examples/hybrid_quantum_algorithms/QAOA/QAOA_braket.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Use Braket SDK Cost Tracking to estimate the cost to run this example\n",
    "from braket.tracking import Tracker\n",
    "t = Tracker().start()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM (QAOA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we show how to (approximately) solve binary combinatorial optimization problems, using the __Quantum Approximate Optimization Algorithm (QAOA)__, as introduced in Ref.[1]. \n",
    "The QAOA algorithm belongs to the class of __hybrid quantum algorithms__ (leveraging both classical as well as quantum compute), that are widely believed to be the working horse for the current __NISQ (noisy intermediate-scale quantum) era__.\n",
    "In this NISQ era QAOA is also an emerging approach for benchmarking quantum devices and is a prime candidate for demonstrating a practical quantum speed-up on near-term NISQ device [1,4]. \n",
    "To validate our approach we benchmark our results with exact results as obtained from classical QUBO solvers. \n",
    "\n",
    "We provide a step-by-step walkthrough explaining the QAOA quantum algorithm and show how to build the corresponding parametrized quantum circuit ansatz using the ```Braket``` SDK, with simple modular building blocks (that can be re-used for other purposes). \n",
    "We use open-source off-the-shelf ```scipy``` optimizers for classical numerical optimization. \n",
    "While we demonstrate our proof-of-concept approach using classical simulators for circuit execution, our code could in principle be run on actual quantum hardware by simply changing the definition of the ```device``` object (provided that the gate set used in the ansatz is supported by the device, as is the case here for IonQ; for Rigetti we need to apply one more extra trick as shown below). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BACKGROUND: HYBRID QUANTUM ALGORITHMS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quantum computers hold the promise to outperform even the most-powerful classical computers on a range of computational problems in (for example) optimization, chemistry, material science and cryptography.\n",
    "The canonical set of quantum algorithms (such as Shor's or Grover's quantum algorithms), however, comes with hardware requirements (such as a large number of quantum gates) that are currently not available with state-of-the-art technology. \n",
    "Specifically, these algorithms are typically believed to be feasible only with fault-tolerance as provided by quantum error correction. \n",
    "In the current __noisy intermediate-scale (NISQ) era__, near-term quantum computers do not have a large enough number of physical qubits for the implementation of error correction protocols, making this canonical set of quantum algorithms unsuitable for near-term devices. Against this background, the near-term focus has widely shifted to the class of __hybrid quantum algorithms__ that do not require quantum error correction. \n",
    "In these hybrid quantum algorithms, the noisy __near-term quantum computers are used as co-processors__ only, within a larger classical optimization loop, as sketched in the schematic figure below. \n",
    "Here, the undesired effects of noise are suppressed by deliberately limiting the quantum circuits on the quantum processing unit (QPU) to short bursts of the calculation, and the need for long coherence times (as required for the standard set of quantum algorithms) is traded for a classical overhead due to (possibly many) measurement repetitions and (essentially error-free) classical processing. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div align=\"center\"><img src=\"hybrid_quantum.png\"/></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Variational Quantum Algorithms__: Specifically, variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) [1] belong to this emerging class of hybrid quantum algorithms. \n",
    "These are widely believed to be promising candidates for the demonstration of a __quantum advantage__, already with near-term (NISQ) devices in areas such as quantum chemistry [2], condensed matter simulations [3], and discrete optimization tasks [4].\n",
    "\n",
    "__Variational Quantum Computing vs. Deep Learning__: The working principle of variational quantum computing is very much reminiscent of training deep neural networks: \n",
    "when you train a neural network, you have an objective function that you want to minimize, typically characterized by the error on your training set. \n",
    "To minimize that error, typically you start out with an initial guess for the weights in your network. \n",
    "The coprocessor, in that case a GPU, takes these weights which define the exact operation to execute and the output of the neural network is computed. \n",
    "This output is then used to calculate the value of your objective function, which in turn is used by the CPU to make an educated guess to update the weights and the cycle continues. \n",
    "Variational quantum algorithms, a specific form of hybrid algorithms, work in the very same way, using parametrized quantum circuits rather than parametrized neural networks and replacing the GPU with a QPU. \n",
    "Here, you start with an initial guess for the parameters that define your circuit, have the QPU execute that circuit, perform measurements to calculate an objective function, pass this value (together with the current values of the parameters) back to the CPU and have this *classical* CPU update the parameters based on that information. \n",
    "\n",
    "Of course, coordinating that workflow for quantum computers is much more challenging than in the previous case. Quantum computers are located in specialized laboratory facilities, are typically single threaded, and have special latency requirements. \n",
    "This is exactly the undifferentiated heavy-lifting that Amazon Braket handles for us, such that we can focus on our scientific problem. \n",
    "For the sake of this introductory tutorial, we simply use a classical circuit simulator (that mimic the behavior of a quantum machine) as the device to execute our quantum circuits.\n",
    "Within Amazon Braket, the workflow, however, is exactly the same. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BACKGROUND: QUADRATIC BINARY OPTIMIZATION PROBLEMS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Combinatorial optimization__: \n",
    "Combinatorial optimization problems are ubiquitous across many areas of science and application areas. \n",
    "Applications can be found (for example) in logistics, scheduling, planning, and portfolio optimization.\n",
    "In a nutshell combinatorial optimization problems are problems involving a large number of yes/no decisions with each set of decisions yielding a corresponding objective function value, like a cost or profit value. \n",
    "Because of the combinatorial explosion of the solution space with the number of variables, finding good solutions is a daunting task and extremely difficult.  \n",
    "\n",
    "__QUBO problems__: The QUBO ([Quadratic Unconstrained Binary Optimization](https://en.wikipedia.org/wiki/Quadratic_unconstrained_binary_optimization)) model unifies a rich variety of NP-hard combinatorial optimization problems: \n",
    "Famous examples include Quadratic Assignment Problems, Capital Budgeting Problems, Task Allocation Problems and Maximum-Cut Problems. \n",
    "For more details we refer to the excellent review and tutorial on QUBO problems presented in Ref.[5].\n",
    "\n",
    "__Maximum Cut__: Among the class of QUBO problems, Maximum Cut (MaxCut) is paradigm combinatorial optimization problem. \n",
    "Given a graph $G=(V,E)$ with vertex set $V$ and edge set $E$, we seek partition of $V$ into two subsets with maximum cut. \n",
    "In short, we have to color every node either blue or red and we score a point whenever an edge connects two nodes with different colors. \n",
    "We then would like to find the solution with the highest score. \n",
    "Applications thereof can be found in, for example, (i) clustering for marketing purposes (segment your customer base into different clusters for targeted marketing) or (ii) portfolio optimization in finance (vertex corresponds to asset, with color referring to sell or buy decisions. \n",
    "Again, the problem in this specific graph coloring problem is that there are $2^𝑁$ possible solutions for $N$ nodes (an exponential explosion in possibilities), making it impossible to enumerate all possible candidates for relevant system sizes. \n",
    "\n",
    "__Ising Hamiltonian__: Importantly, there is a fundamental correspondence between QUBO problems and Ising problems in physics. \n",
    "Specifically, we can encode the Maximum Cut problem as a __minimization problem__ of an Ising Hamiltonian, where the (classical) cost function reads \n",
    "\n",
    "$$H_{C}=\\sum_{i>j} J_{i,j} z_{i} z_{j},$$\n",
    "\n",
    "with Ising variables $z_{i}=-1,1$ and the Ising matrix $J$ encoding the weights of the edges. \n",
    "For the sake of this discussion, we ignore potential linear terms and constant offsets (that do not affect the optimal solution $z$ anyway). \n",
    "In short, the cost Hamiltonian $H_{C}$ assigns a number to every bitstring $z=(z_{1},z_{2},\\dots)$, and we would like to find the lowest number possible. \n",
    "This will be the optimal assignment and solution to our problem. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BACKGROUND: THE QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we will try to solve for the optimal _classical_ bitstring $z$ using the Quantum Approximate Optimization Algorithm (QAOA). \n",
    "To this end, we first promote the classical spin variables $z_{i}=-1,1$ to quantum-mechanical variables $\\sigma_{i}^{z}$ (with the Pauli matrix $\\sigma_{i}^{z}$ representing the observable corresponding to spin along the $z$ coordinate axis in three-dimensional Euclidean space $\\mathbb{R}^{3}$). \n",
    "This leads to the following quantum mechanical cost Hamiltonian encoding the optimization problem\n",
    "\n",
    "$$\\hat{H}_{C}=\\sum_{i>j} J_{i,j} \\sigma_{i}^{z} \\sigma_{j}^{z},$$\n",
    "\n",
    "which can be written as a matrix of size $(2^{N}, 2^{N})$ with diagonal elements only corresponding to all possible classical values for the cost function $H_{C}$. \n",
    "The ground state of $\\hat{H}_{C}$ corresponds to the optimal solution of the classical combinatorial problem.\n",
    "\n",
    "__QAOA ansatz__: Finding this ground state is generically hard. \n",
    "To approximate this groundstate, QAOA prepares a parametrized ansatz state (corresponding to a parameterized  gate  sequence),  whose  parameters  are iteratively updated by a classical optimizer in a closed loop. \n",
    "Specifically, QAOA involves a specific ansatz wavefunction parametrized by a parameter family $(\\vec{\\beta}, \\vec{\\gamma})$, embedded into a larger classical optimization loop to find the optimal values for these parameters. \n",
    "As shown in Ref.[1], good approximate solutions to the problem class considered here can be found by preparing the variational state \n",
    "\n",
    "$$|\\gamma, \\beta \\rangle = U_{x}(\\beta_{p})U_{zz}(\\gamma_{p}) \\cdots U_{x}(\\beta_{1})U_{zz}(\\gamma_{1}) |s\\rangle$$\n",
    "\n",
    "with single qubit rotations induced by $U_{x}(\\beta) = \\exp(-i\\beta \\sum_{i}\\sigma_{i}^{x})$, \n",
    "and interactions described by $U_{zz}(\\gamma) = \\exp(-i\\gamma H_{C})$,\n",
    "starting initially from a product of $\\sigma^{x}$ eigenstates, i.e.,\n",
    "$|s\\rangle =|-,-,\\dots\\rangle$, with $|-\\rangle = (|0\\rangle -|1\\rangle  )/\\sqrt{2}$. \n",
    "The family of states $|\\gamma, \\beta \\rangle$ is prepared by alternating single-qubit operations $U_{x}(\\beta_{p})$ with targeted spin-spin interactions generated by the cost Hamiltonian $H_{C}$. \n",
    "The depth $p$ can be interpreted as a hyperparameter. \n",
    "For $p$ layers of QAOA blocks, there are $2p$ classical parameters to optimize over, \n",
    "since each layer $k$ is characterized by just two variational parameters, $\\gamma_{k}$ and $\\beta_{k}$. \n",
    "The preparation step outlined above is followed by a measurement in the computational basis, giving a classical string $z$, with which one can evaluate the objective function $H_{C}$ of the underlying combinatorial problem at hand. \n",
    "Taking several measurements shots one can build the expectation value $E(\\beta, \\gamma) = \\langle H_{C} \\rangle$ that we report as the objective function to the classical minimizer (while other choices could be possible as well). \n",
    "Repeating this procedure will provide an optimized string $z$, with the quality of the result improving as the depth of the quantum circuit $\\sim 2p$ is increased [1]. \n",
    "In fact, in principle (in the absence of noise and other imperfections), QAOA can reach the global optimum of any cost function in the limit $p \\rightarrow \\infty$ [1], approaching the adiabatic protocol. \n",
    "Thus, in theory the computational power of QAOA increases with $p$, but in practice the number of layers that can be executed without errors on NISQ devices is limited due noise and imperfections. \n",
    "\n",
    "__Optimization__: Since we are primarily interested in solving the classical optimization problem, within this routine it is sufficient to keep track of the best classical bitstring. \n",
    "This means that the wavefunction prepared by the quantum circuit $|\\gamma, \\beta \\rangle$ has to have some overlap with the optimal solution $|z^{*} \\rangle$ that we can read out as bitstring $z^{*}$ in the measurement shots. \n",
    "To this end, in principle (i.e., without any training), we could just sample from a completely uniform state that is prepared in a superposition of all computational basis states, as prepared by applying Hadamard gates to all qubits: $|\\mathrm{uniform}\\rangle = 1/\\sqrt{2^{N}}\\sum_{i}|z_{i}\\rangle$. \n",
    "In that case (assuming a single optimal solution) the success probability per shot amounts to $p_{\\mathrm{success}}=1/2^{N}$. \n",
    "We can then amplify our success chances by just taking many measurement shots. \n",
