Knapsack.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting cplex\n",
      "  Using cached cplex-22.1.1.2-cp310-cp310-macosx_11_0_arm64.whl.metadata (56 kB)\n",
      "Using cached cplex-22.1.1.2-cp310-cp310-macosx_11_0_arm64.whl (29.2 MB)\n",
      "Installing collected packages: cplex\n",
      "Successfully installed cplex-22.1.1.2\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install cplex\n",
    "pip install docplex\n",
    "pip install openqaoa-core\n",
    "pip install openqaoa-qiskit\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from docplex.mp.model import Model\n",
    "import docplex\n",
    "from openqaoa.problems.converters import FromDocplex2IsingModel # function to translate docplex problems into Ising Hamiltonians\n",
    "import openqaoa\n",
    "import qiskit\n",
    "import scipy\n",
    "from collections import defaultdict\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit import Aer\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "backend = Aer.get_backend(\"qasm_simulator\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numpy version: 1.26.4\n",
      "Docplex version: 2.25.236\n",
      "qiskit version: 0.46.2\n",
      "scipy version: 1.13.1\n"
     ]
    }
   ],
   "source": [
    "print(f\"Numpy version: {np.__version__}\")\n",
    "print(f\"Docplex version: {docplex.__version__}\")\n",
    "# print(f\"Openqaoa version: {openqaoa.__version__}\")\n",
    "print(f\"qiskit version: {qiskit.__version__}\")\n",
    "print(f\"scipy version: {scipy.__version__}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Knapsack(values, weights, max_weight):\n",
    "    mdl = Model(\"Knapsack\")\n",
    "    x = mdl.binary_var_list(len(values), name=\"x\")\n",
    "    mdl.minimize(-mdl.sum(var * values[i] for i, var in enumerate(x)))\n",
    "    mdl.add_constraint(mdl.sum(var * weights[i] for i, var in enumerate(x)) <= max_weight)\n",
    "    return mdl\n",
    "\n",
    "def cost_kp(bitstring, list_values, list_weights):\n",
    "    value = 0\n",
    "    weight = 0\n",
    "    for n, i in enumerate(bitstring):\n",
    "        if i == \"1\":\n",
    "            value += list_values[n]\n",
    "            weight += list_weights[n]\n",
    "    return value, weight\n",
    "\n",
    "def objective_KP(samples_dict, problem_data):\n",
    "    list_values =  problem_data[\"values\"]\n",
    "    list_weights =  problem_data[\"weights\"]\n",
    "    max_weight = problem_data[\"max_weights\"]\n",
    "    optimal_value, optimal_weight = cost_kp(problem_data[\"sol\"], list_values, list_weights)\n",
    "    optimal_ising_value, optimal_ising_weight = cost_kp(problem_data[\"sol_ising\"], list_values, list_weights)\n",
    "    results = []\n",
    "    total_counts = 0\n",
    "    probability = 0\n",
    "    probability_ising = 0\n",
    "    for bitstring, counts in samples_dict.items():\n",
    "        value, weight = cost_kp(bitstring, list_values, list_weights)\n",
    "        results.append([value, weight, counts, weight <= max_weight])\n",
    "        if abs(value - optimal_value) < 1e-6 and abs(weight - optimal_weight) < 1e-6:\n",
    "            probability += counts\n",
    "        if abs(value - optimal_ising_value) < 1e-6 and abs(weight - optimal_ising_weight) < 1e-6:\n",
    "            probability_ising += counts\n",
    "        total_counts += counts\n",
    "    probability /= total_counts\n",
    "    probability_ising /= total_counts\n",
    "    return {\"results\":np.array(results), \"optimal\":(optimal_value, optimal_weight), \"optimal_ising\":(optimal_ising_value, optimal_ising_weight), \"probability\":probability, \"probability_ising\":probability_ising}\n",
    "\n",
    "def qaoa_circ(hamiltonian, gammas, betas, n_qubits):\n",
    "    p = len(gammas)\n",
    "    qc = QuantumCircuit(n_qubits)\n",
    "    qc.h(range(n_qubits))\n",
    "    for ii in range(p):\n",
    "        for qbits, value in hamiltonian.items():\n",
    "            if len(qbits) == 1:\n",
    "                qc.rz(2*gammas[ii]*float(value), qbits[0])\n",
    "        for qbits, value in hamiltonian.items():\n",
    "            if len(qbits) == 2:\n",
    "                qc.rzz(2*gammas[ii]*float(value), *qbits)\n",
    "        qc.rx(-2*betas[ii], range(n_qubits))\n",
    "    qc = qc.reverse_bits()\n",
    "    qc.measure_all()\n",
    "    return qc\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------- 10 ------------\n",
      "--------- 11 ------------\n",
      "--------- 12 ------------\n",
      "--------- 13 ------------\n",
      "--------- 14 ------------\n"
     ]
    }
   ],
   "source": [
    "problems = {}\n",
    "np.random.seed(123)\n",
    "lambdas = [0.9603,0.08] # From the paper the lambdas found: https://arxiv.org/abs/2211.13914    \n",
    "# Random Cases with the following values for the problems:\n",
    "values_lim = (5, 63) # Values of the items limits\n",
    "weights_lim = (1, 20) # Weight of the items limits\n",
    "nodes_list_qubo = range(10, 15)\n",
    "num_random_cases = 10 # Number of random cases per problem size\n",
    "# Generate graphs with the above condition for different number of nodes\n",
    "for nodes in nodes_list_qubo: \n",
    "    problems[nodes] = defaultdict(dict)\n",
    "    print(f\"--------- {nodes} ------------\")\n",
    "    for kk in range(num_random_cases):\n",
    "        values = np.random.randint(values_lim[0], values_lim[1], nodes) # Random items' values\n",
    "        weights = np.random.randint(weights_lim[0], weights_lim[1], nodes) # Random items' weights\n",
    "        problems[nodes][kk][\"values\"] = values\n",
    "        problems[nodes][kk][\"weights\"] = weights\n",
    "        problems[nodes][kk][\"max_weights\"] = int(np.sum(weights) * 0.5) # Maximum weight in the knapsack allowed\n",
    "        mdl =  Knapsack(values, weights, problems[nodes][kk][\"max_weights\"])\n",
    "        mdl.solve() # Solving the model using CPLEX: To find the optimal solution - The solution is guarantee to be the optimal by B&B\n",
    "        problems[nodes][kk][\"sol\"] = \"\".join(str(round(mdl.solution.get_value(var))) for var in mdl.iter_binary_vars()) # The solution in binary\n",
    "\n",
    "        qubo = FromDocplex2IsingModel(mdl, unbalanced_const=True, strength_ineq=lambdas) # Convert the CPLEX model into an Ising Hamiltonian model using the unbalanced penalization approach\n",
    "        mdl_ising = qubo.qubo_docplex\n",
    "        mdl_ising.solve() # Solve the new model to find the optimal solution of the Ising Hamiltonian\n",
    "        problems[nodes][kk][\"sol_ising\"] = \"\".join(str(round(mdl_ising.solution.get_value(var))) for var in mdl_ising.iter_binary_vars()) # Optimal solution of the new Ising Hamiltonian (In an ideal case it must be the CPLEX solution found before but in practice it is a solution close to the optimal one in terms of the Hamming distance)\n",
    "        ising_hamiltonian = qubo.ising_model\n",
    "        max_w = np.max(np.abs(ising_hamiltonian.weights))\n",
    "        problems[nodes][kk][\"hamiltonian\"] = {tuple(t):w/max_w for t, w in zip(ising_hamiltonian.terms,ising_hamiltonian.weights) if abs(w) > 1e-10} # Ising Hamiltonian after a normalization \n",
