Hq17/z0dO6LcPfKEeHRLUo32CenRIUEhIcBxbCLY8AGB+NMMAAEDSqUZ30bu79Y83dyp7/7Fq1ykrd2juq1uqHl99WYruGdNOw664WKGhdbsprKx06MO1eXp+yXat+mp/teucLHfolff36JX390iSmjWpp7tvbKvbR7ZWYqMof4YLAKglmmEAAIJcZaVDz76+XX+bv1GlJyrd2vbjr/br46/2q12LBvrXzCvUu/NFPorStzZu+1njZ3yhbXuPurVdbn6x7n9mox75x7d69Pfd9adbOwTNkWIAqOuo1gAABLG9+4p05YQP9ec537jdCP/Sjh+P6rLbluu+/9mgk+We78ffyssd+tuzG3XpLR+43Qj/0omySt379AZdPm659uQWei9AAIDP0AzDJcnJyXrkkUeUnJxsdCgA4HdmrYHf7rCrzy0faN23B7yyP4fDqaf+tUXXT1mt46UVXtmnL50oq9DoqZ/qiZe/U2Wl0yv7XP/9z+pz6wfauO1nr+wvkJg1DwAEL5rhs+Tk5GjhwoW6++671b17d4WHh8tisWj8+PFGh2aouLg4DRkyRHFxcUaHAgB+Z8YauHXPYQ2a+JF+PnLC6/te+WWeRk/9NKCPEJeXO/Trv3ymZZ//5PV9HzpapqsmfqTvdh3y+r6NZMY8ABDcaIbPMm/ePN1xxx1asGCBsrKyVF5ebnRIAeHIkSN68803deTIEaNDAQC/M1sNLD5ermsnr9bhwjKfjbHyyzzd/8xGn+2/th54fpM++K/3G+HTjh47qRF/+ERFxSd9Noa/mS0PAIBm+CwJCQkaOnSoHnroIX3wwQe65557jA4pIBw4cEBz5szRgQPeOZUOAOoSs9XAv87LrHG26JpkZlyrfZ/cpMyMa13e5n8Wb/XaKdje9M33BzXnlS0XXvEXPHn9+2wluvfpDe6GF7DMlgcAQDN8lhkzZmjFihV6+OGHNXz4cDVs2NDokAAA8Jq1m2x6fskOt7dLSohWauMYJSVEu7yN0yn99sEvAup06YoKh3774Fo5HO5dI+zJ65ekl97apTXf5Lu1DQLD45O7y/n97frt9a2qXf7ZwqE6sXG8OqTzWTEYVFQ4dOjoCZUcL5fT6Z05BgJdMOSA6Zthu92uadOmKT09XZGRkbr44os1ZcoUlZSU6Pbbb5fFYtFzzz1ndJgAAPjFU//63q/j7ckt0ruf5vp1zPNZ9vlP2vHjUb+O6e/3HN7x8Avfasuew3r6L72V0vjML0H+eEsH9e+ZrIdeyNK2Hzht3KwcDqc+/ipP10/5RBE9XlFCv/+o3qWvKX3Ym5rzr+916Kj351wIJMGQA6Zuhjdv3qxOnTppzpw5stlsat++vcrLy/Xss89qzJgx2rHj1DfjXbt2NTZQAAD8IGf/Ma1Yu8/v476w1P0j0b5iRCyrvtqvH34q8vu4qJ3yCofGzfhCMVFhWvjwFVXPt24ep8f/0EPrPTjdHnXH4cIyDbzjQ11z9yq9/9lPZ5xN8mPeMU37n0w1vXqp3v8scL7s87ZgyAHTNsN2u10jRoyQzWbT1KlTVVBQoKysLNlsNs2ePVsrVqxQZmamLBaLOnfubHS4AS86Olq9e/dWdLR7p4cBgBmYpQYuem+3jDi774tNNu3OMf7eu9l5x/SpQacsv/zOLkPG9Saz5IE7vt1xSLMWfqdr+qbqzlFtZLVa9Nrj/WSxSONmfOH26faoG4qPl+uqiSv134228653/ESFbvjTp6ZuiM2eA6FGB+ArkydPVl5eniZNmqS5c+eesWzatGl6/fXX9d133yktLU3169c3KMq6o2nTppo/f77RYQCAIcxSA7/MMm7io3WbD6h1c2NvybNus4GvPwAnEnOXWfLAXY++9K2u7d9Uc6f2Ute28erd6SL9ec43AfEFD3xjxvxNytrh2q3RHA6nxv71c+V9cpMa1I/wcWTGMHMOmPLI8I4dO7R06VIlJCRo1qxZ1a7TvXt3SVKXLl1qPd7nn38ui8Vyzo+ZTr+urKxUcXGxKisDZxIUAPAXM9RAp9OprJ3G3fd203a7YWMHQgzf7jykykqHYeN7gxnywBMVFU6Nm/GFIiNCdM+YdlqbZdO8f281Oiz4SPHxcv3r/d1ubVNSWqHFy3/wUUTGM3MOmLIZzsjIkMPh0NixY1WvXr1q14mKipLknWb4tOeff15ff/111c/ixYu9tm+j7dmzRwMHDtSePXuMDgUA/M4MNTBnf7EKjxl3z9tvDWzEAyGGktIK7d3n3u2sAo0Z8sBThcUnVXby1JcAH67dZ8jlBvCPpR/9qKLicre3+8ebO30QTeAwaw6Y8jTpNWvWSJIGDBhQ4zp5eXmSvNsMt2/fXpdeeqnX9tejRw/ZbOe/VsFTo0ePdmv9gwcPSpJWrlypTZs2ubTNyJEj3Y4LAPzFnTroSQ2UAqsOngxJkuJ+V+2yzIxrL3jLoKSEqKrf+z65qcb1bPbj6vmbZec8v2HTVqWmVj++vxysf7cUmlztsgu9B66+fqnm9+DyK69WeOV+NyL2LbN+FnAoTGo0w6v7/NfMKxQeFqLte49oxsSuemNVtn7M896XG61at5ZV7jdg/jDyt39UTL36KrAVKDU19ZzHZnM0+hop8jK3t9v+w2GlpF4si4zvEoMtB5KSkrRx40aPtjVlM5ybe+oi9mbNmlW7vKKiQuvWrZPk3WbY22w2m/bv980/miUlJW6tX1paWvXb1W19FTsAeIM7ddCTGigFWB2MCpNquGT39D10