    "For large systems, however, this approach is not scalable as we would need to take an exponentially increasing number of measurements. \n",
    "That is why we train our circuits, update the parameters, with the goal to increase our success chances to find the optimal bitstring. \n",
    "We can quantify our success chances as follows [6]. \n",
    "For a given wavefunction $|\\gamma, \\beta \\rangle$ the probability to find the optimal solution in a single shot is given by \n",
    "\n",
    "$$ p_{\\mathrm{success}}(\\gamma, \\beta) = |\\langle z^{*}|\\gamma, \\beta \\rangle |^{2},$$\n",
    "\n",
    "where $z^{*}$ denotes the optimal bitstring. \n",
    "If we perform $M$ repeated measurements, the overall probability $P$ for observing this solution at least once is given by \n",
    "\n",
    "$$ P = 1 - (1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}, $$ \n",
    "\n",
    "since the term $(1-p_{\\mathrm{success}}(\\gamma, \\beta))^{M}$ gives the probability of _not_ obtaining $z^{*}$ in repeated $M$ trials. \n",
    "Therefore, to have an overall success chance up to $\\epsilon$ close to 100%, i.e., $P \\geq 1-\\epsilon$, the number of required shots has to be \n",
    "\n",
    "$$ M \\geq \\frac{\\log(\\epsilon)}{\\log(1-p_{\\mathrm{success}}(\\gamma, \\beta))}.$$\n",
    "\n",
    "Let us illustrate this results as follows: \n",
    "If we do not know anything and just resort to a uniform superposition $|\\mathrm{uniform}\\rangle$, for a small system with $N=10$ qubits we can find the optimal solutions with 80% success probability by taking at least $\\sim 1650$ shots. \n",
    "For just $N=20$ qubits, however, this number amounts to $\\sim 1.7 \\times 10^{6}$, making this naive approach unfeasible. \n",
    "Conversely, if we can train the quantum circuit to obtain $p_{\\mathrm{success}}(\\gamma, \\beta) \\sim 0.1$, we only need $\\sim 15$ shots to have $P\\geq 80\\%$. \n",
    "Below we will track and illustrate the best classical optimum as our algorithm proceeds towards a local or (ideally) global optimum.  \n",
    "\n",
    "__Objective function__: Finally, some more details on the definition of the cost function are in order. \n",
    "Following the standard approach [1, 4], QAOA tries to minimize the expectation value $\\langle \\hat{H}_{C} \\rangle$, but does _not_ explicitly maximize the success probability [6]. \n",
    "However, a low expectation value for $\\langle \\hat{H}_{C} \\rangle$ does not necessarily translate to a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, as can be understood from the following example:\n",
    "Consider (for example) a variational state that is a linear combination of low energy excited eigenstates of the cost Hamiltonian $\\hat{H}_{C}$ other than the ground state $|z^{*}\\rangle$. \n",
    "By definition, this state will have a relatively low expectation value $\\langle \\hat{H}_{C} \\rangle$ while the success probability is zero (as this low energy state does not have any overlap with the ground state). \n",
    "Similarly, a variational state that is a linear combination of the ground state with very high energy eigenstates could have a high success probability $p_{\\mathrm{success}}(\\gamma, \\beta)$, while (at the same time) reporting a high cost value to the classical optimizer.\n",
    "To address this issue, alternative methods for the optimization of the variational parameters have recently been proposed. \n",
    "While for simplicity we follow the majority of the literature and take $\\langle \\hat{H}_{C} \\rangle$ as cost value that we report to the classical optimizer, here we do mention a potential alternative for future research: \n",
    "One approach is to use the Gibbs objective function, defined as $\\mathrm{cost}=-\\mathrm{log} \\langle \\exp(-\\eta \\hat{H}_{C})\\rangle$, with the hyperparameter $\\eta>0$ [7]. \n",
    "As compared to the simple expectation value $\\langle \\hat{H}_{C} \\rangle$, this definition of the cost value shows stronger rewards for low energy states, thereby increasing the success probability. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IMPORTS and SETUP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For classical benchmarking we will be using the python library ```pyqubo```, as used in our helper script ```utils_classical```. If not already present in your virtual environment, you can install this library simply with ```pip install pyqubo```. Similarly, as ```seaborn``` are not expected to be present in the virtual environment by default, we will install them via ```pip install seaborn```. Note the ```-q``` to suppress install updates from ```pip```."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If these have already been installed, this cell can be commented out.\n",
    "!pip install pyqubo -q\n",
    "!pip install seaborn -q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# general imports\n",
    "import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import seaborn as sns\n",
    "import time\n",
    "from datetime import datetime\n",
    "import pickle\n",
    "import random\n",
    "\n",
    "# magic line for producing visualizations in notebook\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fix random seed for reproducibility\n",
    "seed = 42\n",
    "np.random.seed(seed)\n",
    "random.seed(a=seed)\n",
    "\n",
    "# switch to trigger writing training results to disk\n",
    "store_results = False\n",
    "# switch to trigger printing results of each optimization cycle\n",
    "verbose = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# AWS imports: Import Braket SDK modules\n",
    "from braket.circuits import Circuit, Observable, FreeParameter\n",
    "from braket.aws import AwsSession, AwsDevice\n",
    "from braket.devices import LocalSimulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils_classical import plot_colored_graph, plot_colored_graph_simple, solve_classical_ising\n",
    "# auto reload external files, so that we can edit the external .py file and immediately see the changes here\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set up device: Local Simulator\n",
    "device = LocalSimulator()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "## example code for other backends\n",
    "## choose the on-demand simulator to run your circuit\n",
    "# device = AwsDevice(\"arn:aws:braket:::device/quantum-simulator/amazon/sv1\")\n",
    "## choose the Rigetti device to run your circuit\n",
    "# device = AwsDevice(\"arn:aws:braket:us-west-1::device/qpu/rigetti/Aspen-M-3\")\n",
    "## choose the Ionq device to run your circuit\n",
    "# device = AwsDevice(\"arn:aws:braket:us-east-1::device/qpu/ionq/Harmony\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PROBLEM SETUP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider a graph coloring problem.\n",
    "Given a graph $G=(V,E)$, made of a set vertices (also called nodes) $V$ and edges $E$, our goal is to color each node red or blue, then score a point for each node that is next to a node of different color. \n",
    "We strive to find the optimal coloring that scores the largest number of points.\n",
    "To this end, we will address the dual problem of finding the minimum energy of the corresponding Ising Hamiltonian. \n",
    "To get started, we first use the open-source ```networkx``` library to visualize the problem graph. \n",
    "Feel free to play with the parameters $n$ (for the number of nodes) and $m$ (for the number of edges) below to consider other graphs of your choice. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SBMuWLUN0dLTQURljjDEuKBWdvr6+3By9KC3Ozs549OgRBgwYgN9++w0tWrTA/fv3hY710ypWrIhBgwbh6NGjePfuHXx9fVGzZk0sXrwYFhYWsLa2xoIFCxAeHs5HQDLGGBMEF5QKTl9fH6mpqcjLyxM6ilTp6Ohg06ZNuHbtGjIzM2FjY4MZM2YgMzNT6GjFUr58ebi6uuLgwYN49+4dAgIC0KBBA6xbtw7169eHhYUFZsyYgdDQUC4uGWOMlRhelKPggoKC4OTkhLdv38LQ0FDoODKRm5uL1atXY9GiRahatSq2bt2KTp06CR1LqnJycnD+/Hn4+/vjyJEjSEpKgomJCXr27AkXFxfY2dlBLObPj4wxxmSDrzAKTp7P85YWVVVVzJo1C+Hh4ahRowY6d+6M/v374927d0JHkxo1NbXC7Ybevn2L8+fP49dff4Wfnx9atWoFIyMjjBkzBufPn0d+fr7QcRljjJUxPEKp4KKjo2FhYYFLly6hTZs2QseROSLC7t27MXnyZIhEIqxZswYDBgwodVsM/SiJRILr168XbqQeGxuLihUrwsnJCS4uLrC3t4eamprQMRljjJVyXFAquKSkJOjr68Pf3x89e/YUOk6JSUxMxKRJk7Bv3z60b98e27Ztg6mpqdCxZIqIEBYWVlhcxsTEoHz58vj111/h4uKCLl26QFNTU+iYjDHGSiG+5a3gKlSoALFYXKZveX+JgYEB9u7di1OnTuH58+ewtrbGsmXLytzipH8TiUSF2w09fvwY4eHhmDRpEsLDw+Hi4oJKlSqhV69e8PX1xcePH4WOyxhjrBThglLBKSkpQVdXV+EKyk86d+6M8PBwjB8/HnPnzoWNjQ1u3LghdCyZE4lEqFevHubPn48HDx7g8ePHmDt3Ll6+fAl3d3dUqlQJv/76K3bt2lXmtpVijDEmfVxQsjK5F2VRaGlpYeXKlQgNDYWqqirs7Owwfvx4hRqlMzc3L9xu6MWLF1i+fDlSU1MxdOhQGBoaomPHjti6dSvevn0rdFTGGGNyiOdQMrRs2RK1a9fG7t27hY4iuIKCAmzcuBGzZ89GhQoVsHHjRvTo0UPoWIJ58+YNAgMD4e/vj0uXLkEikaBly5bo2bMnevbsCRMTE6EjMsYYkwNcUDI4OTmhoKAAx44dEzqK3IiNjcWYMWNw/PhxODs7Y8OGDTAyMhI6lqDev3+PoKAg+Pv74+zZs8jLy4OtrS1cXFzg4uIiF4uaMnLy8SIpA7n5Eqgqi1FDTwtaaspCx2KMsTKPC0qGoUOHIiIiQiHmDhYFEeHQoUMYP348srKysGzZMowaNYo3CAeQmpqKY8eOISAgACdPnkRWVhbq169fWFzWrVu3xLZiiklIw76bsbj4OBGxyZn49xuaCIBJRU20szBAv2YmMDPULpFMjDGmaLigZJg2bRoCAgLw5MkToaPIpZSUFMyYMQPe3t5o0aIFvL29Ua9ePaFjyY2MjAycOnUK/v7+OHbsGNLS0mBhYVF4Sk/jxo1lUly+Ss7ErMPhCH7yHkpiEQokX38r+/R4K1N9LHW2RrWKvD0SY4xJEw+1MIVflPM9urq62LZtG65cuYKUlBQ0atQIc+bMQXZ2ttDR5IKWlhZcXFzg4+ODxMREHD16FC1atMDWrVvRpEkT1KpVC5MnT0ZISAgkEolU+vQLjYX9ussIefbP9+23isl/Px7yLAn26y7DLzRWKjkYY4z9g0coGXbu3ImhQ4ciLy8Pyso83+xbcnJysHz5cixduhTVq1fHtm3b0K5dO6FjyaW8vDxcunQJAQEBOHz4MBISElClShU4OzvDxcUFrVu3/qnvt40XY7D6THSx803pZI5x7cyK3Q5jjDEeoWQA9PT0AADJyckCJ5F/ampqmD9/Pu7du4fKlSujffv2GDJkCI/wfoGKigo6duyILVu24PXr17hy5Qr69OmDo0ePokOHDqhSpQqGDRuGkydPIjc394fa9AuNlUoxCQCrz0RjP49UMsaYVPAIJcO1a9fQsmVLREREoG7dukLHKTUkEgl27NiBqVOnQlVVFV5eXnBzcyuz54JLCxEhNDS08AjIp0+fQkdHB927d4eLiws6d+4MDQ2N/7zuVXIm7NddRk6+dG6bA4CashjnPNvwnErGGCsmHqFk0NfXBwCFPS3nZ4nFYgwfPhxRUVFo3749+vXrh65du+L58+dCR5NrIpEITZs2xYoVKxATE4N79+5h4sSJuHv3LpydnaGvr4/evXvDz88PaWlpha+bdTgc+d+ZK1lU+RLCrMPhUm2TMcYUEY9QMrx//x6VKlVCQEAAnJ2dhY5Tah0/fhxjxozBu3fvsGjRIvz22288J7WIHj9+XDhyeefOHaipqaFTp05o9WsfbHquK7N+z3m2hqkBbynEGGM/i0coGXR1dSESiXiEspgcHBwQERGBUaNGYfr06bC1tcXt27eFjlWqWFhYYNasWQgLC8OzZ8+wdOlSJCUlYdnBYJCkQCZ9KolF2HuD51IyxlhxcEHJoKSkBF1dXV5YIgXlypXD2rVrcfPmTQBAs2bN4OnpifT0dIGTlT41a9bEpEmTcO3aNVh26AWRWEkm/RRICBejE2XSNmOMKQouKBmAf+ZR8gil9DRp0gShoaFYsWIFtm3bBisrKxw/flzoWKVSek4+4lN/bBX4z4pNykRGTr5M+2CMsbKMC0oGgAtKWVBWVsaUKVMQEREBS0tL/Prrr+jbty/evn0rdLRS5WVSBmQ90ZsAvEjKkHEvjDFWdnFByQD8sxcl3/KWjZo1a+LkyZPYt28fLl68CEtLS/z5559SOzWmrMuV4jZB8tAPY4yVRVxQMgA8QilrIpEI7u7uiIyMhLOzM0aMGIG2bdsiKipK6GhyT1W5ZN6mSqofxhgri/gdlAH4Z4SSC0rZ09PTw86dO3HhwgW8efMGDRo0wMKFC5GTkyN0NLlVQ08Lst4qXvR//TDGGPs5XFAyAP+MUPIt75LTrl07PHjwAFOnTsXixYvRsGFDBAcHCx1LLmmpKcNExifZVNIUQUOF3w4ZY+xn8TsoA/BPQZmSkoL8fF7pWlI0NDSwePFi3L17F7q6umjdujVGjBiBlJQUoaPJnXYWBhDLaphSUoAnV47AxMQEU6ZMwZ07d8DnPTDGWNFwQckA/HMrFgAXMwKoV68erl69is2bN8PPzw+WlpY4cOAAFzX/Jy4uDo+CtkHKpy7+f2Il/DmtP5ydnfH333/DxsYGlpaWWLRoEWJiYmTUKWOMlS1cUDIAfJ630MRiMUaPHo3IyEj88ssv6Nu3LxwdHREbq7gnuHz8+BFz5syBubk5Lh7xRXW1LChJeZhSSSxCK1N9uHRsiQ0bNiA+Ph6nT59G8+bNsXr1apibm6Np06ZYt24d4uPjpdo3Y4yVJVxQMgBcUMoLIyMj+Pv74/Dhw7h79y7q1q0LLy8vFBTI5thBeZSXl4fNmzfD1NQUa9asgaenJ54+fYq9E7pBWcoFpbJYhKXO1v//98rK6NSpE/766y8kJCTg4MGDMDY2xowZM2BsbIwOHTpgx44d+PDhg1RzMMZYaccFJQPw/29588Ic+dCjRw88evQIgwcPxqRJk9C8eXPcvXtX6FgyRUQIDAxEvXr1MG7cODg4OCAmJgZLlixB+fLlUa2iJhY6Wkm1z0WOVqj2lQU/Ghoa6NWrFwICApCQkIDt27dDJBJh+PDhMDQ0hLOzMw4ePIisrCypZmKMsdKIC0oGANDV1YVIJOIRSjlSvnx5bNiwASEhIcjOzoatrS2mTZuGzMxMoaNJ3c2bN9GmTRs4OzujevXquHv3Lnbt2gVjY+PPntfD2gBaTy9Ipc+pnSzQ19bkh55boUIFDBkyBOfOnUNcXBxWrFiB169fo0+fPjA0NMTAgQNx+vRpXtTGGFNYXFAyAP/c6qtQoQKPUMqh5s2b486dO/j999/xxx9/oF69ejh9+rTQsaTi2bNncHV1RfPmzfHhwwecOnUKZ86cQYMGDf7zXCLC6NGj8ezoZoy2KQ81ZXGR51QqiUVQUxZjRU9rjG1n+lOZq1atit9++w23bt1CdHQ0pkyZgps3b6JLly4wMjLC+PHjcf36dV5UxRhTKFxQskJ8Wo78UlFRwcyZMxEeHo6aNWuiS5cu8PDwQGJiotDRfkpycjImTZqEOnXqIDg4GDt37sTdu3fRuXPnr75m06ZN+Ouvv+Dt7Y3pvVrhnGcb2NX6Z6rG9wrLT4/b1dLDOc82Pzwy+T1mZmaYN28eIiMjERYWhv79++Pw4cOws7NDrVq1MHv2bEREREilL8YYk2ci4o/R7P/Y2dnBwsICu3btEjoK+wYiwt9//41JkyYBANasWYOBAwdCJJL1eTLFl52djY0bN2LJkiXIz8/HjBkz4OnpCU3Nb29cfunSJdjb22PChAlYu3btZ4/FJKRh381YXIxORGxSJv79hiYCYKKniXbmBvBobgJTA23pf1H/QyKR4MqVK/Dx8cGhQ4eQkpKC+vXrw93dHa6urqhevbrMMzDGWEnjgpIV6t69O0QiEYKCgoSOwn7Au3fvMGnSJOzduxft2rXDtm3bYGZmJnSsL5JIJNi/fz9mzZqFV69eYcSIEZg/fz4MDQ2/+9rY2FjY2Nigfv36OH36NJSVlb/63IycfLxIykBuvgSqymLU0NOCltrXny9rOTk5OH36NHx9fXHkyBFkZWWhZcuWcHNzQ+/evVGpUiXBsjHGmDTxLW9WiG95ly6VKlXCnj17cObMGbx8+RLW1tZYsmQJcnNzhY72mcuXL6NZs2Zwd3dHgwYN8PDhQ2zevPmHismsrCw4OztDS0sL+/fv/2YxCfxzTKNVVR00MtGFVVUdQYtJAFBTU4OjoyN8fX2RmJiIvXv3onz58pgwYQKqVKmCbt26Ye/evUhLSxM0J2OMFRcXlKyQnp4eL8ophTp27Ijw8HD89ttvmD9/Pho3bozr168LHQuRkZFwdHRE27ZtIRKJcPnyZQQGBqJOnTo/9HoiwogRIxAZGYnAwMDCvVJLq3LlyqFfv344fvw43rx5gw0bNiAtLQ39+/eHoaEhXF1dERQUJHcfCBhj7EdwQckK8Qhl6aWpqYnly5fj9u3b0NTUxC+//IKxY8ciNTW1xLMkJCRg9OjRsLa2Rnh4OHx9fXHjxg20bt26SO14eXlh79692LlzJxo2bCibsAKpVKkSRo8ejeDgYLx48QLz589HZGQknJycULlyZYwYMQKXLl2CRCIROipjjP0QnkPJCm3fvh0jRoxAXl4elJSUhI7DflJBQQE2bdqEWbNmQUdHBxs3boSzs7PM+83IyMDatWuxcuVKqKioYM6cORg7dizU1NSK3Nb58+fRuXNnTJo0CStXrpRBWvn08OFD+Pr6wsfHBy9evICRkRFcXV3h7u6ORo0alYqFV4wxxcQFJSt0+PBh9OzZE+/evSv1txfZP4tZxo4di2PHjqFHjx7YsGHDfzYKl4aCggL89ddfmDt3LpKSkjB+/HjMnj0burq6P9Xe8+fPYWtrCxsbG5w4cUIhP9wQEW7cuAEfHx/s378f7969g4WFBdzd3eHm5ia3i68YY4qLb3mzQnyed9liYmKCoKAgHDx4EDdu3EDdunWxadMmqZ0LTkQ4efIkGjZsiGHDhqFNmzaIiorC6tWrf7qYzMzMhLOzM3R0dODr66uQxSQAiEQitGjRAhs2bEB8fDxOnTqFZs2aYdWqVTA3N0fTpk3h5eWFN2/eCB2VMcYAcEHJ/uVTQckLc8oOkUiEXr16ITIyEu7u7hg3bhxatmyJ8PDwYrV77949dOrUCd26dUPFihVx69Yt+Pr6ombNmj/dJhFh6NChiImJQWBgICpWrFisjGWFsrIyOnfujN27dyMxMREHDhyAsbExpk+fDiMjI9jb22PHjh348OGD0FEZYwqMC0pWSE/vn1NHeISy7KlQoQK2bt2K4OBgpKamonHjxpg9ezaysrKK1M6rV68wcOBANG7cGHFxcThy5AguXboEW1vbYmdcvXo1/Pz8sHv3blhbWxe7vbJIQ0MDvXv3RkBAABISErB9+3YAwPDhw2FoaAhnZ2ccPHiwyP+ujDFWXFxQskKfRoS4oCy7WrZsibt372Lu3LlYvXo16tevj/Pnz3/3dampqZg5cybMzc1x6tQpbN68GeHh4XB0dJTKQpEzZ85gxowZmDlzJnr16lXs9hRBhQoVMGTIEJw7dw5xcXFYsWIFXr9+jT59+sDQ0BADBw7E6dOnkZ+fL3RUxpgC4EU57DO6urqYOXMmpk2bJnQUJmNRUVEYOXIkrly5goEDB2LNmjWFo9Sf5OXlYdu2bVi4cCEyMjIwefJkTJs2Ddra0jvC8OnTp7C1tUXz5s1x9OhRhZ03KS0xMTGFK8UfP34MAwMD9OnTB+7u7mjevDmvFGeMyQQXlOwzZmZmcHZ2VqitWhSZRCLBrl27MGXKFCgrK2PdunXo168fgH9W/c+YMQNPnjzB4MGDsWjRIhgZGUm1//T0dLRo0QLZ2dkIDQ1FhQoVpNq+IiMi3L17Fz4+PvD19UV8fDxq1qwJNzc3uLu7w8rKSuiIjLEyhAtK9pkWLVrA0tISO3fuFDoKK0Fv376Fp6cn/Pz8YGtri4KCAty5cwddunTBypUrZTKnkYjQp08fnDp1Cjdu3OACR4YKCgoQHBwMHx8fHDp0CCkpKahfvz7c3d3h6uqK6tWrCx2RMVbKcUHJPvPrr79CSUkJR44cEToKK2FPnjzBoEGDcO3aNYhEIgwZMgRbtmyBioqKTPpbtmwZZs2ahYCAgBLZeJ39IycnB6dPn4aPjw+CgoKQlZWFli1bwt3dHb179+Y9aBljP4UX5bDP8PGLiuf9+/eYOHEi6tati5cvX2Lr1q2YOHEidu3aBVtbW4SGhkq9zxMnTmD27NmYO3cuF5MlTE1NDY6OjvDz80NCQgL27NmD8uXLY/z48ahSpQocHBywd+9epKWlCR2VMVaKcEHJPqOnp8f7UCqI7OxsrFy5Eqampti1axcWLlyI6OhojBw5EuvWrcOtW7cgFovRvHlz/Pbbb1IrMGJiYuDu7g4HBwcsWLBAKm2yn6OtrQ0PDw8cP34cb968wR9//IGPHz+if//+MDQ0hKurK4KCgpCbmyt0VMaYnONb3uwzy5Ytw5o1a3iUsgyTSCTw8fHB7NmzER8fj1GjRmHevHmoVKnSf56bn5+P9evXY968edDT08OmTZvQvXv3n+47LS0NzZo1g0Qiwc2bN6Gjo1OcL4XJyMuXL+Hn5wcfHx88ePAAurq66NWrF9zd3dG6dWuIxTwWwRj7HL8rsM/o6+sjOTlZasfzMfly4cIF2Nraon///rCxsUFERAQ2bNjwxWIS+OeUlsmTJ+Phw4ewsrKCo6Mj+vTp81NH/kkkEgwYMABxcXEIDAzkYlKOVa9eHdOnT8f9+/cRHh6O0aNH4+zZs2jXrh1MTEwwZcoU3LlzBzwewRj7hAtK9hk9PT0QER/jVsZERETg119/RYcOHaCqqorg4GAEBATA3Nz8h15fs2ZNnDhxAj4+Prh06RIsLS3h7e0NiUTywxkWL16MwMBA7Nu3D3Xq1PnZL4WVsHr16mHJkiV49uwZQkJC4OzsjL///hs2NjawtLTEokWLEBMTI3RMxpjAuKBkn/m0wpNveZcNb968wYgRI1C/fn1ERkbiwIEDCAkJQcuWLYvclkgkgpubG6KiotCrVy+MHDkSrVu3xqNHj7772qCgIMyfPx+LFi0q1i1zJhyRSIQWLVpgw4YNiI+Px6lTp9CsWTOsWrUK5ubmaNq0Kby8vH5q9JoxVvpxQck+86mg5IU5pVt6ejoWLFgAMzMz+Pv7Y+3atYiMjETv3r2LfVJKxYoVsX37dly8eBHv3r1Dw4YNMX/+fGRnZ3/x+VFRUfDw8ECPHj0we/bsYvXN5IOysjI6d+6M3bt3IzExEQcOHICRkRGmT58OIyMj2NvbY+fOnXyngzEFwoty2GcSEhJQuXJlHDlyBI6OjkLHYUWUn5+PnTt3Yv78+UhJScGECRMwa9YsmZ1Ak52djaVLl2L58uWoVasWvL290bp168LHU1NT0bRpUygrK+PGjRtSPbKRyZ+UlBQEBATA19cXFy5cgIqKChwcHApX9WtoaAgdkTEmIzxCyT5TsWJFAHzLu7QhIhw/fhwNGjTAyJEj0aFDBzx+/BgrV66U6XGG6urqWLRoEe7evQs9PT20adMGw4cPR0pKCiQSCTw8PJCQkIDAwEAuJhWArq4uhg4dinPnziEuLg4rVqxAXFwcevfuDUNDQwwcOBBnzpxBfn6+0FEZY1LGBSX7jIqKCnR0dPiWdyly584ddOjQAb/++isMDQ1x+/Zt7N27t0SP07OyskJwcDC2bNmCAwcOwNLSEr1798bx48fh6+sLMzOzEsvC5EPVqlXx22+/4datW4iOjsaUKVNw48YNdO7cGUZGRhg/fjyuX7/OK8UZKyO4oGT/wafllA4vX76Eh4cHbGxs8PbtWxw7dgznz5+HjY2NIHnEYjFGjRqFyMhI1KxZEwEBATAzM0PdunUFycPkh5mZGebNm4eoqCiEhYWhf//+CAgIgJ2dHWrXro3Zs2cjIiJC6JiMsWLggpL9h76+Po9QyrEPHz5g2rRpsLCwwLlz57Bt2zY8ePAADg4OxV5wIw0pKSl4+PAh7OzskJ6ejrp162LdunV8m5NBJBKhcePGWL16NWJjY3Hx4kXY29tj8+bNqFevHho0aIAVK1bg5cuXQkdljBURL8ph/+Hg4AAVFRUEBgYKHYX9S25uLrZs2YJFixYhOzsbU6dOxZQpU1CuXDmhoxVKSUlB06ZNoaGhgZCQEEgkEsyZMwcbN25E48aN8eeff6JRo0ZCx2RyJicnB6dPn4aPjw+CgoKQlZWFli1bwt3dHb179y7cfYIxJr94hJL9B9/yli9EhIMHD6Ju3bqYNGkSXFxc8OTJEyxYsECuismCggL069cPSUlJOHz4MMqVK4fy5cvjjz/+wPXr15GbmwtbW1tMmTIFGRkZQsdlckRNTQ2Ojo7w8/NDQkIC9uzZA21tbYwfPx5VqlSBg4MD9u3bh/T0dKGjMsa+ggtK9h96enp8y1tOXLt2DXZ2dujTpw8sLCzw4MEDeHt7o0qVKkJH+4+5c+fi9OnT8PPzQ+3atT97rFmzZggLC8PixYuxadMmWFlZ4dSpUwIlZfJMW1sbHh4eOHHiBN68eYP169cjNTUVHh4eMDAwgJubG44ePYrc3FyhozLG/oULSvYfPEIpvOjoaPTs2RMtW7ZETk4Ozp8/j+PHj8PKykroaF908OBBLFu2DMuXL0enTp2++BwVFRXMmDEDDx8+hJmZGbp27Qp3d3ckJCSUcFpWWlSqVAljxozB1atX8eLFC8yfPx+PHj2Co6MjKleujJEjR+Ly5ctFOgKUMSYbXFCy/9DX10dycjK/SQvg3bt3GD9+PKysrBAWFoY9e/bg9u3baN++vdDRvurBgwcYNGgQXF1dMWXKlO8+v3bt2jhz5gz+/vtvnDlzBpaWlti5cydvH8O+qXr16pg+fTru37+P8PBwjB49GmfOnEHbtm1hYmKCKVOm4M6dO/x9xJhAeFEO+w9/f3/06tULSUlJhRudM9nKysqCl5cXli9fDpFIhFmzZmHChAlQV1cXOto3JScno0mTJtDR0cG1a9egqalZpNe/f/8ekydPxt9//422bdti27ZtMDc3l1FaVtYQEW7cuAEfHx/s378f7969g4WFBdzd3eHm5sb7nzJWgniEkv3HpxWVfNtb9iQSCXbv3g1zc3PMmzcPgwcPxpMnTzBt2jS5Lybz8/Ph6uqKjx8/4vDhw0UuJoF/vtd2796Ns2fPIjY2FvXr18fixYt5fhz7ISKRCC1atMCGDRsQHx+PU6dOoVmzZli1ahXMzc3RtGlTeHl54c2bN0JHZazM44KS/cengpIX5sjWuXPnYGNjg0GDBqF58+aIjIyEl5dXqdkiZdasWbhw4QL279+PGjVqFKste3t7hIeHw9PTEwsWLECjRo0QEhIinaBMISgrK6Nz587YvXs3EhMTceDAARgZGWH69OkwNjaGvb09du7ciQ8fPggdlbEyiQtK9h96enoAeIRSVsLDw9G1a1d07NgRmpqaCAkJwcGDB2Fqaip0tB/m6+uLVatWYfXq1ejQoYNU2tTU1MSyZctw584dlCtXDr/88gvGjBmD1NRUqbTPFIeGhgZ69+6Nw4cP4+3bt/D29gYRYdiwYTA0NETPnj1x6NAhZGVlCR2VsTKDC0r2H1xQysbr168xdOhQNGzYEE+ePMGhQ4dw9epVtGjRQuhoRXLv3j0MHToUHh4emDhxotTbr1+/PkJCQvDHH39gz549sLS0REBAAC+2YD9FV1cXQ4cOxfnz5xEXF4fly5fj1atX6N27NwwNDTFo0CCcOXOGT3JirJi4oGT/oaKigvLly/MtbylJS0vD3LlzYWZmhiNHjsDLywsRERFwcXGRi6MSi+L9+/fo0aMHLC0t4e3tLbP8SkpKGD9+PB49egRbW1u4uLjA2dkZcXFxMumPKYaqVavC09MToaGhiI6OxpQpU3D9+nV07twZRkZGmDBhAm7cuMEfXhj7CVxQsi/ivSiLLz8/H1u3boWpqSlWr16NiRMn4unTpxg/fjxUVVWFjldk+fn56NOnDzIzM3H48GFoaGjIvM9q1aohMDAQhw4dwq1bt2BpaYkNGzagoKBA5n2zss3MzAzz5s1DVFQUwsLC0L9/f/j7+6NFixaoXbs2Zs+ejYiICKFjMlZqcEHJvkhfX59HKH8SESEoKAjW1tYYM2YMunTpgsePH2PZsmXQ0dEROt5Pmzp1KoKDg3Hw4EGYmJiUWL8ikQguLi549OgRPDw8MGHCBNjZ2eHBgwclloGVXSKRCI0bN8bq1asRGxuLixcvwt7eHps3b0a9evXQoEEDrFixAi9fvhQ6KmNyjQtK9kV6eno8QvkTQkND0bZtWzg5OcHIyAhhYWHYvXt3iRZgsrBnzx54eXlh3bp1aNOmjSAZKlSogC1btuDq1atIT0+HjY0NZs6cyQsrmNQoKSmhbdu28Pb2xtu3b3HkyBFYWlpi4cKFqFGjBlq1aoUtW7bweyNjX8AFJfsivuVdNC9evIC7uzuaNm2K5ORknDhxAmfPnkWjRo2EjlZst2/fxvDhwzFo0CCMHTtW6Dj45ZdfcPfuXcyfPx9r166FtbU1zp07J3QsVsaoqanB0dERfn5+SEhIwJ49e6CtrY3x48ejSpUqcHBwwL59+5Ceni50VMbkAheU7Iv4lvePSUlJwZQpU2BhYYFLly5h+/btuHfvHrp27VrqFtx8SWJiIpydnVG/fn1s2bJFbr4mVVVVzJkzBw8ePICxsTE6duyIgQMH8ocgJhPa2trw8PDAiRMn8ObNG6xfvx6pqanw8PCAgYEB3NzccPToUd6Qnyk0LijZF/Et72/LycnB2rVrUbt2bWzduhVz5sxBTEwMhg4dCiUlJaHjSUVeXh569+6NvLw8BAQEyOXJPRYWFrh48SJ27NiBo0ePok6dOvj77795lS6TmUqVKmHMmDG4evUqnj9/jnnz5iEiIgKOjo6oXLkyRo4cicuXL0MikQgdlbESxQUl+yJ9fX0kJyfzm+L/ICLs378flpaWmDZtGvr06YMnT55g7ty50NLSEjqeVE2aNAkhISE4dOgQjI2NhY7zVSKRCEOGDEFkZCQ6deqEgQMHolOnTnj69KnQ0VgZV6NGDcyYMQMPHjxAeHg4Ro8ejTNnzqBt27YwMTHBlClTcOfOHf6AwxQCF5Tsi/T09FBQUMCnlPxLcHAwmjdvDldXV9SrVw/h4eHYunUrKleuLHQ0qdu1axc2btyIDRs2oGXLlkLH+SGGhobw8fHBiRMnEBMTg3r16mHFihXIy8sTOhpTAPXq1cOSJUvw7NkzhISEwNnZGX///TdsbGxgaWmJRYsWISYmRuiYjMkMF5Tsiz6dJ823vYHHjx+jR48eaN26NSQSCS5evIigoCBYWloKHU0mbt68iVGjRmH48OEYOXKk0HGKrGvXroiIiMDYsWMxa9YsNGnSBDdv3hQ6FlMQIpEILVq0wIYNGxAfH49Tp06hWbNmWLVqFczNzdG0aVN4eXnhzZs3QkdlTKq4oGRf9KmgVOSFOYmJiRgzZgysrKxw7949+Pj44ObNm2jbtq3Q0WTm7du36NmzJ2xsbLBhwwa5WYRTVFpaWli9ejVCQ0OhrKyMFi1aYMKECUhLSxM6GlMgysrK6Ny5M3bv3o2EhAQcOHAARkZGmD59OoyNjWFvb4+dO3fiw4cPQkdlrNi4oGRfpMjneWdmZmLJkiWoXbs2fH19sXz5ckRFRcHNzQ1icdn9kcnNzUWvXr1ARDh06BDU1NSEjlRsjRs3xs2bN7FmzRrs2LEDdevWRVBQkNCxmALS1NRE7969cfjwYbx9+xbe3t4gIgwbNgyGhobo2bMnDh06xPuqslKr7F4dWbF8KigVaYSyoKAAu3btgrm5ORYuXIjhw4fjyZMnmDJlilyucJa2iRMnIjQ0FAEBAahatarQcaRGWVkZnp6eiIiIgLW1NZycnNCrVy/Ex8cLHY0pKF1dXQwdOhTnz59HXFwcli9fjlevXqF3794wNDTEoEGDcObMGeTn5wsdlbEfxgUl+yJVVVVoa2srzAjl6dOn0ahRIwwZMgQtW7ZEVFQU1q5dW1hYl3Xe3t7YunUrNm3ahObNmwsdRyZq1KiB48ePw8/PD8HBwbC0tMTWrVt5JwMmqKpVq8LT0xOhoaF4/PgxJk+ejOvXr6Nz584wMjLChAkTcOPGDV4pzuQeF5TsqxThtJz79++jU6dO6NKlC3R0dHDjxg34+fmhVq1aQkcrMSEhIRg3bhxGjx6NYcOGCR1HpkQiEfr27YvIyEj06dMHo0ePRqtWrRARESF0NMZgbm6O+fPnIyoqCrdv34aHhwf8/f3RokUL1K5dG7Nnz+bvVSa3uKBkX1WWT8uJi4vD4MGD0ahRI7x8+RKHDx/GlStX0KxZM6Gjlaj4+Hi4uLigWbNm8PLyEjpOialYsSL+/PNPXLp0Ce/fv0ejRo0wb948ZGdnCx2NMYhEItjY2GDNmjWIjY3FhQsXYG9vj82bN6NevXpo0KABVqxYgZcvXwodlbFCIuJxdPYVXbt2hYaGBgICAoSOIjUfP37EihUrsG7dOpQrVw4LFizA8OHDoaKiInS0EpeTk4O2bdvi1atXCAsLg6GhodCRBJGdnY1ly5Zh2bJlqFmzJrZt21amV/Kz0isnJwenT5+Gj48PgoKCkJWVhZYtW8Ld3R29e/cu3J2DMSHwCCX7qrJ0yzsvLw+bNm2Cqakp1q5di0mTJuHJkycYM2aMQhaTRISxY8fi7t27OHz4sMIWkwCgrq6OhQsX4t69e6hUqRLatWuHYcOGITk5WehojH1GTU0Njo6O8PPzQ0JCAvbs2QNtbW2MHz8eVapUgYODA/bt24f09HShozIFxAUl+6qycMubiBAYGIh69eph/PjxcHBwQExMDBYvXozy5csLHU8wW7duxY4dO7B161bY2toKHUcu1K1bF1euXMHWrVtx6NAhWFpaws/PjxdDMLmkra0NDw8PnDhxAm/evMH69euRmpoKDw8PGBgYwM3NDUePHkVubq7QUZmC4IKSfZWenl6pHqG8efMmWrduDWdnZ9SoUQN3797Frl275Ppc6pIQHByMCRMmYPz48Rg0aJDQceSKWCzGyJEjERkZidatW8PNzQ3dunXDixcvhI7G2FdVqlQJY8aMwdWrV/H8+XPMmzcPERERcHR0ROXKlTFy5EhcvnyZdzRgMsUFJfuqTyOUpW2E5tmzZ+jbty+aN2+Ojx8/4vTp0zh9+jQaNGggdDTBxcXFoVevXvjll1+wZs0aoePIrSpVquDgwYM4cuQIHj58CCsrK6xZs4b3BWRyr0aNGpgxYwYePHiABw8eYNSoUTh9+jTatm0LExMTTJ06FXfv3i117+tM/nFByb5KT08PBQUFSE1NFTrKD0lKSoKnpyfq1KmDq1evYteuXbhz5w46deokdDS5kJ2dDWdnZ6irq+PgwYMKOXe0qBwdHfHo0SMMHz4cU6dORdOmTREWFiZ0LMZ+iLW1NZYuXYrnz5/j2rVr6NGjB3bv3o3GjRujbt26WLRoEWJiYoSOycoILijZV31aMSjvt72zs7OxatUqmJqaYseOHZg/fz5iYmIwaNAgKCkpCR1PLhARRo0ahYcPH+Lw4cOoVKmS0JFKDW1tbXh5eeHGjRsoKChA06ZNMXnyZF74wEoNkUgEOzs7bNy4Ea9fv8bJkyfRtGlTrFq1Cubm5mjatCm8vLzw5s0boaOyUowLSvZVnwpKeV2YI5FI4OPjgzp16mDmzJlwd3fHkydPMHv2bGhqagodT65s3LgRu3fvxp9//onGjRsLHadUatq0KW7fvo1ly5YV7gd44sSJYrebkZOPiPhU3I1NQUR8KjJy+LY6kx0VFRV06dIFu3fvRkJCAg4cOAAjIyNMnz4dxsbGsLe3x86dO/Hhwweho7JShvehZF8VHx8PIyMjHDt2DA4ODkLH+cylS5cwZcoUhIWFoUePHli+fDksLCyEjiWXLl26BHt7e0ycOJHnTUrJ06dPMXr0aJw9exaurq7w8vIq0tZLMQlp2HczFhcfJyI2ORP/fhMWATCpqIl2Fgbo18wEZobaUs/P2P9KSUlBQEAAfHx8cPHiRaioqMDBwQHu7u5wcHCAhoaG0BGZnOOCkn1VTk4O1NXVsXv3bgwYMEDoOACAyMhITJs2DceOHUPTpk2xevVqtGrVSuhYcuvly5do0qQJGjRogFOnTkFZWVnoSGUGEWHfvn3w9PREfn4+Vq9ejSFDhkAkEn31Na+SMzHrcDiCn7yHkliEAsnX334/Pd7KVB9Lna1RrSKPurOSER8fj/3798PHxwe3b9+GtrY2evbsCXd3d7Rv357fR9gX8S1v9lVqamooV66cXMyhfPv2LUaNGgVra2tERETAz88PN27c4GLyGzIzM+Hs7Ixy5crBz8+PLwJSJhKJ4OHhgcjISDg5OWHYsGFo164dHj9+/MXn+4XGwn7dZYQ8+2cKybeKyX8/HvIsCfbrLsMvNFa6XwBjX1G1alV4enoiNDQUjx8/xuTJk3H9+nV07twZRkZGmDBhAm7cuMErxdlnuKBk3yT0aTkZGRlYtGgRTE1NceDAAaxatQqRkZHo27fvN0eCFB0RYcSIEYiKikJgYCAfySZD+vr6+Ouvv3Du3DnExcWhfv36WLRoEXJycgqfs/FiDGYEhCMnX/LdQvJ/FUgIOfkSzAgIx8aLvCKXlSxzc3PMnz8fUVFRuH37Njw8PODv748WLVqgdu3amDNnDh49eiR0TCYH+JY3+yZbW1s0btwY27ZtK9F+CwoKsGvXLsybNw9JSUmYMGECZs2aBV1d3RLNUVqtXbsWkydPhq+vL1xdXYWOozCysrLw+++/Y9WqVTAzM4O3tzfi1EwwIyBcan2s6GmNvrYmUmuPsaIqKCjAlStX4OPjg0OHDuHDhw9o0KAB3Nzc4OrqiurVqwsdkQmAC0r2TV26dIGWlhb8/f1LpD8iwsmTJzFt2jRERETAzc0NS5YsQc2aNUuk/7Lg3Llz6Ny5M6ZMmYIVK1YIHUchPXjwACNGjEBY1AtUG+UNiUh621epKYtxzrMNz6lkciEnJwenTp2Cj48PgoKCkJ2djZYtW8Ld3R29e/fmuyMKhAtK9k0eHh6Ii4vDpUuXZN7X3bt3MXXqVJw/fx5t2rTB6tWr0aRJE5n3W5Y8f/4cTZo0QZMmTXDixAneh1NABQUFaP97AF5kqUEklt6/g5JYBLtaetgztJnU2mRMGtLS0hAYGAgfHx+cPXsWIpEInTp1gru7O5ycnFCuXDmhIzIZ4jmU7JtKYg5lbGwsBgwYABsbG7x+/RpBQUG4ePEiF5NFlJGRgR49eqBChQrw9fXlYlJgz95n4mWOplSLSeCfOZXBT97jSWKaVNtlrLi0tbXRv39/nDx5Em/evMH69euRmpoKDw8PGBgYwM3NDUePHkVubq7QUZkMcEHJvklPT09mBWVqaipmzJgBc3NznD59Gps3b0Z4eDi6d+/OC26KiIgwdOhQPH36FIGBgahYsaLQkRTevpuxUBLL5vtYSSzC3hu86pvJr0qVKmHMmDG4evUqnj9/jnnz5iEiIgKOjo6oXLkyRo4cicuXL0MikQgdlUkJF5Tsm8pXrISP4vK4I8VTPHJzc/HHH3+gdu3a2LBhA6ZNm4YnT55g1KhRvLXNT1q1ahX279+Pv/76C9bW1kLHYQAuPk4s8oruH1UgIVyMTpRJ24xJW40aNTBjxgw8ePAADx48wKhRo3D69Gm0bdsWJiYmmDp1Ku7evcvbEJVyPIeS/ce/T/F4mZyBf87u+EdxTvEgIgQEBGDGjBl49uwZBg8ejEWLFqFq1arS/yIUyOnTp9G1a1fMnDkTS5YsEToOA5Cekw/rBachyzdXEYCHCzpDS40/hLHSh4hw/fp1+Pj4YP/+/Xj//j3q1KkDd3d3uLm5wdTUVOiIrIi4oGSFZHmKx/Xr1zFlyhSEhISgS5cuWLlyJY+kScGTJ09ga2sLOzs7BAUF8bxJgeXl5SEjIwN3X7zD4P3RMu/v+PiWsKqqI/N+GJOlvLw8nD9/Hj4+Pjh8+DDS09PRtGlTuLm5oW/fvqhSpYrQEdkP4IKSAfjnFI/5QRHIl1CRbtMpiUVQFouw0NEKrl/YG+/JkyeYMWMG/P390bBhQ6xatQr29vbSjK6w0tPT0bx5c+Tm5uLWrVuoUKGC0JFKhYKCAmRmZiI9PR0ZGRmFv773+x95zqfFBqpVzFFl4FqZfy16YTthoJSJChUq/PAvNTU1medi7GdlZmbi2LFj8PHxwYkTJ1BQUIB27drB3d0dPXv25Pc5OcYFJcPGizFYfab4oylTOpljXDszAMD79+/x+++/Y/PmzahcuTKWLFkCDw8PiMU8bVcaiAi9e/fG6dOncfPmTdStW1foSFIlkUiQlZX104Xdt36fnZ393f7FYjG0tLSgpaWFcuXKFf7/l37/pT9LgRaW3pH9W2vT5PMoeP8SHz58+M+vry12UFdXL1IBygUpE0pKSgr8/f3h4+ODS5cuQUVFBQ4ODnB3d4eDgwM0NDSEjsj+hQtKBecXGivVUzx+714H8cGHsHTpUgDAzJkzMXHiRP7Bl7KlS5di9uzZOHz4MHr06CFIBiJCdnZ2sQq9rz0nMzPzhzJ8r7D7mWKwXLlyUFNTK9ZOAxk5+agn4BxKIkJ6evoXC80f/cUFKZMnr1+/xoEDB+Dj44Pbt29DW1sbPXv2hLu7O9q3by/Igs6MnHy8SMpAbr4Eqspi1NDTUug5zVxQKrBXyZmwX3cZOfnS2raBQPl5SNg1DiPcXTB37lxUqlRJSm2zT44fP47u3btj7ty5WLhw4Xefn5ubK5XbuV96zY9s+aGurv7Thd23fq+hoSHXI95tVl3Ey+QfK4x/RnU9TVye0k4mbXNByuRZdHQ0fH19sW/fPsTExMDAwAB9+/aFu7s7mjVrJtNt5/69aDU2OfOzD43FWbRaFnBBqcD677iJkGdJ0t3ahCRobFQOAeNlc6Erq/Lz83+okHvx4gXWr18PY2NjdOzY8YtzAf/3Nfn539/qSVVV9acLu28Vh5qamgq7UGjO4fvYd+sVCNK/uCmJRejfrDoWOFpJvW1p4IKUlQQiwp07d+Dj4wM/Pz/Ex8ejZs2acHd3h7u7u1SnAsly0WpZwQWlgopJSENHrysya/+cZ2uYGpStT2cSiUTqizg+/f5HTo74NBonFothYmICHR0dqY368f6f0pObm4sdO3Zg8YYdUHH6/gjyzyqLP2OffK8gTUlJ+WYxmpqaygWpgikoKMCVK1fg4+ODQ4cO4cOHD2jQoAHc3d3h6uoKE5P/Lhr9UbJatFrWcEGpoBYERWDPzZcy2XhZyNETIkJmZqZUF3F8+pWVlfXd/kUikVRu537p9q6bmxsuXryIW7duwcLCogT+NllR5OfnY+/evVi4cCFevnyJfv36IbPZENx7kyXVnzM+y/v7JBJJsUZIuSAt3XJycnDq1Cn4+PggKCgI2dnZaNWqFdzd3dGrVy/o6+v/cFuyWLRaVnFBqaCEnN9FRMjJyZHqIo5P/5+ZmflDpy1oampKdRHHp/9XV1eXyfydRYsWYcGCBQgKCsKvv/4q9fbZz5NIJDhw4ADmz5+P6OhouLi4YOHChbCyspLBPGVATVmMc55tFOY2mhCELEh1dXW/+piOjg4XpEWUlpaGwMBA+Pj44OzZsxCJROjUqRPc3d3h5OSEcuXKffW10l60uqKnNfqW4ZFKLigVUEmc4gEimN7bgqy0D18s/n50MYc0F3F8+jN5X8zxv4KCguDk5ITff/8dc+bMEToO+z9EhKCgIMydOxfh4eHo1q0bfv/9dzRu3Piz5/FFSfEUtyD98OHDVz8Ya2ho/PToqKIXpImJiTh48CB8fHwQEhICTU1NODo6wt3dHZ07d4aqqmrhc/nDYNFxQamAIuJT4bDhqsz7sYoNQiWVnJ8qBrW0tBR2Mce/RUVFoWnTprC3t8ehQ4dKVSFcVhERzp49izlz5iA0NBTt2rXD4sWLYWdn99XXSOu22dROFhjbjo+kK+vktSCtUKHCZ0VXafbixQv4+flh3759ePjwIXR1ddG7d2+4u7ujVatWGLgrVOqLVsv6dBUuKBXQ3dgUOG8JkXk/h0fboZGJrsz7KatSU1PRtGlTKCsr48aNG9DWLpsLMEqT4OBgzJkzB1euXEHz5s2xZMkStG/f/ode+7MT+0UgqCorYZGjFY9Msh/CBWnRhIeHw9fXFz4+Pnj58iWM6jaBsuMCmfVXVhfUcUGpgEpqhJLPGf55EokEjo6OuHbtGkJDQ2FqyqNSQgoNDcXcuXNx+vRpNGzYEIsXL0a3bt2KPF/2Z7YeyXl5D/7Te8GuAS/EYiVDUQtSIsL169cxy/8unitXg0gs/btk8r7lV3HwXiEKqIaeFkSAzE/xqKGnJcMeyrb58+fjxIkTOHHiBBeTAgoPD8fcuXNx5MgRWFpa4uDBg+jZs+dPTz2oVlETe4Y2+/+bI0cn4mVSBvCvvSpFAEz0NNHO3AA9G1RCt19GYl3ePdgdPCidL4qx7xCLxShfvjzKly//U9vtFLUgffv2LaKiogQvSEUiEezs7EDXciCS0aLVAgnhYnQiFqDsFZQ8QqmgZL3Ku5quOoKndZBZ+2VZQEAAXFxcsGzZMsyYMUPoOAopOjoa8+fPx/79+1GzZk0sWLAA7u7uMpnX+9uU6TgRHIr9B/2/eHzb3r170b9/f1y6dAlt2rSRev+MyRuJRIK0tLSfHh1NTU396YJUU6citn+oA8jgQIJPvnVsamnGBaWCkuU+lCQpQHb4GfSqSRg7dqxUTyso6x4+fIjmzZujW7du2L9/v0yPEGP/9eLFCyxatAi7d+9G1apVMXfuXAwePBgqKioy63P06NG4desWwsLCvvi4RCKBnZ0dsrOzERYWxovVGPuO4hSkH5XKQ7v3UplnLItTwrigVFCyPinHSeUB9nuvR0JCAtq3b49x48ahe/fufCLLN6SkpMDW1haampq4fv06tLR4ykBJiY+Px5IlS/Dnn39CV1cXs2fPxogRI6Curi7zvgcMGIDnz58jODj4q8+5efMmmjdvDm9vbwwfPlzmmRhTVLxo9efxHiQKysxQG61M9aEklu4ImJJYhFam+li/aCZiY2Ph4+OD7Oxs9OzZE7Vq1cKyZcvw7t07qfZZFhQUFMDd3R3JyckIDAzkYrKEvHv3DlOmTEHt2rXh6+uL33//Hc+ePcOECRNKpJgEgIyMjO/+ezdr1gz9+/fH7NmzkZqaWiK5GFNEqsolUxaVVD8lqex9ReyHLXW2hrKUC0plsQhLna0BAKqqqnBzc8O1a9cQFhYGe3t7LFy4ENWqVcOgQYNw+/ZtqfZdms2ZMwdnzpzB/v37UatWLaHjlHkfPnzAnDlzULNmTXh7e2P69Ol4/vw5pk+fXuLFfGZm5g/1uWzZMmRkZOD3338vgVSMKaZPi1ZlqawuWuWCUoFVq6iJhVLeumCRo9UXTwFo3Lgxdu7cidevX2PRokW4dOkSbG1t0bx5c+zduxc5OTlSzVGaHDhwAMuXL8eKFSvQsWNHoeOUaenp6ViyZAlq1qyJtWvXYuzYsXj+/DkWLFgAHR1h5jP9yAglABgZGWHmzJn4448/EBMTUwLJGFMsRISH98KgKZHdglXgn10cytqCHIALSoXnamuCKZ3MpdLW1E4W3914WU9PD9OmTcPTp09x5MgRlC9fHv3790e1atUwZ84cxMXFSSVLafHgwQMMHjwYbm5umDx5stBxyqysrCysXbsWNWvWxKJFi9C/f388e/YMK1asgJ6enqDZMjIyoKn5Y0exTZ48GVWrVuXvFcakhIjw4MEDzJo1C7Vr10bz5s2RGnUdIpLekYv/piQWoZ25gUzaFhoXlAzj2plheU9rqCmLizynkgryoSr+53zhohwJp6SkBEdHR5w5cwaRkZHo27cv1q9fjxo1aqB37964fPnyV7d9KCuSkpLQo0cPmJubY/v27byiWwZyc3OxZcsWmJqaYtq0aXB2dkZMTAz++OMPVK5cWeh4AH78ljfwz5Ynq1atwtGjR3HmzBkZJ2Os7IqJicHvv/8OKysrNGjQAFu3boW9vT3Onz+Pc1vng0SyKY8KJASP5mXzxCsuKBmAf0Yqz3m2gV2tf0ZrvldYfnpcKekpKt32Rp8m1X667zp16mDDhg14/fo11q9fj4cPH6Jt27aoX78+tm3bhoyMjJ9uW17l5+fD1dUVHz9+xOHDh394hIr9mPz8fPz111+wsLDA2LFj0b59e0RFRcHb2/unNmqWpR+95f1Jr1690KpVK3h6eiI/P1+GyRgrW169eoXVq1fDxsYG5ubmWLlyJWxsbHDs2DG8ffsW3t7eaN++PepU0ZHpotWyeOwiwAUl+5dPp3ic/a01+jerjup6mv+ZnCwCUF1PE/2bVcc5z9bY1MsSIWeCEBgYWOz+y5cvj7Fjx+LRo0c4d+4cTE1NMWbMGBgZGcHT0xNPnjwpdh/yYubMmbh48SIOHDiAGjVqCB2nzJBIJPDz84OVlRUGDx4MGxsbhIeHY8+ePXJ74lBRC0qRSIT169cjMjISW7dulWEyxkq/hIQEbNq0Ca1atYKJiUnhYryDBw8iISEBe/bsgYODw39O0JH1otWyiPehZN+UkZOPF0kZyM2XfPEUDwDo0qULnjx5gkePHkn9nNWXL19iy5Yt2L59O5KSktC1a1eMGzcOXbp0+enj74Tm4+ODfv36Yd26dfjtt9+EjlMmEBGCgoIwd+5chIeHo1u3bvj999/RuHFjoaN9l7q6OlatWoXx48cX6XXDhw9HQEAAYmJiULFiRRmlY6z0+fDhAwICAuDn54fz589DLBajU6dOcHV1hZOTE8qXL/9D7czZdQJ7o6VXIq3oaf3ddQalWem8IrMSo6WmDKuqOmhkogurqjpfXJm2evVqPH/+HBs3bpR6/9WrV8fy5cvx6tUr7Nq1CwkJCXBwcIC5uTnWrl2LlJQUqfcpS3fv3sXQoUPRv39/TJw4Ueg4pR4R4cyZM2jWrBl69OgBfX19XLt2DcePHy8VxWRBQQFycnJ+aquixYsXIy8vDwsWLJB+MMZKmYyMDPj6+sLJyQmGhoYYNmwY8vPzsWXLFrx58wbHjx9H//79f7iYDAoKwqpRzjBMuCWVfD+yaLW044KSFVu9evUwYsQILFq0CO/fv5dJHxoaGoV7V16/fh3NmzfHjBkzYGxsjJEjR+LBgwcy6Vea3r17hx49esDKygrbtm3jRTjFFBwcjDZt2qBz585QUlLC+fPnceHCBdjZ2Qkd7YdlZv6zPcnPFJSGhoaYO3cuNm/ejIiICGlHY0zu5eTk4MiRI3B1dYWBgQHc3d2RkJCAlStXIi4uDhcuXMCIESOgr69fpHYPHToEFxcXODo6Injr7J9etKokFkFNWVzkRaulFd/yZlKRmJgIMzMzDBgwABs2bCiRPhMSEuDt7Y2tW7ciPj4erVu3xrhx49CjRw+Znr38M/Ly8tC5c2c8fPgQYWFhqFbt5xcxKbrQ0NDCjeAbNmyIxYsXo1u3bqWyQH/79i2qVKmCoKAgdO/evcivz8nJgZWVFWrXro1Tp06Vyr8DxooiPz8fFy5cgK+vLw4fPozU1FTUr18frq6ucHV1Rc2aNYvVvo+PD/r37w9XV1fs3r278LjgV8mZmHU4HMFP3kNJLEKB5Oul06fHW5nqY6mz9Rf3Zi6TiDEpWbFiBSkpKVFkZGSJ9pubm0sHDhyg1q1bEwCqWrUqLVq0iN68eVOiOb5l4sSJpKysTJcvXxY6Sql1//59cnJyIgBkaWlJhw4dooKCAqFjFcuTJ08IAJ0/f/6n2zhy5AgBoKNHj0oxGWPyo6CggK5cuUJjxoyhSpUqEQAyNTWluXPnUkREhNT62blzJ4lEIho0aBDl5+d/8TnRbz/S/CMPqfWqC1RjxjGq/q9fNWYco9arLtD8Iw8pJuGj1HKVFlxQMqnJysqiGjVqkIODg2AZ7t+/TyNGjCANDQ1SUVGhfv360fXr10kikQiWaffu3QSANm7cKFiG0iwqKopcXV1JJBJRrVq1aM+ePV99sy9tHjx4QADoxo0bP92GRCIhe3t7MjMzo5ycHCmmY0w4EomEQkNDafLkyWRsbEwAyNjYmKZMmUK3b9+W+nv61q1bCQCNHDnyhz+opmfn0cPXH+jOy2R6+PoDpWfnSTVTacMFJZOqAwcOEAA6c+aMoDmSk5NpzZo1VKtWLQJANjY2tGvXLsrMzCzRHKGhoaSmpkaDBw8WtKgtjZ4/f06DBw8msVhMxsbG5O3tTbm5uULHkqrr168TAAoPDy9WO+Hh4SQWi2n16tVSSsaYMB4+fEhz5swhU1NTAkAGBgY0duxYCg4OltkdCS8vLwJAEydO5PfpYuCCkkmVRCKhX375haytreViFKmgoICOHz9OXbt2JQCkp6dH06dPpxcvXsi877dv35KxsTE1bdqUsrKyZN5fWfH69WsaM2YMqaiokIGBAa1fv77M/v2dO3eOANDTp0+L3daYMWOofPnylJCQIIVkjJWcp0+f0pIlS8ja2poAkI6ODg0ZMoTOnDlDeXmyHfVbsWIFAaBp06ZxMVlMXFAyqbt58yYBIG9vb6GjfCY6Opo8PT1JR0eHxGIx9ejRg86dOyeTN5Hc3Fxq1aoVGRoaUlxcnNTbL4sSExNp8uTJpK6uTrq6urR8+XJKT08XOpZMBQUFEQB6+/Ztsdt6//496erq0ogRI6SQjDHZiouLo7Vr11LTpk0JAGlqapKbmxsdOXKEsrOzSyTDokWLCADNmzePi0kp4IKSyUS/fv3IwMCAUlNThY7yH2lpabR161aqV68eAaA6derQxo0b6eNH6U2iHjt2LKmoqNDVq1el1mZZlZKSQrNnzyYtLS3S1tam+fPn04cPH4SOVSJ8fX0JAKWlpUmlvfXr15NIJKK7d+9KpT3GpOndu3e0ZcsWatOmDYlEIlJVVSUnJyfy8/Mr0Q+PEomEZs+eTQBoyZIlJdZvWccFJZOJ2NhYUldXp5kzZwod5askEgldunSJevXqRUpKSqStrU3jxo0r9ir1HTt2EADaunWrlJKWTWlpabR48WKqUKECaWho0LRp0+j9+/dCxypR27dvJwBSmxuWm5tLlpaW1KZNGx5xYXIhNTWVdu/eTV26dCElJSVSUlKiTp060a5duyglJaXE80gkEpo8eTIB4DnHUsYFJZOZOXPmkJqaGj1//lzoKN/16tUrmjNnDhkYGBAA6tixIx05cqTI80Bv3LhBqqqqfNvxGzIzM2nNmjWkr69PqqqqNH78eLna4qkkrV+/ntTV1aXa5smTJwkAHTp0SKrtMvajMjIy6MCBA+Ts7ExqamoEgFq1akWbNm0SdI5vQUEBjR07lnfdkBEuKJnMpKWlUeXKlcnV1VXoKD8sOzub9uzZQ82aNSMAVL16dVqxYsUPjZy9efOGqlatSi1atCixOUClSU5ODm3evJmqVq1KSkpKNHz4cHr58qXQsQS1bNky0tPTk3q7Dg4OVKNGjTK7mInJn5ycHDp69Cj169ePypUrRwCoSZMmtHr1aoqNjRU6HhUUFNCwYcNIJBLJ3fz+soILSiZTn27/hoSECB2lyG7dukUDBw4kNTU1UldXp8GDB1NYWNgXn5uTk0N2dnZUpUoVio+PL+Gk8i0vL4927dpFNWrUIJFIRB4eHhQTEyN0LLkwZ84cMjExkXq7UVFRpKyszPPDmEzl5+fTuXPnaNiwYaSrq0sAqG7duvT7779TdHS00PEK5efn04ABA0gsFtPu3buFjlNmcUHJZCo/P58aNmxIzZo1K7VzuhITE2nZsmVUrVo1AkB2dna0b9++zzaRHjlyJKmqqtL169cFTCpfCgoKyNfXl8zNzQkAubi40MOHD4WOJVc8PT2pTp06MmtbS0uLXr9+LZP2mWKSSCR07do1Gj9+PBkaGhIAqlWrFs2aNYsePHggdLz/yM3NJVdXV1JSUiJfX1+h45RpXFAymbtw4QIBIB8fH6GjFEteXh4FBARQ+/btCQAZGhrSvHnzCvcx2759u9AR5YJEIqHAwMDCPeW6dev21ZFdRTdy5EiysbGRSdspKSmkr69PAwcOlEn7THFIJBK6c+cOTZs2japXr154xK2npyfdvHlTbgcLcnJyyNnZmVRUVCggIEDoOGUeF5SsRDg5OZGJiUmJn1QjKxERETRmzBjS0NAgAFS7dm26cuWK3L6xlgSJREKnT58mW1tbAkDt2rWja9euCR1Lrnl4eFDr1q1l1v6n4+Ru3bolsz5Y2RUVFUXz588nCwuLwoMhRo0aRZcuXZKLgyu+JSsrixwcHEhNTY2OHTsmdByFICIiAmMyFh0dDSsrKyxcuBCzZs0SOo5UvH79Go0bN0a5cuWgpKSEmJgY1K9fH+PGjYO7uzu0tLSEjlhigoODMXv2bAQHB6N58+ZYsmQJ2rdvL3QsudezZ09kZ2fjxIkTMmm/oKAAjRs3hpaWFq5duwaRSCSTfljZ8fLlS/j5+cHPzw/37t1D+fLl4ezsDFdXV3To0AEqKipCR/yuzMxM9OjRA1evXkVgYCA6deokdCSFIBY6AFMM5ubmGDduHJYtW4a3b98KHafYcnJy4OLiAlVVVYSEhCAqKgqnT59G9erVMXLkSBgbG2PKlCl4+vSp0FFlKjQ0FJ07d0br1q2RlpaGY8eOISQkhIvJH5SRkQFNTU2Zta+kpAQvLy9cv34dvr6+MuuHlW5v377Fhg0bYGdnhxo1amDBggUwMzNDQEAAEhIS8Ndff6FLly6lophMT0+Hg4MDQkJCcOLECS4mS5LQQ6RMcSQlJZGuri4NGzZM6CjFIpFIaMiQIaSmpvbFW4nPnj2jqVOnkq6uLolEInJwcKCTJ09KbfNqeXD//n1ycnIiAGRpaUmHDh0qU19fSWnZsiUNGDBA5v307NmTjI2Ny/xRluzHJSUl0Z9//knt27cnsVhMKioq9Ouvv9LevXulempYSfrw4QPZ2dmRtrY2n1ImAC4oWYn6dDTcvXv3hI7y0zZt2kQAvrv9REZGBu3YsYMaNmxIAMjU1JTWrVsnyOkQ0hIVFUWurq4kEomoVq1atGfPHrmfSyXPGjVqRKNHj5Z5P0+fPiVVVVWaP3++zPti8uvjx4+0d+9e+vXXX0lFRYXEYjF16NCB/vzzT0pKShI6XrEkJyeTra0tVahQgW7evCl0HIXEBSUrUbm5uWRubk4dOnQolQtYLl++TMrKyjRhwoQffo1EIqGrV6+Sq6srKSsrk5aWFo0aNYrCw8NlmFS6nj9/ToMHDyaxWEzGxsbk7e1Nubm5Qscq9czNzWny5Mkl0teMGTNIXV1d4TeTVzRZWVnk7+9PvXv3LlxEaGdnR3/88UeZOaHq3bt31LBhQ9LT06M7d+4IHUdhcUHJSlxQUBABoKNHjwodpUhiY2PJwMCA2rZt+9PFVHx8PC1YsIAqV65MAKht27Z06NAhysvLk3Ja6Xj9+jWNHj2aVFRUyNDQkNavX8+nr0iRkZERzZs3r0T6+vjxY6k7uYr9nNzcXDpx4gQNGDCAtLW1CQA1atSIVqxYUSqOwi2Kt2/fkpWVFRkYGJSqD+llEReUrMRJJBJq3749WVhYlJpRrszMTLKxsSETExNKTEwsdns5OTnk5+dHv/zyCwEgY2NjWrx4saDn3P5bYmIiTZo0idTV1UlXV5eWL1/O8+9kQFdXl1asWFFi/e3atYsAUHBwcIn1yUpGfn4+Xbp0iUaOHEl6enoEgCwsLGjBggUUGRkpdDyZiIuLIwsLC6pSpUqZ/RpLEy4omSDu3btHIpGI/vjjD6GjfJdEIqEBAwaQurq6TDbovnPnDg0dOpTU1dVJVVWV+vfvL9gcoOTkZJo9ezZpaWmRtrY2LViwgD58+CBIFkWgqqpKGzduLLH+CgoKqEmTJmRjY8OLqMoAiURCN2/epN9++42qVq1KAKh69eo0ffp0unv3bqmcVvSjXr58SbVr16Zq1arxUa5yggtKJpihQ4dSxYoVKTk5Wego37R+/XoCQHv37pVpP0lJSbRq1SqqUaMGASBbW1vavXt3idxi/vjxIy1evJgqVKhAGhoaNH36dHr//r3M+1VkeXl5BIB27txZov1evXpVkH6ZdEgkEnrw4AHNmjWLatWqVXhq1/jx4ykkJKRMF5GfPH36lKpXr041a9Ysc7fwSzMuKJlg3rx5Q1paWuTp6Sl0lK+6cOECKSkp0aRJk0qsz/z8fDp69Ch16tSJAJC+vj7NnDmTYmNjpd5XZmYmrVmzhvT19UlVVZUmTJhQZibqy7vU1FQCQPv37y/xvl1dXaly5cqldnsYRRQTE0O///471a1blwAUbsF2/vx5hdpp4fHjx2RkZERmZmb06tUroeOwf+GCkglq8eLFpKKiQtHR0UJH+Y8XL16Qvr4+dejQQbBFM1FRUTRhwgTS1tYmsVhMPXv2pAsXLhR7FCInJ4c2b95MVatWJSUlJRo+fDiv/i1h8fHxBECQY+FevnxJGhoaNGPGjBLvm/242NhYWr16NdnY2BAA0tLSon79+tHRo0cpJydH6HglLiIiggwNDalu3boUHx8vdBz2P7igZILKzMykatWqUY8ePYSO8pmMjAxq1KgR1ahRQy5u/X78+JE2b95cODpRt25d2rx5M6WlpRWpnby8PNq1axfVqFGDRCIReXh48PwjgcTExBAAunjxoiD9z58/n1RVVenJkyeC9M++LCEhgTZt2kQtW7YkAKSmpkY9e/akAwcOUEZGhtDxBHPv3j3S19en+vXry83iRfY5LiiZ4Pbt20cA6MKFC0JHIaJ/5ii5u7uThoaG3G3ALpFI6MKFC+Ts7ExisZjKly9PEyZMoMePH3/zdQUFBeTr60vm5uYEgFxcXOjhw4cllJp9yb179wiAYAuwMjIyyNjYmJydnQXpn/1/KSkptHPnTurUqRMpKSmRkpISde3alXbv3s2L4ogoNDSUdHV1ycbGRi4+4LMv44KSCU4ikVCzZs2oYcOGcjEXaPXq1QSA/Pz8hI7yTS9fvqSZM2eSvr4+AaDOnTvT0aNHP/s7lEgkFBgYSNbW1gSAunXrJpOV6qzoQkJCCICghb28fZhTJOnp6eTr60tOTk6kqqpKIpGI2rZtS1u3bqV3794JHU9uhISEUPny5al58+al+pQxRcAFJZML165dk4uVp2fPniWxWEzTp08XNEdRZGVl0e7du6lJkyYEgGrWrEkrV66kgwcPkq2tLQGgdu3a0bVr14SOyv7l7NmzBEDQVaoSiYTs7Oyofv36cru5flmSnZ1NR44cIVdXV9LU1CQA1KxZM1q3bh3FxcUJHU/uXL58mcqVK0etWrXiBWSlABeUTG707duXqlSpUuR5gdLy9OlTqlixInXu3FkuRkp/xs2bN6lTp04kEokIAFWqVIm2bdsmdCz2BYGBgQRA8Plgt27dIgC0ZcsWQXOUVXl5eXTmzBkaPHgw6ejoEACytrampUuX0tOnT4WOJ7fOnTtHGhoa1L59ez5UoZTggpLJjefPn5OamhrNnTu3xPtOT08na2trql27NiUlJZV4/9Jw69atwq2GrKysqH///mRkZEQAqGXLluTn51dqTiZSBJ9uN8vDxXLgwIGkr6/PtxSlpKCggIKDg2nMmDFUqVIlAkCmpqY0d+5cnrv8A06cOEFqamrUpUsXyszMFDoO+0FcUDK5MmPGDNLQ0JDJnotfI5FIqE+fPqSlpVUqz4K9f/8+OTk5EQCytLSkQ4cOFZ6CkpeXR4cOHaK2bdsSAKpSpQotWLCAt9yQA3/++ScBkIsTa16/fi33e8LKO4lEQrdv36YpU6ZQtWrVCo9UnTx5Mt2+fVshNhyXhsDAQFJVVSVHR0fKzs4WOg4rAi4omVxJTU0lAwMD8vDwKLE+ly9fTgDo0KFDJdanNERFRZGrqyuJRCKqVasW7dmz55u36h88eEAjR44kTU1NUlZWJldXV7p27Rpf6ATi5eVFmpqaQscotHTpUlJWVqaoqCiho5QqERERNHfuXDIzMyucZjJmzBi6cuWKXHxYKE0OHDhAysrK1Lt3b76bUgpxQcnkzrZt2wgA3bp1S+Z9nTx5kkQiEc2ePVvmfUnL8+fPafDgwSQWi8nY2Ji8vb2L9OabkpJC69atI1NTUwJAjRo1oh07dvCtpRK2ZMkS0tfXFzpGoaysLKpZsyZ169ZN6Chy7+nTp7R06VKqX78+ASAdHR0aPHgwnT59mhc3/aS9e/eSWCymfv368d9hKcUFJZM7+fn5ZG1tTb/88otMR89iYmKoQoUK5ODgUCoW4bx+/ZpGjx5NKioqZGhoSOvXry/WOd8FBQV08uRJcnBwIJFIRBUrVqSpU6fSs2fPpJiafc3s2bOpevXqQsf4zKFDhwgAnTx5Uugocuf169e0bt06atasGQEgTU1NcnV1pcDAQL41W0w7duwgkUhEgwcPLhXvxezLuKBkcunMmTMEgA4ePCiT9j9+/EhWVlZkZmYm9wsREhMTadKkSaSurk66urq0fPlyqS/kiImJoUmTJlGFChVIJBJR9+7d6cyZM3zLToZ+++03qlu3rtAxPiORSKhNmzZUp04dvuVIRO/fv6etW7dS27ZtSSQSkaqqKjk5OZGvr69cLKYqC7Zs2UIAaNSoUfx+U8pxQcnkloODA9WsWbNYo3BfIpFIqGfPnqStrU2PHj2SatvSlJycTLNnzyYtLS3S1tamBQsWyPzUjPT0dPL29i7cCN3CwoL++OMPSk1NlWm/imj48OFka2srdIz/uHv3LonFYvLy8hI6iiBSU1Pp77//pq5du5KysjKJxWLq2LEj7dy5U+4/fJY269atIwA0ceJEnstdBnBByeTWo0ePSElJiVauXCnVdhcvXkwAKDAwUKrtSsvHjx9p8eLFVKFCBdLQ0KDp06eX+HFjEomErly5Qn369CElJSUqV64cjRkzhiIiIko0R1nm7u5Obdq0ETrGF40YMYIqVKigMCe2ZGZm0sGDB6lnz56kpqZWuNXWpk2bBN8ntKz6tBhy+vTpXEyWEVxQMrk2btw4Kl++vNTe1I8dO0YikYjmz58vlfakKTMzk9asWUP6+vqkqqpKEyZMoDdv3ggdi+Li4mju3LlkYGBAAKh9+/Z0+PBhnjhfTD169JDbBTAJCQlUvnx5GjNmjNBRZCYnJ4eOHTtG/fr1o3LlyhEAsrGxodWrV5fotmWKRiKR0MKFCwkAzZ8/n4vJMoQLSibX3r17Rzo6OjR69OhitxUVFUXly5cnR0dHuZqrk5OTQ5s2baIqVaqQkpISDR8+XC4vaNnZ2bRv3z5q0aIFASATExNatmyZwoxiSVvHjh2pd+/eQsf4qjVr1pBYLKYHDx4IHUVq8vPz6fz58zR8+HCqWLFi4d6tixYtoujoaKHjlXkSiYRmzZpFAGjJkiVCx2FSxgUlk3ufLmzFOWEiNTWV6tSpQ3Xq1JGb+YB5eXm0c+dOql69OolEIvLw8KCYmBihY/2Q27dv0+DBg0lNTY3U1NRo4MCBFBoaKnSsUsXOzo4GDhwodIyvysnJIXNzc+rQoUOpHkWSSCQUEhJCEyZMoMqVKxeedz9z5ky6f/9+qf7aShOJREKTJk0iALRmzRqh4zAZ4IKSyb3s7GyqXbs2denS5adeX1BQQI6OjlS+fHm52LS5oKCAfH19ydzcnABQr169Su3cxHfv3tHy5cvJxMSEAFCzZs1o7969vI3KD2jQoIHc31I+evSoXM83/hqJREJ3796l6dOnU/Xq1QtPifrtt9/oxo0bXESWsIKCAhozZgwBoI0bNwodh8kIF5SsVAgICPjp/fEWLFhAIpGIjh07JoNkP04ikVBgYGDhCmoHBwcKCwsTNJO05OfnU2BgINnb2xMAMjAwoDlz5tCrV6+Ejia3zMzMaOrUqULH+CaJREKdOnWi2rVrl4oPCY8fP6YFCxZQnTp1CADp6enRyJEj6eLFi7y/oUDy8/Np2LBhJBKJ6M8//xQ6DpMhLihZqfBpf7y6desWaTFIYGAgAaDFixfLMN23SSQSOn36NNna2hYuarl27ZpgeWTt0aNHNG7cOCpXrhwpKSlRr1696NKlSzwq9D+qVq1KCxYsEDrGd0VERMhktwVpefHiBa1YsYIaNWpEAEhbW5sGDBhAJ06c4L00BZaXl0f9+/cnsVhMu3fvFjoOkzEuKFmpERYWRiKRiDZv3vxDz3/06BGVK1eOevbsKVgxc+XKFWrVqhUBoObNm9P58+cFySGE1NRU2rBhA1lYWBAAsra2pm3btvGG0P9HR0dHbou0/zV+/HjS1tamt2/fCh2FiIjevn1Lf/zxB9nZ2REAUldXp969e5O/vz8fISoncnNzqW/fvqSkpER+fn5Cx2ElgAtKVqoMHDiQ9PX1v7vBd0pKCpmZmZGVlRV9/PixhNL9f7du3aJOnToRAGrYsCEdO3ZMYUfoJBIJnT17lpycnEgsFpOOjg55enqWmgVIsqKiokKbNm0SOsYPSUpKoooVK9LQoUMFy5CcnEzbt2+nDh06kFgsJmVlZXJwcKC9e/cK8jPOvi47O5t69OhBKioqFBAQIHQcVkK4oGSlSlxcHGlqan5z7ll+fj5169aNKlSoUOJFy/3798nJyalwO5JDhw7J1RZFQnv+/DlNnz69cMuWrl270vHjxxXu7yg3N5cA0F9//SV0lB+2YcMGEolEdOfOnRLrMy0tjfbt20e//vorqaiokEgkovbt29Off/5JSUlJJZaD/bisrCzq1q0bqampCT5vnZUsLihZqbNgwQJSVVWlp0+ffvHx2bNnk0gk+qkFPD8rKiqKXF1dSSQSUa1atWjPnj28COAbMjMzaefOnYXz3mrXrk1r166l5ORkoaOViJSUFJmeVS8LeXl5ZGVlRa1atZLpaHtWVhYFBARQnz59SENDgwBQixYtaP369RQfHy+zflnxZWRkkL29PWloaNCZM2eEjsNKGBeUrNRJT08nIyMj6tWr138eO3ToEAGg5cuXl0iW58+f0+DBg0ksFpOxsTF5e3vzQoAi+LRHoLu7O6moqJCmpiaNGDGC7t+/L3Q0mYqLiyMAdPz4caGjFMmZM2cIAO3fv1+q7ebm5tLJkydp4MCBVL58+cKpIsuXL6fnz59LtS8mG2lpadSmTRvS0tKiixcvCh2HCYALSlYq7d69mwBQcHBw4Z+Fh4eTlpYW9enTR+bzFV+/fk2jR48mFRUVMjQ0pPXr11NWVpZM+yzr3rx5Q4sWLaKqVasSAGrdujUdOHCgTBbo0dHRBIAuXbokdJQi6969O5mYmBR78UtBQQFdunSJRo0aRfr6+gSAzM3Naf78+fTo0SMppWUl4cOHD2RnZ0fly5cv0ztYsG/jgpKVSgUFBWRjY0NNmjShgoICSk5Optq1a1P9+vVluoo4MTGRJk2aROrq6qSrq0vLly/nVctSlpubS/v37y9cHW9kZES///673Kwwloa7d+8SgFJ5ulB0dDSpqKjQ77//XuTXSiQSunXrFnl6epKRkVHhEZ7Tpk2jO3fuKOzCtdIsKSmJmjRpQhUqVKBbt24JHYcJiAtKVmpduXKFANDu3bupc+fOVLFixa/Oqyyu5ORkmj17NmlpaZG2tjYtWLDguyvNWfHdu3ePhg8fThoaGqSiokL9+vWj69evl/rC4+rVqwSg1J6QNGXKFNLU1KS4uLgfen54eDjNmjWLatWqRQDI0NCQxo8fT9euXVO4BVllSWJiIjVs2JD09PTo7t27QsdhAuOCkpVqLi4upK2tTSKRiM6ePSv19j9+/EiLFy+mChUqkIaGBk2fPp3ev38v9X7YtyUnJ9OaNWsKCxIbGxvatWtXqZ1m8Gku4osXL4SO8lM+fPhAlSpVIg8Pj68+JyYmhhYvXkxWVlYEgCpUqEBDhw6lc+fOFelwAiaf3rx5Q1ZWVmRgYEDh4eFCx2FygAtKVqp5eXkRAOrcubNU283MzKQ1a9aQvr4+qaqq0oQJE+jNmzdS7YMVXX5+Ph07doy6dOlSeLTejBkzSl1hdvjwYQJA7969EzrKT/P29iYAdP369cI/e/XqFa1Zs4aaNGlCAEhLS4vc3d3p6NGjlJOTI2BaJk1xcXFkYWFBVatWpcjISKHjMDkhIiICY6XQ/fv3YWdnh+rVq+Ply5eIiYlB1apVi9Vmbm4utm/fjsWLFyMxMRFDhgzB3LlzUa1aNSmlZtISExODzZs3Y+fOnUhPT4ejoyPGjRuH9u3bQyQSCR3vm/bt2wcPDw9kZmZCQ0ND6Dg/paCgADY2NlBWVsbgwYNx4MABBAcHQ1VVFd26dYObmxscHBygqakpdFQmRS9fvkT79u2Rn5+PCxcuoHbt2kJHYnJCLHQAxn5GUlISevToAXNzc5w7dw6ampqYM2fOT7eXn5+PXbt2wdzcHOPGjUOHDh0QFRUFb29vLibllJmZGdatW4fXr19j8+bNiImJgb29PaysrLBp0yakpaUJHfGrMjIyIBKJoK6uLnSUn/Lhwwfs2bMHqqqqCAsLw/jx46GpqYldu3YhISEBAQEB6N27NxeTZczTp0/RunVrAMCVK1e4mGSfE3qIlLGiysvLow4dOpC+vn7hrc5NmzaRSCSisLCwIrVVUFBAvr6+ZG5uTgCoV69epXahhKKTSCR08eJFcnFxISUlJdLW1qbx48dTVFSU0NH+Y926daSlpSV0jCLJyMggPz8/6tGjB6mqqpJIJKI2bdpQ48aNqXLlypSWliZ0RCZDUVFRZGRkRObm5vTq1Suh4zA5xCOUrNSZMWMGLl26hAMHDqB69eoAgBEjRqBOnTqYPHky6AdmcRARjhw5goYNG8LNzQ1mZmYICwvDwYMHUbduXVl/CUwGRCIR2rZti0OHDuH58+eYMGEC/Pz8UKdOHXTq1AlBQUEoKCgQOiaAf0YotbS0hI7xXTk5OQgKCoK7uzsMDAzg6uqK+Ph4LF++HK9evcKlS5fg7++PlJQUrFixQui4TEYiIiLQpk0b6Ojo4NKlSzA2NhY6EpNHQle0jBXF3r17CQB5eXn957ETJ04QADp8+PBXXy+RSOjUqVOFiwbat2/PG/GWYdnZ2fT3339T06ZNCQBVr16dVqxYIfhK/ZkzZ1KNGjUEzfA1eXl5dPbsWRoyZAhVqFCBAJC1tTUtWbKEnjx58sXXzJ49m9TV1flUmzLo3r17pK+vTw0aNKDExESh4zA5xgUlKzXCwsJIXV2dBgwY8MV9CCUSCXXq1IlMTU2/uKL08uXLhZtlt2jRgs6fP18SsZmcuHnzJg0YMIBUVVVJXV2dhgwZQnfu3BEky4QJE8jKykqQvr+koKCArl69SmPHjiUDA4PC89XnzJlDDx8+/O7r09LSqEqVKtS7d+8SSMtKSmhoKOnq6pKNjQ0lJSUJHYfJOS4oWamQmJhIJiYm1KRJk28e+RYeHk5isZjWrl1b+Gc3b96kTp06EQBq1KgRHT9+vNRvjM1+XmJiIi1dupSqVatGAMjOzo58fHxKbFub9Ow86jtyMjWyd6aHrz9QerYwezJKJBIKCwujqVOnkomJSeGpRJMnT6bQ0NAi/4x8Og718uXLMkrMSlJISAiVL1+emjdvzoc4sB/C2wYxwWTk5ONFUgZy8yVQVRajhp4WtNSU//O8vLw8dOrUCY8ePcLt27e/u+p61KhR2L9/P44cOYI1a9YgKCgIdevWxaJFi+Ds7AyxmKcOs39W9gcFBWHjxo24ePEiDA0NMXLkSIwcObLY20/9r5iENOy7GYuLjxMRm5yJf7/pigCYVNREOwsD9GtmAjNDban2/b8iIyPh5+cHPz8/REdHQ19fH71794abmxt++eWXn/75kEgkaNGiBfLy8hAaGgolJSUpJ2cl5cqVK+jWrRsaN26M48ePQ1tbtt+TrGzggpKVqJ+5sE6cOBGbN2/G+fPnC7es+JaQkBC0adMG+fn5qF27NhYsWAA3Nze+wLGvioiIwKZNm/D3338jJycHLi4uGDduHH755Zdi7Wn5KjkTsw6HI/jJeyiJRSiQfP3t9tPjrUz1sdTZGtUqSm/LnefPn2P//v3w8/PD/fv3Ub58efTs2RNubm5o3749lJX/+0HuZ1y/fh12dnbYvn07hg4dKpU2Wck6d+4cHB0dYWdnhyNHjpSKxWNMPnBByUrEz15YbSTR8BwxAJs2bcKYMWO+2ceLFy+wcOFC/P333yhXrhzS09Nx7949WFtbS/vLYWVUamoqdu/ejY0bNyImJgYNGjTAuHHj4O7uXuQ9Ff1CYzE/KAL5Evrm9/v/UhKLoCwWYaGjFVxtTYr6JRR68+YNDhw4AD8/P9y4cQMaGhpwdHSEq6srunTpIrM9MD08PHD27FnExMSgfPnyMumDycaJEyfQs2dPtG/fHv7+/qV2030mDC4omcz97IVVLAIKcnNgmRWBkxvnfHWkKD4+HosXL8b27dtRsWJFzJo1CwMGDECjRo1Qr149HD16VFpfClMQEokEZ8+excaNG3H8+HFUqFABQ4YMwZgxY1CrVq3vvn7jxRisPhNd7BxTOpljXDuzH35+UlIS/P394efnh0uXLkFZWRldu3aFq6srunfvjnLlyhU70/fExcXBwsICY8eOxcqVK2XeH5OOI0eOoHfv3ujWrRv2798PNTU1oSOxUoYLSiZTxb6wEgEi0RcvrO/evcPy5cuxefNmaGhoYPr06Rg3blzhLZoDBw6gb9++OHv2LOzt7YvzZTAF9uzZM2zZsgU7duzAhw8f4ODggHHjxqFjx45fnG/oFxqLGQHhUut/RU9r9P3GSGVaWhoCAwPh5+eHM2fOQCKRoEOHDnB1dYWzszN0dXWlluVHLVq0CIsXL8ajR49gampa4v2zojlw4AD69esHZ2dn7Nu3DyoqKkJHYqUQF5RMZmR1YU1JScGaNWvg5eUFsViMyZMn47fffoOOjs5nzycitGzZEmlpabh79y7PoWTFkpmZCV9fX2zYsAH379