    "# np.save(\"./Data/KP/problems.npy\", problems)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "problems = np.load(\"./Data/KP/problems.npy\", allow_pickle=True).item()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Running QAOA circuits using p = Nq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-------- nodes: 10 ----------\n",
      "-------- nodes: 11 ----------\n",
      "-------- nodes: 12 ----------\n",
      "-------- nodes: 13 ----------\n",
      "-------- nodes: 14 ----------\n"
     ]
    }
   ],
   "source": [
    "shots = 1000\n",
    "delta = 0.5\n",
    "results = {}\n",
    "for nodes in problems.keys():\n",
    "    results[nodes] = defaultdict(dict)\n",
    "    print(f\"-------- nodes: {nodes} ----------\")\n",
    "    for kk in problems[nodes].keys():\n",
    "        hamiltonian = problems[nodes][kk][\"hamiltonian\"]\n",
    "        p = nodes\n",
    "        gammas = np.arange(1, p+1) * delta/p # Annealing linear ramp schedule: cost hamiltonian term\n",
    "        betas = np.arange(1, p+1)[::-1] * delta/p # Annealing linear ramp schedule: mixer term\n",
    "        qc = qaoa_circ(hamiltonian, gammas, betas, nodes) # QAOA circuit\n",
    "        solutions = backend.run(qc, shots=shots).result().get_counts() # Samples results\n",
    "        results[nodes][kk][\"samples\"] = solutions\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Postprocessing: Cost function and constraints analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = np.load(\"./Data/KP/results.npy\", allow_pickle=True).item()\n",
    "for nodes in problems.keys():\n",
    "    print(f\"-------- nodes: {nodes} ----------\")\n",
    "    for kk in problems[nodes].keys():\n",
    "        samples = results[nodes][kk][\"samples\"]\n",
    "        results[nodes][kk][\"postprocessing\"] = objective_KP(samples, problems[nodes][kk])\n",
    "np.save(\"./Data/KP/results.npy\", results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Solutions found using LR-QAOA 1000 shots for 24 items and case 1')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nodes = 24\n",
    "case = 1\n",
    "problems = np.load(\"./Data/KP/problems.npy\", allow_pickle=True).item()\n",
    "results = np.load(\"./Data/KP/results.npy\", allow_pickle=True).item()\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "values = results[nodes][case][\"postprocessing\"][\"results\"][:,0]\n",
    "weights = results[nodes][case][\"postprocessing\"][\"results\"][:,1]\n",
    "counts = results[nodes][case][\"postprocessing\"][\"results\"][:,2]\n",
    "max_weight = problems[nodes][case][\"max_weights\"]\n",
    "for sample in results[nodes][case][\"postprocessing\"][\"results\"]:\n",
    "    ax.plot(sample[0], sample[1], marker=\"o\",linewidth=0, markersize=sample[2])\n",
    "\n",
    "ax.plot(results[nodes][case][\"postprocessing\"][\"optimal\"][0], results[nodes][case][\"postprocessing\"][\"optimal\"][1], marker=\"X\",linewidth=0, markersize=8, color=\"None\", markeredgecolor=\"black\", label=\"optimal\")\n",
    "ax.plot(results[nodes][case][\"postprocessing\"][\"optimal_ising\"][0], results[nodes][case][\"postprocessing\"][\"optimal_ising\"][1], marker=\"P\",linewidth=0, markersize=8, color=\"None\", markeredgecolor=\"black\", label=\"optimal Ising\")\n",
    "\n",
    "ax.plot([min(values), max(values)], [max_weight, max_weight], linestyle=\"--\", color=\"red\", label=\"Maximum weight\")\n",
    "\n",
    "ax.set_xlabel(\"Total value in the Knapsack\")\n",
    "ax.set_ylabel(\"Weight in the knapsack\")\n",
    "ax.legend()\n",
    "ax.set_title(f\"Solutions found using LR-QAOA 1000 shots for {nodes} items and case {case}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16a7380d0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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F92HVLC/tnqzZxUxh92StLma8dE+yag2QXn8txtf/Y9Rd1O4WAE6si+TFyeAkeqjdbQKvG/+yHiPDavq89B4w7aS4i96U541/1WHWGiVCZVDFFhv+/v7Yu3cvruSYo83GfJiEvEKbjfm4+qoO9u7dC39/ftYRioiIwPBunrgimoInB5bjimgKhndrwdv0fVakrXJLzipulVt6jp9WuaXTxqKNT0+k//vXcPrmJ2jb9TMsnf61SutVFyyb5aXdky/K6p6M4qd7klVrgLpcf0pWHrSM3q5qL13dXsvQjNdxiqzHyLAaoqBOA9bVZZsVSoR4ZujcGrpDwmA5eCnMfWfAcvBS6Hz5MwydVbuJrJR0LaPWZvJrGbUye8brWkYs/NcqV4TPd8q3yn2+8w3+TCzipVVOIBBg/7Zw1NA1wr3F92CsVwMRWzeqtE51wbpZXto9qS80VNg9aaDNz2BdVq0B6nL90iTAyMUbtuO3wKhhO17HKarDGBlWQxTUZcA66xa5kigR4tnqE0nQ0hJC374JjFw7QN++CbS0hLw0CUtnTX1WX6hw1lSv+toqnTWlDvz9/eEx8jucyDCVa5U7kWEKj5Hf8dYqx3qwMqvNHtWhWd7CwgK/rl+vsHvyt/X8/CxYTlhQh+tnOU6RdTIuxWrPQUA9BqyzbpEriRZULIeyFlSUqjf3CIolpV9ybS0B7i7t9dHnf5/Tp0+jU6dOb1uAbEvvrnLxQTHabMzHqVOn0LFjR5XGwpI67PfGkmwhN/zbJfPvv2FDmql82xOO49Cvfz8cPnEYdb+vW2qbj3vz7qF3t94q326kZBz2s+yRtiwNvbuqvl4p1ovpsb5+gN1+f+q0qCPLBQ1Z3gNlLiz700No3VPewrK0oOJHUvZgaSmh1rt/B76/XJlYz5pSFz3crLF+mCeaerVFrSad0NSrrcYkQcDbVklIxHiddhN58WfwOu0mIBHz0ir53mb5zfw1y7NeS4n1Ynqsr1+KxRo60jEyL08qHif1kqdxUqy7hljdA+rSIlcSJUJlUMVgaQAQK2gNel+5MqnDrCl10cPNGkcnt8ed73vi6OT2GpMEAUDs2WN48ssoZOyYi6w/ViBjx1w8+WUUrkcf46V+CwsLjJsTXLpZ/mo2xs0O5u0vYtbdk6zvQZbXz3INHYFAAN/evijKK8LjTY9l5RzH4fGmxyjKL0Lvz3qrPA516BpicQ+oQ/f4u6hrrBzK7hrrsToat5+8KlXuYm2Mo5Pbf/T530e235lBBg4MYrvfGWEjIiIC/fr1Q29nbczz1oWbhRBxmWJ8f7YIhxOLsG/fPl7GSXVfdQbnwuag4PFVOM1xQEpwKvQ+8UT78cEq/z0g7PVYHY07T17JtQEJBEBDK/7eB2sVPca1dEmpPfeaWQvxQtdGpe+DfHUNqSNpl9yffx3Gp0tKd48nz7sHXyV1j1PXmJqa4lMfgPwgQYCfQYIl1zJSPGuKv7WMCP/K22LkMxVvMVLS/Wf5qPXOOjK1uk6o9tu8kLdSsvIgkYjx5t/u2TdpNyERi3n5+UtXmF/XUw9+LtrI2Pz47Z57mx/D31Ub63rqqXSFeXXqGmIxaULaJceJdRXOXOQkerx301IixDPWYwP8/f3hPuJbhbOm3Ed8y9usKdZYzZpiqbwtRuapeIuRkpzMjaD9zjoy2jXMqv02L+Qtw8cxyHinezbjl1EwfByj8rqlYyAbW2oj7DN9GEokuLc4GUYSCX7upa/ysZLq0jXEsnvSwsICNX0mKJy5WLPLBN5bw0pPHSIq18PNWuWzc94n36Y5LL/+rdSsqXxdHWYx8endWVPSNwA+Zk2xpE6D5af41Me4rddQw9UbRi7eTLZ5iYxLx+oTSUjJyoOTuRGm+NTn9ecvFotx9uxZpKenw9raGt7e3hrRGhsREYEb4QvwWX0h5vU3LNE9m40j4QsQ0dtVpX+QlRwr2cpWG+t76WPy8QKs6aYHCyMtXHxQLHecskkHax8+cRi1u9Qu1TXE14KGskkTJT4H9O0a4ceoJF5+DwwbesPw9lk83nwVep/oybZZMXLhd5sVgMYIlUkkEkEkEkEsFiMxMVFpY4TUQduQKDx6+aZUuW1NA5yb1ZmXGFh+CLEcn8CSui2fwGr6tLRuVksIAG+TgYDAQDwpkXRaWVtDtG5dtW6VlY1T1M/Agf+xGaeoDmMl1WGMkE3/b/D8xHoUZGfJyvRMzVHLZywe7/1epXUDbz+H0h49wePfxoIT50OgbQSbr8LgYGuttM8hGiP0kVQ1a0ydcTxNX2XZJAuwW9WXNXXZYkSK5awpVltcAP+t7t7C+Knc6u7NjbOq/eru0u7Zud46Crtn57RVffesOoyVZL2gYUREBJ5ELEFXy5dy96CPZTaeRCzh5R6c39sVwne6x4VGZvjmM1eV1/0uSoQ0UFZuoeLyV4rLlU3hOjYcP+vYAGxX9ZUSi8U4ffo0duzYgdOnT/MyQFn6AXA4SfEWI4eT+NliRB2wSobLW939s2q+uru6dM/6+/vD+YsFCsdKNvhyIS+tcgMHDoSfvx8ytma8Hay9NQP+/fwxcOBAldb73z2oU8Y9yM+kCel42Rade+HTidvQolNPXsfLlkRjhDSQk7lR6a4h8JcI3Dx3XGGTbKHPWICHrinp+JR3V/Xla3xKREQEpk2djPtpD2Vljva2+GHVjyp/A/b394eV/zycOLEehzfKv/5W/mN57ZZh2T2q8HeAh2RY2iKyY5ShwhaRue100Gbj2xaR6ri6+7vjc97F51pmBbaeCsdKvtHi5w8B6eypBi4NcG/xPZgam/IyW0rd7kEWi2q+i1qENFAHZ/PSfw0DaF+/jsrrVocm2R5u1hjb3gm6wre3v65QC2Pb1+XlLxFpt0hj/Qy5629skMFbt0iTdt1g9fVvchv/Wo39De7e3VRetxTr7lHpXlcl8ZEMq0uLCCvS7tnvy+ieXcJz96zgnX0fBTwlQVIsFjRUl3uQ9XtASZQIaaAziVkKy6OTnqq0XnVpko2MS8f66BQUFksAAIXFEqyPvqfyX0DZOj71tXHgf/py139gkD56O/PTLTLFpz6gJYSBw9sPAAOHJoBAyOuMLZZjdN5PtX+RqtPq7iyWkJB2zx4po3v2CI/dszZm+orLayouV5WBAwci/VE6BgwYwEt96nIPqtN7ACVCGiglS/E4CFWPj/hvHRvFAyXn8rSODatfQHUYKAqwbRGTYj1gXXoPlMTHPaAuLSIs/xr39/fH4DmrFY7PGTxH9d3DUvN7Kx6UO/8z1U5bL4lFMiq9B5eeU3wPBp/n5x5k/R5QEiVCDLBezI/VYGF1aZJl9QuoLtcvbREr+LdFrICnFrGSWA9YZ3UPqEuLCOu/xp/VaQrLd7pnLb/+Dc8tPHipH/hvsK6L9dvFbV2s+V3cllUyWnLWXN9d8vdg31387TDA+j2gJEqEeKYO/aLS8RElt/ngY3yEujTJmtfQ/aByZVGX6//uz/gPKlcFVveglJO54jdbPt6E385YWqiwRcSZpxlLLLe4kNavaHwO360BmrqEg7+/P/bu3Yt/XlvK3YNxb6ywd+9eXu5B1u8BJdGssTKUXFBRmd538/O2oOC/fwnxvZjdf90CGTj0P2Gphcz4Hij5LoHg3b9PlOu/dXwycFDB9fO1js9jBYtpvq9cFVjdg1IdnM0Vbn7Mx4QBAOAcvWD5dbNSM5Y4nlZ3N3wcg9SIH0vN3HTxnwygp8rrZzVrT52w7hry9/dHnz59mK1uzvo9oCRKhMoQEBCAgIAA2cqUysL65pdisc2HtEm2X79++HwnMK+djmx5/SXnpLufq75Jtqx1lJ6+KlBpvepy/eqC5VYzZxKzAIkYb0puL2DbCNFJTzEHLiqv38ncCLefvIK+fRO5cj4SAdZbXADsl7BQB+qQDAqFQqbLNLDebkqKEiGeqcPNz5K/vz++mLsa+0Tfl1rH5ou583lpkmX5M/D390edvnNx4tQvpa6/Tt+vebl+GzN9hVusfFLTQOV1qwvWa1mxapF6d+aitFXy7cxNIfrueoPpQVPQp08flSbk0gH74RdSUVAsga5QCyPaOPLeGsByLaspPvUxdvOVUq2CmpQMqgtKhHhGfwkBQwcPxLkip1JvAEMHe/JSP+ufQX2vznhY36vU9dvVrsFL/fN7u2Lc1mulyvle2p7Vh5B0LavP6muXbhGJWIKIiGYqT0j/vKl4TODhf9Ixp5fqWqTKW0xvTlt+FtOTDtiXkg7Yb2pvxlsiwnrz5fzEiyjcGoiMd/aby2+1DnCrvvvNlcR642MpGizNM2m/aEOrtzMVGlrxO1NBHaw+kQStdwZKagmFvM1YYf0z6N3EWuFA0c8a8ztGjNVsGYDdpAF1WcuqrPFYj168Vmm96jJzUR0G7KvDfnOexllyC6t6mlT//eakIuPSMXbzFcRePo/nN08h9vJ5jN18hcmCitQixIC69Iuyog7jpK6nvcC9p3koKJbg3tM8XE97zlsi8L4FLfkYnwKwvwdZTRpQt+0F+KYuW1yow4B91vvNKeqePDCIv+5J1uaE/oYMBQP252RNRo+N3/AaC7UIEd6VNU29jrEeL/UHH4lXsI5OCoKP8PPXKKsFLdWJpq/lxGpVY3VZTE8dsFrHRl0WVmUpIiICsb/PV7jVUuzv83lvEaNEiKgNjqcN98IvpH5QubKp00JirDiZG72dtVViHRtwYpW/BuqylhOrVY3VZTG9shJBPgfss1rHRl2ScVZkLWLO2gq7p3s789M9XRIlQoR3GTmKp6lnZKt2+rqUtCWoouXKxmrDz5JYr27uiSQ8+WUUMnbMRdYfK5CxYy6erB+FFhw/W1ywbhFhOU5LHRbTKysR5HPAPqutZtQlGWflv62WdJlutVQSjREivBNqCVAsKd36I9RS7YKGUnraWgqTHj1t1n8X8NMixnq2TEREBJYEjSk1a2vJ2WwsCRqDpvY1VfZhLG0R6d+/P/rueoM5bf9byyn4fBH+TCzG3r38rOXEcpwWLab338w16btOIU8z1/5LxjNwYFDphVWre/ekOraIsX7nV7kHDx6gY8eOcHV1RZMmTbBnzx7WITH/a5x1DGIFSdD7ypVtRBuHMsodeamf1Yaf79bPYrZMyYGiB/+nL9csfvB/+ujtrK3yZnF1aBFRB38lZCIkVguLbpkhJFYLfyVk8lo/y+0tAHa/B+rSPcmKOraIVftESFtbG6tXr0Z8fDyOHz+OKVOmIC+P3aBUddhrjHUM9SxqlE4EANS35GcdnTm9XDG2vZOsBUhP+22TuCrXbymJ9aw5lvWry0BRf39/3L13H6dOncL27dtx6tQpJCWnaEwSxPo9QB2w/D3Q5GT8v62GFHdP87XVUEnVPhGytraGh4cHAMDKygrm5uZ4/vw5s3hY7/qsDjEoHKQIfsfINLWvCSdzI+hpa8HJ3AhN7c14q5v1YGmW9atTs7h0e4HBgwejY8eO1fYvcEVYvweoA9a/h5qajEtbxA4nFePznfItYp/vfIPDSfy3iDFPhKKjo+Hr6wsbGxsIBAIcOHCg1DEikQiOjo7Q19eHl5cXLl++XKm6YmJiIBaLYWdn95FRVx7r1gB1iIH1goas/xpmvesyy/rVsVlcE7F+D1AHrH8PAc1NxqUtYjGvzOVaxK7l1mHSIsZ8sHReXh7c3d3x1VdfKbz4Xbt2ISgoCGFhYfDy8sLq1avRvXt33LlzBxYWFgAADw8PFBcXl/re48ePw8bGBgDw/PlzDBs2DBs2bHhvPAUFBSgo+G/2Uk5OzsdcXinqsNeYOsTAcqAoq8X8pFgPFGVZv7RZ/PuzGTj0v9IDRZcwaBbXROrwHsAa699DTcd6wH5JzBOhnj17omfPnmU+HxoaijFjxmDkyJEAgLCwMBw+fBgbN27E7NmzAQCxsbHvraOgoAB9+/bF7Nmz0aZNm/ceGxwcjMWLF3/YRXwA1vtcqUsMLPeYUZe/hqXd42//5WegOOv6pc3i/fr1w+c7gXnt/pu1teRcEQ4nFmHfPn6axYOPxMs2/dTT1sKINg6Y04vf/dZYkb4HlKRpex4CbFeYJ/+1iLHGvGvsfQoLCxETEwMfHx9ZmZaWFnx8fHDx4sUKnYPjOIwYMQKdO3fG0KFDyz1+zpw5yM7Olj0ePHhQ6fgVYd0tpA4xsO6aYj02gPX1s67f398fHiO/w4kMU7lm8RMZpvAY+R0vzeKsVxdn7XraizLK2Y2f5Jum3wPkP8xbhN4nKysLYrEYlpaWcuWWlpa4fft2hc5x/vx57Nq1C02aNJGNP9qyZQsaN26s8Hg9PT3o6al2qwfW+zyxjoF11xTrFjHW18+6fgAIDhqFseZNUPDwFsS5LyCsURN6to0QPKwlL/W/b3VxTWgV0vTrB+g1ANjv/s66fim1ToSUoV27dpBIPnzFYJFIBJFIxOsy35qCddcU67EBrK+fdf1SAi0h9O2bvBsJL3WzXl2cNU2/foBeA9YLq7KuvyS17hozNzeHUChERkaGXHlGRgasrFT7oRUQEID4+HhcuXJFpfVoItZdUwDbxdxYXz/r+gH2i0qWtYY5P2ubs6fp1w+UvZI8+xXm+cF6CQXW9Zek1j9xXV1dNG/eHFFRUbIyiUSCqKgotG7dWqV1i0QiuLq6wtPTU+nnVoeVpVlSh2mrLLHea0wdXn/WrVKCMj7xyyqvbjT9+gH2K8yzxvp3kHX9JTFPhHJzcxEbGyub+ZWSkoLY2FikpaUBAIKCgrBhwwZs2rQJCQkJGD9+PPLy8mSzyFRFVS1CrAeqqgPWg7XVFz/dQurw+pvX0FVYXsdYtePzpKxNFe9+bmPG3+7nLDlbGissb2CluLw6Yr3CPGusW4ZZ118S8zFCV69eRadOnWRfBwUFAQCGDx+O8PBwDBo0CE+fPsWCBQvw5MkTeHh4IDIystQA6qpCHQaqqgN1GDDOyrv3AMD/PaCurz/HYBkBdaqfL6wnDKiLOb1cNWZg9LtY3wOs6y+JeYtQx44dwXFcqUd4eLjsmMDAQKSmpqKgoACXLl2Cl5eXyuNSVdeYOjUHEjboHgCycgsVl79SXF7d6mdNHVoFCVus7wHW9ZfEvEVIXQUEBCAgIAA5OTkwNTVV2nlpRVdC9wD714B1/epAXVsFCb9YLuyqLvcg8xYhTaMOA1UJW3QPsH8NWNdPCGs0XvU/lAjxTJ2aAwkbdA+wfw1Y108Ia+o0fZ01AcdxmjE68AOVXFAxMTER2dnZMDExYR0WIYQQ8tEafHNU4eKRetpauPN92ft/ViXSoS3lfX7TGKEyqGqMECHkLXVZXp9oLk2+B53MjXD7yatS5Zo0Tk6KusYIIbyj8QmENU2/Bzs4myssb1+/Ds+RsEeJECGEdzQ+gbCm6ffgmcSs0gsaAohOesoiHKYoESqDKrfYIETT0VpKhDVNvwcVXj805/pLokSoDLTpKiGqo07L6xPNpOn3oKZff0mUCBFCeEfr+NDmy6xp+j3IevNnQH1+BygRIoTwTtPX8dH0gbrqQNPvwbLxs6KOOv0O0DpC5ajoOgSEEFJRPVZHK9zio6GVMY5Obs8sLqI5WN+DfNRf0c9vahEqAw2WJoSoiqYP1CXssb4HWddfEiVCZaDB0oQQVaGBqoQ11vcg6/pLokSIEEJ4pukDdQl7rO9B1vWXRFtsEEKYCD4Sj/ALqSgolkBPWwsj2jhgTi9X3upnub1CDzdrjG3vJLt+XaEWRrRxpIG6Gob1PdjV1QIn4jPfFnBAV1dLXjc+VpffAWoRIoTwLvhIPNZHp8g2fSwolmB9dAqCj8TzUj/rGSuRcelYH52Cwn+vv7BYgvXR92jWmAZhfQ8GH4nHX/GZcitr/xWfwevvoLr8DlAiRAjhXfiF1A8qVzbW2yuwrp+wx/oe0PTfwZIoESoDzRojRHWkLUEVLVc21jNWWNdP2GN9D2j672BJlAiVgWaNEaI6etqK33rKKlc21jNWWNdP2GN9D2j672BJlAgRQng3oo1DGeWOvNTPesYK6/oJe6zvAU3/HSyJVpYuB60sTYhqlJ415og5vVx4qz8yLh0/RiXh3tM81K1jhMldnHmdscK6fsIe63uguv8OVvTzmxKhclAiRAghhFQ9tMUGIYQQQkg5aEFFwgTLhcTUgaZfP6F7YMzmKzjx7zo2AgA+rhbYMEyzZumyvgdY168uqGusHNQ1pnzShcSka0hI/w0b0kwjfgk1/foJ3QNjNl/BX9IVjUvoqkHJEOt7gHX9fKCuMaK21GkhLRY0/foJ3QMnFCRB7yuvjljfA6zrVyeUCJWBFlRUHXVaSIsFTb9+QvdAWd0QmtQ9wfoeYF2/OqFEqAy0oKLqqNNCWixo+vUTugfevfbyyqsj1vcA6/rVCSVChHfqtJAWC5p+/YTuAR9XC4XlXV0teY6EHdb3AOv61QkNli4HDZZWDdYLibGm6ddP6B54d9ZYV1dL/DKsBeuweMX6HmBdv6rRgopKQokQIYQQUvXQrDFCCCGEkHJQIkQIIYQQjUWJECGEEEI0FiVChBBCCNFYlAgRQgghRGNV+0To5cuXaNGiBTw8PODm5oYNGzawDokQQgghaqLa7z5vbGyM6OhoGBoaIi8vD25ubvD390ft2rVZh0YIIYQQxqp9i5BQKIShoSEAoKCgABzHgZZOIoQQQgigBi1C0dHRWLFiBWJiYpCeno79+/ejb9++cseIRCKsWLECT548gbu7O9auXYuWLVtWuI6XL1+iQ4cOSEpKwooVK2Bubq7kq6h6IuPSsfpEElKy8uBkboQpPvXRw82adViEEJ4EH4lH+IVUFBRLoKethRFtHDCnlyvrsHjF+n3w83VncfNhjuzrJrYmOBTozVv9rK+fdf1SzFuE8vLy4O7uDpFIpPD5Xbt2ISgoCAsXLsS1a9fg7u6O7t27IzMzU3aMdPzPu4/Hjx8DAMzMzHDjxg2kpKRg+/btyMjI4OXa1FVkXDrGbb2GO09eoaBYgjtPXmHc1muIjEtnHRohhAfBR+KxPjoFBcUSAEBBsQTro1MQfCSecWT8Yf0++G4SBAA3H+bg83Vneamf9fWzrr8k5olQz5498f3338PPz0/h86GhoRgzZgxGjhwJV1dXhIWFwdDQEBs3bpQdExsbi7i4uFIPGxsbuXNZWlrC3d0dZ8+WfaMVFBQgJydH7qEqBw4cwNq1a/H69WuV1aHI6hNJEACQdhBKN977MSqJ1zgIIWyEX0j9oPLqiPX74LtJUHnlysb6+lnXXxLzROh9CgsLERMTAx8fH1mZlpYWfHx8cPHixQqdIyMjA69evQIAZGdnIzo6Gg0aNCjz+ODgYJiamsoednZ2H3cRZZBIJJg7dy4mTZoER0dHhISEqDTpKiklKw/vjpLiOODe0zxe6ieEsCVtCapoeXWk6e+DrK+fdf0lqXUilJWVBbFYDEtLS7lyS0tLPHnypELnSE1Nhbe3N9zd3eHt7Y2JEyeicePGZR4/Z84cZGdnyx4PHjz4qGsoi0QikSVBmZmZmDNnDuzt7TF//nxkZWWppE4pJ3MjCN4pEwiAunWMVFovIUQ96Gkrfusvq7w60vT3QdbXz7r+kqr9Xd+yZUvExsbixo0buHnzJsaOHfve4/X09GBiYoItW7agVatW6NKli0ri0tbWxrhx45CYmIjNmzfDxcUF2dnZ+P777+Hg4ID169erpF4AmOJTX9YMiX//5ThgchdnldVJCFEfI9o4lFHuyG8gDLF+H2xiq3g3dHdbU17qZ339rOsvSa0TIXNzcwiFwlKDmzMyMmBlZaXSugMCAhAfH48rV66otB4dHR0MHToUcXFx2LdvH5o1a4b8/HzUrVtXdoyyp/v3cLNG2JBmaGhlDD1tLTS0MkbYkObo4aba15QQoh7m9HLF2PZOshYgPW0tjG1fF3N6uTCOjD+s3wcPBXqXSobcbU1xMLAdL/Wzvn7W9Zck4NRoUR2BQFBq+ryXlxdatmyJtWvXAnjbpWRvb4/AwEDMnj1b5THl5OTA1NQU2dnZMDFRnMErE8dxOHv2LLy9vSH4N1VetGgR7t69i9mzZ8PNzU3lMRBCCCFVXUU/v5m3COXm5iI2NhaxsbEAgJSUFMTGxiItLQ0AEBQUhA0bNmDTpk1ISEjA+PHjkZeXh5EjR6o0LpFIBFdXV3h6eqq0nncJBAK0b99elgTl5+dj9erV2LZtGxo3bgw/Pz+Vt1IRQgghmoJ5i9Dp06fRqVOnUuXDhw9HeHg4AGDdunWyBRU9PDywZs0aeHl58RIf3y1CisTExCA4OBgRERGybrKuXbti3rx5ckkTIYQQQt6q6Oc380RI3alDIiSVkJCAkJAQbNu2DWKxGAAQEhKCWbNmMY2LEEIIUTdVpmtMXbHqGnsfFxcXbNq0CUlJSRg/fjyMjIwwYMAA2fPPnz+XJUiEEEIIKR+1CJVDnVqE3pWTkyMXU//+/REXF4fZs2fjyy+/hI6ODsPoCCGEEHaoRUgDlPzBZmdn4/Tp07hz5w5GjhyJevXqQSQS8b59ByGEEFKVUCJUBnXsGnsfU1NTpKSkYPny5bC0tERaWhoCAwPh5OSE5cuX87Z9ByGEEFKVUNdYOdS5a6wsb968wcaNG7F8+XKkpr7dRHH16tWYPHky48gIIYQQflDXmAbT19fHhAkTkJSUhPDwcLRt2xajR4+WPX/t2jU8fvyYYYSEEEKIeqhUIpSXpxm781Z1Ojo6GD58OM6dOwcjo7cb2XEchxEjRsDJyQnjxo3DvXv3GEdJCCGEsFOpRMjS0hJfffUVzp07p+x41EZVGyNUUc+ePYOpqSkKCwuxfv16ODs7Y+jQoYiPj2cdGiGEEMK7SiVCW7duxfPnz9G5c2c4OzsjJCSk2nW18LXpKt/Mzc1x9uxZREdHo3v37hCLxdi6dSsaNWoEf39/xMXFsQ6REEII4U2lEqG+ffviwIEDePToEcaNG4ft27fDwcEBvXv3RkREBIqLi5UdJ1Eyb29vREZG4urVq/D39wcA7N+/X7bHGyGEEKIJlDZrbO3atZgxYwYKCwthbm6OcePGYfbs2TA0NFTG6ZmpirPGKiM+Ph7btm3D999/L9u7bPPmzTA3N0fPnj1pPzNCCCFVCi97jWVkZGDTpk0IDw9Hamoq/Pz8MGrUKDx8+BDLli2DjY0Njh8/XtnTqwVNSYTe9erVKzg4OODFixdo2rQp5s6dCz8/PwiFQtahEUIIIeVS6fT5iIgI+Pr6ws7ODtu3b8eECRPw6NEjbN26FZ06dcLQoUNx8OBBnD59urLxM1ddB0tXlFgsxqhRo2BkZITr169jwIABaNSoETZt2oSioiLW4RFCCCFKUakWIVNTU/zvf//D6NGjy0wUXr9+jeXLl2PhwoUfHSRLmtoiJPXs2TOsWbMGa9aswcuXLwEADg4O2LhxIzp37sw2OEIIIaQMKu0ay8/Pr/JjfypK0xMhqZycHISFhSE0NBSZmZlISEhAgwYNWIdFCCGEKKTSrjFjY2NkZmaWKn/27BmNIammTExMMHPmTKSkpODIkSNySVBgYCAWLlyIZ8+eMYyQEEII+XCVSoTKakQqKCiArq7uRwVE1JuBgQF69Ogh+/revXv4+eef8e2338LBwQHTp09Heno6wwgJIYSQitP+kIPXrFkDABAIBPj1119Ro0YN2XNisRjR0dFo2LChciMkas3BwQG7du3CkiVLEBsbix9++AHr1q3DyJEjMXPmTDg5ObEOkRBCCCnTB40Rkn6opaamwtbWVq4bTFdXF46Ojvj222/h5eWl/Eh5JhKJIBKJIBaLkZiYqPFjhMrDcRwiIyOxZMkSnD9/HgAgFAqxf/9++Pr6Mo6OEEKIplHpYOlOnTohIiICNWvW/KggqwIaLP1hOI7D2bNnsWTJEly+fBmpqamy1y0vL0+2+SshhBCiSrwsqKgJKBGqvIyMDFhaWgJ4myB5enrC3Nwc8+bNg7e3N+PoCCGEVGcV/fyu8BihoKAgfPfddzAyMkJQUNB7jw0NDa14pKTakiZBAPDPP/8gNjYWYrEYx44dQ7t27TBv3jx0796dtu8ghBDCTIUToevXr8tWFL5+/XqZx9GHGlGkSZMmSExMxPLly/H777/j3Llz6NmzJ5o1aybbvkNLq1KTGAkhhJBKo66xclDXmPI9evQIoaGhCAsLQ35+PgDg8OHD6NWrF+PICCGEVBc0RkhJKBFSnaysLKxZswanTp3CmTNnZC1C169fh4uLC/T19RlHSAghpKpSeiLk7+9f4cojIiIqfKy6o0RI9TiOk3Wp5ufnw9HREUKhENOmTcPYsWNhbGzMOEJCCCFVjdK32DA1Na3wg5APUXJcWVJSEvT19fHkyRPMmDEDDg4OWLx4MZ4/f84wQkIIIdUVdY2VgRZUZKewsBDbtm1DSEgIEhMTAQA1atTA+PHjMX36dFhYWDCOkBBCiLqjMUJKQl1j7IjFYuzbtw9Lly7FjRs3AABxcXFo1KgR48gIIYSoO6WvI9SsWTNERUWhZs2aaNq06XunyV+7du3DoiVEAaFQiIEDB2LAgAE4cuQI/v77b7kk6LfffkPbtm1pfztCCCGVVuFEqE+fPtDT0wMA9O3bV1XxEFKKQCDAZ599hs8++0xWdv/+fYwdOxYSiQT9+vXD3Llz0bRpU4ZREkIIqYqoa6wc1DWmnpKSkjBjxgwcPHhQVtazZ0/MnTsX7dq1YxgZIYQQdcDLGKGrV68iISEBAODq6ormzZtX9lRqixIh9fbPP/8gJCQEO3fuhEQiAQC0b98ev/76K+rXr884OkIIIayoNBF6+PAhBg8ejPPnz8PMzAwA8PLlS7Rp0wY7d+6Era1tpQNXN5QIVQ3JyclYtmwZwsPDoa+vj9TUVNSsWZN1WIQQQhhR+jpCJY0ePRpFRUVISEjA8+fP8fz5cyQkJEAikWD06NGVDpqQyvr000/xyy+/4N69e9i+fbssCeI4DiNGjMDWrVtRXFzMOEpCCCHqplItQgYGBrhw4UKpwakxMTHw9vaW7R9VHVCLUNV2+vRpdOrUCQDg5OSEWbNmYfjw4bR9ByGEVHMqbRGys7OT7URfklgsho2NTWVOSYhKNG3aFEuXLkWdOnWQkpKCcePGoW7duvjhhx+Qm5vLOjxCCCGMVSoRWrFiBSZOnIirV6/Kyq5evYrJkydj5cqVSguOkI9lamqKOXPm4P79+/jxxx9ha2uL9PR0TJ8+HQ4ODrLB/oQQQjRThbvGatasKbeIYl5eHoqLi6Gt/XYpIun/jYyM1HJfqPz8fLi4uGDAgAEflKxR11j1UlhYiC1btiAkJARaWlqIj4+HUCgEABQVFUFHR4dxhIQQQpRB6StLr169WhlxMbNkyRK0atWKdRiEMV1dXYwaNQojRozAgwcPZEnQmzdv4Obmhp49e8paiwghhFR/FU6Ehg8frso4VCopKQm3b9+Gr68v4uLiWIdD1IBQKISjo6Ps6z/++APJyclYt24dwsLCMGTIEMyePRsNGjRgFyQhhBCVq9QYoZLevHmDnJwcuceHiI6Ohq+vL2xsbCAQCHDgwIFSx4hEIjg6OkJfXx9eXl64fPnyB9Uxffp0BAcHf9D3EM3Sv39/REVFoUuXLiguLkZ4eDhcXFwwcOBAxMbGsg6PEEKIilQqEcrLy0NgYCAsLCxgZGSEmjVryj0+9Fzu7u4QiUQKn9+1axeCgoKwcOFCXLt2De7u7ujevTsyMzNlx3h4eMDNza3U4/Hjxzh48CCcnZ3h7OxcoXgKCgo+KrEjVZNAIEDnzp1x4sQJXLx4EZ9//jk4jsOePXvQtGlTJCcnsw6REEKIKnCVMGHCBM7FxYXbu3cvZ2BgwG3cuJH77rvvOFtbW27r1q2VOSX376Btbv/+/XJlLVu25AICAmRfi8VizsbGhgsODq7QOWfPns3Z2tpyDg4OXO3atTkTExNu8eLFZR6/cOFCDkCpR3Z2dqWuiVRdN2/e5AYPHsz5+vrKlSckJHASiYRRVIQQQioiOzu7Qp/flVpQ0d7eHps3b0bHjh1hYmKCa9euoV69etiyZQt27NiBI0eOVCopEwgE2L9/v2x3+8LCQhgaGmLv3r1yO94PHz4cL1++lNtwsyLCw8MRFxf33lljBQUFKCgokH2dk5MDOzs7mjWmwcRisWxQ9aNHj1C3bl24u7tj7ty5+Pzzz6Gl9dE9zIQQQpRMpQsqPn/+HHXr1gUAmJiYyKbLt2vXDtHR0ZU5pUJZWVkQi8WwtLSUK7e0tMSTJ0+UVk9Jenp6MDExwZYtW9CqVSt06dJFJfWQqkOaBAHA5cuXIRQKceXKFfj5+aFJkybYtm0bbd9BCCFVVKUSobp16yIlJQUA0LBhQ+zevRvA25k30k1Y1dGIESMqvIZQQEAA4uPjceXKFRVHRaoSPz8/3L9/H3PnzoWJiQlu3bqFIUOGwNnZGevXr5drTSSEEKL+KpUIjRw5Ejdu3AAAzJ49GyKRCPr6+pg6dSpmzJihtODMzc0hFAqRkZEhV56RkQErKyul1UPIh7CwsMCSJUuQmpqKJUuWwNzcHCkpKQgKCsKrV69Yh0cIIeQDVHgdoZKmTp0q+7+Pjw8SEhJk44SaNGmitOB0dXXRvHlzREVFycYISSQSREVFITAwUGn1KCISiSASiSAWi1VaD6m6zMzMMHfuXEyePBm//vorXr9+DXNzc9nz4eHh6Nu3r1q3khJCiKar1GBpZcrNzcXdu3cBvN0gMzQ0FJ06dUKtWrVgb2+PXbt2Yfjw4Vi/fj1atmyJ1atXY/fu3bh9+3apsUOqQFtskMo4d+4cvL29YWxsjICAAEyZMoWX+5UQQshbKh0sDQBRUVHo3bs3Pv30U3z66afo3bs3Tpw48cHnuXr1Kpo2bYqmTZsCAIKCgtC0aVMsWLAAADBo0CCsXLkSCxYsgIeHB2JjYxEZGUkfKkStFRcXw83NDa9evUJISAgcHR0xadIkpKWlsQ6NEEJICZVqEfrpp58wefJk9O/fH61btwYA/P3339i7dy9WrVqFgIAApQfKt5JdY4mJidQiRD6YRCLBn3/+iSVLlshWQ9fW1sbQoUMRGhpKXWaEEKJCFW0RqlQiZGtri9mzZ5capyMSibB06VI8evTowyNWU9Q1Rj4Wx3GIiorC0qVLcerUKTg5OSExMRHa2pUaokcIIaQCVNo19vLlS/To0aNUebdu3ZCdnV2ZUxJSbQkEAvj4+ODkyZO4cOECfvrpJ1kSVFhYiJEjR+LixYuMoySEEM1UqUTo888/x/79+0uVHzx4EL179/7ooNSBSCSCq6srPD09WYdCqpHWrVvL/RGxdetWhIeHo02bNrK9zhjPXyCEEI1S4a6xNWvWyP6fk5ODlStXom3btnJjhM6fP49p06bhm2++UU20DFDXGFGlu3fvIjg4GJs3b5atTt2yZUvMnTsXvr6+tH0HIYRUktLHCDk5OVWoYoFAgHv37lUsyiqAEiHCh7S0NKxcuRIbNmzAmzdvAABubm44f/483XeEEFIJKh0srUkoESJ8yszMxKpVqyASidCqVSscP35c9hzHcRAIBAyjI4SQqkPl6whJcRxXLcc00BghwoKFhQWCg4ORlpaGsLAwWfmTJ0/g7OyM1atXIy8vj2GEhBBSvVQ6Edq8eTMaN24MAwMDGBgYoEmTJtiyZYsyY2OKNl0lLJmZmaFu3bqyr9evX4+7d+9i6tSpcHR0xNKlS/Hy5Ut2ARJCSDVRqUQoNDQU48ePR69evbB7927s3r0bPXr0wLhx47Bq1Splx0iIxps9ezbWr1+PunXrIisrC/PmzYODgwPmzZuHp0+fsg6PEEKqrEqNEXJycsLixYsxbNgwufJNmzZh0aJFSElJUVqArNEYIaJOiouLsWvXLgQHB+PWrVsAgFq1auHhw4cwMDBgHB0hhKgPlY4RSk9PR5s2bUqVt2nTBunp6ZU5JSGkArS1tfHll1/i5s2b2L9/P1q0aIHBgwfLJUHVaWV3QghRtUolQvXq1cPu3btLle/atQv169f/6KDUAQ2WJupMS0sLffv2xeXLl7Fy5UpZ+ZUrV2Bvb4/Bgwfjn3/+YRghIYRUDZXqGtu3bx8GDRoEHx8ftG3bFgBw/vx5REVFYffu3fDz81N6oKxQ1xipSpYuXYp58+bJvvb19cW8efPg5eXFMCpCCOGfSrvG+vXrh8uXL8Pc3BwHDhzAgQMHYG5ujsuXL1erJIiQqmbu3Lm4fv06Bg4cCIFAgD/++AOtWrVCly5dcPLkyWq51AUhhHyMD24RKioqwtixYzF//vwKrzZdlVGLEKmqEhMTERISgi1btqC4uBh2dna4e/cudHV1WYdGCCEqp7IWIR0dHezbt++jgiOEqJ6zszM2btyI5ORkBAYG4ptvvpElQcXFxdi3bx/EYjHjKAkhhK1KdY317dsXBw4cUHIohBBVsLe3x9q1a/H111/Lynbu3In+/fujYcOG+PXXX1FYWMgwQkIIYUe7Mt9Uv359fPvttzh//jyaN28OIyMjuecnTZqklOAIIapRUFCA2rVr4+7duxgzZgwWL16M6dOnY8yYMTA0NGQdHiGE8KbSCyqWecJqsvu8SCSCSCSCWCxGYmIijREi1U5ubi42bNiAlStX4vHjxwCAOnXqYOrUqZg5cyaEQiHjCAkhpPJ4231e+u3VdVdsGixNqruCggKEh4dj2bJlSElJQfv27XHmzBnWYRFCyEdR+e7zv/32G9zc3KCvrw99fX24ubnh119/rezpCCGM6OnpYezYsUhMTMSWLVuwZMkS2XNZWVmYNm0aHj58yDBCQghRnUolQgsWLMDkyZPh6+uLPXv2YM+ePfD19cXUqVOxYMECZcdICOGBtrY2hgwZgnbt2snKfvzxR4SGhqJu3br4+uuvcffuXYYREkKI8lWqa6xOnTpYs2YNBg8eLFe+Y8cOTJw4EVlZWUoLkDXqGiOa7NSpU1i0aBGio6MBvN3a43//+x/mzJkDNzc3xtERQkjZVNo1VlRUhBYtWpQqb968OYqLiytzSkKIGurUqRPOnDmDs2fPomfPnpBIJNi+fTsaN26MgQMH0krVhJAqr1KJ0NChQ/Hzzz+XKv/ll1/w5ZdffnRQhBD10q5dOxw5cgTXrl1D//79IRAIYGZmVm0nSRBCNEelusYmTpyIzZs3w87ODq1atQIAXLp0CWlpaRg2bBh0dHRkx4aGhiovWgaoa4yQ0m7fvo0aNWrA1tYWABAbG4sJEyZg7ty5+OyzzyhBIoQwp9Lp8506darQcQKBACdPnvzQ06sVSoQIKd8XX3yBHTt2AACaNGmCuXPnon///rQWESGEGd7WEaquaEFFQiruyZMnWLVqFX766Sfk5uYCeLsC/ezZszFkyBDa6JUQwjtKhJSEWoQIqbjnz59j3bp1+PHHH/H8+XMAgJeXFy5evEjdZYQQXql8QUVCCHlXrVq1sGDBAqSmpmLlypWwsrLCgAEDZEmQWCxGTk4O4ygJIeQ/lAgRQpSuRo0amDZtGlJSUjBhwgRZ+b59+2Bvb4/58+dXq/XGCCFVFyVChBCV0dfXh4GBgezrvXv3Ijs7G99//z0cHBwQFBSER48eMYyQEKLpKBEihPBm586d2LdvH5o1a4b8/HysWrUKdevWxdixY3Hv3j3W4RFCNBAlQoQQ3mhpacHf3x9Xr15FZGQkvL29UVhYiF9++QXDhw9nHR4hRANRIkQI4Z1AIED37t0RHR2N6Oho9OzZE7NmzZI9//LlS1y5coVhhIQQTUGJECGEKW9vbxw5cgS9e/eWla1duxYtW7ZEt27dcPr