XREaYnV53V+qqHAY/35EO2r85OPqe+Dp65ekn+2HpeOB8zdh2s8ClnCpkfd294eb22tAryaa/uxGvf9ZrrKWXq9FM69Q/wkfem2Mgvx8yWncmRvn4/i/0+IdlZXav3//OY9Np8kJKdKD7SxW5efbJGeF10NyPxZywFWmbIZPF+jTRftsS5culd1uV2xsrNLS0rw27pgxY2S32xUfH69rr71WTz75pBISEjzeX1JSktdiO1tMjHv/kJ9+T6OiolzeNiUlxe24AMBf3KmDntRAKbDqYHlIQx2sYZnNfvyC2yclRCk0xKqKSods9ur/fT3fvkJDpMYGvx8HQ1XjcYcLvQeuvv7z7SsxoYHCKwPnb8KsnwUcClOBl/aV3rS+Zk3poQ1bftbsRd/L4XDq4RezNGtKT/3h5vaa//p2r4yT3KRJwB4ZtoaEVP1OSUk557HZFEVZ5cnxTovzhJo0aez1eDwRbDlQm57JlM1wUlKSjhw5oqysLPXp0+eMZQUFBbr33nslSZ07d5bFYqn1eHFxcbr33nvVr18/1atXT19//bVmzZql9evXa+PGjYqM9OTrJXl8uN8VmZmZbq2/c+dOZWRkaMiQIWrbtq1L28ybN8+DyADAP9ypg57UQCmw6mDx8XLV7/Natdd5VXdK79n2fXKTUhvHyGYv1cVXLXF7/OsGX6q3nv6b29t502+mfaYlH/1Y7bILvQe1ff2StGfrOsXFhnu0rS+Y9bNAyfFy1bv0tVrvx2KRXnm0n0KsFo2b8d+qW8g89a8tuuFXzTVrSg+t+GKfV04V3bN7t2Kiw2q9H1944vn/qKi4RMlJycrLyzvnsdls2X1YnUe/6/Z240d20qKZgfF+kAOuM+UEWoMGDZIkzZ49W7t3//9scJmZmRowYIDs9lOzSXprtudu3brpqaee0vDhw9W/f3/df//9+s9//qNt27YpIyPDK2MYLT09XatWrVJ6errRoQCA35mhBtaLDlPbtAaGjd+9vednSpkhhvSm9QOqEfaEGfLAHVPHdVLfbo314AtZ2pn9/7eQcTicGv/AFwoNsWrRzCsMjBC+0Kl1I11xiftHeO8Z084H0RgrGHLAlM3wtGnTFB8fr3379qlDhw7q1KmTWrVqpV69eqlFixYaOHCgpOqvF163bp0SEhKqfp5++mlJ0pIlS854/vQ1xzUZPny4YmJifHp0159CQ0PVsGFDhYaa8mQCADgvs9TAHgY2g93bxxs29mk9OgT3668ts+SBK9qmxenR31+ir787qL+/eu4tZLbvPaqHX8zSlT2S9Yeb2xsQIXxp5u+7KzTE9bNHb/hVc/XokOjDiPwvWHLAlM1wamqq1q5dq2HDhikyMlI5OTlq1KiRFixYoBUrVlQdLa6uGS4vL9ehQ4eqfk5fd1xWVnbG8+Xlrp3T7o3TsANBXl6epk6dasrTYQDgQsxSA0df1dyQcRMaRurKHtXP4uxPl3W9qGpWaH+78SrvzVFiFLPkgSt2ZhcqqueruuzWD6pODT3bkwu/l6XzQq9dM4nA0b9nsl57/EqXGuKBvZK1+Ikr/RCVfwVLDpiyGZakdu3aafny5Tp27JiOHTumb775RhMnTlRJSYlycnJktVrVsWPHc7br37+/nE7nBX/69+9/3vGXLVumkpIS9erVy0ev0L+Ki4u1du1aFRcXGx0KAPidWWrgsH4Xq2myZzMh18YdN7RWRHiI38c9W3hYiO4c1cbv4za5KFrX9q/+Dhd1iVnyAHDFb4a21JqXh2rQpU2qXZ6cGK1H7rlEK1+8RtFR5j9bwqyC7v/ctm3b5HQ61bp1a0VHn/+eiq665ZZb1KJFC11yySVVE2g99dRT6tq1q2666fz3IgQAwF9CQqy6+8Z2mv6s/y7hsVotmjjK9UnHfG3iqLaatfA7VVT4716gd41uq7Aw0x5/AEzriu5J+uSlIdqVfVTvf/aTHn3pWxUfr1Cj+uHK/WgMeW0CQfd/cMuWLZK8e3/hDh066N1339Vtt92mIUOGaNGiRbrzzjv1+eefKzy8bk+WAQAwlz/e0kGtm9Vww2EfuO+3nZWWGuu38S4kNSlG02/v6rfxWqTGaupt556JBqDuaJPWQNMmdFZcvVOf66MiQ2mETSLo/i/6ohm+//77tWXLFhUVFam8vFzZ2dl6+umnFRfnvw8bAAC4IioyVItmXiF/TGnRoWUDPfS7br4fyE1/m9hFXdo08stYi2ZeEbC3zAGAYEczDJckJiZqypQpSkw010x5AOAKs9XAvt0a68G73GtSbfbjyjtQIpv9uEvr14sO0+InrgyIa4XPFh4WosWPX6nYGNebVHdfvyTdf3uXgJg4zFvMlgcAEHTXDK9Zs8boEOqk+Ph4jR071ugwAMAQZqyBD/2umw4Vlum5DNdmAe35m2Uu7zsqMkTvPzNI3doZf2/hmnRq3UjL51+lob//WCWlFRdc353XL0l33dhWj0/u7ml4AcmMeQAguAXdkWF4pqioSKtXr1ZRUZHRoQCA35mxBlosFj3710v1wF1dvbrfxIaR+mTBEA3sXf0MrIGkX49krX5piBrHe/d2S3+9vbNenHGZaW6veJoZ8wBAcKMZhkvy8/M1ffp05efnGx0KAPidWWugxWLRzN93138XDVXLi2s/ydWvr0nTtndvUN9ujb0QnX9c2uUibXv3Bt08tGWt95WWEqs1Lw/RrCk9TdcIS+bNAwDBi2YYAIAg169Hsr57c6Qe/l03JSe6f9vBvt0a671