+HmZkZxo4di0GDBhV+771KzoT9usvIyZdIrV81ZTHOebb5bE5lVlYWTpw4AV9fXxw/fhzZ2dn45Zdf4Obmhl69esHQ0FBq/f+MzMxMWFpaolGjRggMDBQ0C/u2vXv3YuDAgXBzc8Nff/0ltfm0TPFwQclkQlYX1h6qD+G9dilycnIwYcIETJ06FXp6el99za1bt9CsWTN4e3tj+PDhUsvCFBcR4dq1a9i4cSP8/f2hpqaG/v37Y9y4cVh+Ix0hz5KKNLXje5TEItjV0sPOAY1x9uxZ+Pn5ITAwEGlpaWjcuDHc3NzQp08fmJj8/HxLWdi/fz9cXV35DoEc27lzJ4YNG4bBgwfD29ubP3SzYuGCkslE/x03pX5hJUkBcmLD0dcgETNnzkTlypV/6HWfFgk8efKEt79gUhUfHw9vb29s27YNSXkqqDp8i8z6yjgwA++fPYSlpSXc3NzQt29fmJuby6y/4iIitG7dGikpKbh37x6PfMmZLVu2YMyYMRg9ejQ2btzI26mxYuOCkkldTEIaOnpdkVn75zxbw9TgxwvD2NhYWFhYwNPTE0uXLpVZLqa4cnNzMWjDcYS8UwZEMrgwSwpgLk7AardmsLa2LtZWRiUpLCwMtra22Lhx43d3aWAlZ926dZg0aRJ+++03rF27ttR8PzH5xh9JmNTtuxkLJbFs3qCUxCLsvRFbpNeYmJhgypQpWLt2LV6+fCmTXEyxqaqq4rWkgmyKSQAQKyFHzxT169cvVRd/GxsbDB48GHPnzkVycrLQcRiA5cuXY9KkSZg+fToXk0yquKBkUnfxcaJUb3X/W4GEcDE6scivmz59OnR1dTFjxgwZpGKKLj0nH7HJmTLtIzYpExk5+TLtQxaWLFmCvLw8LFy4UOgoCo2IsHDhQsycORPz58/HsmXLuJhkUsWTWphUleSF9UvHNH5NuXLlsGTJEgwdOhQTJkxAixYtZJhQMRERJBLJT/23OK+Vhzbis8QgVJDt3y+AF0kZsKqq893nypPKlStj9uzZmD17NkaNGgVLS0uhIykcIsLs2bOxbNkyLF26FDNnzhQ6EiuDeA4lk6qI+FQ4bLgq8376V4pDJeWcIl30CwoK8Oeff0JJSQkDBw786QKitBc/smhD0d9GVKuYo8rAtTLv5/BoOzQyKfl9JYsrJycHdevWhZmZGU6ePMkjYyWIiDB58mSsW7cOa9euhaenp9CRWBnFI5RMqnKluE3Qt3j9sREFiU8hEokgFot/6L8ikQj5+fl4+/YtvL29Ua5cuR9+7b/bKOprvtaGkpJSsduQRg5uo/htRCVkoMfWGzL/vldVLp2zlNTU1LBmzRo4OzvjxIkTcHBwEDqSQpBIJBg3bhy2bNnyQ8fXMlYcXFAyqSqpC96NkKs/fevPyckJ9+7dw6NHj/isWiYVZpWVIcI/t6VlRQSghp6WDHuQLScnJ7Rv3x6TJk1Cx44doaqqKnSkMq2goAAjR47Ezp078eeff2LYsGFCR2JlXOn8uMvkVg09Lcj8ZhYRtq9bhv379+PZs2dFvt26atUqxMfHw8vLSzb5mMLRUlOGyb9OspEFEz3NIs0bljcikQheXl548uQJNm3aJHScMi0/Px+DBg3Crl27sHv3bi4mWYnggpJJVUlcWNXy0nD4oB9cXV1Ru3Zt6Ovro3PnzpgzZw4CAwPx+vXrb77e3NwcY8eOxdKlS/H27VuZZmWKo52FgUy3y2pnbiCTtkuStbU1RowYgYULF+Ldu3dCxymT8vLy0K9fP/j6+sLX1xf9+/cXOhJTELwoh0ndgqAI7Ln5UiZbBymJRejfrDoWOFrh3bt3uH37NkJDQwv/+6lArFKlCpo0aQJbW9vC/+rr6xe2k5ycDFNTU/Tq1Qve3t5Sz8kUj7xt6C+v3r17B3Nzc/Tt2xdbt24VOk6ZkpOTg759++LEiRM4cOAAevToIXQkpkC4oGRSJ9SFlYgQHx+P0NDQz4rMlJQUAED16tVha2tbWGTeunULs2fPxt27d1G/fn2Z5WWKQxZHjn46y3vP0GZSa1NoXl5emDx5Mv/sSVFWVhZcXFxw4cIFBAQEoFu3bkJHYgqGC0omE/JyYSUiPHv27LORzLCwMKSnpwMAVFRUoKenh+nTp8PW1haNGjWCpqZsb9mzsutVcibs111GjhR3O1BTFuOcZxtUk/FUkpKUl5cHa2trVK1aFefPn+dthIopMzMTTk5OuHbtGo4cOYKOHTsKHYkpIC4omUzI84W1oKAAjx8/xu3bt3HgwAEcP34cysrKyM/Ph5KSEqysrD67XV6/fn1ekcp+mF9oLGYEhEutvRU9rdHX1kRq7cmLkydPolu3bggICICzs7PQcUqttLQ0/PrrrwgLC8Px48fRpk0boSMxBcUFJZOZ0nBhJSLY29sjLi4Oe/bswf379wtHMsPDw5Gfnw9VVVU0aNCgsMi0tbWFpaUllJSUpJqFlR1z/a5hz/0PABFQjNG3qZ0sMLadqfSCyZlu3bohKioKjx49grq6utBxSp3U1FR07doVEREROHnyJOzs7ISOxBQYF5RMpjZejMHqM9FyfWG9d+8eGjdujPXr12P8+PGFf56VlYX79+9/drs8MjISRARNTU00btz4syKzdu3aEIt54wRFl5GRAVtbW0hqNgc17o18CRVp6oeSWARlsQiLHK3K5Mjkv0VFRcHa2hq///47ZsyYIXScUiU5ORmdO3fGkydPcObMGdja2godiSk4LiiZzI338sOROFUoq6qhKFMqS/LCOmzYMBw+fBhPnjyBru7Xj7ZLS0vDnTt3CovM0NBQPHv2DACgo6ODJk2afFZkVqtWjeeHKZihQ4fCz88Pt2/fRjnD6ph1OBzBT95DSSz6ZmH56fFWpvpY6mxdpuZMfstvv/2GHTt2IDo6GlWqVBE6Tqnw7t07dOzYEXFxcTh37hwaNmwodCTGuKBksvXu3TvUqVMH7bv3hnqrwXJ7YX3z5g3MzMwwYsQIrF1btDOZk5OTcfv27c+KzE97YRoYGPxn+yJDQ0NZfAlMDvj4+KBfv37YuXMnBg8eXPjnMQlp2HczFhejExGblPnZiToi/LNpeTtzA3g0NykTWwMVRUpKCszMzNC9e3fs2rVL6Dhy7+3bt+jQoQOSkpJw7tw51KtXT+hIjAHggpLJ2MCBA3Hs2DFERkbCwMBAri+sS5YswcKFCxEREQEzM7NitfXmzZv/7JH5/v17AICxsfFn2xc1adLkm6OirHSIiYlB48aN4eTkhD179nx1ZDojJx8vkjKQmy+BqrIYNfS0SvUJONKwZcsWjBkzBqGhoWjSpInQceTW69ev0b59e6Snp+PChQuwsLAQOhJjhbigZDJz4cIFdOjQATt27MCQIUP+87i8XVizsrJgYWEBGxsbHD58WKptExFiY2M/2yPz9u3b+PjxIwCgdu3anxWZjRs3Rrly5aSagclOTk4OWrRogfT0dISFhUFbW7FGGYsrPz8fjRo1go6ODoKDg3mayBe8fPkS7du3R35+Pi5cuIDatWsLHYmxz3BByWQiOzsb9evXR5UqVXDp0qVSc4H4dMvy4sWLaNu2rUz7kkgkePLkyWdF5p07d5CVlQWxWAxLS8vPbpc3aNCAV8LKqQkTJmDbtm24efMmz2f7SefPn4e9vT18fX3h6uoqdBy58vTpU7Rv3x7Kysq4cOECqlevLnQkxv6DC0omE/PmzcPy5ctx//59WFpaCh3nh0kkErRo0QJ5eXkIDQ0t8a2B8vPz8ejRo89ul9+/fx95eXlQVlZG/fr1P1v0U7duXaioqJRoRva5wMBAODs7Y8OGDRg3bpzQcUo1Z2dn3L59G48fP+YDBv7P48eP0b59e5QrVw7nz5+HsbGx0JEY+yIuKJnUPXr0CA0bNsTMmTOxcOFCoeMUWUhICH755Rfs2rULgwYNEjoOcnJy8ODBg88W/Tx69AgSiQTq6upo1KjRZ0Wmubk5b19UQmJjY9GwYUO0bdsW/v7+pWYkXl49ffoUdevWxaxZszB//nyh4wju4cOHsLe3h56eHs6fP4/KlSsLHYmxr+KCkkmVRCJBmzZtkJiYiPv375faW7R9+/ZFcHAwoqOj5XIuY0ZGBu7evftZkRkTEwMA0NbWho2NzWdFZo0aNbjYkbK8vDy0bdsWcXFxuHfvHi+skpLp06djw4YNePz4MapVqyZ0HMHcu3cPHTt2hJGREc6ePYtKlSoJHYmxb+KCkknV9u3bMXz4cFy4cAHt2rUTOs5Pe/HiBerUqYPp06eXmlHWDx8+ICws7LMiMzY2FgCgp6f3nz0yq1atKnDi0m3WrFlYuXIlgoOD0aJFC6HjlBkfP36Eubk5OnTogH379gkdRxChoaHo3LkzateujdOnT6NixYpCR2Lsu7igZFKTkJCAOnXqwMnJCX/99ZfQcYptxowZ+OOPPxAdHV1q5y0lJib+Z4/MhIQEAECVKlX+s32Rvr6+wIlLhzNnzqBz585Yvnw5pk+fLnScMmfnzp0YOnQorl27pnDHCYaEhKBr166wsrLCyZMnoaOjI3Qkxn4IF5RMavr164fTp08jKiqqTBQmHz9+hKmpKbp06YK///5b6DhSQUR4/fr1f7YvSklJAQDUqFHjsyLTxsYG5cuXFzi1fHn79i0aNGiARo0a4cSJEzxfVQYkEglsbW0hFotx8+ZNhfk7vnz5MhwcHGBjY4Njx47x9lOsVOGCkknFpxGbv/76CwMHDhQ6jtRs27YNo0aNwq1bt8rsWblEhGfPnn1WZIaFhSEjIwMAYGFh8VmR2bBhQ4VdgVtQUIDOnTsjIiIC9+/fh4GBgdCRyqzg4GC0bt26zL2nfM25c+fg6OiIX375BUeOHFHYnzFWenFByYotMzMT1tbWqF69Os6fP1+mFn982nC5QoUKuHLlSpn62r6loKAAUVFRn21fdO/ePeTk5EBJSQn16tX7bI9Ma2trqKqqCh1b5pYsWYK5c+fi7Nmz6NChg9BxyrxPi+MeP35cpkfrTpw4gZ49e6JDhw7w9/cvtYsZmWLjgpIV26xZs7B27Vo8ePAA5ubmQseRuk+jrwcPHkSvXr2EjiOY3NxcPHz48LMiMzw8HAUFBVBTU0ODBg0+KzItLS1LfB9PWQoODkbbtm0xe/ZsLFq0SOg4CuHly5eoU6cOPD09sXTpUqHjyERgYCD69OmDbt26Yf/+/VBTUxM6EmM/hQtKVizh4eFo3Lgx5s2bh7lz5wodR2YcHBwQGRmJyMhIfsP/l6ysLNy7d++zRT+PHz8GEUFLSwuNGzf+rMg0NTUtlaO8SUlJaNiwIWrWrIkLFy5AWVmxz94uSfPmzcPKlSvx/9q784Co6v194M8MKKK4ILiVG8kiIAIjiA4wo2lS3dzS0sTKyu0WftPqdrnaolaYN3cr07J+ZeaaebHUq4axiSPIsINAirgSgoEOyDDM+f3R1/neuZYJzHBmeV7/kuc8UwkP53w+709hYSE8PDzEjmNSu3btQnR0NB5//HFs376dhxSQVWOhpBbT6/WIiIjA9evXkZWVZdNFq7CwEAEBAVixYgX+9re/iR3HotXW1iIzM9OoZJ47dw4A0K1btzvGF/Xt29eiS6YgCJgwYQLS0tKQlZVltTv+rZVGo4GPjw9GjBiBvXv3ih3HZLZt24ZZs2ZhxowZ+OKLL/hLClk9FkpqsdsbVhITE6FQKMSOY3YxMTHYtm0bSktLOWS4maqqqu4YX3T58mUAQM+ePQ1PMG+XTEva7LJu3TosWrQIBw4cwGOPPSZ2HLu0fft2zJw5E8ePH8eoUaPEjtNqW7duxZw5c/D8889j8+bNNrU0hOwXCyW1yJUrV+Dr64upU6fis88+EztOm7h27Ro8PT0xY8YMfPzxx2LHsXqXL1++o2RWVVUBAPr163fHjMxu3bq1ecaMjAzI5XLExMRgzZo1bX5/+o0gCJDL5aivr8fp06etuoB9/PHHeOmll/DXv/4VH374od2MRCLbx0JJLTJ9+nQkJCSgqKjIrk5xWL16NV5//XXk5OTA399f7Dg2RRAEnD9//o4ZmTdu3AAAeHp6GpVMmUyGTp06mS1PTU0NZDIZunfvjtTUVLvYxW7JTp06hbCwMGzevBlz584VO06LrF27Fq+88goWLlyINWvWWPRSD6LmYqGkZjt06BAeffRRfP3114iOjhY7TptqaGiAv78/vLy8cOjQIbHj2Dy9Xo+SkhKjkqlWq1FfXw+pVApfX1+jkhkYGGiStbyCIOCpp57CoUOHoFar8cADD5jg01BrPfPMMzh8+DCKi4tFeWLdGitWrMDixYsRGxuLuLg4lkmyOSyU1CwajQb+/v7w9vbGv//9b7v8prhv3z5MmTIFhw4dwsMPPyx2HLuj0+lQUFBgVDJzcnLQ2NiIdu3aYejQoUY7y/39/Zu94eHTTz/F3LlzsWvXLjz55JNm+iTUXJcuXYKPjw/mzZuH1atXix3nngiCgGXLlmHZsmVYunQp3nrrLbv8vkm2j4WSmuX111/Hxo0bkZeXh0GDBokdRxSCIGDUqFG4du0asrOzuTvTAty6dQs5OTlGMzILCgqg1+vh7OyM4OBgo5Lp7e39h2vX8vLyEBoaimeeeQabN29u409Cf+a9997D0qVLkZ+fb/FzbwVBwOLFi/H+++9jxYoViI2NFTsSkdmwUNI9y87OxrBhw7B8+XIsXrxY7DiiOn36NEJDQ/Hxxx9j/vz5Yseh33Hz5k2o1WqjTT+lpaUAgC5dumDYsGFGO8sHDBiA+vp6wxnSp06dgrOzs8ifgv5bfX09fH19ERAQgAMHDogd5w8JgoBXXnkF69atw5o1a7Bo0SKxIxGZFQsl3ZOmpibI5XJoNBpkZmZygwKAWbNm4eDBgygpKUHXrl3FjkP34Pr16zh9+rRRybxw4QIAwN3dHR06dEBFRQXWrFmDKVOmoE+fPiInpt+zZ88ePPnkkzh8+DCioqLEjnMHvV6PmJgYbNq0CR999BFefPFFsSMRmR0LJd2Tjz76CDExMUhJSUF4eLjYcSzCpUuX4O3tjZiYGKxcuVLsONRCFRUVyMjIwOeff459+/ahc+fOhp3l9913n9GMzJCQELi5uYmcmG4vO6msrER2drZFnTDT1NSEuXPn4osvvsCnn36KF154QexIRG2ChZL+1KVLl+Dr64sZM2bgk08+ETuORVm2bBni4uJQWFjIncBWrKSkBDKZDBMnTsRXX32FS5cu3TG+6NdffwUAeHh4GO0sHzZsGDp37izuB7BDarUaw4YNw/r167FgwQKx4wD4bcPYrFmzsGPHDnz55ZeYOXOm2JGI2gwLJf2pqVOnIiUlBYWFhXB1dRU7jkXRaDTw9vZGeHg4du/eLXYcaoGGhgbI5XLcuHEDp0+f/t1yKAgCfv75Z6OSmZmZCY1GA4lEAh8fH6OSGRQUxPWXbWDOnDn49ttvUVJSIvqT48bGRkRHR2Pfvn345ptvOB2A7A4LJd3VgQMHMGHCBOzcuRPTpk0TO45F+uqrr/Dss88iOTkZERERYsehZnr55ZfxySef4OTJkwgODr7nP9fU1ISioiKjkpmVlQWtVgtHR0cMGTLE6FV5QECARb2atQUVFRXw8vLCs88+i40bN4qWo6GhAdOmTcPBgwexe/duTJo0SbQsRGJhoaQ/dPPmTfj5+cHf3x8HDx7k7LQ/oNfrMXz4cEilUpw8eZJHqVmR/fv3Y/Lkydi4cSNiYmJafT2tVovc3Fyj8UV5eXloamqCk5MTAgMDjZ5kDh482KqPEbQEq1atQmxsLLKzs0U5vaq+vh5TpkxBQkIC9u3bh0cffbTNMxBZAhZK+kOvvvoqNm3ahPz8fHh4eIgdx6IlJSVBqVRi27ZtXDdlJcrLyxEUFIRRo0bh22+/NdsvTHV1dcjKyjLaWX7mzBkAgIuLC2QymdGTzEGDBvGXt2bQarXw9/eHh4dHmx+2oNFoMHHiRJw4cQLx8fEYO3Zsm92byNKwUNLvyszMRGhoKFasWIHXX39d7DhWYcqUKTh16hTOnDmDjh07ih2H7qKxsRGjRo3CxYsXkZWV1eZrg2tra+8YX1RWVgYAcHV1RUhIiFHJ7Nu3L0vmXcTHx2PixImIj4/H+PHj2+SeN27cwGOPPYbMzEz88MMPUCgUbXJfIkvFQkl3aGpqQlhYGBobG5GRkcF1X/fo559/hq+vL9588028+eabYsehu1i8eDH++c9/IikpCXK5XOw4AIBr164ZdpTfLplXrlwBAPTq1ctofFFoaCh69OghcmLLIQgCxo0bh7KyMuTn55t9Tu6vv/6KRx55BAUFBTh8+DBGjhxp1vsRWQMWSrrD+vXrsWjRIpw4cQIjRowQO45Vee2117Bp0yaUlJTgvvvuEzsO/Y6jR48iKioKcXFxFn8U3uXLlw1rMW+XzOrqagBA//79jUrmsGHD0K1bN3EDiygvLw9BQUF4//338dprr5ntPtXV1Rg3bhzOnj2LI0eOICQkxGz3IrImLJRk5MKFC/Dz88MzzzyDjz76SOw4VufXX3+Fp6cnJkyYgM8//1zsOPRfrl69isDAQAQFBeHQoUNWt4FKEASUlZUZ7Sw/ffq0YRC7l5eX0aaf4OBgdOrUSeTUbScmJgbbtm1DSUkJevbsafLrV1ZWYuzYsbh8+TKOHj2KoKAgk9+DyFqxUJKRSZMm4dSpUygsLORxgi300UcfYcGCBTh9+nSzxtCQeTU1NSEqKgr5+fnIzs42S+EQg16vR3FxsVHJVKvVuHXrFqRSKfz8/IxK5tChQ+Hk5CR2bLOoqqqCl5cXpk6dii1btpj02leuXMHYsWNRVVWFH3/8UZQd5USWjIWSDG6PUNmzZw+mTp0qdhyrpdPpMHToUPTq1QsJCQncTGEh3nvvPbz55ps4evQoxowZI3Ycs2psbERBQYFRyczJyYFOp0O7du0wdOhQo5Lp5+cHR0dHsWObxIYNG7Bw4UKT/kJ38eJFjBkzBhqNBgkJCfD29jbJdYlsCQslAfht16mfnx+Cg4MRHx/PEtRKBw8exF/+8hfs378fEydOFDuO3UtJSYFSqcTixYvxzjvviB1HFLdu3UJ2drbRjMyCggIIggBnZ2cEBwcblUwvLy+rWxIA/FamAwMD0aNHD/z0009G38s0DTqUVWmg1enR3lGKgW6d0Mnp7kW6rKwMDz74IJqampCQkIBBgwaZ+yMQWSUWSgLw22khn332GQoKCjBgwACx41g9QRDw8MMP4+zZs22y65T+WFVVFYKCguDh4YGEhASbeRJnCjdv3kRmZqZRySwtLQUAdO3aFcOGDTMaXzRgwACr+GXz3//+Nx5++GHs2bMHgZFR2K4qx/Ezv6C8ug7/+QNPAqB/944Y7dMT0WH94dXL+NjN0tJSjBkzBo6OjkhISOD3RqK7YKEkpKenIywsDKtWrcIrr7widhybkZeXh8DAQKxevRoLFy4UO45dEgTBMHg6KysLffv2FTuSxbt+/fod44suXrwIAHB3d79jfFHv3r1FTvz7xk1+CsVdhwF9fOEglaBJ/8c/6m5/PdLTHXGTA9Cve0cUFRVhzJgxcHFxQUJCAu6///42TE9kfVgo7ZxOp0NoaCgkEglOnTrFpzcmNn/+fOzatQulpaVwc3MTO47dWbduHRYtWoQDBw7gscceEzuO1bp69eodJbOyshIAcP/99xuVzJCQEHTv3l3UvDvTy/HWv/LQ0KiDRHrvR1s6SCVwlEowd1g3/HPeJPTo0QPHjh2z2NJMZElYKO3c6tWr8frrr0OlUnGemhlUVFTAy8sLzz33HNavXy92HLuSkZEBuVyOmJgYrFmzRuw4NkUQBFy4cMFo009GRgZqamoAAA888IBRyZTJZOjcufOfXNU0PjxeglVHilt9nQ7FR5H8yRIOkCe6RyyUduz8+fPw8/PD7NmzWXbMaOXKlXjjjTeQl5cHHx8fsePYhdraWshkMri6uiI1NZVrWNuAXq/Hzz//bFQyMzMzUVdXB4lEgsGDBxtt+gkKCkKHDh1MmmFnejli9+Wa7HorHw/AtND+JrsekS1jobRTgiBg/PjxyMrKQmFhYZs9PbBHt27dgq+vLwICAhAfHy92HJsnCAJmzJiBH374AWq1mrtyRaTT6VBUVGRUMrOzs6HVauHo6IghQ4YYlcwhQ4a0+KjXC9V1GLs2EQ06vcnyOzlKcWyREv26dzTZNYlsFQulndq7dy+eeOIJfPfdd5g0aZLYcWze7t27MW3aNBw7dszmZyCK7bPPPsOcOXOwa9cuPPnkk2LHof/S0NCA3Nxco53l+fn5aGpqgpOTE4KCgoxKpo+PDxwc/nwd5NNbVThxtuqum2+ay0EqgfwBN2x7Icxk1ySyVSyUdqimpga+vr4YPnw49u/fL3YcuyAIAiIiIgxjWu7lByQ1X15eHkJDQ/HMM89g8+bNYsehe1RXVwe1Wm1UMs+cOQMAcHFxuWN80QMPPGA0vqik4gYeWpdktnzHFing2ZNvcYjuhoXSDr300kv46quvUFBQgH79+okdx26oVCqMGDECn376KWbPni12HJtTV1eH0NBQSKVSnDp1Cs7OzmJHolaoqanB6dOnjXaWnz9/HgDQvXt3hISEGEpmSl0ffJdv2qeTtzlIJXg6bACWTuBRi0R3w0JpZ06ePAm5XI61a9fi5ZdfFjuO3YmOjsaPP/6IkpISrls1sdmzZ+Obb75BRkYG/Pz8xI5DZlBZWXnH+KKrV6/ivnlb0M71PrPdd4BbRyS+Ntps1yeyBSyUdqSxsRHDhg1D+/btoVKp+NpVBOXl5fDx8cErr7yC9957T+w4NmPHjh2YMWMGtm7diueff17sONRGBEFASdkFjNuSg9/OvTEPCYC8pVF/ekwjkT2zvoNaqcXWrl2L/Px8bNmyhWVSJP3798err76K1atXG17fUeuUlJRg7ty5iI6OxnPPPSd2HGpDEokEjU5dYc4yCQACgLIqjVnvQWTtWCjtxLlz57B06VIsXLgQMplM7Dh2LTY2Fq6urvjHP/4hdhSr19DQgOnTp6NPnz7YtGmTVZwzTaalNeGYIEu4D5G1YqG0A4Ig4K9//St69OiBZcuWiR3H7rm4uODdd9/Fjh07cPLkSbHjWLXXX38deXl52LVrF9ek2qn2jm3zY6yt7kNkrbiG0g7s3LkTTz31FM8ztiBNTU0YNmwYOnbsiNTUVD5Za4F//etfmDRpEjZs2IAFCxaIHYfakCAIOHfuHBITE/FjUgpSek0GzPh3iGsoif4cC6WNu379Onx9fREREYG9e/eKHYf+Q0JCAsaMGYOdO3di2rRpYsexKuXl5QgKCoJSqcS+fftYyG2cIAgoLi5GYmIiEhMTkZSUhIsXL0IikWDo0KHQRi1BndR8p9lwlzfRn2OhtHHz5s3Djh07UFRUhPvuM99YDWqZiRMnIjs7G0VFRSY/19hWNTY2YtSoUbh48SLUajW6d+8udiQyMb1ej4KCAqMCWVFRAalUCplMBqVSCaVSiYiICLi6umJpfD62qc5zDiWRiPj83oalpqZiy5Yt+PDDD1kmLdQHH3wAf39/rFu3DrGxsWLHsQpvv/02VCoVkpKSWCZtRFNTE3JycgzlMSkpCVVVVXB0dERoaCiee+45KJVKyOVydOnS5Y4/Hx3WH/8vrcw82fQCZo7ob5ZrE9kSPqG0UVqtFsHBwejcuTNSU1M5JsiCLVy4EJ9//jlKSkrQq1cvseNYtKNHjyIqKgpxcXEs4FZMp9MhMzMTSUlJSExMRHJyMmpqatC+fXuMGDECSqUSCoUCI0eORKdOne7pmjzLm0hcLJQ2Ki4uDm+99RYyMzMxdOhQsePQXVRXV8PT0xNTp07Fli1bxI5jsa5evYrAwEAEBQXh0KFDkEq569ZaaLVapKenGwpkamoqbt68CWdnZ8jlcigUCiiVSoSFhbV46ceF6jqMXZuIBhOO93FylOLYIiX6dTff+kwiW8FCaYNKS0sREBCA//mf/8HKlSvFjkP3YP369XjllVegVqv5C8Dv0Ov1iIqKQl5eHrKysvgk18LdunULKpXKsAYyLS0N9fX1cHFxQXh4uGENZEhICNq3b2+y++5ML0fsvlyTXW/l4wGYFsrX3UT3goXSxgiCgHHjxqG0tBR5eXn3/LqIxKXVajFkyBAMGDAAR44c4a7l/xIXF4c33ngDR48exZgxY8SOQ/9Fo9EgLS3NUCBVKhW0Wi26du2KyMhIQ4EMDg6Go6N5l+5/eLwEq44Ut/o6fxvng5dGe5ogEZF9YKG0Mdu3b8fMmTNx8OBBPPLII2LHoWaIj4/HxIkT8f333+Mvf/mL2HEsRkpKCpRKJRYvXox33nlH7DgEoLa2FqmpqYYCmZGRAZ1OBzc3N8Pra6VSiYCAAFHWb+9ML8fb8fnQ6YVmral0kErgKJVg+QR/PpkkaiYWShtSXV2NwYMH48EHH8TOnTvFjkPNJAgCxowZg8uXLyM3Nxft2rUTO5LoqqqqEBQUBA8PDyQkJJj96Rb9vuvXryM5OdmwCzszMxN6vR69evUylEeFQgE/Pz+LWdt6oboOi7/LRXLpNThIJXctlre/HunpjrjJAVwzSdQCLJQ2ZPbs2di7dy+KiorQu3dvseNQC2RlZUEmk2HDhg2IiYkRO46oBEHApEmTkJKSguzsbPTt21fsSHajsrLSML4nMTEROTk5EAQBffv2NSqQ3t7eFr88o6TiBrarynG8+BeUV9XhP3/gSQD0d+uI0d49MXNEf3j25PGdRC3FQmkjkpKSoFQq8cknn2DevHlix6FWeOGFF7B//36UlpbC1dVV7DiiWb9+PRYuXIj4+HiMHz9e7Dg27cqVK4bymJiYiIKCAgCAh4eHoTwqlUp4eHhYfIG8G02DDmVVGmh1erR3lGKgWycep0hkIiyUNqChoQFBQUHo3r07kpOTLeaVE7XMlStX4OXlhXnz5mH16tVixxHF6dOnMXLkSMTExGDNmjVix7E55eXlRgWypKQEAODt7W20BrJfv34iJyUia8FCaQOWL1+Od955B2q1GkOGDBE7DpnAu+++i+XLlyM/Px9eXl5ix2lTtbW1kMlkcHV1RWpqqknHytgjQRBw7tw5Q3lMTExEWVkZAMDf399QIBUKBfr06SNuWCKyWiyUVq64uBgBAQF49dVXERcXJ3YcMpH6+nr4+PggJCQE+/btEztOmxEEATNmzMAPP/wAtVqNQYMGiR3J6giCgOLiYqMCeenSJUgkEgwdOtTw9DEyMhI9evQQOy4R2QgWSit2e1fw+fPnkZeXB2dnZ7EjkQndHgF1/PhxjBo1Suw4beKzzz7DnDlzsHPnTkybNk3sOFZBr9ejoKDAUB6TkpJQUVEBqVQKmUxmKJARERF2vSaXiMyLhdKKffnll5g1axaOHDmChx56SOw4ZGJ6vR4jR45EY2MjMjIybH5tbH5+PkJDQzFz5kweQXkXTU1NyMnJMZTHpKQkVFVVwdHREaGhoYYCKZfL0aVLF7HjEpGdYKG0UteuXcPgwYPx8MMP4+uvvxY7DplJamoqIiIi8MUXX2DWrFlixzGburo6hIaGQiqVQqVSoWNHzgG8TafTITMz01Agk5OTUVNTAycnJ4SFhRnWP44cOZInYxGRaFgordSsWbMQHx+PoqIi9OzZU+w4ZEbTpk1DcnIySkpKbLYwzJkzB9u3b0dGRgb8/PzEjiMqrVaL9PR0wy7s1NRU3Lx5E87OzpDL5YYCGRYWhg4dOogdl4gIAAulVTp+/DgefPBBfPbZZ3jhhRfEjkNmdu7cOQwePBixsbFYtmyZ2HFMbseOHZgxYwa2bt2K559/Xuw4be7WrVtQqVSGNZBpaWmor6+Hi4sLwsPDDa+wQ0JCuOOdiCwWC6WVuXXrFoYOHYrevXvjp59+svl1dfSb2NhYbNiwAcXFxTZ1YkxpaSmCg4MxYcIEfP3111Y9NPteaTQapKWlGQqkSqWCVqtF165dERkZaSiQwcHBPGqSiKwGC6WVefvtt7FixQpkZ2fD19dX7DjURmpra+Hp6YmHH34YX331ldhxTKKhoQFyuRy1tbXIzMxE5862eexdbW0tUlNTDQUyIyMDOp0Obm5uRkPEAwIC4ODgIHZcIqIWYaG0IoWFhQgMDERsbCyWL18udhxqY5s3b8b8+fORnp6OkJAQseO02sKFC7Fp0yakpaVBJpOJHcdkrl+/juTkZMMmmszMTOj1evTq1ctQHpVKJXx9ffmGgYhsBgulldDr9Rg1ahSuXr2KnJwcLsa3QzqdDkFBQXB1dUVSUpJVvx6Oj4/HxIkTsWHDBixYsEDsOK1SWVlp2ECTlJSEnJwcCIKAvn37GhVILy8vq/5vRkR0NyyUVmLr1q2YPXs2fvzxRzz44INixyGRHDlyBFFRUdi7dy+mTJkidpwWKS8vR1BQEJRKJfbt22d