0adrTjBCiMpQIEULUzosXLyAUCvHXX3+hU6dOaNeuHQ4fPkwJESFE6TQiEXJ0dESTJk3g4eFR4e1BCCHshIaG4u7du5gwYQL09PRw4cIF9O7dG02bNsW+fftYh0cIqUY0IhECgAsXLiA2NhanTp1iHQohpAIcHR0hEomQkpKCGTNmoEaNGrhx4wb++OMP1qERQqoRjUmECCFVk7W1NZYvX47U1FQsWrQIs2fPlj0XHx+PdevW4fXr1wwjJIRUZcwToejoaPj6+sLGxgYCgQAHDhwodYxIJIKjoyP09fXh5eWFy5cvf1AdAoEAHTp0gKenJ7Zt26akyAkhfKpVqxYWLlyIhg0bysqWLl2KiRMnwtHREcuWLaPtOwghH4x5IpSXlwd3d3eIRCKFz+/atQtBQUFYuHAhrl27Bnd3d3Tv3h2ZmZmyYzw8PODm5lbq8fjxYwDAuXPnEBMTg0OHDmHp0qW4efNmmfEUFBQgJydH7kEIUU/t27eHg4MDMjMzMXv2bDg4OGDBggV49uwZ69AIIVWEWu0+LxAIsH//fvTt21dW5uXlBU9PT6xbtw4AIJFIYGdnh4kTJ8o1kVfUjBkz0KhRI4wYMULh84sWLcLixYtLldPu84Sop6KiIuzYsQPBwcG4ffs2AMDIyAhz5szBvHnzGEdHCGGlWuw+X1hYiJiYGPj4+MjKtLS04OPjg4sXL1boHHl5eXj16hUAIDc3FydPnkSjRo3KPH7OnDnIzs6WPR48ePBxF0EIUSkdHR0MGzYMcXFx2Lt3L5o2bYq8vDxoaan12xshRE2o9TtFVlYWxGIxLC0t5cotLS3x5MmTCp0jIyMD7dq1g7u7O1q1aoVhw4bB09OzzOP19PRgYmKCLVu2oFWrVujSpctHXQMhhB9CoRD9+vVDTEwMjhw5Irfr/aFDhzB06FDcunWLYYSEEHWkzToAVatbty5u3Ljxwd8XEBCAgIAAWdMaIaRqEAgE6Nmzp+xrjuPw3Xff4erVq9i6dSv8/Pwwb948NG/enGGUhBB1odYtQubm5hAKhcjIyJArz8jIgJWVFaOoCCFViUAgQFhYGPz9/QEA+/fvR4sWLdCjRw9ER0czjo4QwppaJ0K6urpo3rw5oqKiZGUSiQRRUVFo3bq1SusWiURwdXV9bzcaIaRqaN68Ofbt24dbt25h6NChEAqFOHbsGDp06IBx48axDo8QwhDzRCg3NxexsbGIjY0FAKSkpCA2NhZpaWkAgKCgIGzYsAGbNm1CQkICxo8fj7y8PIwcOVKlcQUEBCA+Pp52wCakGnF1dcXmzZuRlJSEcePGQVdXF926dZM9X1BQALFYzDBCQgjfmE+fP336tML9v4YPH47w8HAAwLp167BixQo8efIEHh4eWLNmDby8vHiJr6LT7wghVU96ejosLS1lM8xCQkIQHh6OOXPm4IsvvoCOjg7jCAkhlVXRz2/miZC6EolEEIlEEIvFSExMpESIkGqO4zi4urrK1iJycHDAzJkzMXLkSBgYGDCOjhDyoSgRUhJqESJEc7x69QphYWH44YcfZJM0LC0tERQUhPHjx8PY2JhxhISQiqoWCyoSQgifjI2NMWPGDKSkpEAkEsHe3h4ZGRmYNWsWpkyZwjo8QogKUCJUBpo1RojmMjAwwIQJE3D37l38/vvvaNiwIaZOnSp7/tGjR7K9DAkhVRt1jZWDusYIIRzHQSAQyL7+6quvsG3bNnz11VeYOXMmnJycGEZHCFGEusYIIURJSiZBYrEYKSkpKCwsRFhYGOrXr49hw4YhISGBYYSEkMqiRIgQQj6AUCjEyZMncebMGXTr1g1isRhbtmxBo0aN0K9fP1y/fp11iISQD0CJUBlojBAhpCwCgQDt27fHsWPHcOXKFfj5+YHjOEREROCPP/5gHR4h5APQGKFy0BghQkhF3Lp1C6GhoVixYgVq1aoFALhw4QKys7PRo0cPue41Qojq0RghQgjhUaNGjfDbb7/JkiCO4zBjxgz06tULzZs3x969eyGRSBhHSQh5FyVChBCiAkVFRWjVqhUMDQ1x/fp1DBgwAI0aNcKmTZtQVFTEOjxCyL8oESKEEBXQ1dXFDz/8gNTUVMyfPx9mZma4ffs2RowYgfr162Pv3r2sQySEgBKhMtFgaUKIMpibm+Pbb79FamoqQkJCYGFhgdTUVBQXF7MOjRACGixdLhosTQhRptevX2PHjh0YPnw4hEIhAODXX3/Fo0ePMHHiRNkYI0LIx6FNV5WEEiFCiCoVFBSgbt26ePz4MWrUqIHx48cjKCgIVlZWrEMjpEqjWWOEEFIFaGtrY9WqVXB3d0dubi5WrFgBR0dHBAQE4P79+6zDI6Tao0SIEEIYEgqFGDhwIK5fv44///wTrVu3RkFBAX766SfUq1cPP/30E+sQCanWKBEihBA1IBAI8Nlnn+H8+fM4deoUunbtCrFYjFatWsmOEYvFDCMkpHqiRIgQQtSIQCBAx44dcfz4cSQkJKBZs2ay5wIDA9GrVy+cO3eOYYSEVC+UCJWBps8TQlhr2LCh7P/Z2dnYvHkzjh49Cm9vb3To0AHHjh0DzXch5OPQrLFy0KwxQoi6SE5OxrJlyxAeHi5bnbp58+aYO3cu+vbtCy0t+tuWECmaNUYIIdXMp59+il9++QX37t3DlClTYGBggJiYGPTr1w+hoaGswyOkSqJEiBBCqhhbW1usWrUKqamp+Oabb2BjY4Phw4fLnn/w4AHevHnDMEJCqg5KhAghpIqqU6cOvvvuO6SmpqJOnTqy8mHDhqFu3boIDQ1Fbm4uwwgJUX+UCBFCSBWnra0t+//Tp09x9+5dpKenY9q0aXBwcMC3336LFy9eMIyQEPVFiRAhhFQjderUQXJyMn799VfUq1cPz58/x8KFC2Fvb49Zs2bhyZMnrEMkRK1QIkQIIdWMrq4uRo0ahdu3b2Pnzp1o0qQJcnNzsXz5cvz111+swyNErdD0+XJUZPqdRCJBYWEhz5ERoho6OjqyXdFJ9cBxHA4fPoxNmzZh+/bt0NHRAQBERUXB1tYWDRo0YBwhIcpHu89/JJFIBJFIBLFYjMTExDJfyMLCQqSkpEAikTCIkhDVMDMzg5WVFQQCAetQiIoUFRWhXr16ePDgAfr37485c+agadOmrMMiRGkoEVKS972QHMchLS0NRUVFsLGxocXMSJXHcRzy8/ORmZkJMzMzWFtbsw6JqEhmZibGjBmDQ4cOycp69eqFuXPnom3btgwjI0Q5KBFSkve9kEVFRbh79y5sbGxgamrKKEJClO/Zs2fIzMyEs7MzdZNVc//88w+Cg4Oxa9cuWct2hw4d8MMPP6B58+aMoyOk8mhlaR5Id4LW1dVlHAkhymVoaAgAsm0cSPXVuHFjbN++Hbdv38bo0aOho6ODM2fOoLi4mHVohPCCEiEloHEUpLqhe1rz1K9fHxs2bEBycjLWrl0LLy8v2XM//PADtm3bRskRqZYoESKEECJjZ2eHwMBA2deZmZn45ptvMGTIEDRo0AC//PILCgoKGEZIiHJRIkQIIaRMBgYGmD9/PszNzXHv3j2MHTtWtn1HXl4e6/AI+WiUCKkBsYTDxeRnOBj7CBeTn0EsofHrhBD1YGxsjLlz5+L+/ftYvXo1PvnkEzx+/Fi2fceJEydYh0jIR9Eu/xCiSpFx6Vj8RzzSs//bKdraVB8LfV3Rw42mLhNC1IORkREmT56McePGYcuWLQgJCcHDhw/RqFEj2TEcx9H4MlLlUIsQQ5Fx6Ri/9ZpcEgQAT7LfYPzWa4iMS1dZ3RKJBMuXL0e9evWgp6cHe3t7LFmyBAAwa9YsODs7w9DQEHXr1sX8+fPlZg/duHEDnTp1grGxMUxMTNC8eXNcvXpV9vy5c+fg7e0NAwMD2NnZYdKkSdSETkg1oaenh9GjR+P27ds4e/as3FpT/v7+mDRpEtLS0hhGSMiH0YhEKCUlBZ06dYKrqysaN26ssg9ljuOQX1hcocerN0VYeOgWFHWCScsWHYrHqzdFFTrfhy4HNWfOHISEhGD+/PmIj4/H9u3bYWlpCeBtU3h4eDji4+Px448/YsOGDVi1apXse7/88kvY2triypUriImJwezZs2VL9icnJ6NHjx7o168fbt68iV27duHcuXNygy8JIVWftrY2PD09ZV/HxcXhwIEDWLt2LT799FOMGjUKiYmJDCMkpGI0YkHFDh064Pvvv4e3tzeeP38OExMTaGtXrFfwfQsyvXnzBikpKXBycoK+vj7yC4vhuuCYKi6hXPHfdoehbsWu6dWrV6hTpw7WrVuH0aNHl3v8ypUrsXPnTlmrj4mJCdauXYvhw4eXOnb06NEQCoVYv369rOzcuXPo0KED8vLyoK+vX8ErIiy9e28TUh6O43Dy5EksXboUJ0+eBABoaWlhwIABmDNnDtzd3RlHSDQNLaj4r1u3bkFHRwfe3t4AgFq1alU4CaquEhISUFBQgC5duih8fteuXWjbti2srKxQo0YNfPPNN3JN3UFBQRg9ejR8fHwQEhKC5ORk2XM3btxAeHg4atSoIXt0794dEokEKSkpKr82QggbAoEAXbp0QVRUFC5evAhfX19IJBLs2rULHh4eiIyMZB0iIQoxbxGKjo7GihUrEBMTg/T0dOzfvx99+/aVO0YkEmHFihV48uQJ3N3dsXbtWrRs2bJC5z9w4ADCw8MhFovx6NEj9O/fH3Pnzq1wfB/SIsRxHF4XiSt03sspzzHi9yvlHhc+0hMtnWqVe5yBjrDCgxT/+ecfNGnSBPfu3YOTk5PccxcvXoS3tzcWL16M7t27w9TUFDt37sQPP/yAly9fyo5LTEzE4cOHcfToUZw5cwY7d+6En58fXFxc0LVrV0yaNKlUvfb29rQKdxVBLUJEGW7evImlS5fi4sWLSEpKkv3+P3nyBJaWljSwmqhURVuEmDeN5OXlwd3dHV999RX8/f1LPb9r1y4EBQUhLCwMXl5eWL16Nbp37447d+7AwsICAODh4aFwxdPjx4+juLgYZ8+eRWxsLCwsLNCjRw94enqia9euCuMpKCiQWywsJyenwtciEAgq3D3lXb8OrE318ST7jcJxQgIAVqb68K5fB0It5b5Z1K9fHwYGBoiKiirVNXbhwgU4ODhg3rx5srLU1NRS53B2doazszOmTp2KwYMH4/fff4efnx+aNWuG+Ph41KtXT6kxE0KqniZNmmDnzp3Iy8uTJUHFxcVo27YtzM3NMXfuXPj6+tKG1YQp5olQz5490bNnzzKfDw0NxZgxYzBy5EgAQFhYGA4fPoyNGzdi9uzZAIDY2Ngyv/+TTz5BixYtYGdnB+Dt7sqxsbFlJkLBwcFYvHhxJa+m4oRaAiz0dcX4rdcgAOSSIWnas9DXVelJEADo6+tj1qxZmDlzJnR1ddG2bVs8ffoUt27dQv369ZGWloadO3fC09MThw8fxv79+2Xf+/r1a8yYMQP9+/eHk5MTHj58iCtXrqBfv34A3s44a9WqFQIDAzF69GgYGRkhPj4ef/31F9atW6f0ayGEqD8jIyPZ/2/cuIHHjx/j3r176Nu3L9zc3DBnzhwMHDhQ44ctEDbUOg0vLCxETEwMfHx8ZGVaWlrw8fHBxYsXK3QOT09PZGZm4sWLF5BIJIiOjoaLi0uZx8+ZMwfZ2dmyx4MHDz76OsrSw80aPw9pBitT+a4HK1N9/DykmUrXEZo/fz6mTZuGBQsWwMXFBYMGDUJmZiY+//xzTJ06FYGBgfDw8MCFCxcwf/582fcJhUI8e/YMw4YNg7OzMwYOHIiePXvKkscmTZrgzJkzSExMhLe3N5o2bYoFCxbAxsZGZddCCKk6mjdvjtTUVMyePRvGxsaIi4vDl19+iYYNG2LDhg20fQfhHfMxQiUJBAK5MUKPHz/GJ598ggsXLqB169ay42bOnIkzZ87g0qVLFTrv0aNHMXPmTHAch27duiE0NLTCMX3IGKHKEks4XE55jsxXb2BhrI+WTrVU0hJESEXRGCHCh5cvX2LdunVYvXo1nj17BgA4e/Ys2rVrxzgyUh1UmTFCfCiv+00RkUgEkUgEsbhig58/hlBLgNaf1lZ5PYQQok7MzMzwzTffYOrUqfjll19w6dIluSToxIkTaNGiBczMzNgFSao9te4aMzc3h1AoREZGhlx5RkYGrKysVFp3QEAA4uPjceVK+TO7CCGEVJ6RkRGmTp2KnTt3ysqePXuGPn36wMHBAXPnzkVmZibDCEl1ptaJkK6uLpo3b46oqChZmUQiQVRUlFxXmSqIRCK4urrKrZxKCCGEHw8fPoSTkxNycnIQHBwMR0dHTJ48WaXjNolmYp4I5ebmIjY2VjbzKyUlBbGxsbIF/IKCgrBhwwZs2rQJCQkJGD9+PPLy8mSzyFSFWoQIIYQdd3d33Lx5EwcOHICnpydev36NNWvW4NNPP8Xo0aPx6NEj1iGSaoJ5InT16lU0bdoUTZs2BfA28ZHONAKAQYMGYeXKlViwYAE8PDwQGxuLyMhI2b5YhBBCqictLS306dMHly5dwl9//YWOHTuiqKgImzdv/uD9FQkpi1rNGlMnJQdLJyYmqnTWGCHqhu5toq4uXLiA69evIyAgQFa2ZMkSdOnSBa1atWIYGVE3FZ01RolQOfiYPk+IuqF7m1QVN27cgIeHBwCgc+fOmDdvHjp16kTbdxDadJUQQkj1Z2ZmhpEjR0JbWxsnT55Ely5d0Lp1a/zxxx/UfUYqhBIhQgghVZaDgwM2btyI5ORkBAYGQl9fH5cuXcLnn38Od3d3JCUlsQ6RqDlKhMrA5/R5sViM06dPY8eOHTh9+jQvizgS4P79+xAIBO/dq64q1UOIJrO3t8fatWtx//59zJo1C8bGxnj69Klsn0lCykKJUBn4mj4fERGBenUd0alTJ3zxxRfo1KkT6tV1REREhErr1TQjRoyQbd0iZWdnh/T0dLi5ubEJihCidJaWlggJCUFqaioiIiJkY9zEYjG6du2KH3/8Efn5+YyjJOqEEiGGIiIi0L9/fzTWz8DFUYZ4NccYF0cZorFBBvr370/JkIoJhUJYWVnRjteEVEM1a9aUW3j34MGDOHHiBKZMmQIHBwcsXboU2dnZDCMk6oISIWXiOKAwr0IP8escTJsyCb3ra+PA//TRylYbNXQFaGWrjQOD9NHbWRvTp06G+HVOxc75AYMCO3bsiIkTJ2LKlCmoWbMmLC0tsWHDBtlClcbGxqhXrx6OHj0q931xcXHo2bMnatSoAUtLSwwdOhRZWVmy5yMjI9GuXTuYmZmhdu3a6N27N5KTk2XPS7uIIiIi0KlTJxgaGsLd3R0XL158b7xpaWno06cPatSoARMTEwwcOFBu25VFixbBw8MD69evh52dHQwNDTFw4EDZm9yiRYuwadMmHDx4EAKBAAKBAKdPny7VZXX69GkIBAIcO3YMTZs2hYGBATp37ozMzEwcPXoULi4uMDExwRdffCH3F2V5100IYe+zzz7D+vXr4eTkhKysLMybNw8ODg745ptv8PTpU9bhEYYoESpDpcYIFeUDS20q9Dg73hr3HzzCXG8daL0zzVNLIMCctjpISXuIs+OtK3bOog9r6t20aRPMzc1x+fJlTJw4EePHj8eAAQPQpk0bXLt2Dd26dcPQoUNlH/gvX75E586d0bRpU1y9ehWRkZHIyMjAwIEDZefMy8tDUFAQrl69iqioKGhpacHPzw8SiUSu7nnz5mH69OmIjY2Fs7MzBg8ejOLiYoVxSiQS9OnTB8+fP8eZM2fw119/4d69exg0aJDccXfv3sXu3bvxxx9/IDIyEtevX8eECRMAANOnT8fAgQPRo0cPpKenIz09HW3atCnztVm0aBHWrVuHCxcu4MGDBxg4cCBWr16N7du34/Dhwzh+/DjWrl37wddNCGFHT08PX3/9NRITE7Flyxa4uroiOzsbS5YsgYODA+7evcs6RMIKR94rOzubA8BlZ2eXeu7169dcfHw89/r167cFBbkct9CkQo/t/gYcAO7VHGOFz+fMNuYAcNv9DSp2zoLcCl9Thw4duHbt2sm+Li4u5oyMjLihQ4fKytLT0zkA3MWLFzmO47jvvvuO69atm9x5Hjx4wAHg7ty5o7Cep0+fcgC4f/75h+M4jktJSeEAcL/++qvsmFu3bnEAuISEBIXnOH78OCcUCrm0tLRS33P58mWO4zhu4cKFnFAo5B4+fCg75ujRo5yWlhaXnp7OcRzHDR8+nOvTp4/cuaXxXL9+neM4jjt16hQHgDtx4oTsmODgYA4Al5ycLCsbO3Ys1717d4Xxvu+6pfVUBaXubUKqGbFYzO3fv59r0aIF5+XlxUkkEtlzit7vSdXzvs/vkmhwhDLpGAJzH1foUOsz0UBEL8RlitHKtvSPIS7z7cwx63H7gA7tK1b3B2jSpIns/0KhELVr10bjxo1lZdItTKQ7Pt+4cQOnTp1CjRo1Sp0rOTkZzs7OSEpKwoIFC3Dp0iVkZWXJWkTS0tLkBiSXrNva2lpWT8OGDUudOyEhAXZ2dnIzP1xdXWFmZoaEhARZi529vT0++eQT2TGtW7eGRCLBnTt3YGVl9QGvjHx8lpaWMDQ0RN26deXKLl++LPu6otdNCFEfWlpa6Nu3r6zFWboA48uXL1G3bl306NEDc+bMkXtfJNUTJULKJBAAukYVOtS7czc42tti6bkMHBgklOsek3Acgs8XwcnBDt6duwFCodJD1dHRkftaIBDIlUnfFKQf6rm5ufD19cWyZctKnUuazPj6+sLBwQEbNmyAjY0NJBIJ3NzcUFhYWGbd79ajDt6NT9FrVTLeil43IUT9CAQC1K5dW/b1kSNH8OLFC+zYsQM7duzA559/jnnz5qFly5YMoySqRGOEGBEKhfhh1Y/4M7EYfXe9wcUHxXhVwOHig7df/5lYjJWhqyFUQRJUGc2aNcOtW7fg6OiIevXqyT2MjIzw7Nkz3LlzB9988w26dOkCFxcXvHjx4qPrdXFxwYMHD/DgwQNZWXx8PF6+fAlXV1dZWVpaGh4//q817u+//4aWlhYaNGgAANDV1VXJ+kyqum5CCBtffPEFrl+/jgEDBkAgEODQoUPw8vKCj48PTp06RatVV0OUCJWBjwUV/f39sXfvXvzz2hJtNubDJOQV2mzMR9wbK+zduxf+/v4qq/tDBQQE4Pnz5xg8eDCuXLmC5ORkHDt2DCNHjoRYLEbNmjVRu3Zt/PLLL7h79y5OnjyJoKCgj67Xx8cHjRs3xpdffolr167h8uXLGDZsGDp06IAWLVrIjtPX18fw4cNx48YNnD17FpMmTcLAgQNl3WKOjo64efMm7ty5g6ysLBQVFX10bABUdt2EEHY8PDywe/duJCQkYMSIEdDW1kZUVBS6du2KR48esQ6PKBklQmXga0FFf39/3L13H6dOncL27dtx6tQpJCWnqFUSBAA2NjY4f/48xGIxunXrhsaNG2PKlCkwMzODlpYWtLS0sHPnTsTExMDNzQ1Tp07FihUrPrpegUCAgwcPombNmmjfvj18fHxQt25d7Nq1S+64evXqwd/fH7169UK3bt3QpEkT/PTTT7Lnx4wZgwYNGqBFixaoU6cOzp8//9GxAVDZdRNC2GvQoAF+//133L17FwEBARg1ahRsbW1lz589e5Z2AqgGaPf5ctDu8+pv0aJFOHDgAG1hoUR0bxNSGsdxsnGN8fHxaNSoEerXr4/Zs2djyJAh0NXVZRwhKYl2nyeEEEKUSFBiUktSUhJq1aqFpKQkjBo1CvXq1cPatWtp+44qiBIhQggh5AP16dMHqampWLlyJaysrPDgwQNMmjQJjo6OCAkJQV5eHusQSQVR11g5qGuMaCK6twmpuDdv3iA8PBzLli3D/fv3YW5ujvv378PIqGLLqRDVoK6xj8THrDFCCCFVn76+PsaNG4fExERs3rwZy5YtkyVBEokES5cupdlmaoxahMpBLUJEE9G9TYhyHDx4EH379oWuri5GjBiBmTNn4tNPP2UdlkagFiFCCCGEMQsLC7Rv3x6FhYX45Zdf4OzsjCFDhiAuLo51aORflAgRQgghKtK6dWucOXMGZ8+eRY8ePSCRSLBt2zY0btwYfn5+yMnJYR2ixqNEiBBCCFGxdu3a4ejRo4iJiUG/fv0gEAiQlpYGY2Nj1qFpPEqE1MTu3bth/Yk19uzZwzoUQgghKtKsWTPs3bsXt27dws8//yxbm+jVq1fo2bMnDh8+TPuZ8YwSITWQmZmJsePHIjPr338zM1mHpFYEAgEOHDig9GPV0enTpyEQCPDy5ctqUQ8hRDEXFxe5He3DwsIQGRmJ3r17o2nTpti9ezdt38ETSoQY4zgO48aPQ35xPuourIu8ojyMnzCedVhqJT09HT179lT6sax17NgRU6ZMkStr06YN0tPTYWpqyiYoQggTQ4YMwYwZM1CjRg3cuHEDgwYNgqurK37//XelbRJNFKNEiLHdu3djf8R+WA6xhP4n+rAcYomIfRHYvXs369DUhpWVFfT09JR+rDrS1dWFlZWV3FL+hJDqz9raGsuXL0dqaioWLVqEmjVrIjExEV999RUaNGhAW3eoECVCZajMgoocxyG/KL/Cj/uP7mPchHEw9TSFacu3LQAmniYw9TTF2Aljcf/R/Qqf60P6lDt27IiJEydiypQpqFmzJiwtLbFhwwbk5eVh5MiRMDY2Rr169XD06FG574uLi0PPnj1Ro0YNWFpaYujQocjKypI9HxkZiXbt2sHMzAy1a9dG7969kZycLHv+/v37EAgEiIiIQKdOnWBoaAh3d3dcvHjxvfGW7O4qLCxEYGAgrK2toa+vDwcHBwQHBys8tqL1bdiwAXZ2djA0NISfnx9CQ0NhZmb23pj++ecfdO7cGQYGBqhduza+/vpr5Obmyp4fMWIE+vbti8WLF6NOnTowMTHBuHHjUFhYKHv+zJkz+PHHHyEQCCAQCHD//v1SXVbh4eEwMzPDn3/+iQYNGsDQ0BD9+/dHfn4+Nm3aBEdHR9SsWROTJk2Sa0bfsmULWrRoAWNjY1hZWeGLL76gLldCqoBatWph4cKFSE1NxYoVK2BlZQUvLy8YGhrKjikoKGAYYfWjzToAdRUQEICAgADZgkwV8br4Nby2e1XoWI7j8ED0AHlFeag/tL6sXCAQwHqoNZLmJsG9rzvsA+0rdL5LX1yCoY5h+Qf+a9OmTZg5cyYuX76MXbt2Yfz48di/fz/8/Pwwd+5crFq1CkOHDkVaWhoMDQ3x8uVLdO7cGaNHj8aqVavw+vVrzJo1CwMHDsTJkycBAHl5eQgKCkKTJk2Qm5uLBQsWwM/PD7GxsdDS+i/nnjdvHlauXIn69etj3rx5GDx4MO7evQtt7fJvxzVr1uDQoUPYvXs37O3t8eDBAzx48OC93/O++s6fP49x48Zh2bJl+Pzzz3HixAnMnz//vefLy8tD9+7d0bp1a1y5cgWZmZkYPXo0AgMDER4eLjsuKioK+vr6OH36NO7fv4+RI0eidu3aWLJkCX788UckJibCzc0N3377LQCgTp06uH//fqn68vPzsWbNGuzcuROvXr2Cv78//Pz8YGZmhiNHjuDevXvo168f2rZti0GDBgEAioqK8N1336FBgwbIzMxEUFAQRowYgSNHjpT7GhNC2DM2Nsb06dMRGBgoN8U+MTERbdq0wYQJEzBp0iSYm5szjLKa4Mh7ZWdncwC47OzsUs+9fv2ai4+P516/fs1xHMflFeZxbuFuFXrU+74eB4Cr06eOwufr9KnDAeDqLalXofPlFeZV+Jo6dOjAtWvXTvZ1cXExZ2RkxA0dOlRWlp6ezgHgLl68yHEcx3333Xdct27d5M7z4MEDDgB3584dhfU8ffqUA8D9888/HMdxXEpKCgeA+/XXX2XH3Lp1iwPAJSQklBkvAG7//v0cx3HcxIkTuc6dO3MSiaTcYytS36BBg7jPPvtM7hxffvklZ2pqWmY8v/zyC1ezZk0uNzdXVnb48GFOS0uLe/LkCcdxHDd8+HCuVq1aXF7efz+Xn3/+matRowYnFos5jnv7c5g8ebLcuU+dOsUB4F68eMFxHMf9/vvvHADu7t27smPGjh3LGRoacq9evZKVde/enRs7dmyZMV+5coUDIPued+t517v3NiFEPcyZM4cDwAHgDA0NuaCgIO7Ro0esw1JL7/v8LolahJTIQNsAl764VKFjOY7DFzFfIDIqErW71Ia2yX8/iuKcYmSfzEYf/z7YPmN7hev+EE2aNJH9XygUonbt2mjcuLGszNLSEgBk3Sk3btzAqVOnUKNGjVLnSk5OhrOzM5KSkrBgwQJcunQJWVlZkEgkAIC0tDS4ubkprNva2lpWT8OGDcuNe8SIEejatSsaNGiAHj16oHfv3ujWrVuFr/Xd+u7cuQM/Pz+541u2bIk///yzzPMlJCTA3d1dbkPFtm3bQiKR4M6dO7LXzt3dXa45u3Xr1sjNzcWDBw/g4OBQ7rVKGRoayi3Jb2lpCUdHR7mfhaWlpVzXV0xMDBYtWoQbN27gxYsXcj8LV1fXCtdNCFEv33//PZo3b44lS5bg+vXrCA0Nxbp16zBy5EjMnDkTdevWZR1ilUNjhJRIIBDAUMewQg8jXSNsCNsAQ21DpG9Jl52D4zikb0mHka4Rfvn5lwqf70MH1+ro6JSKvWSZ9HzSD9Dc3Fz4+voiNjZW7pGUlIT27dsDAHx9ffH8+XNs2LABly5dwqVLb5NC6bgYRXW/W095mjVrhpSUFHz33Xd4/fo1Bg4ciP79+1f4Wj+0PnVQ3s9KWia9JmnXnYmJCbZt24YrV65g//79AEr/LAghVYuWlhb69euHmJgYHD16FO3atUNhYSHWr1+PVq1a0e94JVAixJCFhQXCfgpD9pVsZF/OBgDkXMlB9pVshP0UBgsLC8YR/qdZs2a4desWHB0dUa9ePbmHkZERnj17hjt37uCbb75Bly5d4OLighcvXqgkFhMTEwwaNAgbNmzArl27sG/fPjx//rxS52rQoAGuXLkiV/bu1+9ycXHBjRs3kJeXJys7f/48tLS00KBBA1nZjRs38Pr1a9nXf//9N2rUqAE7OzsAb2eIqWKdkNu3b+PZs2cICQmBt7c3GjZsSAOlCalmBAIBevTogbNnzyI6Oho9evTAhAkToKurC+DtH9U3b95kHGXVQIkQYwMHDoSfvx8ytmbgzaM3yNiaAf9+/hg4cCDr0OQEBATg+fPnGDx4MK5cuYLk5GQcO3YMI0eOhFgsRs2aNVG7dm388ssvuHv3Lk6ePImgoCClxxEaGoodO3bg9u3bSExMxJ49e2BlZVXuLK+yTJw4EUeOHEFoaCiSkpKwfv16HD169L0tbF9++SX09fUxfPhwxMXF4dSpU5g4cSKGDh0q6xYD3ra+jBo1CvHx8Thy5AgWLlyIwMBA2cBxR0dHXLp0Cffv35frSvxY9vb20NXVxdq1a3Hv3j0cOnQI3333nVLOTQhRP97e3jh69CgWLFggKzt27Bjc3d3RvXt3nDlzhlarfg9KhBgTCAQI+zkMhtqGuLf4Hox0jPDzTz+zDqsUGxsbnD9/HmKxGN26dUPjxo0xZcoUmJmZQUtLC1paWti5cydiYmLg5uaGqVOnYsWKFUqPw9jYGMuXL0eLFi3g6emJ+/fv48iRI3Kz0j5E27ZtERYWhtDQULi7uyMyMhJTp06Fvr5+md9jaGiIY8eO4fnz5/D09ET//v3RpUsXrFu3Tu64Ll26oH79+mjfvj0GDRqEzz//HIsWLZI9P336dAiFQri6uqJOnTpIS0ur1DW8q06dOggPD8eePXvg6uqKkJAQrFy5UinnJoSor5Lvgzdu3IBQKMTx48fRsWNHeHt748iRI5QQKSDg6FV5L+n0+ezsbJiYmMg99+bNG6SkpMDJyem9H5wVsXv3bkyeOhlrVq/BgAEDPupc5OOMGTMGt2/fxtmzZyt9jhEjRuDly5dVdrsPZd7bhBA2UlJSsHz5cmzcuFE2dsjDwwNz585Fv379Kv0HZFXxvs/vkqr3q1CFDBw4EOmP0ikJYmDlypW4ceMG7t69i7Vr12LTpk0YPnw467AIIeSjODk54eeff8b9+/cxffp0GBkZITY2VrZ2GXmr2idCd+7cgYeHh+xhYGBQZf9KJ6px+fJldO3aFY0bN0ZYWBjWrFmD0aNHsw6LEEKUwtraGitWrEBqaioWLlyIb7/9VtYalJeXh7CwMLmJHZpGo7rGcnNz4ejoiNTUVLk1YN6Hr64xQtQJ3duEaIbVq1dj6tSpsLS0RFBQEMaPHw9jY2PWYSkFdY0pcOjQIXTp0qXCSRAhhBBSndWpUwf29vbIyMjArFmzYG9vj4ULF+LZs2esQ+MN80QoOjoavr6+sLGxkdswsySRSARHR0fo6+vDy8sLly9frlRdu3fvlu3FRAghhGi6L7/8Enfv3kV4eDgaNGiAly9f4ttvv4WDgwNmzJihEbPMmCdCeXl5cHd3h0gkUvj8rl27EBQUhIULF+LatWuydRFKLhDn4eEBNze3Uo/Hjx/LjsnJycGFCxfQq1ev98ZTUFCAnJwcuQchhBBSXeno6GD48OG4desW9uzZAw8PD+Tl5eHevXsfvGtBVaRWY4QEAgH279+Pvn37ysq8vLzg6ekpW6NFIpHAzs4OEydOxOzZsyt87i1btuDYsWPYunXre49btGgRFi9eXKqcxggRTUL3NiGai+M4REZGws7OTrZPZEpKChYvXoxZs2bBxcWFcYQVUy3GCBUWFiImJgY+Pj6yMi0tLfj4+ODixYsfdK6KdovNmTMH2dnZsseDBw8+OG5CCCGkqhIIBOjZs6fcZtnLly/Hpk2b0KhRI/Tv3x8xMTEMI1QutU6EsrKyIBaL5bYtAN7utP3kyZMKnyc7OxuXL19G9+7dyz1WT08PJiYmcg9CCCFEk40aNQp+fn7gOA779u1DixYtZHudVXVqnQgpi6mpKTIyMmSb0VWESCSCq6srPD09VRhZ9TdixAi5rk5CCCFVT4sWLRAREYG4uDgMGTIEQqEQx44dQ/v27eHr61ulB1WrdSJkbm4OoVCIjIwMufKMjAxYWVmptO6AgADEx8eXuxM5IYQQoikaNWqELVu2IDExEWPHjoWuri6aNGkiG1TNcZzSNpDmi1onQrq6umjevDmioqJkZRKJBFFRUWjdurVK69akFiHpHjSEEEJIRdStWxdhYWFISUnBtGnTZOUnT56Em5sbNm/ejKKiIoYRVhzzRCg3NxexsbGIjY0F8HZkemxsrGwn7qCgIGzYsAGbNm1CQkICxo8fj7y8PIwcOVKlcX1Mi1BeXl6Zjzdv3lT42HeXPC/ruA/VsWNHBAYGYsqUKTA3N0f37t0RGhqKxo0bw8jICHZ2dpgwYQJyc3Nl3xMeHg4zMzMcO3YMLi4uqFGjBnr06IH09HTZMWKxGEFBQTAzM0Pt2rUxc+bMUs2lBQUFmDRpEiwsLKCvr4927drJvcanT5+GQCDAsWPH0LRpUxgYGKBz587IzMzE0aNH4eLiAhMTE3zxxRfIz8//4GsnhBCiPDY2NqhVq5bs6zVr1iAhIQHDhw+Hs7Mzfv7551Kfe2qHY+zUqVMcgFKP4cOHy45Zu3YtZ29vz+nq6nItW7bk/v77b97iy87O5gBw2dnZpZ57/fo1Fx8fz71+/VquXNH1SB+9evWSO9bQ0LDMYzt06CB3rLm5ucLjPlSHDh24GjVqcDNmzOBu377N3b59m1u1ahV38uRJLiUlhYuKiuIaNGjAjR8/XvY9v//+O6ejo8P5+PhwV65c4WJiYjgXFxfuiy++kB2zbNkyrmbNmty+ffu4+Ph4btSoUZyxsTHXp08f2TGTJk3ibGxsuCNHjnC3bt3ihg8fztWsWZN79uwZx3H/3Q+tWrXizp07x127do2rV68e16FDB65bt27ctWvXuOjoaK527dpcSEjIB187qZiy7m1CCHmf7OxsLiQkhLOwsJB9RllZWXErVqzgcnJyeI+lrM/vkpgnQupq3bp1nIuLC+fs7FwtE6GmTZu+95g9e/ZwtWvXln39+++/cwC4u3fvyspEIhFnaWkp+9ra2ppbvny57OuioiLO1tZWlgjl5uZyOjo63LZt22THFBYWcjY2NrLvkyZCJ06ckB0THBzMAeCSk5NlZWPHjuW6d+/+gVdOKooSIULIx8jPz+fWrl3L2dnZyT6r2rRpw2sMFU2EtJXavFSNBAQEICAgQLYg04co2aX0LqFQKPd1yRWy3yXdHVjq/v37HxTH+zRv3lzu6xMnTiA4OBi3b99GTk4OiouL8ebNG+Tn58PQ0BAAYGhoiE8//VT2PdbW1rL4s7OzkZ6eDi8vL9nz2traaNGihax7LDk5GUVFRWjbtq3sGB0dHbRs2RIJCQly8TRp0kT2f0tLSxgaGqJu3bpyZZXdaoUQQohqGRgYIDAwEF9//TW2bduGkJAQfP3117Ln37x5g5cvX6p84lNFMB8jVB0ZGRmV+Xh3ld73HWtgYFChYysbo9T9+/fRu3dvNGnSBPv27UNMTIxsy5OSA6l1dHTkziEQCFQ2ZbJkXQKBQGHdVW1mAiGEaBpdXV2MHDkS8fHxGDJkiKx848aNcHR0REBAgFL/yK8MSoQIYmJiIJFI8MMPP6BVq1ZwdnaW26etIkxNTWFtbY1Lly7JyoqLi+VWH/3000+hq6uL8+fPy8qKiopw5coVuLq6fvyFEEIIUUtCoVCuRyQ6OhoFBQX46aefcPDgQYaRUSJUJk2aPl+vXj0UFRVh7dq1uHfvHrZs2YKwsLAPPs/kyZMREhKCAwcO4Pbt25gwYQJevnwpe97IyAjjx4/HjBkzEBkZifj4eIwZMwb5+fkYNWqUEq+IEEKIOtuxYwdOnTqF/v37Y8yYMUxjoUSoDJq0oKK7uztCQ0OxbNkyuLm5Ydu2bQgODv7g80ybNg1Dhw7F8OHD0bp1axgbG8PPz0/umJCQEPTr1w9Dhw5Fs2bNcPfuXRw7dgw1a9ZU1uUQQghRcwKBAB07dsSePXtk41CZxcKpapBHNfG+3Wtph25SXdG9TQip6qrF7vOEEEIIIapEiVAZNGmMECGEEKKpKBEqgyaNESKEEEI0FSVChBBCCNFYlAgpAY03J9UN3dOEEE1BidBHkC4OVXL1ZUKqg/z8fAClVxMnhJDqhvYaK4NIJIJIJIJYLC7zGG1tbRgaGuLp06fQ0dEptTcYIVUNx3HIz89HZmYmzMzMSu2NRwgh1Q2tI1SO8tYhKCwsREpKCu17RaoVMzMzWFlZQSAQsA6FEEIqpaLrCFGL0EfS1dVF/fr1qXuMVBs6OjrUEkQI0RiUCCmBlpYWrb5LCCGEVEE0qIUQQgghGosSIUIIIYRoLEqEykBbbBBCCCHVH80aK0d2djbMzMzw4MGD9446J4QQQoj6yMnJgZ2dHV6+fAlTU9Myj6PB0uV49eoVAMDOzo5xJIQQQgj5UK9evXpvIkQtQuWQSCR4/PgxjI2NlbqmijRT1eSWJk1/DTT9+gF6Dej6Nfv6AXoNVHn9HMfh1atXsLGxee+Cx9QiVA4tLS3Y2tqq7PwmJiYaefOXpOmvgaZfP0CvAV2/Zl8/QK+Bqq7/fS1BUjRYmhBCCCEaixIhQgghhGgsSoQY0dPTw8KFC6Gnp8c6FGY0/TXQ9OsH6DWg69fs6wfoNVCH66fB0oQQQgjRWNQiRAghhBCNRYkQIYQQQjQWJUKEEEII0ViUCBFCCCFEY1EipGLR0dHw9fWFjY0NBAIBDhw4IPc8x3FYsGABrK2tYWBgAB8fHyQlJbEJVgXed/1FRUWYNWsWGjduDCMjI9jY2GDYsGF4/Pgxu4BVoLx7oKRx48ZBIBBg9erVvMWnahW5/oSEBHz++ecwNTWFkZERPD09kZaWxn+wKlLea5Cbm4vAwEDY2trCwMAArq6uCAsLYxOsCgQHB8PT0xPGxsawsLBA3759cefOHblj3rx5g4CAANSuXRs1atRAv379kJGRwShi5Srv+p8/f46JEyeiQYMGMDAwgL29PSZNmoTs7GyGUStPRX7+UhzHoWfPnuW+VyoTJUIqlpeXB3d3d4hEIoXPL1++HGvWrEFYWBguXboEIyMjdO/eHW/evOE5UtV43/Xn5+fj2rVrmD9/Pq5du4aIiAjcuXMHn3/+OYNIVae8e0Bq//79+Pvvv2FjY8NTZPwo7/qTk5PRrl07NGzYEKdPn8bNmzcxf/586Ovr8xyp6pT3GgQFBSEyMhJbt25FQkICpkyZgsDAQBw6dIjnSFXjzJkzCAgIwN9//42//voLRUVF6NatG/Ly8mTHTJ06FX/88Qf27NmDM2fO4PHjx/D392cYtfKUd/2PHz/G48ePsXLlSsTFxSE8PByRkZEYNWoU48iVoyI/f6nVq1crdTurCuEIbwBw+/fvl30tkUg4KysrbsWKFbKyly9fcnp6etyOHTsYRKha716/IpcvX+YAcKmpqfwExbOyXoOHDx9yn3zyCRcXF8c5ODhwq1at4j02Pii6/kGDBnFDhgxhExADil6DRo0acd9++61cWbNmzbh58+bxGBl/MjMzOQDcmTNnOI57+76no6PD7dmzR3ZMQkICB4C7ePEiqzBV5t3rV2T37t2crq4uV1RUxGNk/Cjr+q9fv8598sknXHp6eoU+L5SFWoQYSklJwZMnT+Dj4yMrMzU1hZeXFy5evMgwMnays7MhEAhgZmbGOhTeSCQSDB06FDNmzECjRo1Yh8MriUSCw4cPw9nZGd27d4eFhQW8vLx4axJXF23atMGhQ4fw6NEjcByHU6dOITExEd26dWMdmkpIu3xq1aoFAIiJiUFRUZHce2HDhg1hb29fLd8L373+so4xMTGBtnb12xJU0fXn5+fjiy++gEgkgpWVFa/xUCLE0JMnTwAAlpaWcuWWlpay5zTJmzdvMGvWLAwePFijNh9ctmwZtLW1MWnSJNah8C4zMxO5ubkICQlBjx49cPz4cfj5+cHf3x9nzpxhHR5v1q5dC1dXV9ja2kJXVxc9evSASCRC+/btWYemdBKJBFOmTEHbtm3h5uYG4O17oa6ubqk/gKrje6Gi639XVlYWvvvuO3z99dc8R6d6ZV3/1KlT0aZNG/Tp04f3mKpfqkmqpKKiIgwcOBAcx+Hnn39mHQ5vYmJi8OOPP+LatWv894urAYlEAgDo06cPpk6dCgDw8PDAhQsXEBYWhg4dOrAMjzdr167F33//jUOHDsHBwQHR0dEICAiAjY2NXCtJdRAQEIC4uDicO3eOdShMlHf9OTk5+Oyzz+Dq6opFixbxGxwPFF3/oUOHcPLkSVy/fp1JTNQixJC0+e/dmREZGRm8Nw2yJE2CUlNT8ddff2lUa9DZs2eRmZkJe3t7aGtrQ1tbG6mpqZg2bRocHR1Zh6dy5ubm0NbWhqurq1y5i4tLtZo19j6vX7/G3LlzERoaCl9fXzRp0gSBgYEYNGgQVq5cyTo8pQoMDMSff/6JU6dOwdbWVlZuZWWFwsJCvHz5Uu746vZeWNb1S7169Qo9evSAsbEx9u/fDx0dHQZRqk5Z13/y5EkkJyfDzMxM9j4IAP369UPHjh1VHhclQgw5OTnBysoKUVFRsrKcnBxcunQJrVu3ZhgZf6RJUFJSEk6cOIHatWuzDolXQ4cOxc2bNxEbGyt72NjYYMaMGTh27Bjr8FROV1cXnp6epabSJiYmwsHBgVFU/CoqKkJRURG0tOTfjoVCoazFrKrjOA6BgYHYv38/Tp48CScnJ7nnmzdvDh0dHbn3wjt37iAtLa1avBeWd/3A2/f+bt26QVdXF4cOHapWsybLu/7Zs2eXeh8EgFWrVuH3339XeXzUNaZiubm5uHv3ruzrlJQUxMbGolatWrC3t8eUKVPw/fffo379+nBycsL8+fNhY2ODvn37sgtaid53/dbW1ujfvz+uXbuGP//8E2KxWDYeoFatWtDV1WUVtlKVdw+8m/zp6OjAysoKDRo04DtUlSjv+mfMmIFBgwahffv26NSpEyIjI/HHH3/g9OnT7IJWsvJegw4dOmDGjBkwMDCAg4MDzpw5g82bNyM0NJRh1MoTEBCA7du34+DBgzA2Npb9npuamsLAwACmpqYYNWoUgoKCUKtWLZiYmGDixIlo3bo1WrVqxTj6j1fe9UuToPz8fGzduhU5OTnIyckBANSpUwdCoZBl+B+tvOu3srJS2PJnb2+vMGlUOl7mpmmwU6dOcQBKPYYPH85x3Nsp9PPnz+csLS05PT09rkuXLtydO3fYBq1E77v+lJQUhc8B4E6dOsU6dKUp7x54V3WbPl+R6//tt9+4evXqcfr6+py7uzt34MABdgGrQHmvQXp6OjdixAjOxsaG09fX5xo0aMD98MMPnEQiYRu4kpT1e/7777/Ljnn9+jU3YcIErmbNmpyhoSHn5+fHpaenswtaicq7/rLuDwBcSkoK09iVoSI/f0Xfw9f0ecG/FRJCCCGEaBwaI0QIIYQQjUWJECGEEEI0FiVChBBCCNFYlAgRQgghRGNRIkQIIYQQjUWJECGEEEI0FiVChBBCCNFYlAgRQgghRGNRIkQI0Sj379+HQCCQ7WekyOnTpyEQCEptAkoIqX4oESKEkHe0adMG6enpMDU1BQCEh4fDzMyMbVCEEJWgTVcJIeQdurq6CjeBJIRUP9QiRAipUvLy8jBs2DDUqFED1tbW+OGHH9CxY0dMmTIFACAQCHDgwAG57zEzM0N4eLhc2e3bt9GmTRvo6+vDzc0NZ86ckT1Xsmvs9OnTGDlyJLKzsyEQCCAQCLBo0SIAwE8//YT69etDX18flpaW6N+/vwqvnBCiCpQIEUKqlBkzZuDMmTM4ePAgjh8/jtOnT+PatWuVOs+0adNw/fp1tG7dGr6+vnj27Fmp49q0aYPVq1fDxMQE6enpSE9Px/Tp03H16lVMmjQJ3377Le7cuYPIyEi0b99eGZdICOERdY0RQqqM3Nxc/Pbbb9i6dSu6dOkCANi0aRNsbW0/+FyBgYHo168fAODnn39GZGQkfvvtN8ycOVPuOF1dXZiamkIgEMh1l6WlpcHIyAi9e/eGsbExHBwc0LRp04+4OkIIC9QiRAipMpKTk1FYWAgvLy9ZWa1atdCgQYMPPlfr1q1l/9fW1kaLFi2QkJBQ4e/v2rUrHBwcULduXQwdOhTbtm1Dfn7+B8dBCGGLEiFCSLUiEAjAcZxcWVFRkdLrMTY2xrVr17Bjxw5YW1tjwYIFcHd3pyn3hFQxlAgRQqqMTz/9FDo6Orh06ZKs7MWLF0hMTJR9XadOHaSnp8u+TkpKUthS8/fff8v+X1xcjJiYGLi4uCisV1dXF2KxuFS5trY2fHx8sHz5cty8eRP379/HyZMnK3VthBA2aIwQIaTKqFGjBkaNGoUZM2agdu3asLCwwLx586Cl9d/fdJ07d8a6devQunVriMVizJo1Czo6OqXOJRKJUL9+fbi4uGDVqlV48eIFvvrqK4X1Ojo6Ijc3F1FRUXB3d4ehoSFOnjyJe/fuoX379qhZsyaOHDkCiURSqW46Qgg7lAgRQqqUFStWIDc3F76+vjA2Nsa0adOQnZ0te/6HH37AyJEj4e3tDRsbG/z444+IiYkpdZ6QkBCEhIQgNjYW9erVw6FDh2Bubq6wzjZt2mDcuHEYNGgQnj17hoULF8LHxwcRERFYtGgR3rx5g/r162PHjh1o1KiRyq6dEKJ8Au7dznRCCKliOnbsCA8PD6xevZp1KISQKobGCBFCCCFEY1EiRAghhBCNRV1jhBBCCNFY1CJECCGEEI1FiRAhhBBCNBYlQoQQQgjRWJQIEUIIIURjUSJECCGEEI1FiRAhhBBCNBYlQoQQQgjRWJQIEUIIIURj/R/GxzmviJWi4QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "for nodes in problems.keys():\n",
    "    prob = []\n",
    "    prob_ising = []\n",
    "    for kk in problems[nodes].keys():\n",
    "        ax.plot(nodes, results[nodes][kk][\"postprocessing\"][\"probability\"], marker=\"o\", color=\"tab:blue\", markersize=4)\n",
    "        prob.append(results[nodes][kk][\"postprocessing\"][\"probability\"])\n",
    "        prob_ising.append(results[nodes][kk][\"postprocessing\"][\"probability_ising\"])\n",
    "    ax.plot(nodes, np.mean(prob), color=\"tab:orange\", markeredgecolor=\"black\", marker=\"o\")\n",
    "    ax.plot(nodes, np.mean(prob_ising), color=\"tab:green\", markeredgecolor=\"black\", marker=\"d\")\n",
    "ax.plot([],[], marker=\"o\", color=\"tab:blue\", label=\"case\")\n",
    "ax.plot([],[], marker=\"o\", color=\"tab:orange\", label=\"mean optimal\", markeredgecolor=\"black\")\n",
    "ax.plot([], [], color=\"tab:green\", markeredgecolor=\"black\", marker=\"d\", label=\"mean ising optimal\")\n",
    "ax.plot(np.arange(10, 25), [1/2**(i) for i in np.arange(10, 25)], color=\"black\", linestyle=\"--\",label=\"random\")\n",
    "\n",
    "ax.set_yscale(\"log\")\n",
    "ax.set_ylabel(\"probability\")\n",
    "ax.set_xlabel(\"qubits\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Strategy to find optimal  Lagrange multipliers of the unbalanced penalization function using LR-QAOA "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_qaoa(lambdas, mdl, delta, shots):\n",
    "    nodes = mdl.number_of_binary_variables\n",
    "    qubo = FromDocplex2IsingModel(mdl, unbalanced_const=True, strength_ineq=lambdas) # Convert the CPLEX model into an Ising Hamiltonian model using the unbalanced penalization approach\n",
    "    ising_hamiltonian = qubo.ising_model\n",
    "    max_w = np.max(np.abs(ising_hamiltonian.weights))\n",
    "    hamiltonian_dict = {tuple(t):w/max_w for t, w in zip(ising_hamiltonian.terms,ising_hamiltonian.weights) if abs(w) > 1e-10} # Ising Hamiltonian after a normalization \n",
    "    gammas = np.arange(1, p+1) * delta/p # Annealing linear ramp schedule: cost hamiltonian term\n",
    "    betas = np.arange(1, p+1)[::-1] * delta/p # Annealing linear ramp schedule: mixer term\n",
    "    qc = qaoa_circ(hamiltonian_dict, gammas, betas, nodes) # QAOA circuit\n",
    "    samples = backend.run(qc, shots=shots).result().get_counts() # Samples results\n",
    "    return samples\n",
    "\n",
    "def objective_func_lambdas(lambdas, mdl, problem, delta, shots):\n",
    "    samples = run_qaoa(lambdas, mdl, delta, shots)\n",
    "    results = objective_KP(samples, problem)[\"results\"]\n",
    "    samples_satisfy_constraint = np.mean(results[:,2] * results[:,3]) # Maximize the samples that satisfy the constraints\n",
    "    values = np.mean(results[:,0] * results[:,2] * results[:,3]) # Maximize the value of the solutions that satisfy the constraint \n",
    "    print(f\"values: {round(values,2)} | constraints satified:{round(samples_satisfy_constraint,2)} | lambdas: {np.round(lambdas,3)}\")\n",
    "    objective_function = -(values + 10*samples_satisfy_constraint) # This is an example of an objective function that produces lambda parameters for the unbalanced penalization function, which is not necessarily the best choice\n",
    "    return objective_function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "problems = np.load(\"./Data/KP/problems.npy\", allow_pickle=True).item()\n",
    "lambdas0 = [1, 0.2] # Initial condition (Guessing good parameters)\n",
    "nodes = 12 # number of qubits\n",
    "case = 0 # Random case chose\n",
    "shots = 1000 # Shots per LR-QAOA circuit\n",
    "delta = 0.5 # LR-QAOA ramp schedule \n",
    "mdl = Knapsack(problems[nodes][case][\"values\"], problems[nodes][case][\"weights\"], problems[nodes][kk][\"max_weights\"])\n",
    "# Using scipy find a good set of lambda parameters (Based on my experience, they generalize well for other problems)\n",
    "sol = minimize(objective_func_lambdas, x0=lambdas0, args=(mdl, problems[nodes][case], delta, shots), method=\"COBYLA\",options={\"maxiter\":20})\n",
    "lambda_opt = sol.x # Optimal lambda_{1,2} for this problem \n",
    "samples_opt = run_qaoa(lambda_opt, mdl, delta, shots) \n",
    "results_opt = objective_KP(samples_opt, problems[nodes][case])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = np.load(\"./Data/KP/results.npy\", allow_pickle=True).item()\n",
    "fig, ax = plt.subplots()\n",
    "ax.bar(0, results[nodes][case][\"postprocessing\"][\"probability\"], label=r\"$\\lambda_{1,2}$ paper\", edgecolor=\"black\")\n",
    "ax.bar(1, results_opt[\"probability\"], label=r\"$\\lambda_{1,2}$ optimization\", edgecolor=\"black\")\n",
    "ax.set_ylabel(\"probability\")\n",
    "ax.set_xlabel(\"case\")\n",
    "ax.set_xticks([0,1])\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "problems = np.load(\"./Data/KP/problems.npy\", allow_pickle=True).item()\n",
    "results = np.load(\"./Data/KP/results.npy\", allow_pickle=True).item()\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "values = results[nodes][case][\"postprocessing\"][\"results\"][:,0]\n",
    "weights = results[nodes][case][\"postprocessing\"][\"results\"][:,1]\n",
    "counts = results[nodes][case][\"postprocessing\"][\"results\"][:,2]\n",
    "max_weight = problems[nodes][case][\"max_weights\"]\n",
    "for sample in results[nodes][case][\"postprocessing\"][\"results\"]:\n",
    "    ax.plot(sample[0], sample[1], marker=\"o\",linewidth=0, markersize=sample[2]/5, color=\"grey\", alpha=0.3)\n",
    "for sample in results_opt[\"results\"]:\n",
    "    ax.plot(sample[0], sample[1], marker=\"p\",linewidth=0, markersize=sample[2]/5, color=\"red\", alpha=0.3)\n",
    "\n",
    "ax.plot([], [], marker=\"o\",linewidth=0, markersize=10, color=\"grey\", alpha=0.3, label=r\"$\\lambda_{1,2}$ paper\")\n",
    "ax.plot([], [], marker=\"p\",linewidth=0, markersize=10, color=\"red\", alpha=0.3, label=r\"$\\lambda_{1,2}$ optimization\")\n",
    "\n",
    "ax.plot(results[nodes][case][\"postprocessing\"][\"optimal\"][0], results[nodes][case][\"postprocessing\"][\"optimal\"][1], marker=\"X\",linewidth=0, markersize=8, color=\"None\", markeredgecolor=\"black\", label=\"optimal\")\n",
    "ax.plot(results[nodes][case][\"postprocessing\"][\"optimal_ising\"][0], results[nodes][case][\"postprocessing\"][\"optimal_ising\"][1], marker=\"P\",linewidth=0, markersize=8, color=\"None\", markeredgecolor=\"black\", label=\"optimal Ising\")\n",
    "\n",
    "ax.plot([min(values), max(values)], [max_weight, max_weight], linestyle=\"--\", color=\"red\", label=\"Maximum weight\")\n",
    "\n",
    "ax.set_xlabel(\"Total value in the Knapsack\")\n",
    "ax.set_ylabel(\"Weight in the knapsack\")\n",
    "ax.legend()\n",
    "ax.set_title(f\"Solutions found using LR-QAOA 1000 shots for {nodes} items and case {case}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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