nBmnpnIFKbOTdo6z+EN8gUv95sr8+mH+VLvegkW8cH6UH7uqq798eqQG9Av+IOADglKC7ZhgAAJwrJjpMD/3uEk2/o6ve+yxXSz/6UZu225WTX3zOumGhVnVq1VCXdW2s20e2Vte28QZE7H3Dr2yq4Vc21fe7D2vhO7u0bvNBbdlzWCfLHees26xJPXVvl6BfX5Omkb9qpvCwwJsoDABwfjTDAACgSliYVTdenaYbr06TJB06ekJ7cotUWlahEKtFcbHhapvWICBnifaWzq0b6Zm/9pEknSyv1M7sQh0tKlNFpVPRkaFKb1pfCQ0jDY4SAFBbNMNwSUREhNq0aaOIiAijQwEAvwvmGhjfIFLxDYK38QsPC1Hn1v65J3GgC+Y8AGBONMNwSVpamhYvXmx0GABgCGogQB4AMB8m0AIAAAAABB2aYbhk165d6tu3r3bt2mV0KADgd9RAgDwAYD40w3CJ0+lUeXm5nE6n0aEAgN9RAwHyAID5cM0wAAAATCM6KlTF628zOgy3REfxkRzeQw64jswDAACAaVgsFsVEhxkdBmAYcsB1nCYNAAAAAAg6HBmGS5o3b66MjAylpKQYHQoA+B01ECAPAJgPzTBcEhkZqZYtWxodBgAYghoIkAcAzIfTpOGSgoICPfbYYyooKDA6FADwO2ogQB4AMB+aYbiksLBQy5YtU2FhodGhAIDfUQMB8gCA+dAMAwAAAACCDs0wAAAAACDo0AwDAAAAAIIOzTBcYrVa1a1bN1mt/MkACD7UQIA8AGA+VDO4xOFw6Ntvv5XD4TA6FADwO2ogQB4AMB+aYQAAAABA0KEZBgAAAAAEHZphAAAAAEDQoRmGS2JjYzV48GDFxsYaHQoA+B01ECAPAJhPqNEBoG5ISUnRzJkzjQ4DAAxBDQTIAwDmw5FhuKSsrEz79u1TWVmZ0aEAgN9RAwHyAID50AzDJdnZ2Ro1apSys7ONDgUA/I4aCJAHAMyHZhgAAAAAEHS4ZhgAAACm4XQ6dby0wugw3BIdFSqLxWJ0GDAJcsB1NMMAAAAwjeOlFap36WtGh+GW4vW3KSY6zOgwYBLkgOs4TRoAAAAAEHQ4MgyXtG3bVhs2bDA6DAAwBDUQIA8AmA9HhgEAAAAAQYdmGC7Jzc3VhAkTlJuba3QoAOB31ECAPABgPjTDcElpaam2bt2q0tJSo0MBAL+jBgLkAQDzoRkGAAAAAAQdmmEAAAAAQNChGQYAAAAABB2aYbgkOTlZjzzyiJKTk40OBQD8jhoIkAcAzIf7DMMlcXFxGjJkiNFhAIAhqIEAeQDAfDgyfJacnBwtXLhQd999t7p3767w8HBZLBaNHz/e6NAMdeTIEb355ps6cuSI0aEAgN9RAwHyAID5cGT4LPPmzdMzzzxjdBgB58CBA5ozZ446deqkhg0bGh0OAPgVNRAgDwCYD83wWRISEjR06FD17NlTPXr00MqVK/XCCy8YHRYAAAAAwIs4TfosM2bM0IoVK/Twww9r+PDhfPMJAAAQhB6f3F3O72/Xb69vVe3yzxYO1YmN49Uhnc+KZlZR4dD7n+Xqtw98oUNHyyRJRSXlKvj5uMGR+V4w5IDpm2G73a5p06YpPT1dkZGRuvjiizVlyhSVlJTo9ttvl8Vi0XPPPWd0mAAAAAggD7/wrbbsOayn/9JbKY2jz1j2x1s6qH/PZD30Qpa2/cA11Gb1r/d2q8XQN3T9lNV65f09OnGyUpJ0rKRcTa9eot9M+0yHjp4wOErfCYYcMHUzvHnzZnXq1Elz5syRzWZT+/btVV5ermeffVZjxozRjh07JEldu3Y1NtA6IDo6Wr1791Z0dPSFVwYAk6EGAsGXB+UVDo2b8YViosK08OErqp5v3TxOj/+hh9Z/f1BzXtliYITwpZn/+FYTHlyrfbaSapdXVDq15KMfddmty2Wzm/MocTDkgGmbYbvdrhEjRshms2nq1KkqKChQVlaWbDabZs+erRUrVigzM1MWi0WdO3c2OtyA17RpU82fP19NmzY1OhQA8DtqIBCcefDtjkOatfA7XdM3VXeOaiOr1aLXHu8ni0UaN+MLORxOo0OEDyxZuVcPvZDl0rq7cwt13eTVpv1bMHsOmLYZnjx5svLy8jRp0iTNnTtXsbGxVcumTZumLl26qKKiQs2bN1f9+vUNjLRuqKysVHFxsSorK40OBQD8jhoIBG8ePPrSt9q885DmTu2l+ff3Ue9OF+lv8zdpd06h0aHBB5xOpx57abNb22zY+rM+/SbfNwEFADPngCmb4R07dmjp0qVKSEjQrFmzql2ne/fukqQuXbp4bdx3331Xl112mWJiYhQXF6e+fftq27ZtXtu/kfbs2aOBAwdqz549RocCAH5HDQSCNw8qKpwaN+MLRUaE6J4x7bQ2y6Z5/95qdFjwkbWbbNq296jb272wdIf3gwkQZs4BUzbDGRkZcjgcGjt2rOrVq1ftOlFRUZK81ww/++yz+vWvf63LL79cy5YtU0ZGhgYNGqTS0lKv7B8AAADGKCw+qbL/mzzpw7X75KzbZ4biPD5at9+j7VZ+mSenif8wzJoDprzP8Jo1ayRJAwYMqHGdvLw8Sd5phvfu3at7771X//M//6NJkyZVPT906NBa7bdHjx6y2Wy1Da9ao0ePdmv9gwcPSpJWrlypTZs2ubTNyJEj3Y4LAPzFnTroSQ2UqIMIbGb9LOBQmNRohlf3+a+ZVyg8LETb9x7RjIld9caqbP2Yd8xr+2/VurWsKvfa/rxp5G//qJh69VVgK1Bqauo5j83maPQwKbKX29uVnaxU6sVpsqjCB1G5J9hyICkpSRs3bvRoW1M2w7m5uZKkZs2aVbu8oqJC69atk+SdZnjRokUKCwvTnXfeWet9/ZLNZtP+/Z59O3UhJSXVz4xXk9NHuEtLS13e1lexA4A3uFMHPamBEnUQgc20nwUs4VIj7+3uDze314BeTTT92Y16/7NcZS29XotmXqH+Ez702hgF+fmS86TX9udNjv+7RtxRWan9+/ef89h0kg5LkR5s56xU/v5cr4fjEXLAZaZshk8X6JpOUV66dKnsdrtiY2OVlpZW6/G++uortWnTRv/+97/12GOPad++fWrVqpUefPBB/eY3v/F4v0lJSbWOrSYxMTFurX/6PY2KinJ525SUFLfjAgB/cacOelIDJeogAptZPws4FKYCL+0rvWl9zZrSQxu2/KzZi76Xw+HUwy9madaUnvrDze01//XtXhknuUmTgD0ybA0JqfqdkpJyzmOzKQ0r1GEPtguv2K/EAHk/gi0HatMzmbIZTkpK0pEjR5SVlaU+ffqcsaygoED33nuvJKlz586yWCy1Hq+goED79+/X/fffr9mzZ+viiy/WwoULdfPNNysxMVGDBg3yaL+eHu53RWZmplvrV1RUaPz48YqNjVVoqGt/NvPmzfMgMgDwD3fqoCc1UKIOIrCZ9bNAyfFy1bv0tVrvx2KRXnm0n0KsFo2b8d+qW8g89a8tuuFXzTVrSg+t+GKfV04V3bN7t2Kiw2q9H1944vn/qKi4RMlJycrLyzvnsdmUlzvU9Jolstndm/fn5adu0a0jHvFRVO4hB1xnygm0Tjefs2fP1u7du6uez8zM1IABA2S32yVJXbt29cp4DodDxcXFeumll/Tb3/5WgwYN0uuvv67OnTvr0Ucf9coYRgsNDVXDhg3d+hAIAGZBDQSCLw+mjuukvt0a68EXsrQz+/9vIeNwODX+gS8UGmLVoplXGBghfCEszKpJN7V3a5vkxGjdeHXtzzYNNMGQA6ZshqdNm6b4+Hjt27dPHTp0UKdOndSqVSv16tVLLVq00MCBAyVVf73wunXrlJCQUPXz9NNPS5KWLFlyxvOnrzmWpEaNTp2U/8sjwBaLRYMGDdLWreaYdjwvL09Tp0415TeAAHAh1EAguPKgbVqcHv39Jfr6u4P6+6vnfpbbvveoHn4xS1f2SNYfbnavcULgu29CZ13bv6lL69aLDtWyZwcpMsJcXxIFSw6YshlOTU3V2rVrNWzYMEVGRionJ0eNGjXSggULtGLFiqqjxdU1w+Xl5Tp06FDVz+nrjsvKys54vrz8/89p79ChQ42xnDhxwsuvzhjFxcVau3atiouLjQ4FAPyOGggEVx7szC5UVM9XddmtH1SdGnq2Jxd+L0vnhV67ZhKBIzTUqjf/PlATR7fR+a6obJEaqy/+NUw9OiT6Lzg/CZYcMNdXGL/Qrl07LV++/Jzni4uLlZOTI6vVqo4dO56zvH///m7fI+y6667TokWL9PHHH+uGG26QdOrU6U8++UQ9e/b07AUAAAAAMER4WIgWPHi57r+9i156a5feXZOj3TmFcjiliHCr3n76VxrcN1UhIaY8thg0TNsM12Tbtm1yOp1q3bq1oqOjvbLPESNG6IorrtDEiRN16NAhNW3aVC+//LK2bdumTz75xCtjAAAAAPCv5imxemJKDz0xpYdSB2Vo/8HjSmgQqWH9XDuNGoEt6JrhLVu2SPLO/YVPs1gsWrZsme677z5Nnz5dRUVF6tKliz788MOq65MBAAAAAIGDZthLGjRooAULFmjBggVe3W+gSExM1JQpU5SYaL5rIgDgQqiBAHkAwHxohuGS+Ph4jR071ugwAMAQ1ECAPABgPkF3xfeaNWvkdDo1bNgwo0OpU4qKirR69WoVFRUZHQoA+B01ECAPAJhP0DXD8Ex+fr6mT5+u/Px8o0MBAL+jBgLkAQDzoRkGAAAAAAQdmmEAAAAAQNChGQYAAAAABB2aYbgkIiJCbdq0UUREhNGhAIDfUQMB8gCA+QTdrZXgmbS0NC1evNjoMADAENRAgDwAYD4cGQYAAAAABB2aYbhk165d6tu3r3bt2mV0KADgd9RAgDwAYD40w3CJ0+lUeXm5nE6n0aEAgN9RAwHyAID50AwDAAAAAIIOE2gBAADANKKjQlW8/jajw3BLdBQfyeE95IDryDwAAACYhsViUUx0mNFhAIYhB1xHMwyXNG/eXBkZGUpJSTE6FADwO2ogQB4AMB+aYbgkMjJSLVu2NDoMADAENRAgDwCYDxNowSUFBQV67LHHVFBQYHQoAOB31ECAPABgPjTDcElhYaGWLVumwsJCo0MBAL+jBgLkAQDzoRkGAAAAAAQdmmEAAAAAQNChGQYAAAAABB2aYbikUaNGGjdunBo1amR0KADgd9RAgDwAYD40w3CJ1WpVWFiYrFb+ZAAEH2ogQB4AMB+qGVxit9v18ssvy263Gx0KAPgdNRAgDwCYD80wAAAAACDo0AwDAAAAAIIOzTAAAAAAIOjQDMMlsbGxGjx4sGJjY40OBQD8jhoIkAcAzCfU6ABQN6SkpGjmzJlGhwEAhqAGAuQBAPPhyDBcUlZWpn379qmsrMzoUADA76iBAHkAwHxohuGS7OxsjRo1StnZ2UaHAgB+Rw0EyAMA5sNp0gAAADANp9Op46UVRofhluioUFksFqPDgEk4nU5VVlYaHYZbQkJCDMkBmmEAAACYxvHSCtW79DWjw3BL8frbFBMdZnQYMInKykq9/fbbRofhllGjRik01P+tKadJAwAAAACCDs0wAAAAACDocJo0XNK2bVtt2LDB6DAAwBDUQIA8AGA+HBkGAAAAAAQdmmG4JDc3VxMmTFBubq7RoQCA31EDAfIAwc3hcMrhdEo6NVszzIHTpOGS0tJSbd26VaWlpUaHAgB+Rw0EyAMEl53ZR/Xup7natN2uTdvtyskvrlpWYC/VFeOWq3v7BF1xSWON6N9U4WEhBkYLT9EMAwAAAAh6DodT736aoxeW7tCaDQU1rud0Sl9+e0BffntAz/xnmxrHR+nOUW10z5h2Sk6M9mPEqC1OkwYAAAAQ1LLzjmnQnSs1euqa8zbC1TlwqFSPvbRZ7a5/W/96bzenUdchNMMAAAAAgtar7+9Rp1Hv6LNM95rgsxUeO6kJD67V8Ekf62hRmZeigy/RDMMlycnJeuSRR5ScnGx0KADgd9RAgDyAOf391S0a/8AXKimt8No+P1ybp/63f6ifD3N9faCjGT5LTk6OFi5cqLvvvlvdu3dXeHi4LBaLxo8fb3RohoqLi9OQIUMUFxdndCgA4HfUQIA8gPm8uHSH/vJ339w7+7tdhzX4d6tUVHzSJ/uva+x2uxwOh9FhnIMJtM4yb948PfPMM0aHEXCOHDmi1atXa9CgQWrYsKHR4QCAX1EDAfIA5vLtDrsmz/7ap2Nk7TikP835RgsfucKn4/jK4cOH9cMPP+jHH3/UTz/9pNLSUjmdTkVERKhJkyZq0aKFWrZsqeTkZFkslhr3k5ubq8cee0y9e/fWhAkTZLUGzvFYmuGzJCQkaOjQoerZs6d69OihlStX6oUXXjA6LMMdOHBAc+bMUadOnfgHEEDQoQYC5AHM42R5pcY/sFYVFe5NdJWZca2SEqJlsx9Xz98sc2mbRe/u1uhBzTXkios9CdXvHA6HsrKy9Mknn+i7776rcb1fLmvevLmuvvpqXXbZZYqMjDxjvdON8LFjx7R69Wo1btxYI0aM8Fn87qIZPsuMGTPOeLx+/XqDIgEAAIBRHp/cXdPv6KoJD36hf72355zlny0cqj5dLlL3m97Xth+OGBAhPDVv8TZ9v/uw29slJUQrtXGM29tNnLlOez+8MeDvRbxr1y4tWLBA+fn5bm2Xk5Ojl156SRkZGRo3bpz69u0ri8VyRiMsSenp6frVr37li9A9Zvpm2G6366mnntI777yjvLw8JSYm6oYbbtATTzyhyZMna9GiRZo/f74mTZpkdKgAAAAIEA+/8K1GXNlUT/+ltz7+er/2HzheteyPt3RQ/57J+uu8TBrhOqaiwqHnlmz365h5B0r07qe5GjO4hV/HdVV5ebmWLFmiDz/88IzbQl100UXq06ePWrZsqbS0NMXFxclisaikpES5ubnKzs5WZmam9u7dK0k6duyYnnvuOX3zzTcaPHiw5s2bd0YjPH36dEVHB9Z9mE3dDG/evFlDhgyRzWZTTEyM2rdvr/z8fD377LPau3evDh8+9Y1Q165djQ0UAAAAAaW8wqFxM77QN/++VgsfvkKDf7dKktS6eZwe/0MPrf/+oOa8ssXgKOGu5V/8pH22Er+P+8LSHQHZDJ84cUJz587V1q1bq55r2bKlRo8erS5dulR7fW+DBg3UoEEDdenSRddff7327t2r999/Xxs2nJqMLDMzUxs3bqxqrAO1EZZMPJu03W7XiBEjZLPZNHXqVBUUFCgrK0s2m02zZ8/WihUrlJmZKYvFos6dOxsdbsCLjo5W7969A/KPGAB8jRoIBGcefLvjkGYt/E7X9E3VnaPayGq16LXH+8likcbN+EIOh3vXnMJ4iz/Ya8i4X2yyKTf/mCFj1+TkyZOaM2dOVSMcFhamsWPHaubMmerWrZvLE121bNlSf/7zn/WnP/1JMTGnTiM/3Qg3b948YBthycRHhidPnqy8vDxNmjRJc+fOPWPZtGnT9Prrr+u7775TWlqa6tevb1CUdUfTpk01f/58o8MAAENQA4HgzYNHX/pW1/ZvqrlTe6lr23j17nSR/jznG+3OKTQ6NHhgw9afDRs7c6tdzZrEGjb+2V555RVt27ZNkhQTE6P77rtPrVu39nh/SUlJ1c4qHRER4fE+fc2UR4Z37NihpUuXKiEhQbNmzap2ne7du0uSunTpUuvx+vfvL4vFUu3P3XffXev9B4LKykoVFxersrLS6FAAwO+ogUDw5kFFhVPjZnyhyIgQ3TOmndZm2TTv31svvCECzsFDpco74P9TpE/buN1u2Nhn++6777RmzRpJp5rVv/71r7VqhE9PllVcXCxJCg09dcw1JydHy5a5NvO2EUzZDGdkZMjhcGjs2LGqV69etetERUVJ8k4z/MILL+jrr78+4+f0rNTDhw+v9f4DwZ49ezRw4EDt2XPubIoAYHbUQCC486Cw+KTKTp76EuDDtfvk5OzoOmnbXmMnOwuUydZOnDihl156qerxLbfcolatWnm8v+pmjb7vvvuqjhK/9dZb2r9/f+2C9hFTniZ9+luOAQMG1LhOXl6eJO80w+3btz/nuccff1yJiYkaPHiwx/vt0aOHbDZbbUKr0ejRo91a/+DBg5KklStXatOmTS5tM3LkSLfjAgB/cacOelIDJeogAptZPws4FCY1mnHhFd3wr5lXKDwsRNv3HtGMiV31xqps/Zjnves/W7VuLavKvbY/bxr52z8qpl59FdgKlJqaes7juqQ0rLUUO7baZafvIXw+SQlRVb/3fXJTjevVdB/ijz/9QqmpE9yI2DPh4eE1nh0rSV9++aUOHTokSerQoYMGDRrk8VjVNcKnrxEePny4PvjgA1VWVmrFihWaOHFijftp3bq1Tp486VEMSUlJ2rhxo0fbmrIZzs3NlSQ1a9as2uUVFRVat26dJO80w2f7+eef9dFHH+mee+6pOkXAEzabzWffopSUuHeKSGlpadVvV7cN1G+AAEByrw56UgMl6iACm2k/C1jCpUbe290fbm6vAb2aaPqzG/X+Z7nKWnq9Fs28Qv0nfOi1MQry8yWnZ42Arzn+77R4R2Wl9u/ff87jOiU2Xqrhkl137iEcGmL16H7DJ8tO+OU9O981uk6nUx9//HHV41tuuaXa63xdcb5GWJJGjRql1atXq7S0VF9++aXGjh1bNcHW2fLz81VWVuZRHLVhymb4dIE+XbTPtnTpUtntdsXGxiotLc3r42dkZKiiokK33nprrfaTlJTkpYjOVdMfYk1Ov6dRUVEub5uSkuJ2XADgL+7UQU9qoEQdRGAz62cBh8JU4KV9pTetr1lTemjDlp81e9H3cjicevjFLM2a0lN/uLm95r/unfvVJjdpErBHhq0hIVW/U1JSznlcl5SFxqqmq3Zt9uM1LPl/SQlRCg2xqqLSIZu9+j7jfPuKDLcq3g/vWXh4eI3L9u7dq59++knSqebV017oQo2wJEVGRqpfv35atWqVTp48qS+//FLXXHNNtftr0qRJrY4Me8qUzXBSUpKOHDmirKws9enT54xlBQUFuvfeeyVJnTt39vibkPNZvHix2rVrpx49etRqP54e7ndFZmamW+vv3LlTGRkZGjJkiNq2bevSNvPmzfMgMgDwD3fqoCc1UKIOIrCZ9bNAyfFy1bv0tVrvx2KRXnm0n0KsFo2b8d+q2yg99a8tuuFXzTVrSg+t+GKfV06X3rN7t2Kiw2q9H1944vn/qKi4RMlJycrLyzvncV3y8+FSXdT/9WqXVXda89n2fXKTUhvHyGYv1cVXLXF7/D/+7kbNmvKU29u5q6KiQm+//Xa1y3bu3Fn131deeaVH+3elEf7lGKtWraoau6ZmePfu3bU6o9ZTppxA6/R577Nnz9bu3burns/MzNSAAQNkt5/6Tqhr165eH3vnzp3auHFjrY8KB5r09HStWrVK6enpRocCAH5HDQSCLw+mjuukvt0a68EXsrQz+/9vo+RwODX+gS8UGmLVoplXGBgh3JXYKEoXJ7l/erO3dG+XYNjYp/34449V/+3JpFnuNMLSqctWw8JOfdGTnZ3tQcS+ZcpmeNq0aYqPj9e+ffvUoUMHderUSa1atVKvXr3UokULDRw4UFL11wuvW7dOCQkJVT9PP/20JGnJkiVnPH/6muOzLV68WBaLRWPHVn9xfl0VGhqqhg0bGvKNDQAYjRoIBFcetE2L06O/v0Rff3dQf3/13Nsobd97VA+/mKUreyTrDzefO5EqAlevjonGjd3JuLFPy8nJkSSFhYW5PQGau42wJIWEhKh58+aSTs2HVNNlrEYxZTOcmpqqtWvXatiwYYqMjFROTo4aNWqkBQsWaMWKFVVHi6trhsvLy3Xo0KGqn9P/w8rKys54vrz83Os6nE6n/vOf/6h///5q2rSpb1+kn+Xl5Wnq1Kl17nQYAPAGaiAQXHmwM7tQUT1f1WW3flB1evTZnlz4vSydF3rtumH4x20jjDmzoX/PZDVNrv6Wr/50+tr/Bg0auPXFlieN8Gnx8fHnjB8oTPvVXrt27bR8+fJzni8uLlZOTo6sVqs6dux4zvL+/fvL6eHN47744gvl5ubqoYce8mj7QFZcXKy1a9fqzjvvNDoUAPA7aiBAHsAchvW7WE2TY/RTgX+bsnvGtPPreDWZOnWqysrKZLW6d0z0888/96gRlqTrrrtOAwYMUHh4uOrXr+92zL5k2ma4Jtu2bZPT6VTr1q1d/h/oqsWLFysqKsrt+/YBAAAA8L2QEKsm39xBf/n7Br+N2TQ5RtcPqP6Wr/7WunVrj7a79dZbdfz4ce3fv9+tRliST+7e4y1B1wxv2bJFkvfvL3zixAm99dZbuv766xUbW8MNzAAAAAAYavLNHfSfFXv17c5Dfhnv5YevUFhY3b461Wq16q677tLJkycVGRlpdDheQzPsJZGRkTp69KhX9wkAAADAu8LCrHrlsX7qcdP7Kq9wuLzd6fsHu3JP4tMmjm6jq/rUrfsx18RqtZqqEZZohuGixMRETZkyRYmJxs+CBwD+Rg0EyAOYS+fWjfT89D6aOLP6O8RUx5V7EZ+xfscE/f0vvd0NDX4UdM3wmjVrjA6hToqPjzfd7aIAwFXUQIA8gPncObqtjp+o0B+f+sbr+76kXbxWvnCN6kWHeX3f8J66ffI6/KaoqEirV69WUVGR0aEAgN9RAwHyAOY05ZaO+vesKxUb472m9dr+TbXm5aGKb2CuU4rNiGYYLsnPz9f06dOVn59vdCgA4HfUQIA8gHmNHZaure/coKv6NKnVfhrWD9e/Z12p954ZpLjYcC9FB18KutOkAQAAAOCXmibX06p/DNYHn/+kF5bu0Kqv9ru8bcpF0brrxra6a3RbXRQf5cMo4W00wwAAAACCnsVi0bUDmunaAc20J7dQ73/2kzZtt2vTDrv27jsmh8MpSWoQG65ubePVvX2CrriksYZecbFCQznhti6iGQYAAACAX2jVLE5/Gd/pjOfKyx0KCbHIarUYFBW8jWYYLomIiFCbNm0UERFhdCgA4HfUQIA8AMLCOPprNjTDcElaWpoWL15sdBgAYAhqIEAeADAfvt4AAAAAAAQdmmG4ZNeuXerbt6927dpldCgA4HfUQIA8AGA+NMNwidPpVHl5uZxOp9GhAIDfUQMB8gCA+XDNMAAAAEwjOipUxetvMzoMt0RH8ZEc3hMSEqJRo0Z5bX9zFizVsZISxcbE6N67xpzz2BtCQkK8sh93kXkAAAAwDYvFopjoMKPDAAxjsVgUGuq9Ns8pyeE89Ts0NPScx3UZp0kDAAAAAIJO3W7l4TfNmzdXRkaGUlJSjA4FAPyOGgiQBwDMh2YYLomMjFTLli2NDgMADEENBMgDAObDadJwSUFBgR577DEVFBQYHQoA+B01ECAPAJgPzTBcUlhYqGXLlqmwsNDoUADA76iBAHkAwHxohgEAAAAAQYdmGAAAAAAQdGiGAQAAAABBh9mkg1TPnj3dWj81NVUPPfSQBg0apOTkZB9FBQD+404dpAbCjPgsACDY0QzDJcnJyXr44YeNDgMADEENBMgDAObDadIAAAAAgKBDMwwAAAAACDo0wwAAAACAoEMzDAAAAAAIOjTDAAAAAICgQzMMAAAAAAg6NMMAAAAAgKBDMwwAAAAACDo0wwAAAACAoEMzDAAAAAAIOjTDAAAAAICgQzNch82ZM0d9+vRRw4YN1aBBA11++eX66KOPjA4LAAAAqNGHH36orl27KiIiQs2bN9fTTz9tdEjwsy+++ELXXXedmjVrJovFoscee8yQOGiG67A1a9ZowoQJ+uyzz7RhwwZddtllGj58uNatW2d0aAAAAMA5Nm7cqOuuu05DhgzR5s2b9fDDD2v69On6xz/+YXRo8KPi4mK1b99eTz31lJKSkgyLI9SwkVFrK1euPOPxU089pY8++kjvvPOO+vbta1BUAAAAQPWefvpp9ezZU7NmzZIktWvXTtu2bdOTTz6pu+++2+Do4C9Dhw7V0KFDJUn33XefYXFwZNhEHA6HioqKFBMTY3QoAAAAwDnWrVunwYMHn/Hc4MGDlZubq7y8PIOiQrDiyLCJPPHEEzp69KgmTpxodCgAAACoQ5xOp/b+lC+Hw3nG8xWVlVW/d2fnnfP4l+rXi1ZSYqPzjlNQUHDOabGnHxcUFCg1NbVWrwOeKys7qdz8g+c8787fQOOEhoqLrTsH5miGTeKFF17QE088oWXLllFEAAAA4BaLxaKcPJtWf7mp2uXHS09o0Rsf1vjYarXonluv93WY8KGw8DCt3fCd9uTsr3b5hf4GGtSvpz9OGO3zOL2J06RNYO7cubr33nu1bNkyDRo0yOhwAAAAUAcN6NNNFycnerTtr/p2V2rShbdNTk6WzWY747kDBw5ULYNxrBaLRg/tr8iIcLe3tUi6cZhn2xqJZriOe/DBB/XII4/oww8/pBEGAACAx0KsVv16+ACFhYa4tV3TJhep/6VdXVq3b9++WrVq1RnPffTRR2rWrBlnNwaAuNgYjbz6cre369uzk1o2beKDiHyLZrgO++Mf/6g5c+Zo8eLFatOmjWw2m2w2mwoLC40ODQAAAHVQYqMGGjrgUpfXDwsL1a+HD1CI1bW24k9/+pM2bNigv/3tb9q5c6deffVVzZ8/X3/96189DRle1qV9urq0a+ny+o0TGuqafj3dGqO4uFibN2/W5s2bdfLkSdlsNm3evFk//PCDu+HWisXpdDovvBqqU1RUpCeeeEJvv/229u3bp7i4OF1++eW6//771aNHD5+Pb7FYqn1+3LhxeuWVV3w+PgAAAMzH6XTqX2+uPGdypOqMvOZy9e7a3q39r1ixQtOnT9fOnTuVlJSkKVOm6M9//rOn4cIHjpee0LxFb6uouOS864VYrfr9bderSeMEt/b/+eefa8CAAec8f+WVV+rzzz93a1+1QTPsoYMHD+qyyy7T3r17FRkZqfbt2ys/P182m02hoaFasmSJRo0aZXSYAAAAgNuKjpVo3qK3dPxEWY3rtGlxscaPHlzjARrUbXuy87TwFxNkVWfwlb1cPkU+EHGatIcmTJigvXv3qnfv3srNzdWmTZuUl5enRx99VBUVFbrtttu0f3/1M7EZYb/NrpLjJ4wOAwAAAHVA/dgYXX/NFTUuj46K0KghV9IIm1irtFRd1r1DjcubpTRWv16d/RiR99EMe2DTpk1asWKFQkNDlZGRoYsuukiSFBISohkzZmjAgAE6fvy45s6da3Ckp1Q6HMpY9qlmL8jQjz/lGx0OAAAA6oDObVuoa/v0apeNvOYK1a8X7eeI4G+Dr+ytxEZx5zwfHh6mXw8fIKuL14oHqrodvZdVVlZq8eLFuvrqq5WYmKiIiAg1bdpUgwcP1ssvv6zK/7vB9Ntvvy1J+tWvfqW0tLRz9nPnnXdKkt566y3/BX8e323/QfYjhQoNsSrFhSnvAQAAAEm67qq+iouNOeO5Szq2Uqc2LQyKCP4UHhaqMcMHymo98wyA4QP7KL5BfYOi8h6a4f9TVFSkq666Srfddps++eQThYeHq0uXLnI4HPr4449155136tixY5Kk9evXS5Iuv7z6acdPP5+Xl6e8vAtPPOBLlQ6H1nz1rSSpX68uiggPMzQeAAAA1B1RkRG6cWj/qscN6tfTtYP6GhcQ/C41OVEDL7uk6nG79Kbq2bmNgRF5D83w/7n99tv12WefKTU1VWvWrNH+/fu1YcMG5eXlqaCgQI8//rjCwk41krt375YktWxZ/ZTjqampCg8PP2Ndo5w+KhwdFaE+l9R8zj8AAABQnfTmKerbo6Mskm4c1l+REeFGhwQ/G9Cnmy5OTlRMdKRuGNzPNNeKM5u0Tl0D3KNHD4WGhurbb79Vx44dz7t+TEyMjh8/rpUrV2rw4MHVrtO4cWMdPHhQb731lsezSs9/9R0dKy71aNtTnCouKZXD6VREeJgiwilcAAAAcJ/T6VR5RYXCwzjLMFhVOhxyOBwKCw01OpQzxNaL0h/G3eDRtoH1Sgzy3nvvSZKGDRt2wUZYkk6cODUrc/h5msuIiAhJUmmp583sseLSC97by1VlJ8tVdrLcK/sCAABAcDpRdtLoEGCwUtV8u626hmZY0vbt2yVJffr0cWn9yMhIHT9+XCdP1lwMyspO/ZFERUV5HFdsPc+35agwAAAAALOrTc9EM6xTk2dJUlzcudOGV6dhw4Y6fvy4jhz53/bu36XuK47j8BuxhJsQcQpiJOAiRJeSoRoy6GacoiQo9C/olC10yhSQLKV/gNVBcLEQyBBx0OoQdBMsjRSpZvFyEwj4Y8ik3g5JpaVpGq7FJjnPM95z4J47vjjfz/fuvnO9Xq9nb2/vZG+jGr3uT5K1XzYz+2Q55yvn8u03X3txFgAAwJ+I4SQtLW9eC76/v/9B+7u6ulKtVrO1tfXO9Z2dnZNb466urobP1fjM8Jtb4SQ5OjrOdxOzDZ8BAADgY2Vm+JR6enry6NGjrK6uftD+3t7eLC0t5enTp+9c/+Pzy5cvp6Ojo+Fz/Rczw2aFAQAA/k4MJxkZGcmDBw8yNzeXjY2NdHd3v3f/7du38/DhwywuLub58+fp7Oz8y/rExESS5M6dO6c6V2PPv5sVBgAAynCamWF/rfTW2NhYZmdnc+XKlUxPT6e/v/9k7eXLl5mamsrdu3dz4cKFJMnQ0FDm5+fT19eXx48f59KlSzk+Ps74+Hju37+fSqWSzc3NU90MN8KsMAAAwL8Tw28dHBzk1q1bWV5eTvLmEef29vbUarVUq9XU6/Xs7u6mtbU1SfLixYvcuHEj29vbqVQquXr1amq1Wmq1WpqbmzMzM5PR0dEz/Q1Hx8f5/ocf82p3Pzf7v8pA35dn+v0AAACfiqb/+wAfi5aWliwsLGRycjIDAwN5/fp11tfX09TUlMHBwUxOTubixYsn+9va2rK2tpZ79+6lvb09z549y+HhYYaHh7OysnLmIZwk6xu/5dXufs5XzuX6tZ4z/34AAIBPhZvhz8jPv27nyU+ruX6tx60wAADAe4jhz8zh0VHq9Xq+aPZuNAAAgH8ihgEAACiOmWEAAACKI4YBAAAojhgGAACgOGIYAACA4ohhAAAAiiOGAQAAKI4YBgAAoDhiGAAAgOKIYQAAAIojhgEAACiOGAYAAKA4YhgAAIDiiGEAAACKI4YBAAAojhgGAACgOGIYAACA4ohhAAAAiiOGAQAAKI4YBgAAoDhiGAAAgOKIYQAAAIojhgEAACiOGAYAAKA4YhgAAIDiiGEAAACKI4YBAAAojhgGAACgOGIYAACA4ohhAAAAiiOGAQAAKI4YBgAAoDhiGAAAgOKIYQAAAIojhgEAACiOGAYAAKA4YhgAAIDiiGEAAACKI4YBAAAojhgGAACgOL8D5IFG3SPu8QYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1225.45x785.944 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1476.28x451.5 with 1 Axes>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# QFT as quantum adder\n",
    "\n",
    "quantum_bits = QuantumRegister(4)\n",
    "classical_bits = ClassicalRegister(4)\n",
    "\n",
    "qft_circuit = QuantumCircuit(quantum_bits, classical_bits)\n",
    "\n",
    "qft_circuit.h(2)\n",
    "qft_circuit.cs(3, 2)\n",
    "qft_circuit.h(3)\n",
    "qft_circuit.barrier()\n",
    "qft_circuit.cz(0, 2)\n",
    "qft_circuit.cs(1, 2)\n",
    "qft_circuit.cz(1, 3)\n",
    "qft_circuit.barrier()\n",
    "qft_circuit.h(3)\n",
    "qft_circuit.cs(3, 2).inverse()\n",
    "qft_circuit.h(2)\n",
    "qft_circuit.barrier()\n",
    "qft_circuit.measure(0, 0)\n",
    "qft_circuit.measure(1, 1)\n",
    "qft_circuit.measure(2, 2)\n",
    "qft_circuit.measure(3, 3)\n",
    "\n",
    "\n",
    "# Plot circuit\n",
    "\n",
    "qft_circuit.draw(output='mpl')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "qiskit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}