1JevKlSuG8piYmIiCggIAgIeHh2EHtlKphIeHh9V9NiKilmKhtAK//PILBg8ejPHjx+PLL78UOw6J7NFHH8WZM2dQUFAAJycnseM0i06nw6hRo3DhwgWo1Wp0795d7Eh/qry83FAeExMTUVJSAgDw9vY2KpD9+vUTOSkRkXhYKK3AzJkzcfjwYRQVFcHd3V3sOCSygoICDB06FO+//z5ee+01seM0y5IlS7By5UokJSVBLpeLHecOgiDg3LlzRudgl5WVAQD8/f0N5VGhUKBPnz7ihiUisiAslBbu6NGjGDdunM2flELN89JLL+Hrr79GaWkpevToIXace3Ls2DGMGzcOcXFxiI2NFTsOgN8KZHFxsVGBvHTpEiQSCYYOHWpY/xgZGWk1/56JiMTAQmnB6uvrERAQgH79+iEhIYHrscigsrISXl5eiI6OxkcffSR2nD919epVBAUFITAwEIcOHRJtd7Ner0dBQYGhPCYlJaGiogJSqRQymcxQICMiIuDq6ipKRiIia8RCacGWLFmCVatWIScnBz4+PmLHIQuzatUqxMbGIicnx6KPK9Tr9YiKikJeXh6ysrLQq1evNrt3U1MTcnJyDAUyOTkZVVVVcHR0RGhoqKFAyuVydOnSpc1yERHZGhZKC5WXl4fg4GC8+eabeOutt8SOQxaooaEBfn5+8PHxwcGDB8WO84fi4uLwxhtv4OjRoxgzZoxZ76XT6ZCZmWl4+picnIyamho4OTkhLCzMUCBHjBhhs+eiExGJgYXSAun1ekRGRqK6uhpZWVlWt5OX2s63336LqVOn4vDhw4iKihI7zh1SU1OhVCoRGxuLd9991+TX12q1SE9PNxTI1NRU3Lx5E87OzpDL5YYNNGFhYZzdSkRkRiyUFmjLli2YN28eEhMToVAoxI5DFkwQBCiVSsMvH5Z09nN1dTWCgoIwYMAAHD9+3CTZbt26hZMnTxrG+KSlpaG+vh4uLi6IiIgw7MIOCQlB+/btTfApiIjoXrBQWpirV69i8ODBmDJlCrZu3Sp2HLICGRkZCA0NxaZNmzB//nyx4wD4rehOmjQJKSkpyM7ORt++fVt0HY1Gg7S0NMMaSJVKBa1Wi27duiEyMtJQIIODgy2qTBMR2RsWSgvz1FNP4dixYygqKoKbm5vYcchKPPvsszh06BBKSkrQtWtXseNg/fr1WLhwIeLj4zF+/Ph7/nO1tbVITU01FMiMjAzodDq4ubkZyqNSqURAQAAcHBzM+AmIiKg5WCgtyOHDh/HII49g27ZtmDlzpthxyIpcvHgR3t7eWLBgAVauXClqltOnT2PkyJF46aWXsHbt2rv+s9evX0dycrKhQKrVauj1evTq1cvoHGxfX1/RRg0REdGfY6G0EHV1dfD398egQYNw9OhRzpykZlu6dClWrFiBoqIieHh4iJKhtrYWMpkM3bp1Q2pq6h0byiorK42OMczNzYUgCOjbt69RgfTy8uLfASIiK8JCaSH+/ve/Y/369cjLy4Onp6fYccgKaTQaeHt7Izw8HLt3727z+wuCgOjoaHz//fdQq9UYNGgQrly5YtiBnZiYiIKCAgCAh4eHUYEcOHAgCyQRkRVjobQAOTk5kMlkWLZsGZYsWSJ2HLJiX375JWbNmoWUlBSEh4e36b23bt2K2bNn48UXX4RWq0ViYiJKSkoAAN7e3obyqFAo0K9fvzbNRkRE5sVCKbKmpiaEh4fjxo0bUKvVHHVCraLX6xEaGgoHBwecPHnSrOsOBUHA2bNnkZSUhP379+PAgQO4/e3E39/fUB4VCgX69OljthxERCQ+ztkQ2ebNm6FSqZCcnMwySa0mlUqxZs0ajBo1Cjt27EB0dLTJri0IAoqLiw3rHxMTE3Hp0iUAQIcOHeDq6ooPP/wQY8eORY8ePUx2XyIisnx8Qimiy5cvw9fXF9OnT8fmzZvFjkM25PHHH0d6ejrOnDmDjh07tugaer0eBQUFhvKYlJSEiooKSKVSyGQywyvsPXv2YO/evcjIyLDoM8WJiMh8WChF9MQTTyA5ORmFhYVwdXUVOw7ZkNLSUvj5+eGtt97CG2+8cU9/pqmpCTk5OYYCmZycjKqqKjg6OiI0NNRQIOVyObp06QIA2LlzJ5566ils3boVzz//vDk/EhERWTAWSpF8//33GD9+PHbs2IHp06eLHYds0KuvvorNmzejuLgY99133x1f1+l0yMzMNBTIlJQU1NTUwMnJCWFhYYYCOWLECHTq1OmOP19aWgqZTIbx48fj66+/5i5tIiI7xkIpgps3b8Lf3x++vr44dOgQfxCTWfz666/w9PTExIkTsXXrVmi1WqSnpxsK5IkTJ3Dz5k04OztDLpcbCuTw4cPRoUOHu167oaEBcrkctbW1yMzMROfOndvoUxERkSXiphwRLF26FJWVlfjpp59YJslsOnTogOjoaGzcuBG5ubnIy8tDfX09XFxcEBERgSVLlkChUCAkJKTZG8L+/ve/Iy8vD2lpaSyTRETEQtnW1Go11q1bh/fee0+000zINmk0Gpw4ccIwRFylUkGr1UIqleLs2bNYtmwZRo0aheDgYDg6tvyvfnx8PNavX4/169dDJpOZ8BMQEZG14ivvNtTU1IQRI0agoaEBp0+fRrt27cSORFastrYWqamphlfYGRkZ0Ol0cHd3N8x/VCqVuHDhAiZMmID9+/dj4sSJrbrnhQsXEBQUhMjISHz33Xd8wk5ERABYKNvUhg0bsHDhQqSmpmLkyJFixyErc/36dSQnJxsKpFqthl6vR69evYyOMfT19TUaaC4IAqKiolBWVoa8vLwWzzvV6XQYNWoULly4ALVaje7du5vqoxERkZVjoWwjFy9ehK+vL55++ml8/PHHYschK1BZWWl4fZ2YmIjc3FwIgoC+ffsaFUgvL68/fVKYm5uLoKAgrF69GgsXLjT6mqZBh7IqDbQ6Pdo7SjHQrRM6Od35SnzJkiVYuXIlkpKSIJfLTflRiYjIyrFQtpHJkyfj5MmTKCoqQteuXcWOQxboypUrRkPECwoKAAAeHh5GBXLgwIEtetU8b9487NmzB6WlpahqbIftqnIcP/MLyqvr8J/fBCQA+nfviNE+PREd1h9evTrj2LFjGDduHN577z384x//MM0HJiIim8FC2Qb279+PyZMnY/fu3XjiiSfEjkMWory83KhAlpSUAAC8vb0N5VGhUKBfv34muV9FRQV8ZHJ4Rb+FSgd3OEglaNL/8V//218f3r8zkle/iIAH7sPhw4fNej44ERFZJxZKM7tx4wb8/PwQGBiIAwcOcBODnRIEAWfPnjV6hV1WVgYA8Pf3N5RHhUKBPn36mCXDzvRyLNmXDZ1egETq0IzweghNOix52AtzxwwxSzYiIrJuHBtkZm+++Saqq6vx4YcfskzaEUEQcObMGaMCeenSJUgkEgQGBmLChAlQKpWIjIxEjx49zJ7nw+MlWHWkGIAUkuY+YJRIIXFsj7hj56GVOiFmtJc5IhIRkRVjoTSjjIwMbNy4Ef/85z8xcOBAseOQGen1euTn5xsKZFJSEioqKuDg4ACZTIbp06dDqVQiIiKizc9t35le/r9lsvVWHSlGDxcnTAvtb5LrERGRbeArbzPR6XQYPnw4BEFAenp6qwZJk+VpampCTk6O4eljcnIyqqqq4OjoiNDQUMMayPDwcFFPkrlQXYexaxPRoNOb7JpOjlIcW6REv+4dTXZNIiKybmw5ZrJhwwZkZWVBpVKxTNoAnU6HzMxMQ4FMSUlBTU0NnJycEBYWhhdffBFKpRIjR45Ex46WU7QWf5cL3V023rSETi9g8Xe52PZCmEmvS0RE1otPKM3g/Pnz8PPzwwsvvIANGzaIHYdaQKvVIj093VAgT5w4gZs3b8LZ2RlyudzwBHL48OHo0KGD2HF/V0nFDTy0Lsls1z+2SAHPnjzHm4iIWChNThAETJgwAWq1GgUFBejSpYvYkege1NfXQ6VSGdY/pqWlob6+Hi4uLoiIiDDswg4JCWnxSTNtbWl8Prapzt91NFBLOUgleDpsAJZO8Df5tYmIyPrwXayJ7du3D99//z327dvHMmnBNBoNTpw4YdhEo1KpoNVq0a1bN0RGRuKdd96BQqFAcHCw1S5ZOH7mF7OUSQBo0gs4XvwLloKFkoiI+ITSpGpqauDr64vQ0FDs37+fY4IsSG1tLVJTUw2vsDMyMqDT6eDu7m6Y/6hUKhEQEAAHh2bMaLRQNxt0CFj6b5jzL7cEQN7SqN89ppGIiOwLfxKY0JIlS1BbW8uZkxaguroaKSkphgKpVquh1+vRq1cvKJVKPP3001AqlfD19bXJk1/OV2nMWiYBQABQVqWB/308SpSIyN6xUJqISqXCxx9/jDVr1pjsqDy6d5WVlUZDxHNzcyEIAvr27QulUol58+ZBqVTCy8vLLsq+1oRjgizhPkREZNlYKE2gsbERc+fOhUwmw4IFC8SOYxeuXLlidA52QUEBAMDDwwNKpRKLFi2CUqnEwIED7aJA/rf2jm3z1LWt7kNERJaNhdIE1q1bh7y8PKSnp9vE+jtLVF5eblQgS0pKAADe3t5QKpVYvHgxFAoFnw7/r4FunSABzL6GcqBbJzPegYiIrAULZSudO3cOb7/9Nl5++WXIZDKx49gEQRBw9uxZowJZVlYGAPD398dDDz2Ed999F5GRkejTp4+4YS1UJydH9O/eEeer68x2j/5uHbkhh4iIALBQtoogCHjxxRfh7u6O5cuXix3HagmCgDNnzhjKY2JiIi5dugSJRILAwEBMnDgRCoUCkZGR6NGjh9hxrcZon55mnUM52runya9LRETWiYWyFXbv3o3Dhw8jPj4eLi4uYsexGnq9Hvn5+YbymJSUhIqKCjg4OEAmk2H69OlQKpWIiIiAq6ur2HGtVnRYf/y/tDKzXLtJL2DmiP5muTYREVkfzqFsoV9//RWDBw9GeHg4vv32W7HjWLSmpibk5OQYXmEnJyejqqoKjo6OCA0NNRxjGB4ejs6deZSfKT29VYUTZ6tM+pTSQSqB/AE3nuVNREQGLJQtNH/+fHzzzTcoLCzE/fffL3Yci9LY2Ai1Wm0okCkpKaipqYGTkxPCwsIMBXLkyJHo2LGj2HFt2oXqOoxdm4gGE473cXKU4tgiJfp15387IiL6DQtlC5w4cQLh4eHYuHEjYmJixI4jOq1Wi/T0dEOBTE1NhUajgbOzM+RyuaFADh8+HB06dBA7rt3ZmV6O2H25JrveyscDMC2Ur7uJiOj/sFA2U2NjI2QyGTp27IgTJ07Y5Zig+vp6qFQqw/rHtLQ01NfXw8XFBREREYYCOWzYMLRv317suATgw+MlWHWkuNXX+ds4H7w02tMEiYiIyJZwU04zrVq1CoWFhcjIyLCbMqnRaHDixAlDgVSpVNBqtejWrRsiIyPxzjvvQKFQIDg4GI6O/F/KEsWM9oK7ixPejs+HTi80a02lg1QCR6kEyyf488kkERH9Lj6hbIaff/4ZQ4YMQUxMDD744AOx45hNbW0tUlJSDLuwMzIyoNPp4O7uDoVCAaVSCYVCgYCAALsp1bbiQnUdFn+Xi+TSa3CQSu5aLG9/PdLTHXGTA7hmkoiI/hAL5T0SBAFRUVEoLi5Gfn4+OnWynRNCqqurkZKSYlgDqVarodfr0bt3b0N5VCqV8PX1hVTKo/ZsQUnFDWxXleN48S8or6ozOlFHgt+Glo/27omZI/rDsyd33hMR0d2xUN6jb775BtHR0fjhhx/w6KOPih2nVX755RckJycbCmRubi4EQUDfvn0N6x+VSiW8vLzs8hxse6Np0KGsSgOtTo/2jlIMdOvEE3CIiKhZWCjvQXV1NQYPHozRo0dj165dYsdptitXrhjKY2JiIgoLCwEAHh4eRgVy4MCBLJBERETUbCyU92DOnDnYs2cPCgsLreLs6PLycqMCWVpaCgDw9vY2lEeFQoF+/fqJnJSIiIhsgd0Xyj973ZecnAyFQoFNmzZh/vz5Iib9fYIg4OzZs4bymJSUhLKyMgCAv7+/UYHs3bu3uGGJiIjIJtlloTRsSDjzC8qrf2dDQveOGO3TE08E98bUcb+dJ52SkmIRG1IEQcCZM2cM5TExMRGXLl2CRCJBYGCgoUBGRkbC3d1d7LhERERkB+yqULZkZMqtMjW2/c9f8NDI4DZM+n/0ej3y8/MNBTIpKQkVFRVwcHCATCYzPH2MiPit+BIRERG1NbsplDvTy1s01FkCPdo7OmLZBH9Mb4Ohzk1NTcjOzjY8fUxOTkZVVRXatWuH0NBQwwif8PBwdO7McS5EREQkPrsolKY6du61cd6IGe1lgkT/p7GxEWq12rAGMiUlBTU1NXByckJYWJjhFfbIkSPRsSMHSxMREZHlsflCuTO9HLH7ck12vZWPB7Tq+DmtVov09HRDgUxNTYVGo4GzszPkcrmhQA4fPhwdOnQwWW4iIiIic7HpQnmhug5j1yaiQac32TWdHKU4tkh5z8fQ1dfXQ6VSGQpkWloabt26BRcXF0RERBgK5LBhw9C+fXuT5SQiIiJqKzZdKJ/eqsKJs1XNWjP5ZxykEsgfcMO2F8J+9+sajQYnTpwwFMhTp05Bq9WiW7duiIyMNBTIoKAgODryNBIiIiKyfjbbaEoqbiC59JrJr9ukF5Bceg2lv9yAZ8/OqK2tRUpKimETTUZGBnQ6Hdzd3aFQKPDBBx9AoVAgICAADg4OJs9DREREJDabfUK5ND4f21TnTfp08jYpBHg0XURNwmdQq9XQ6/Xo3bu3YYSPUqmEr6+vRcytJCIiIjI3m31CefzML2YpkwCghwSlGicofH0xb948KJVKeHl58RxsIiIisks2WShvNuhQXl1n1ntIu/TEJ2u+MDqmkYiIiMge2eQ72fNVGpj7Pb4AoKxKY+a7EBEREVk+myyUWhOOCbKE+xARERFZMpsslO0d2+ZjtdV9iIiIiCyZTTaigW6dYO7tMZL/vQ8RERGRvbPJQtnJyRH97/Ekm5bq79aRG3KIiIiIYKOFEgBG+/SEg9Q8zykdpBKM9u5plmsTERERWRubLZTRYf3NNoeySS9g5oj+Zrk2ERERkbWx2ULp1aszIj3dTf6U0kEqQaSnOzx7djbpdYmIiIislc0WSgCImxwARxMXSkepBHGTA0x6TSIiIiJrZtOFsl/3jlg2wd+k11w+wR/9zLzhh4iIiMia2HShBIDpof3x2jhvk1zrb+N8MC2UayeJiIiI/pNEEARzn1JoEXaml+Pt+Hzo9EKzNus4SCVwlEqwfII/yyQRERHR77CbQgkAF6rrsPi7XCSXXoODVHLXYnn765Ge7oibHMDX3ERERER/wK4K5W0lFTewXVWO48W/oLyqDv/5L0CC34aWj/buiZkj+nM3NxEREdGfsMtC+Z80DTqUVWmg1enR3lGKgW6deAIOERERUTPYfaEkIiIiotax+V3eRERERGReLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQqLJRERERE1CoslERERETUKiyURERERNQq/x/6+tCJfDntYQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# setup Erdos Renyi graph\n",
    "n = 10  # number of nodes/vertices\n",
    "m = 20  # number of edges\n",
    "\n",
    "# define graph object\n",
    "G = nx.gnm_random_graph(n, m, seed=seed)\n",
    "# positions for all nodes\n",
    "pos = nx.spring_layout(G)\n",
    "\n",
    "# choose random weights\n",
    "for (u, v) in G.edges():\n",
    "    G.edges[u,v]['weight'] = random.uniform(0, 1)\n",
    "\n",
    "# draw graph\n",
    "nx.draw(G, pos)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set Ising matrix \n",
    "Jfull = nx.to_numpy_array(G)\n",
    "\n",
    "# get off-diagonal upper triangular matrix\n",
    "J = np.triu(Jfull, k=1).astype(np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IiIiIyGhxpZCIiIioCGNdKeSkkIiIiKgIfs2dwK1btxPLl29BcnI6fH29MGnSF/Dz89F1WSr6tvTCoDa14WJrgSsPMzHl9/M4fy+9xP6VLM0wukM9hPlXgZ2VGR6l5+K7Tedx6HJisb6D3/PBNx3rY+XBm/hu84XyjKExQxgbTRhCnv1bjmLXrweRmZaN6rWq4JOvOqNmvRpq+x76Ix7H9pzEg9sJAADPOlXR7fN2yv6FhTJsWRqL88evIOlRGqysLVCvqQ+6D24PB2e7CstUWvo2PuvX7cbKFX8iJSUDdXxrYPyET+Hn511i/z274/Hj/I14+DAZNWq4I+Lrj9GyVWMAQEFBIeb/sAFH/jqDBw+SYGNjheDghhj1dR+4ujoqj/Fem2F49ChZ5bhfRfTBoEGdyiVjaenb2Kjzz59HcGzzATxJz4KblwfaDemKqnXU/9k5ufsYzsX9i6R7jwEAVbyroU3/D1X6S3Ol2L/yT1yNP4+n2U/h4OaIoI9a4q32b1dIntIyhLGhN2cUU+HY2COIiVmGYcN6Y+vWefD19cLAgZORmpqh69KU2jf2wPjODTF/11V0mH4QVx5mYvWwEDjZmKvtb2YiwprhzVHV0QrDlv+D0O/2I3L9aSRk5hbr61fdHr2be+LKg8zyjqExQxgbTRhCnn/izmDDgu3oNCAM0csiUM27CmZ9/TOy0rPV9r969haCQhtj7PyhmLhkJBxd7THz65+QnpwBAMjPy8e96w/xUf+2iF4egeHfD0DC/ST8MG55BaYqHX0bn12xxzBj+i8YOqwbft88HXXq1MAXg75Haqr6P6tnzlzDmNE/oEvX1ti0ZTpat3kLI0bMxI3r9wEAeXn5uHL5DgYP6YrfN0/HD/O/xp27jzB86Ixixxo+ogcO/fWzcvv44/fLNevr6NvYqHPx8GnsWboV7/QJwxc/joF7zSpYM2kxnmSo/7Nz9/xNNGzVGANihuOz2aNg62yPNRMXIyslQ9lnz9KtuHnqCrqM6YvhP0WiWad3ELt4M64e159/vBvC2GibSCTW+mYIDKPKN7Ry5Tb06BGGrl1D4e1dHdHRQ2FhIcHmzft0XZrSwNbe2HjsLjYdv4+bCdmYuOEscvNl6B7sqbZ/9+AasLMywxc/H8ep22l4mPYUJ26m4urDLJV+VuYmmDvgLYz/9Qwyc/MrIIlmDGFsNGEIefZsPIxWHZqhRftAeHi5o//objC3MMNfO0+o7T948ido07k5atT2QJUabvh0bE8o5ApcPnUDAGBlY4kxcwcjsHUAKld3hXd9T3wyqgvuXnuA1MSSV7p1Qd/GZ/XqHejWvQ06d3kX3t5VETVlECwszLFly0G1/df+Eou33w7ApwM/Qq1aVTHyy16oV7cm1q/fDQCoVMkKy1ZMwvsfhMDLqwr8A3wwYeKnuHTpNh49SlE5lrW1JVxc7JWblZVFued9FX0bG3WObT2EJu+HoFHbZnCt7o4Ph/eAmcQcZ/YeV9u/2zf9EPhhC1SuVRUu1dzQ8cveUMjluH3uurLPf1fuwL9NILz8asPBzQlNPwiBW80qeHjtfkXFei1DGBvSDo0nhSkpKZgxYwY6d+6M4OBgBAcHo3Pnzpg5cyaSk5Nff4AKlp9fgEuXbiIkxF/ZJhaLERISgDNnrumwshfMTERoUM0ef1978fNTKIC/ryWjkZej2n1CG1bGmTtpiO7pjxNTP8Cu8W0wtK0PxC+9hD26ZwAOXkxQOba+MISx0YQh5CksKMTd6w9Qr8mLyz5isRj1m/rg1qW7pTqGVJoPWaEM1pWsSuyTm5MHkUgEKxvLNy1Za/RtfPLzC3H50m0EBzdUqadZcEOcO3td7T5nz11HsyL9AaD52/44e/ZGied5kv0UIpEItraq47Vs2TaENPsUXbt8gxXL/0BhoewN0rwZfRsbdQoLCvH45n+oGaD6Z6dmgA/+u3q3VMcokOZDJpPD0ubFWFSr64Vr/1xAVkoGFAoF7py7gdSHyajVuI62I5SJIYxNeTDWlUKN7in8999/ERYWBisrK4SGhsLH59kfjsTERMyfPx/Tpk3Dnj170LRp03IptizS07Mgk8nh5OSg0u7kZI/btx/oqCpVDjYSmJqIkZItVWlPycpDLTcbtftUc7JGsI8Ltv/7Hz5dHI8aLtb4tmcATE3EmL/rKgDgwyYeaFDNDh1nHCrvCGViCGOjCUPIk52ZA7lMDjvHSirttg6V8PheUqmO8fviHbB3tkO9purvJ8qXFuC3xTsQFNoIlta6XX0qSt/GJyPjeT32xeq5c+eR2n1SUjLg9NJ9mk5OdkgtcjmyKKk0H3Nmr0O79s1hU2Qi8nHfD1Cvnhfs7Gxw9sw1zJv7K5KT0zF2XP83ylRW+jY26jzNyoFcLoeNg+qfHRv7Skj5r3R/dvat/AOVHG1Rs9GLCV+7Id3wx/wNmN0vCmITMUQiET76shc8G5Z8X2lFMoSxKQ+GMonTNo0mhSNGjED37t2xZMmSYt8LqFAoMHjwYIwYMQLx8fGvPI5UKoVUqjoBkkgkkEg0qca4icUipGZLMf7XM5ArgIv/ZcDd3hKD2tTG/F1XUdneEpO7+qHfgr+RXyjXdbkkEDvWxuGfuDMYN38YzCVmxT4vLJRhUdQvgEKB/l9300GF9FxBQSEiRs2FQgFMjvpM5bMBAz5U/u86dWrAzMwU0VOWYlREH5ibFx9XenNHftuHi4fPYMD04TAr8jP+54+/8ODqPfSJGgQ7Vwfcu3gLOxdtQiVHO9RqpB+rhWQ8NJoUnjt3DqtWrVL7RdEikQijRo1Co0aNXnucmJgYREdHq7RFRUVhypQ+mpRTKg4OtjAxESM1VfXeptTUDDg7O5SwV8VKfyJFoUwO50qqs2JnWwskZ0nV7pOUmYdCmRxyxYu2mwnZcLWzeHY5uro9nG0t8MfYd5Wfm5qIEVjLGX1b1oTvV9tV9tUFQxgbTRhCnkp21hCbiJGZpnpjfFZ6NuycKpWw1zO7fj2Inevi8M3cIajmXaXY54WFMiyavBqpCWkY+8NQvVolBPRvfOztn9eToaYee7X7ODvbIzUl86X+mXB6qX9BQSG+HjUXjx6lYOXKySqrhOr4+dVGYaEMDx8mw8ur+NiWN30bG3WsbK0hFovx5KUHsp5kZMPG8dV/dv7efABHf49Dv++Hwt3LQ9leIM1H3Ood6DVxIHwC6wMA3L08kHDrIY5tOaAXk0JDGJvyIELxeY4x0Gh91N3dHSdOqL8ZHQBOnDgBNze31x4nMjISmZmZKltkZKQmpZSaubkZ6tf3Rnz8eWWbXC5HfPw5NNKDP3AAUCBT4OJ/GQip46JsE4mAEB8XnLmTpnafU7dTUcPFGkXn516uNkjMzEWBTIFj15Lx/vf78eG0A8rt/L10bD/5Hz6cdkDnE0LAMMZGE4aQx9TMFJ4+VZUPiQDParx86gZq1fcscb/YdQfwx+p9+HrW5/DyrVbs8+cTwsQHKRgzdwhs7KzLo/w3om/jY25uinr1a+L48Ysq9fxz/CL8A9Rfmg/w98Hxl55KjT92HgEBtZW/fj4hvHcvActXTIK9w6snLABw9epdiMUiODraljHNm9G3sVHH1MwUlb2rqTwkIpfLcefsdVTz9Sxxv6O/x+Hwr3vwyXeD4eFTXeUzmUwOWaGs2EKLyEQMhT78JQ3DGBvSHo1WCkePHo3PP/8cp06dQps2bZQTwMTERMTFxWHp0qWYNWvWa4/z7FJxxV0rDg/vhLFj56JBA2/4+flg9ertyM3NQ5cuoRVWw+ssP3ATs/o2wYX7GTh3Nx3h79aClcQEm47fAwDM6tsEiZm5mPnHZQDAuiN30LdlTUzu5odfDt+Gp4s1hrb1warDtwAAOdJCXH+s+i/ap/mFyMjJL9auS4YwNpowhDxhPVth6dRf4eVbDTXrVsfe3w9DmpuPFu0CAQA//289HJxt0X3ws0uMO9fFYevy3fhi8idwdndERuqzJ9wtLCWwsJKgsFCGhZNW4d71h/hq+kDI5XJlHxtbK5ia6c/rUPVtfPr3/xDjIxeifoOaaNjQG2t+iUVurhSdO78DAIgcuwCubo4YFfHsKson/dphQL8pWLXyT7Rs1Ri7Yv/GxUu3MCX6cwDPJoSjvpqDK5fvYOHisZDJ5Ej+/1cH2dnZwNzcFGfPXMf58zcQGFQf1taWOHf2OqZPW40PO7SAnZ36e5grgr6NjTohnd/B1jnr4FG7Ojx8qiN++2HkS/PR6L0gAMCWWWtRyckO74V3AAAc+X0/Dq6JRbdv+sHe1RHZac/+XJhbSiCxlMDCygKeDb2xd8V2mErMYO/qiLsXbuJc3L8I0/E7I4syhLHRNt5TWArDhg2Ds7Mz5s6di0WLFkEme/a0momJCZo0aYJVq1ahR48e5VLom2jXrgXS0jIxf/46JCeno27dmli2LFqvlr53nn4IRxsJRrWvC+dKElx5mIkBC48pHz6p4mgJueLFvxwfZ+RiwKJjmNilIWIjWyMhIxerDt3Ckn3qn1rUV4YwNpowhDxBbRohO+MJti7fjcy0LFT39sDXsz5XPnySmpiusnJxYNsxFBbIsHDSapXjdAxvi86fvo/05EycOXoJADA5fLZKn7Hzh6JuI/24YR7Qv/H5oF0I0tKzsGD+b0hJyYBvXU/89PN45eXjx49TICrySoFGjepgxsyRmP/DBsyb+ytq1KiMH38cg9r/vwKVlJSGgwdOAgC6dv5G5VwrV0chMLA+zM1NsSv2GBYt/B35+QXwqOqKfv3bo3+R+wx1Qd/GRp0GrRojJ+sJDqyJxZP0LLjXrIq+3w6GjcOzFdbM5HSV8Tq582/ICmXYOHWlynHe6fM+3v3kAwBAt7H9sX/Vn9g8cw1ys5/C3tUBbfq1x1vtmldcsNcwhLHRNmOdFIoUCkWZ1qgLCgqQkvLsvVfOzs4wM9PGzcmGNaEpmQ9qDt+q6yK05vaCzhDO2ACAD4SWJz5pp66L0Ipg1/YQ2tgUys/pugitMRX7Qzjj44MNt3brugit6VXrfQhnbIBnf0/rjlvdMVo/ZuKVmVo/praV+bqOmZkZKleurM1aiIiIiHTOWFcK9edmHyIiIiK9YJyTQuNMTUREREQquFJIREREVISxXj42ztREREREpIIrhURERERFGOtKISeFREREREWIjPRCqnGmJiIiIiIVXCkkIiIiKsJYLx8bZ2oiIiIiUsGVQiIiIqIiin7/uzHhpJCIiIioCF4+JiIiIiKjxUkhERERUREiiLW+lcXChQvh6ekJCwsLBAUF4cSJE6/sP2/ePNSpUweWlpaoVq0aRo0ahby8vFKfj5NCIiIiIj2zceNGREREICoqCqdPn4a/vz/CwsKQlJSktv/69esxbtw4REVF4cqVK1i+fDk2btyI8ePHl/qcnBQSERERFSESibW+aWrOnDkYNGgQwsPDUa9ePSxZsgRWVlZYsWKF2v7Hjh1D8+bN0adPH3h6eqJt27bo3bv3a1cXi9KzB018dF2A1txe0FnXJWiZcMbmGWHlCXZtr+sStEhYY2Mq9td1CVomnPHpVet9XZegZcIZG10rjwdNpFIppFKpSptEIoFEIinWNz8/H6dOnUJkZKSyTSwWIzQ0FPHx8WqPHxISgrVr1+LEiRMIDAzE7du3ERsbi759+5a6Rj2bFF7XdQFa4gPhZAGEmKfj/iO6LkJrtoe2gHDGxweW1Xvrugityb3/K7IK9uu6DK2xNQuFkH6v1X5vua6L0Job+wai1se/6roMrbm1Tjh/DzwXExOD6OholbaoqChMmTKlWN+UlBTIZDK4ubmptLu5ueHq1atqj9+nTx+kpKTg7bffhkKhQGFhIQYPHszLx0RERERlVR4PmkRGRiIzM1NlK7oS+KYOHTqEqVOnYtGiRTh9+jS2bNmCnTt34rvvviv1MfRspZCIiIhIeEq6VKyOs7MzTExMkJiYqNKemJgId3d3tftMmjQJffv2xWeffQYAaNiwIXJycvD5559jwoQJEItfvw7IlUIiIiKiokRi7W8aMDc3R5MmTRAXF6dsk8vliIuLQ3BwsNp9nj59WmziZ2JiAgBQKBSlOi9XComIiIiK0IdvNImIiED//v3RtGlTBAYGYt68ecjJyUF4eDgAoF+/fvDw8EBMTAwAoEOHDpgzZw4aNWqEoKAg3Lx5E5MmTUKHDh2Uk8PX4aSQiIiISM/07NkTycnJmDx5MhISEhAQEIDdu3crHz65f/++ysrgxIkTIRKJMHHiRDx8+BAuLi7o0KEDvv/++1Kfk5NCIiIioiJEIpGuSwAADB8+HMOHD1f72aFDh1R+bWpqiqioKERFRZX5fLpfHyUiIiIineNKIREREVERZf2uYkPHSSERERFREfrwoIkuGGdqIiIiIlLBlUIiIiKiovTkQZOKxpVCIiIiIuJKIREREZEKI10yM5pJ4bp1O7F8+RYkJ6fD19cLkyZ9AT8/H12XVWZCymMIWdIPH0Dq/j2QZWVC4lENbj16w9Kz5mv3yzp5Ao9W/gwbvwBU/eLZu6YUskIk/7kNOZcuID8lGSaWlrCqUw8uHbvCzN6+nJNozhDG54t+72HUFx3g5mKHC1fuI2LyKpw8d6vE/sMHfoBBn4SimoczUtOysTX2H0yavgFSaQEAwMbaAlGje+CjsKZwcbbDuYt3MXrKapw6f1vrtf/262GsXbkfqSlZqF3HA2PG90D9hp4l9t+/5zSWLNiBxw9TUa2GK0aM6ojmLRsoP3/6NA8L5m7H4QPnkZmRgyoeTuj58Tvo2rMFAODRw1R0DJus9tgxswciNKyxVvNpwhB+r338UV181r0hXBwtcfVWGr5dGI/z11LU9l07qx2C/CsXaz/0z38YNHFvsfZvvwxB7w/r4vtFx7Fq6yWt1/6yT96rjUHtfeFiZ4kr99MRvfoUzt9OK7F/JSszfN3DD2FNq8HOxhyPUnLwvzWncejcYwCAWCTCl10boGNzT7jYWyAxPRdb/rqDBdvKP4vW8fKxcMXGHkFMzDIMG9YbW7fOg6+vFwYOnIzU1Axdl1YmQspjCFmyTp1A0pbf4NyuAzzHTYakajX8t2AeCrOzXrlffmoKkrb+DstatVXa5fn5yPvvHpze/xCe4ybDY9BQ5Ccm4OFPP5ZnjDIxhPHp1qEZpk/qi+/nbUZw+/E4f+Ue/lg7Di5Otmr79+wYgu/G9sLUeZsR0PprDB7zE7p1CMa33/RU9lk843O0btEQn361CE3f+wb7j5zHzvUTUMXNQau17911CvNmbMFnQ9phze/jULtOVYz4YgHSUrPV9j935jYmfrMSHTsHY+3vkWjV2g+jR/6MmzceKfvMnbEF8Ucv49uY/vjtj0no1fddzJz6Gw4fPA8AcHN3wK5DU1W2z4e1h5WVBCEt6mk1nyYM4fdau1ZeGP9FEBasPYNOQ7bjyu00rIh5H472Fmr7D4vej+Ae65XbB59tRqFMjl1/3SnW973mNRBQ1xUJKTnlHQMA0L5ZdYz/uBHmb7mIjybuxtX7GVg17l042UrU9jczEeOXce+iqrM1hs8/ivdG78T4ZSeQkJ6r7PNFh7roE1obU1afQtsxsZix4RwGfVgX/cP0a2JPJTOKSeHKldvQo0cYunYNhbd3dURHD4WFhQSbN+/TdWllIqQ8hpAlLW4f7EJawD74bUgqV4F7r08gNjdHZvzREvdRyOV4vGopnNt/BDNnF5XPTCytUH3E17Bt8hYkbu6w9KoFt559kHf/HgrSUss7jkYMYXxGftYeK389gDW/H8bVGw8xInI5cnPz0b/nO2r7N2vig/hT17Fx+zHcf5CCuCMX8Nv2Y2gaUAsAYCExQ6cPAjFh6nr8feIqbt9LxPdzN+PWvQQM6vueVmtf/0scOnULwUedg1GzVmVETu4FCwtz/LE1Xm3/DWsPIrh5PfT99D141XLHkBEd4FuvGn5ff1jZ5/zZ22jfsRmaBPqgiocTunR/G7XreODyhXsAABMTMZyd7VS2Q3HnEBrWGFZW6ic3FcEQfq992rUBNu66hs17buDm/QxM/uFv5EoL0a2ESU9mdj5S0nOV29uNPZCXV1hsUujmZIXJw4IREXMIhYXyioiCTz+og40Hb2HzX3dw82EWJq7491mWVuqvgHR7pybsbMwxeO4RnLqegocpOThxNRlX72co+zT2ccb+Uw9w6OwjPEzJwe4T/+HohQT41XSqkExaJRJpfzMAgp8U5ucX4NKlmwgJ8Ve2icVihIQE4MyZazqsrGyElMcQsigKC5H33z1Y+75YQRGJxbDyrYvc2yVfSkyJ/RMmlWxhH9KiVOeR5+YCIhHEllZvXLO2GML4mJmZoFFDLxw4elHZplAocODoRQQ2rq12n+OnrqNRAy809X82CfSs7oqwdwOw+8BZAICpqQlMTU2QJ81X2S8vLx8hb9XRWu0FBYW4evk/BDbzVbaJxWIENvPFhXPqf29dOHcHbwWr1tAspC4unHsxyfALqIm/Dp5HUmIGFAoFTp64jvt3kxAU4vvy4QAAVy7dx/WrD/BRlxAtpCobg/i9ZipGfR9nHDv9YlVWoQCOnX6ERvVcS3WMbh/4YMeh28jNK1S2iUTAzLGtsOz3C7h5L0PbZatlZiJGAy9HHLuYoGxTKIBjFxPRqLaz2n1CG3vgzI1URA9oin8WdcauaR9gyEf1IC4y2Tl9PQUh9d3g6V4JAOBb3R5N67jg8LlHao9J+kfr9xT+999/iIqKwooVK7R96DJJT8+CTCaHk5PqZR8nJ3vcvv1AR1WVnZDyGEKWwidPALkcppVUL0WaVrLF04QEtfs8vXkDmfFH4Rmp/r6tl8kLCpC0bRNsmwTCxNLyjWvWFkMYH2dHW5iamiApJVOlPSklE3VqVVG7z8btx+DkWAlxm6dAJALMzEzx85p9mLlwOwDgSU4ejp+8jsiRXXDt5iMkJmegR8fmCGrsg1t31Y95WWSkP4FMJoejUyWVdkenSrh7R/15UlOy4PTSZXFHZ1ukpry4lWHM+O6YOuVXtG8zASamYohFYkyY0geNm6qfJG/fcgxeNd3h3+j198iWF0P4veZgZwFTEzFSilwuBYDU9FzUqmb32v396jijjpcjxs8+otL+eU8/yOQKrK6Aewifc6gkeZYlM0+lPSUrDzWrVFK7TzVXGwTXs8b2Y3cxcMYh1HCvhOgBTWFqKsaPW579o2zJn5dhY2mGfTPbQyZXwEQswuzfz+OPY/fKPZPWCX7JTD2tTwrT0tKwevXqV04KpVIppFKpSptEIoFE/a0MRAZDlpeHx78sh3uffjC1Uf+Xa1EKWSEeLV8CAHDr9Ul5l0cAWjSrizHDOuHLiSvw75mbqOXphllT+uPxyM6YNn8rAODTUQvx08zBuP3vIhQWynD24h38tv0YGjX00nH1r7dx3WFcOH8HsxcMRuXKjjhz6gZmfL8Rzq52CApWXS3My8vHntiTGPjF+zqq1nh0f78Ort5OU3kopX5tJ/TvXB+dhm7XYWWlIxYBqVl5mLDsX8gVCly8mw43B0sMal9XOSlsH1QdHZvXwKiFx3D9YSbq1XDAxE8aIyk9F1uOFL+PUp8pDORyr7ZpPCn8448/Xvn57VdcUnsuJiYG0dHRKm1RUVGYMqWPpuW8loODLUxMxEhNTVdpT03NgLOzdm8arwhCymMIWUxtbACxuNhDJYXZWTC1Lb46UJCchILUFDxYUuShEYUCAHB1xOeoOfl/MHd5dqlJISvEw+U/oSAtFdVHjtarVULAMMYnJS0LhYUyuDqrjoWrsx0SkjPU7hM1ugd+3XIEqzYcBABcuvYfrKwssHDaZ5j+4zYoFArcuZeEtj2+hZWlBLaVLJGQlIE1C0fizv0krdVu72ADExNxsYdK0lKz4eSs/iEZJ2dbpKaq/l5MS8lS9s/Ly8eiH/7AzB8+x9utnj2RXLuOB65ffYi1q/YXmxQe2HsGebn5aP9RkLZilYkh/F5Lz8xDoUwOZwfVP6dODpZIfmn18GWWFqZo/25N/LD6tEr7Ww3c4WRvicPrXjzkZGoixrgvAtG/S3282/c37QUoIj1b+iyLneo9pM62Fkh+afXwuaSMZ/nl///3GQDcepQFVwdLmJmIUSCTY1yfACz58wp2HL8PALj+XyY8nK0x+KN6BjcpNFYaTwo7deoEkUgERZHfGC8TvWaGHRkZiYiICJU2iUQCQPtLzObmZqhf3xvx8ecRGhoMAJDL5YiPP4dPPmmv9fOVNyHlMYQsIlNTWFSrgZxrV1DJvxGAZw+RPL12FQ6t3i3W39y9MrwmqP6DJ/nPrZDn5cGte2+YOTg+O8b/TwjzkxJR/csxMLGxKf8wGjKE8SkokOHMhTt4t3kD/Ln3JIBnf/+827w+lqwu/soPALC0NFf5DxsAyGXy/99XOYcHADzNleJprhT2dtYIbemHCTHrtVa7mZkpfOtVw7//XMM7bZ7dSyeXy/HvP9fQvXcrtfs09PfCv8evoU/f1sq2f+KvoqH/sxXMwkIZCgtlEIlV/w4Wm4igkBf/O3v7lni0fLchHBxfv6pdngzi91qhHJeupyC4UWXs///LoSIRENKoCtZsv/zKfT9o6QVzMzG277+p0r5t/038fUb1frsVMWHYvv8mNu+5od0ARRTI5Lh4Jw0h9d2x79RDAM+yBDdww5q919Xuc+p6Mj4KqaHyZ8TLvRIS05+i4P///FiYm0L+0u8zmVwBsSEuuhlizVqg8aSwcuXKWLRoETp27Kj287Nnz6JJkyavPMazS8UVd604PLwTxo6diwYNvOHn54PVq7cjNzcPXbqEVlgN2iSkPIaQxbHNe3j8ywpYVq8BC08vpB/YD7lUCrtmzQEAj1Yvh6m9PVw7doXYzAySKh4q+z9/eOR5u0JWiIdLlyDvv3uoOmQkIJejMPPZPXEm1tYQmerP60MNYXzmL9uJpbOH4NSF2zh59iaGD/wAVlYS/PLbsydyl80dgkcJ6Zg8fQMAIHb/aYz8rB3OXbyLE2dvopanOyaP7o7Y/aeV/0ELbekHkUiE67cfoZanO6aO74Prtx4pj6ktffq1QfSEX1C3fnXUb+CJX9ceQG6uFB06NQMAREWuhourPYaPevb3ba9P3sUX4XOxdtV+vN2yAfbuOoUrl+5j/P9fZbGxsUTjprUxf/ZWWEjM4F7FEadP3kDsHyfw1ZguKuf+734Szpy6iXmLh2g1U1kZwu+1FZsvYsY3LXHxegrOX0vGgM4NYGlhis17nk2kZnzTEokpTzF7xUmV/bq974N9f99HRrbqbVMZ2dJibYWFcqSk5eLOA9X7ZLWeZdc1zPyiGS7cScO5W6kIf78OrCSm2HT42YrerMHNkJCei1kbzwEA1u+/ib5tfTC5bxOs3nsdnu6VMKRjfaze8+JBoANnHmJop/p4lPoUNx5kor6nAz79oA42Hdb++z2pfGj8X58mTZrg1KlTJU4KX7eKqAvt2rVAWlom5s9fh+TkdNStWxPLlkXrzWUJTQkpjyFksW0SCFn2EyTv2A5ZdhYkHtVQbdhXysvHBempGr1uoCAjA08unAUA3I1RXVWs9uVoWPuof0pUFwxhfDb9eRzOjraYHNENbi72OH/5Hjr2naZ8+KRaFWeV1Ytp87dCoQCixvRAFXdHpKRmYef+05gyc6Oyj52tFb4d2wse7o5Iy3yC7bEnEDVzIwoLZVqtve0HTZCRno2fFuxAako2fHw9MH/JMOXl4ITH6Sqrfv6NauJ/08Ox+Mc/seiHP1Gthgtmzf8c3rVfPFTz/axwLJz3ByaNW4WszKdwr+KIISM7KF9e/dwfW+Lh6maPZiF1tZqprAzh91rs4TtwtLfAl/2bwMXBEldupWLg+D1IzXh2ybWKq02x//55VbXDWw3dMWDsLl2UXKKdx+/DsZIEX3VrCGc7C1y5l47w6YeQmvUsS2UnK5UV9cdpTxE+7SAm9G2M2JgPkJD+FKt2X8NPf15R9olefQqjuvnh2/CmcLKVIDE9FxsO3MSPWwzw5dUGubz55kQKDWdwR44cQU5ODt5/X/2NyTk5OTh58iRatVJ/+ePV1C9bGx4fCCcLIMQ8HfcfeX03A7E9tAWEMz4+sKzeW9dFaE3u/V+RVbBf12Voja1ZKIT0e632e8t1XYTW3Ng3ELU+/lXXZWjNrXW6/Xug9rtLtX7MGwcHaf2Y2qbxSmGLFq9+75q1tXUZJ4REREREpCv6c/MSERERkT4wzqvHxvp6RiIiIiIqiiuFREREREUZ6YMmnBQSERERFWWk32jCy8dERERExJVCIiIiIhXGuVDIlUIiIiIi4kohERERkSo+aEJEREREvHxMREREREaLK4VERERERSiM9JU0nBQSERERFWWk9xTy8jERERERcaWQiIiISIVxLhRypZCIiIiIAJFCoVDouggiIiIifeH90WqtH/PmH/21fkxt07PLx9d1XYCW+EA4WQAh5imQn9V1EVpjJg6AcMZHeL/XTiTv1HURWhPo0h7CGR/h/V4TXh4d4oMmRERERKQvFi5cCE9PT1hYWCAoKAgnTpwose8777wDkUhUbGvfvn2pz8dJIREREVFRonLYNLRx40ZEREQgKioKp0+fhr+/P8LCwpCUlKS2/5YtW/D48WPldvHiRZiYmKB79+6lPicnhURERER6Zs6cORg0aBDCw8NRr149LFmyBFZWVlixYoXa/o6OjnB3d1du+/btg5WVFSeFRERERGUmEml/00B+fj5OnTqF0NBQZZtYLEZoaCji4+NLdYzly5ejV69esLa2LvV59exBEyIiIiIdK4evuZNKpZBKpSptEokEEomkWN+UlBTIZDK4ubmptLu5ueHq1auvPdeJEydw8eJFLF++XKMauVJIREREVM5iYmJgZ2enssXExJTLuZYvX46GDRsiMDBQo/24UkhERERUVDksmUVGRiIiIkKlTd0qIQA4OzvDxMQEiYmJKu2JiYlwd3d/5XlycnKwYcMGfPvttxrXyJVCIiIionImkUhga2urspU0KTQ3N0eTJk0QFxenbJPL5YiLi0NwcPArz/P7779DKpXik08+0bhGrhQSERERFVUO9xRqKiIiAv3790fTpk0RGBiIefPmIScnB+Hh4QCAfv36wcPDo9gl6OXLl6NTp05wcnLS+JycFBIREREVpfs5IXr27Ink5GRMnjwZCQkJCAgIwO7du5UPn9y/fx9iseoF32vXruHo0aPYu3dvmc7JSSERERGRHho+fDiGDx+u9rNDhw4Va6tTpw4UCkWZz8dJIREREVERCn73MREREREZK6NZKVy3bieWL9+C5OR0+Pp6YdKkL+Dn56PrsspMSHkMIcuv6/Zg5Yo/kZKSgTq+NTB+Qjga+nmX2H/P7ngsmP8bHj5MRo0a7hj19cdo2aqR8vOFC37H7thjSEhIhZmZKerV88LIr3rBz792RcTRiCGMjyb0Pc++zUcR++tBZKZlo1qtKug3qjNq1auhtu/BP+JxdPdJPLidAADwqlMV3b9op+xfWCjDpp9jce74FSQ9SoOVtQXqN/VBzyHt4eBsV2GZSkvfx0ZTQsojpCylogcPmuiCUawUxsYeQUzMMgwb1htbt86Dr68XBg6cjNTUDF2XViZCymMIWXbFHsOM6b9gyLCu+H3zNNSpUwNfDJqK1NRMtf3PnLmGb0bPR+eu7+L3LdPQus1bGDliJm5cv6/s4+lZGeMnhmPL9pn4ZW00qni44PPPvkdaWlZFxSoVQxgfTeh7nuNxZ7B+wXZ0Dg/Dd8sjUN27CmZE/IzM9Gy1/a+cuYXg0MYY/+NQRP00Eo5u9pgR8RPSkjMAAPl5+bh7/SE69W+L/62IwJffD8Dj+0mYO1azbzmoCPo+NpoSUh4hZSk1UTlsBsAoJoUrV25Djx5h6No1FN7e1REdPRQWFhJs3rxP16WViZDyGEKWX1bvRLfubdC5y7uo5V0Vk6d8BgsLc2zdclBt/7W/7ELztwPw6cCPUKtWVYz4sifq1fXC+vV7lH3af/g2gkP8UK2aG7xrV8M34/rhyZNcXL92r6JilYohjI8m9D3Prg2H8U6HZmjZPhAeXu4IH9MNEgsz/LXjhNr+Q6M+QWiX5qhR2wNVarjhs7E9IZcrcPnkDQCAlY0lxs0bjKA2Aahc3RXeDTzRP6IL7lx7gJSE9IqM9lr6PjaaElIeIWWhVxP8pDA/vwCXLt1ESIi/sk0sFiMkJABnzlzTYWVlI6Q8hpClIL8Qly/dRrPghso2sViMZsENce7sDbX7nDt3HcHBDVTaQt72x7mz10s8x++/xaFSJSvU8VV/mVAXDGF8NKHveQoLCnH3+gPUb/rikpxYLEb9pj64eeluqY4hleZDViiDta1ViX2ePsmDSCSCdSXLNy1Za/R9bDQlpDxCyqIRsUj7mwEQ/KQwPT0LMpkcTk4OKu1OTvZISdGvfymXhpDyGEKW9IznNaref+XkZIeUlAy1+6SkZMDJ2V6lzdnJDikpqpebDx08hbea9EPjgE+wZvVO/Lx8AhwcbLVZ/hsxhPHRhL7nyc7MgVwmh51jJZV2W8dKyEhVf/n4ZRsX7YCDs53KxLKofGkBNi7egWahjWBpbfHGNWuLvo+NpoSUR0hZ6PU0nhTm5ubi6NGjuHz5crHP8vLy8Msvv7z2GFKpFFlZWSqbVCrVtBQigxYYVB+bt8zA2vXfovnbARg9al6J9ykSvc6fa+JwPO4MvpwaDnOJWbHPCwtlWDD5FyigQPjobjqokMiAiETa3wyARpPC69evo27dumjZsiUaNmyIVq1a4fHjx8rPMzMzlV+/8ioxMTGws7NT2V7+mhZtcXCwhYmJGKmpqv+iSU3NgLOzQwl76S8h5TGELA72z2tUnaylpmbC+aXVwOecne2R+tIqYkpqJpxfetrTysoC1Wu4wz/AB999PxgmJibYsvmANst/I4YwPprQ9zyV7KwhNhEjM011VTArLRv2TpVK2OuZnesPYse6OHwzdzCqe1cp9nlhoQwLJq1GSkIaxs4drFerhID+j42mhJRHSFk0wgdNXm/s2LFo0KABkpKScO3aNVSqVAnNmzfH/fv3X79zEZGRkcjMzFTZIiMjNTpGaZmbm6F+fW/Ex59XtsnlcsTHn0OjRnXK5ZzlSUh5DCGLmbkp6tWviX+OX1C2yeVy/HP8IvwD1L8+xt/fB8ePX1Rpiz92Af4Br359g1yhQH5+4ZsXrSWGMD6a0Pc8pmam8PSpisunXtyrKpfLcenUDXjX9yxxvx3rDmD76n0YM+tz1PStVuzz5xPChAcpGDdvCCrZWZdH+W9E38dGU0LKI6Qs9Hoavafw2LFj2L9/P5ydneHs7Iw///wTQ4cORYsWLXDw4EFYW5fuLxuJRAKJRFKmgssiPLwTxo6diwYNvOHn54PVq7cjNzcPXbqEVlgN2iSkPIaQpV//9pgQuQj1G9RCg4a1sPaXWOTmStGp8zsAgMixC+Dq5ohREX0AAJ/0+wDh/aKxauWfaNmqMXbFHsOlS7cwJXoQAODp0zz8/NNWvPtuE7i4OCA9Ixu/rt+DpMQ0hIU101FK9QxhfDSh73k+6NUKP3//K7x8q6Fm3erY89thSHPz0bJ9IABgyXfr4eBii56DPwQA7Fgbh83Ld2No1CdwruyIjNRnrzSysJTAwkqCwkIZfpy4CnevP0TE9IGQy+XKPja2VjA1059X1er72GhKSHmElKXUDOTBEG3T6G+E3NxcmJq+2EUkEmHx4sUYPnw4WrVqhfXr12u9QG1o164F0tIyMX/+OiQnp6Nu3ZpYtizaYJe+hZTHELJ80C4E6elZWDD/N6SkZMC3rieW/BypvHz8+HGqypeSN2pUB9NnjsCPP2zED3M3oEYNd8z/cQxq+1QHAJiYiHHn9kP8se0w0tOzYW9fCQ0a1sLqtVPgXbv4So8uGcL4aELf8zRr0wjZGU+wedluZKZlobq3B8bM/lz58ElqYjpERf5jFbftGAoLZJg/cbXKcTqHt0WXge8jPTkTp49eAgBMDJ+t0mf8/KGo27jkF7BXNH0fG00JKY+QstCriRQafHNyYGAgRowYgb59+xb7bPjw4Vi3bh2ysrIgk8nKWI76V3YYHh8IJwsgxDwF8rO6LkJrzMQBEM74CO/32onknbouQmsCXdpDOOMjvN9rwsujO7UG/q71Y95a3l3rx9Q2je4p7Ny5M3799Ve1ny1YsAC9e/eGBnNMIiIiIr2jEGl/MwQaTQojIyMRGxtb4ueLFi2CXC5/46KIiIiIqGLpz13GRERERPrASB80Efw3mhARERHR63GlkIiIiKgoA/kGEm3jpJCIiIioKF4+JiIiIiJjxZVCIiIioqKMdMnMSGMTERERUVFcKSQiIiIqig+aEBEREREfNCEiIiIio8WVQiIiIqIiFEZ6+ZgrhURERETElUIiIiIiFUa6ZMZJIREREVFRfNCEiIiIiIyVSKFQKHRdBBEREZG+8Br9p9aPeWdWB60fU9v07PLxdV0XoCU+EE4WgHn0nQ/81hzRdRFacb5vCwhtbM6m7tB1EVoT4PQhhDM+PiiUn9N1EVpjKvaHcMYGePb3NFU0PZsUEhEREemYkd5TyEkhERERUVHGOSfkgyZERERExJVCIiIiIhUKXj4mIiIiImO9p5CXj4mIiIj00MKFC+Hp6QkLCwsEBQXhxIkTr+yfkZGBYcOGoXLlypBIJPDx8UFsbGypz8eVQiIiIqKiRLpfKdy4cSMiIiKwZMkSBAUFYd68eQgLC8O1a9fg6uparH9+fj7ee+89uLq6YtOmTfDw8MC9e/dgb29f6nNyUkhERESkZ+bMmYNBgwYhPDwcALBkyRLs3LkTK1aswLhx44r1X7FiBdLS0nDs2DGYmZkBADw9PTU6Jy8fExERERUl1v4mlUqRlZWlskmlUrWnz8/Px6lTpxAaGvqiJLEYoaGhiI+PV7vPH3/8geDgYAwbNgxubm5o0KABpk6dCplMplFsIiIiInpOJNL6FhMTAzs7O5UtJiZG7elTUlIgk8ng5uam0u7m5oaEhAS1+9y+fRubNm2CTCZDbGwsJk2ahNmzZ+N///tfqWPz8jERERFROYuMjERERIRKm0Qi0drx5XI5XF1d8fPPP8PExARNmjTBw4cPMXPmTERFRZXqGJwUEhERERVVDq+kkUgkpZ4EOjs7w8TEBImJiSrtiYmJcHd3V7tP5cqVYWZmBhMTE2Vb3bp1kZCQgPz8fJibm7/2vLx8TERERKRHzM3N0aRJE8TFxSnb5HI54uLiEBwcrHaf5s2b4+bNm5DL5cq269evo3LlyqWaEAJGtFK4bt1OLF++BcnJ6fD19cKkSV/Az89H12WVmZDyCCkLYBh5evpUxoD6VeFsaY7r6U8Qc+IWLqY+Udv3o5qu+F/zOiptUpkcb63/W/nrNtWc0N2nMuo52cBeYobuO07jWnpOuWYoK0MYn5ft2XwUf647hIy0bNTwroLwiM7wrlddbd+47cfx1+6T+O/2s/uOvOpURe/B7Ursr0/0bWzWr9uNlSv+REpKBur41sD4CZ/Cz8+7xP57dsfjx/kb8fBhMmrUcEfE1x+jZavGAICCgkLM/2EDjvx1Bg8eJMHGxgrBwQ0x6us+cHV1BACcOHEJ4f2j1R57w29T0bBhyecub/o2NuVOD15eHRERgf79+6Np06YIDAzEvHnzkJOTo3wauV+/fvDw8FDelzhkyBAsWLAAX375JUaMGIEbN25g6tSpGDlyZKnPaRQrhbGxRxATswzDhvXG1q3z4OvrhYEDJyM1NUPXpZWJkPIIKQtgGHnCajhjTNOaWHL+PnruPINr6TlY0qYBHC3MStwnO78Q7/5+XLmFbVF9gaqlqQnOJGVh3uk75V3+GzGE8XnZsf1n8Mv8P9D107aYtnIUanhXwdRRPyMzLVtt/0tnbiIktBEm/zgE3/00Ak6u9vj+q5+QlpxZwZVrRt/GZlfsMcyY/guGDuuG3zdPR506NfDFoO+Rmqr+53jmzDWMGf0DunRtjU1bpqN1m7cwYsRM3Lh+HwCQl5ePK5fvYPCQrvh983T8MP9r3Ln7CMOHzlAeIyCgDg799bPK1rVba1St6ooGDWpVSG519G1sKoJCJNL6pqmePXti1qxZmDx5MgICAnD27Fns3r1b+fDJ/fv38fjxY2X/atWqYc+ePfj333/h5+eHkSNH4ssvv1T7+pqSGMWkcOXKbejRIwxdu4bC27s6oqOHwsJCgs2b9+m6tDIRUh4hZQEMI0+/eh7YfCMB228l4nbmU3x3/CZyZXJ0quVW4j4KAKl5BcotLa9A5fMdd5Lw04X7OP44o3yLf0OGMD4v27nhL7T5qBne/TAQVb3c8dk3XWEuMcPBHeq/2WDklE8Q1rU5PH084OHphsGRPaCQK3Dh5I0Krlwz+jY2q1fvQLfubdC5y7vw9q6KqCmDYGFhji1bDqrtv/aXWLz9dgA+HfgRatWqipFf9kK9ujWxfv1uAEClSlZYtmIS3v8gBF5eVeAf4IMJEz/FpUu38ehRCgDA3NwULi72ys3e3gYHD5xEp87vQKTDlynr29gYk+HDh+PevXuQSqX4559/EBQUpPzs0KFDWLVqlUr/4OBgHD9+HHl5ebh16xbGjx+vco/h6wh+UpifX4BLl24iJMRf2SYWixESEoAzZ67psLKyEVIeIWUBDCOPqViEuo6VcDwhQ9mmAPDP4wz4u9iWuJ+VqQl2d34Le7sE4od36qGWnVX5F6tlhjA+LyssKMTtaw/QsGltZZtYLEbDt3xw4+K9Uh1DmpePwkIZbGz1d8z0bWzy8wtx+dJtBAc3VKmnWXBDnDt7Xe0+Z89dR7Mi/QGg+dv+OHu25Mn4k+ynEIlEsC1hbA4ePImMjGx07vJuGVJoh76NTYUph/cUGgKNy7xy5QpWrlyJq1evAgCuXr2KIUOG4NNPP8WBAwe0XuCbSk/Pgkwmh5OTg0q7k5M9UlLSdVRV2Qkpj5CyAIaRx0FiBlOxCKm5+SrtqXn5cLZUf/n4blYuouKv48tDlxF59BrEIuCX9/3hZlW6G5f1hSGMz8uyMnIgl8lh51hJpd3O0QYZJVw+ftm6RTvh6GynMrHUN/o2NhkZz+uxV1NPhtp9UlIy4ORs91J/O6SW0F8qzcec2evQrn1z2NionxRu2XQQzZsHwN3dSdMIWqNvY0PlS6MHTXbv3o2OHTvCxsYGT58+xdatW9GvXz/4+/tDLpejbdu22Lt3L1q3bv3K40il0mJv8X72qLbmAYiofJ1Pycb5lBcTkHPJWdj2URN0q10ZC8+VbrWKdGPbL3E4tv8MohYOhbmk5HtGqWIVFBQiYtRcKBTA5KjP1PZJSEjF33+fxey5oyq4OgKgF999rAsarRR+++23GDNmDFJTU7Fy5Ur06dMHgwYNwr59+xAXF4cxY8Zg2rRprz2OJm/1flMODrYwMREjNVX1XzSpqRlwdnYoYS/9JaQ8QsoCGEaedGkBCuUKOFmqrvI5WZgjJbeghL1UFSoUuJr+BNUrWZRHieXGEMbnZbb21hCbiIs9VJKZ9gT2L60evuzP9Qexfe0BTJj3BWp4VynPMt+Yvo2Nvf3zejLU1GOvdh9nZ3ukpmS+1D8TTi/1LygoxNej5uLRoxQsWz6xxFXCrVsOwt6+Et59t2lZY2iFvo1NhRGLtL8ZAI0mhZcuXcKAAQMAAD169EB2dja6deum/Pzjjz/G+fPnX3ucyMhIZGZmqmyRkZGaVV5K5uZmqF/fG/HxL+qSy+WIjz+HRo3qvGJP/SSkPELKAhhGnkK5AlfSshHkbq9sEwEIcrfHueSsUh1DLAJq21sj+aVL0PrOEMbnZaZmpqhZpyounHpxX5pcLsfFkzdQu0GNEvfbvvYANq/cj8g5n6NW3WoVUeob0bexMTc3Rb36NXH8+EWVev45fhH+AepfwxLg74Pjxy+otMUfO4+AgBeX7Z9PCO/dS8DyFZNg76B+Yq9QKLBt6yF81LElzMx0++Y4fRsbKl8a/257/gSUWCyGhYUF7Oxe3ENRqVIlZGa+/rUHmrzVWxvCwzth7Ni5aNDAG35+Pli9ejtyc/PQpUvo63fWQ0LKI6QsgGHk+eXyQ/yveR1cTs3GhZRsfFLXA5amYmy79ezN+d+H+CAxNx/zz9wFAHzRsDrOp2ThfnYebM1NMKBeVVS2lmDLzRdv2rc1N0Vlawlc/n8F0tPWEgCQkpuP1LzSrUBWBEMYn5e179USi/63AbV8q6FWveqI3fgXpHn5eOfDQADAgm/Xw9HFDn2GtAcAbF9zAL8t242RUz6Ba2UHZKQ+m+xbWEpgYaW/9+jo29j07/8hxkcuRP0GNdGwoTfW/BKL3FwpOnd+BwAQOXYBXN0cMSqiDwDgk37tMKDfFKxa+SdatmqMXbF/4+KlW5gS/TmAZxPCUV/NwZXLd7Bw8VjIZHIkJ2cAAOzsbGBu/uI/x/8cv4gHD5LQtVubioxcIn0bmwphICt72qbRpNDT0xM3btxArVrP3pcUHx+P6tVfvBD1/v37qFy5snYr1IJ27VogLS0T8+evQ3JyOurWrYlly6INdulbSHmElAUwjDx77qXAwcIMQ/1rwNnSHNfSn2DIgUvK18y4W0sgL9LfVmKKqGa14Wxpjqz8QlxOfYJ+u8/hduZTZZ93qjqqvOB6Zsu6AIDF5+5h8fn7FZKrNAxhfF4WEtoIWRk5+G3pHmSkZcGztgci5wxSXj5OTcyAuMh/wPZtPYbCAhnmTFitcpxun7ZF98/CKrR2Tejb2HzQLgRp6VlYMP83pKRkwLeuJ376ebzy8vHjxykQFfm5N2pUBzNmjsT8HzZg3txfUaNGZfz44xjU9nn238ikpDQcPHASANC18zcq51q5OgqBgfWVv968+QACGtVBzZoe5ZyydPRtbKj8iBQKhaK0nZcsWYJq1aqhffv2aj8fP348kpKSsGzZsjKWo/5Rf8PjA+FkAZhH3/nAb80RXRehFef7toDQxuZs6g5dF6E1AU4fQjjj44NC+TldF6E1pmJ/CGdsgGd/T+tOjVnaf5vKvdGvfghXH2i0Ujh48OBXfj516tQ3KoaIiIhI1xRGevnYQF6nSERERETlSbePNRERERHpG76nkIiIiIiMFVcKiYiIiIoy0nsKOSkkIiIiKso454S8fExEREREXCkkIiIiUiE20iUzI41NREREREVxpZCIiIioCCN9Iw0nhURERERFGeukkJePiYiIiIgrhURERERFiYx0qZArhURERETElUIiIiKioox0oZCTQiIiIqKijHVSKFIoFApdF0FERESkL2r/9JfWj3nji5ZaP6a26dlK4XVdF6AlPhBOFoB59J2Q8vig5hebdV2E1tz+qSuEMzaA0H6vCScLAPig5qLDui5Ca24PbaXT84uM9IkLI41NREREREXp2UohERERkW4Z6z2FnBQSERERFSE20kkhLx8TEREREVcKiYiIiIoy1svHXCkkIiIiIq4UEhERERVlrCuFnBQSERERFSEy0lkhLx8TEREREVcKiYiIiIriN5oQEREREUQi7W9lsXDhQnh6esLCwgJBQUE4ceJEiX1XrVoFkUiksllYWGh0Pk4KiYiIiPTMxo0bERERgaioKJw+fRr+/v4ICwtDUlJSifvY2tri8ePHyu3evXsanZOTQiIiIqIi9GGlcM6cORg0aBDCw8NRr149LFmyBFZWVlixYsUr6hbB3d1dubm5uWl0TqO5p3Ddup1YvnwLkpPT4evrhUmTvoCfn4+uyyozIeURUhaAeXSh7zs1Meg9H7jYWeDKg0xM2XAW5++ml9i/kqUZRneqj7BGVWBnZY5HaU/x3W/ncehiAgDgyw/r4ssO9VT2uZWQjfei9pZrDk0ZwthognkqVt8GVTAooBpcrMxxJfUJphy5ifNJ2Wr7dq3jhpltfFXapIVy1P35iNr+/2tVG33qV8F3R29i5fmHWq9d6PLz83Hq1ClERkYq28RiMUJDQxEfH1/ifk+ePEGNGjUgl8vRuHFjTJ06FfXr1y/1eY1ipTA29ghiYpZh2LDe2Lp1Hnx9vTBw4GSkpmbourQyEVIeIWUBmEcX2jetivHd/DB/5xV0+D4OVx5kYvXIt+FUSaK2v5mJCGu+ehtVnaww7Kd/EBq1F5FrTiMhI1el37WHmQgcs0O59ZhxqALSlJ4hjI0mmKditfd2wfjmtTD/5F10+P0UrqQ8weoPG8LJ0qzEfbKlhQhceUy5tVhzXG2/tl5OCHCzRcITaXmVX+7KY6VQKpUiKytLZZNK1f+MUlJSIJPJiq30ubm5ISEhQe0+derUwYoVK7B9+3asXbsWcrkcISEhePDgQalza2VSqFAotHGYcrNy5Tb06BGGrl1D4e1dHdHRQ2FhIcHmzft0XVqZCCmPkLIAzKMLA0NrY+PRu9h07B5uPs7GxHWnkZsvQ/eQGmr7d2/uCTtrc3yxKB6nbqXiYepTnLiRgqsPMlX6yeQKpGRJlVt6Tn5FxCk1QxgbTTBPxRroXxUbLz/GpquJuJn+FBMP30BuoRzdfd1L3EcBICW3QGV7mZu1OaJa1MaofVdQKNfvucGriEXa32JiYmBnZ6eyxcTEaK3m4OBg9OvXDwEBAWjVqhW2bNkCFxcX/PTTT6XPrY1CJBIJrly5oo1DaV1+fgEuXbqJkBB/ZZtYLEZISADOnLmmw8rKRkh5hJQFYB5dMDMRoUF1e/x95cWN1woF8PfVJDSq6aR2n1C/KjhzOw3RfRrhxMz22DU5FEM/qAPxS/f8eLraIH56Oxz63/uY++lbqOJgWZ5RNGIIY6MJ5qlYZmIRGrhUwt8PXtxioQDw94N0NHK3LXE/KzMTHOkbhKP9gvDTB/VR28FK5XMRgNltfLH07H+4kf60nKo3XJGRkcjMzFTZil4eLsrZ2RkmJiZITExUaU9MTIS7e8kT96LMzMzQqFEj3Lx5s9Q1anRPYUREhNp2mUyGadOmwcnp2V/Cc+bM0eSw5So9PQsymRxOTg4q7U5O9rh9u/RLqvpCSHmElAVgHl1wsJHA1ESMlOw8lfaUrDzUcq+kdp9qLtYIdnLB9n/u49Mf/0YNVxt82zsApiZizN/x7B+3Z++kYcyqk7iTmA0XO0uM/LAuNo5phfej9yNHWljuuV7HEMZGE8xTsRwszGAqFiHlqepKX0puAWq9NNF77nZGLsYevIarKU9QSWKKQQHVsKlLI4Rt+BcJ/7+KPrhxNcgUCqwSwD2E5fGFJhKJBBKJ+ttaXmZubo4mTZogLi4OnTp1AgDI5XLExcVh+PDhpTqGTCbDhQsX0K5du1LXqNGkcN68efD394e9vb1Ku0KhwJUrV2BtbV2qr4aRSqXFrqM/+2FpUg0RkebEIiA1W4rxa09DrgAu3s+Au70lBrWtrZwUHr704l/nVx9m4eydNByN+QDtm1bFb3/f1VHlRLpzJjELZxKzlL8+nZCFvb3fQu/6VTD3xF00cLHBAL+q6PDbKR1WKSwRERHo378/mjZtisDAQMybNw85OTkIDw8HAPTr1w8eHh7KS9DffvstmjVrBm9vb2RkZGDmzJm4d+8ePvvss1KfU6NJ4dSpU/Hzzz9j9uzZaN26tbLdzMwMq1atQr169V6x9wsxMTGIjo5WaYuKisKUKX00KadUHBxsYWIiRmqq6pOIqakZcHZ2KGEv/SWkPELKAjCPLqQ/kaJQJodzJdUXtDrbWiA5M0/tPkmZeSiUKVD0dqebj7PgamcJMxMRCmTF74PKzi3AncRs1HCx1mr9ZWUIY6MJ5qlY6XkFKJQr4Gyl+lCJs6UZkp+W7t7ZQrkCl5OfwNPu2W0Vb1W2g5OlGY72a6bsYyoWYXxILYT7VUXLtf9oL0AF0IevPu7ZsyeSk5MxefJkJCQkICAgALt371Y+fHL//n2IxS/uAkxPT8egQYOQkJAABwcHNGnSBMeOHSv13AzQ8J7CcePGYePGjRgyZAhGjx6NgoLiN5mWhibX1d+UubkZ6tf3Rnz8eWWbXC5HfPw5NGpUp1zOWZ6ElEdIWQDm0YUCmQIX72cgpK6Lsk0kAkJ8XXDmdqrafU7dSkUNF2uVv/S93CohMSNX7YQQAKwkJqjuYoOkEiaaFc0QxkYTzFOxCuQKXEzORojHiwmqCEBIVQecScgqeccixCKgjpM1kv7/0vHWa4lot/EkPvztxZbwRIqlZ/9D/x3nX3M0/SMSi7S+lcXw4cNx7949SKVS/PPPPwgKClJ+dujQIaxatUr567lz5yr7JiQkYOfOnWjUqJFG59P4PYVvvfUWTp06hWHDhqFp06ZYt25dqS4ZF6XJdXVtCA/vhLFj56JBA2/4+flg9ertyM3NQ5cuoRVWgzYJKY+QsgDMowvL99/ArAFNceFuOs7dTUd4G29YmZti07Fnb/KfNaApEjNyMXPbJQDAusO30fedWpjc0x+/HLgFT1cbDP2gDlYdeHEzdmTXhog7/xgP057Czc4CX3WoB5lcgT///U8nGdUxhLHRBPNUrOXnHmBWa19cSM7GuaRshPt5wMpUjE1Xn73uZFabOkjMycfM43cAACOa1sCZxCzcy8yFrbkpPm9UDR6VJNh45TEAIENaiIyX7rctlCuQ/DQfd1563RPprzK9vNrGxgarV6/Ghg0bEBoaCplMpu26tKpduxZIS8vE/PnrkJycjrp1a2LZsmi9WMYvCyHlEVIWgHl0YefJB3C0kWDUR/XgbPvs5dUD5h9FSvaz+5arOFpBXuS1WY/TczFg/lFM7O6H2MmhSMjIxaoDN7Fk94unQt0dLPHDZ4GwtzZH2hMpTt5MRddpB5H2RH9eS2MIY6MJ5qlYO28mw9HCDKMCPeFsZY4rKU8wYMcF5WtmqthYqNxiYScxRcw7PnC2MkeWtBAXk7PRbctZ3BToU8b6cPlYF0SKN3zJ4IMHD3Dq1CmEhobC2vpN77e5/ob76wsfCCcLwDz6Tkh5fFDzi826LkJrbv/UFcIZG0Bov9eEkwUAfFBz0WFdF6E1t4e20un5A38/qvVjnuj+ttaPqW1v/DV3VatWRdWqVbVRCxEREZHOGetKodF89zERERFRaRjrpNAovvuYiIiIiF6NK4VERERERZTxDTIGjyuFRERERMSVQiIiIqKijPWeQk4KiYiIiIoQGel1VCONTURERERFcaWQiIiIqAhjvXzMlUIiIiIi4kohERERUVEiI10q5KSQiIiIqAgjnRPy8jERERERcaWQiIiISAVXComIiIjIaHGlkIiIiKgIY10pFCkUCoWuiyAiIiLSF212/a31Y8Z90Fzrx9Q2PVspvK7rArTEB8LJAjCPvhNSHiFlAZhHnwkpCwD44J+knbouQmuCXNvrugSjpGeTQiIiIiLdEhvp5WM+aEJEREREXCkkIiIiKkosMs7HLTgpJCIiIiqCl4+JiIiIyGhxpZCIiIioCGNdMTPW3ERERERUBFcKiYiIiIrggyZERERExAdNiIiIiMh4caWQiIiIqAhjXTEz1txEREREVARXComIiIiKMNZ7CjkpJCIiIipCxKePhW3dup1YvnwLkpPT4evrhUmTvoCfn4+uyyozIeURUhaAefSdkPIIKQvAPBVt/5ajiP31IDLTslGtVhX0/aozatWrobbvwT/i8feek3hwOwEA4FmnKrp/3k7Zv7BQhs1LY3Hu+BUkPUqDlbUF6jf1QY/B7eHgbFdhmejNGMU9hbGxRxATswzDhvXG1q3z4OvrhYEDJyM1NUPXpZWJkPIIKQvAPPpOSHmElAVgnop2PO4M1i/Yjk4DwvDtsghU966CmV//jKz0bLX9r569hWahjRE5fygmLxkJJ1d7zPz6J6QlZwAA8vPycff6Q3Ts3xbfLY/AyO8H4PH9JMwdt7wCU2mPWKT9zRAYxaRw5cpt6NEjDF27hsLbuzqio4fCwkKCzZv36bq0MhFSHiFlAZhH3wkpj5CyAMxT0XZvPIx3OjRDy/aB8PByx4DR3SCxMMPhnSfU9h8y+ROEdm6OGrU9UKWGGwaO7Qm5XIHLp24AAKxsLDF27mAEtQ5A5equ8K7viX6juuDutQdISUyvyGiCsnDhQnh6esLCwgJBQUE4cUL9+Lxsw4YNEIlE6NSpk0bnE/ykMD+/AJcu3URIiL+yTSwWIyQkAGfOXNNhZWUjpDxCygIwj74TUh4hZQGYp6IVFhTi7vUHqN/kxaVssViMek19cPPS3VIdQyrNh6xQButKViX2eZqTB5FIBGsbyzctucKJy2HT1MaNGxEREYGoqCicPn0a/v7+CAsLQ1JS0iv3u3v3LkaPHo0WLVpofM43mhTm5ORg5cqVmDBhAhYsWIDU1NQ3OVy5SE/Pgkwmh5OTg0q7k5M9UlIM718vQsojpCwA8+g7IeURUhaAeSpadmYO5DI5bB0rqbTbOVRCZqr6y8cv27h4Bxyc7VC/qfp7JPOlBfht8Q40C20ES2uLN665oolFCq1vmpozZw4GDRqE8PBw1KtXD0uWLIGVlRVWrFhR4j4ymQwff/wxoqOjUbNmTc1za9K5Xr16SEtLAwD8999/aNCgAUaNGoV9+/YhKioK9erVw507d157HKlUiqysLJVNKpVqXDwRERFVrD/XxuGfuDMY+X04zCVmxT4vLJRhYdQvUCgUGPB1Nx1UqJ80mfvk5+fj1KlTCA0NVbaJxWKEhoYiPj6+xHN8++23cHV1xcCBA8tUo0aTwqtXr6KwsBAAEBkZiSpVquDevXs4ceIE7t27Bz8/P0yYMOG1x4mJiYGdnZ3KFhMTU6YAr+PgYAsTEzFSU1X/dZaamgFnZ4cS9tJfQsojpCwA8+g7IeURUhaAeSpaJTtriE3EyEpTXRXMTM+GnVOlEvZ6JvbXg9i5Lg5j5gxGde8qxT4vLJRh4eTVSElIwzdzBxvkKiFQPg+aaDL3SUlJgUwmg5ubm0q7m5sbEhIS1O5z9OhRLF++HEuXLi177rLuGB8fjylTpsDO7tmj5jY2NoiOjsbRo0dfu29kZCQyMzNVtsjIyLKW8krm5maoX98b8fHnlW1yuRzx8efQqFGdcjlneRJSHiFlAZhH3wkpj5CyAMxT0UzNTOHpUxWX/v8hEeBZfZdP3YB3fc8S99u57gC2r96H0bM+R03fasU+fz4hTHiQgrFzh6CSnXV5lF8hyuOewvKc+2RnZ6Nv375YunQpnJ2dy3wcjd9TKBI9e646Ly8PlStXVvnMw8MDycnJrz2GRCKBRCLR9NRlFh7eCWPHzkWDBt7w8/PB6tXbkZubhy5dQl+/sx4SUh4hZQGYR98JKY+QsgDMU9He79kKS6f+Ci/faqhZtzr2/n4Y0tx8tGwXCAD46X/r4eBsix6DPwQA7FgXhy3Ld2PI5E/g7O6IjNQsAICFpQQWVhIUFsrw46RVuHf9ISKmD4RcLlf2sbG1gqmZ0bwWuUSazH2cnZ1hYmKCxMRElfbExES4u7sX63/r1i3cvXsXHTp0ULbJ5XIAgKmpKa5du4ZatWq99rwaj1KbNm1gamqKrKwsXLt2DQ0aNFB+du/ePTg5OWl6yHLXrl0LpKVlYv78dUhOTkfdujWxbFm0Xizjl4WQ8ggpC8A8+k5IeYSUBWCeitasTSNkZzzBluW7kZmWhereHhgz63PY/f/DJ6mJ6cpFIAA4sO0YCgtk+HHSapXjdApviy6fvo/05EycOXoJADAxfLZKn8j5Q1G3kXc5J9IuXb9X0NzcHE2aNEFcXJzytTJyuRxxcXEYPnx4sf6+vr64cOGCStvEiRORnZ2NH374AdWqFV/ZVUekUChK/UhMdHS0yq+bNWuGsLAw5a/HjBmDBw8e4Ndffy3tIV9yvYz76RsfCCcLwDz6Tkh5hJQFYB59JqQsAOCDf5J26roIrQlyba/T8w/467DWj7mqZSuN+m/cuBH9+/fHTz/9hMDAQMybNw+//fYbrl69Cjc3N/Tr1w8eHh4l3pc4YMAAZGRkYNu2baU+p0YrhVFRUa/8fObMmZocjoiIiEjvlOUVMtrWs2dPJCcnY/LkyUhISEBAQAB2796tfPjk/v37EIu1+7ppXuQnIiIiKkLXl4+fGz58uNrLxQBw6NChV+67atUqjc8n+G80ISIiIqLX40ohERERURHGumJmrLmJiIiIqAiuFBIREREVoQ8PmugCJ4VERERERejLgyYVjZePiYiIiIgrhURERERFcaWQiIiIiIwWVwqJiIiIijDWFTNOComIiIiKMNanj411MkxERERERXClkIiIiKgIPmhCREREREaLK4VERERERRjriplIoVAY592URERERGp8c+KA1o85I7C11o+pbXq2Unhd1wVoiQ+EkwVgHn0npDxCygIwjz4TUhZAmHmoounZpJCIiIhIt0R8JQ0RERERGSuuFBIREREVYayvpOGkkIiIiKgIY72Maqy5iYiIiKgIrhQSERERFcHvPiYiIiIio8WVQiIiIqIi+KAJERERERntpJCXj4mIiIiIK4VERERERZnougAd4UohEREREXGlkIiIiKgovpJG4Nat24nWrQeiYcMu6N79a5w/f13XJb0RIeURUhaAefSdkPIIKQvAPPpMSFlKQyzS/mYIjGJSGBt7BDExyzBsWG9s3ToPvr5eGDhwMlJTM3RdWpkIKY+QsgDMo++ElEdIWQDm0WdCykKvZhSTwpUrt6FHjzB07RoKb+/qiI4eCgsLCTZv3qfr0spESHmElAVgHn0npDxCygIwjz4TUpbS4kqhQOXnF+DSpZsICfFXtonFYoSEBODMmWs6rKxshJRHSFkA5tF3QsojpCwA8+gzIWWh19NoUnj69GncuXNH+es1a9agefPmqFatGt5++21s2LBB6wW+qfT0LMhkcjg5Oai0OznZIyUlXUdVlZ2Q8ggpC8A8+k5IeYSUBWAefSakLJowEWl/MwQaTQrDw8Nx69YtAMCyZcvwxRdfoGnTppgwYQLeeustDBo0CCtWrHjtcaRSKbKyslQ2qVRatgREREREWsTLx6Vw48YN1K5dGwCwaNEi/PDDD/jhhx8wePBgzJ07Fz/99BNmz5792uPExMTAzs5OZYuJiSlbgtdwcLCFiYkYqamq/6JJTc2As7NDCXvpLyHlEVIWgHn0nZDyCCkLwDz6TEhZ6PU0mhRaWVkhJSUFAPDw4UMEBgaqfB4UFKRyebkkkZGRyMzMVNkiIyM1KaXUzM3NUL++N+Ljzyvb5HI54uPPoVGjOuVyzvIkpDxCygIwj74TUh4hZQGYR58JKYsmxCKF1reyWLhwITw9PWFhYYGgoCCcOHGixL5btmxB06ZNYW9vD2trawQEBGDNmjUanU+jl1d/8MEHWLx4MZYtW4ZWrVph06ZN8Pd/cfPpb7/9Bm9v79ceRyKRQCKRaFTomwgP74SxY+eiQQNv+Pn5YPXq7cjNzUOXLqEVVoM2CSmPkLIAzKPvhJRHSFkA5tFnQspiSDZu3IiIiAgsWbIEQUFBmDdvHsLCwnDt2jW4uroW6+/o6IgJEybA19cX5ubm2LFjB8LDw+Hq6oqwsLBSnVOjSeH06dPRvHlztGrVCk2bNsXs2bNx6NAh1K1bF9euXcPx48exdetWTQ5ZIdq1a4G0tEzMn78OycnpqFu3JpYtizbYpW8h5RFSFoB59J2Q8ggpC8A8+kxIWUpLH+4BnDNnDgYNGoTw8HAAwJIlS7Bz506sWLEC48aNK9b/nXfeUfn1l19+idWrV+Po0aOlnhSKFAqFRmuaGRkZmDZtGv7880/cvn0bcrkclStXRvPmzTFq1Cg0bdpUk8O9RChvSPeBcLIAzKPvhJRHSFkA5tFnQsoCCDOP7iy6vFfrxxxar22p++bn58PKygqbNm1Cp06dlO39+/dHRkYGtm/f/sr9FQoFDhw4gI8++gjbtm3De++9V6rzavzdx/b29pg2bRqmTZum6a5ERERERkkqlRZ700pJt9OlpKRAJpPBzc1Npd3NzQ1Xr14t8RyZmZnw8PCAVCqFiYkJFi1aVOoJIWAEL68mIiIi0kR5vJKmIt68UqlSJZw9exb//vsvvv/+e0RERODQoUOl3l/jlUIiIiIi0kxkZCQiIiJU2kp66NbZ2RkmJiZITExUaU9MTIS7u3uJ5xCLxcoHfgMCAnDlyhXExMQUu9+wxP1L1YuIiIjISJTHK2kkEglsbW1VtpImhebm5mjSpAni4uKUbXK5HHFxcQgODi51DrlcrtGXg3ClkIiIiKgIffhauoiICPTv3x9NmzZFYGAg5s2bh5ycHOXTyP369YOHh4fyEnRMTAyaNm2KWrVqQSqVIjY2FmvWrMHixYtLfU5OComIiIj0TM+ePZGcnIzJkycjISEBAQEB2L17t/Lhk/v370MsfnHBNycnB0OHDsWDBw9gaWkJX19frF27Fj179iz1OTV+JU35Esrj9EJ8NQDz6C8h5RFSFoB59JmQsgDCzKM7K6/v0foxw31K965AXeJKIREREVER+vDyal3ggyZERERExJVCIiIioqK4UkhERERERosrhURERERFmIj06BncCsRJIREREVERxnoZ1VhzExEREVERXCkkIiIiKoIPmhARERGR0dKzbzQhIiIi0q1Nd3Zr/ZjdvN7X+jG1Tc8uHwvlK3qE+HVDzKO/hJRHSFkA5tFnPqju/z9dF6E1989NhOd3e3VdhtbcndRWp+c31qePefmYiIiIiPRtpZCIiIhIt/igCREREREZLa4UEhERERVhrCuFnBQSERERFWGsk0JePiYiIiIirhQSERERFWXClUIiIiIiMlZcKSQiIiIqQmykL6/mpJCIiIioCGO9jGqsuYmIiIioCK4UEhERERXBV9IQERERkdEympXCdet2YvnyLUhOToevrxcmTfoCfn4+ui6rzISUR0hZAObRd0LKI6QsgGHk6dezCb7oHwwXZxtcuZ6IydP24NzFRyX2H/hxID7p0QQe7rZIy8hF7L4rmD7/AKT5MgBAYOPqGDygGRrWrQw310r47KvfsPfg9QrJ0rdpNXwR7AkXG3NcSXyCqN1XcO5Rltq+3fyqYFbHBipt0kIZ6sTEKX/tbG2OcW1qo0VNJ9hamOHEvXRE7bmKu2lPyzVHeeAraQQsNvYIYmKWYdiw3ti6dR58fb0wcOBkpKZm6Lq0MhFSHiFlAZhH3wkpj5CyAIaRp0NYPUwa/R7m/XQE7Xstw5VriVi7uDecHK3U9u/4QX2M/bI15i35C607L8GYKTvQIawevhn5rrKPlaUZLl9LwsSY3RUVAwDwYT03THyvDn746xbaLz2Oy4nZ+KVPEzhZmZe4T1ZeAd6ac0i5NZ9/ROXzn3sEoJq9FQZtPIv2S+PxMDMXaz9uAkszk/KOo3VikULrmyEwiknhypXb0KNHGLp2DYW3d3VERw+FhYUEmzfv03VpZSKkPELKAjCPvhNSHiFlAQwjz2d9g/DrljP4ffs53Lidgsj/xSI3rwA9OwWo7d8koCpOnf0P23ddwoNHmTgSfxvbd19CQAMPZZ9Df9/CrIWHsOfAtQpK8cxnzTyx4cwD/H7uEW6m5GDCzsvILZChR0CVV+6XnJOv3FJy8pXtXo5WaFzVHhN3Xcb5x1m4nfoUE2KvwMLMBB/Vdy/vOKQlgp8U5ucX4NKlmwgJ8Ve2icVihIQE4MyZiv1DqA1CyiOkLADz6Dsh5RFSFsAw8piZitGwbmUcPX5H2aZQAEeP30VjPw+1+5w6+wAN6laGf4NnE63qHvZ4921vHDhys0JqLomZWIQGlSvh7zupyjYFgL/vpKFxVfsS97MyN8HRES1wbGRLLO0RgNou1srPzE2fTSekhXKVY+YXyvFW9ZKPqa/EIu1vhkDwk8L09CzIZHI4OTmotDs52SMlJV1HVZWdkPIIKQvAPPpOSHmElAUwjDyODlYwNRUjJTVHpT0l9QlcnG3U7rN91yXMWXwYm1f1x62TkTgaOxzHT97DwuV/V0TJJXKwMoepWIyUJ/kq7ck5UrjYSNTuczs1B9/8eQmf/3YWo7ZdgEgkwuYBgXCv9Kz/rZQcPMjIxTeta8PWwhRmYhEGh3iiip0FXEs4JukfjSaFI0aMwJEjR17f8TWkUimysrJUNqlU+sbHJSIi0hfNmtbAsIHNMfH7XWjXaxkGjfodrVt4Y+Tnb+u6NI2dfpiJLecf43JiNv65n47Bv59F2tMC9GlSFQBQKFdg8O9nUdPRCufHtMaVyDYIruGIgzeSITeM2+lUcKWwFBYuXIh33nkHPj4+mD59OhISEsp00piYGNjZ2alsMTExZTrW6zg42MLERIzUVNV/baamZsDZ2aGEvfSXkPIIKQvAPPpOSHmElAUwjDxp6U9RWCiHs5O1Sruzkw2SU56o3Wf0sFbYsuMCNmw9i2s3k7HnwDXM+PEghn3aHCIdThLSn+ajUC6Hs43qQyUu1hIkPyndAk2hXIFLCVnwdHjxkM3FhGy0W3ocDWccQODcw+j/62k4WJnjfrrhPX0sLofNEGhc5969e9GuXTvMmjUL1atXR8eOHbFjxw7I5fLX7/z/IiMjkZmZqbJFRkZqWkqpmJuboX59b8THn1e2yeVyxMefQ6NGdcrlnOVJSHmElAVgHn0npDxCygIYRp6CQjkuXHmM5kFeyjaRCGge5InT5x+q3cfSwgwKheoymUym+P99dTcrLJArcPFxNkI8nZRtIgAhXo44/SCjVMcQiwBf10pIUjOJzJYWIu1pATwdrdCwsi32XU/WUuVU3jR+T2HDhg3Rpk0bzJw5E1u3bsWKFSvQqVMnuLm5YcCAAQgPD4e3t/crjyGRSCCRVNw9BuHhnTB27Fw0aOANPz8frF69Hbm5eejSJbTCatAmIeURUhaAefSdkPIIKQtgGHmWrfkHs7/7CBcuPcbZiw8x8JMgWFma4bdt5wAAc//3ERKSsjF9/kEAwP7DN/BZ3yBcvJqAsxcewbOaA0YPa4X9f12H/P+vqVpZmsGzuqPyHNU87FGvjhsyMnPxKEH9OwO1kuX4Xczu2AAXHmfh7KNMDAysDiszE/x+7tk7F2d3bIDE7DzMOPDsoZiRLWrizMNM3E17ClsLU3wR7AkPOwtsOPNiQtyurhvSnubjYWYefF1tEBXmi73XknDkdqraGvSZLldydanML682MzNDjx490KNHD9y/fx8rVqzAqlWrMG3aNMhkMm3W+MbatWuBtLRMzJ+/DsnJ6ahbtyaWLYvWm8sSmhJSHiFlAZhH3wkpj5CyAIaR5889l+HoYIWIoa3g4myNy9cS0Xfor0hJe/bwSRV3O+VkDwDmLz0ChUKBMcPegbtrJaSmP8X+wzcwc8FBZR+/+lXw2/K+yl9HjWkLAPh9+zl8PfnPcsuy43IiHK3MMapVLbjYSHAlMRv9159WvmbGw9ZCZZXTzsIMMe3rwcVGgqy8Alx4nIWuq07gZsqLB29cbSSY+F4dONuYIylbii0XHuHHv26XWwbSPpHi5bXtVxCLxUhISICrq6vazxUKBfbv34/33nuvjOVUzFvcy58PhJMFYB59J6Q8QsoCMI8+80F1///pugituX9uIjy/26vrMrTm7qS2Oj3/v8k7tX7Mt1zaa/2Y2qbRSmGNGjVgYlLym8lFItEbTAiJiIiIdI+Xj0vhzp07r+9ERERERAbHUJ6SJiIiIqoQ+vJKmoULF8LT0xMWFhYICgrCiRMnSuy7dOlStGjRAg4ODnBwcEBoaOgr+6vDSSERERGRntm4cSMiIiIQFRWF06dPw9/fH2FhYUhKSlLb/9ChQ+jduzcOHjyI+Ph4VKtWDW3btsXDh+pfmaQOJ4VERERERYhECq1vmpozZw4GDRqE8PBw1KtXD0uWLIGVlRVWrFihtv+6deswdOhQBAQEwNfXF8uWLYNcLkdcXFypz8lJIREREVERonLYNPmK3/z8fJw6dQqhoS/e0ykWixEaGor4+PhSZXj69CkKCgrg6Oj4+s7Pz1HqnkRERERUJpp8xW9KSgpkMhnc3NxU2t3c3Er9FcNjx45FlSpVVCaWr1Pml1cTERERCVF5vJImMjISERERKm3l9e1u06ZNw4YNG3Do0CFYWFiUej9OComIiIjKmSZf8evs7AwTExMkJiaqtCcmJsLd3f2V+86aNQvTpk3D/v374efnp1GNvHxMREREVER53FOoCXNzczRp0kTlIZHnD40EBweXuN+MGTPw3XffYffu3WjatKmGZ+VKIREREZEKsR58o0lERAT69++Ppk2bIjAwEPPmzUNOTg7Cw8MBAP369YOHh4fyvsTp06dj8uTJWL9+PTw9PZX3HtrY2MDGxqZU5+SkkIiIiEjP9OzZE8nJyZg8eTISEhIQEBCA3bt3Kx8+uX//PsTiFxd8Fy9ejPz8fHTr1k3lOFFRUZgyZUqpzslJIREREVERerBQCAAYPnw4hg8frvazQ4cOqfz67t27b3w+3lNIRERERFwpJCIiIiqqPF5JYwg4KSQiIiIqwkjnhBApFArNv5CPiIiISKCuZOzQ+jHr2n+o9WNqm56tFF7XdQFa4gPhZAGYR98JKY+QsgDMo8+ElAUAfKDANV0XoTUi1NHx+Y2Tnk0KiYiIiHRLH95TqAt8+piIiIiIuFJIREREVJSRLhRypZCIiIiIuFJIREREpEIkMs4Xs3BSSERERFQELx8TERERkdHiSiERERFREcb6NXdcKSQiIiIirhQSERERFWWsK2acFBIREREVwcvHRERERGS0uFJIREREVISRLhRypZCIiIiIjGhSuG7dTrRuPRANG3ZB9+5f4/z567ou6Y0IKY+QsgDMo++ElEdIWQDmKZ/zfwa/hl3Ro/vo155/966j+OD9IfBr2BUdOozA4cMnVT5XKBSY/8M6tHi7P/z9uiF8wCTcvfuo2HEOHfoXPbqPhr9fNwS+1RvDhn6v8rlvnY+KbTt3/vXmgbVIJNL+ZgiMYlIYG3sEMTHLMGxYb2zdOg++vl4YOHAyUlMzdF1amQgpj5CyAMyj74SUR0hZAOYpj/NPi1mOYcN6YcvWuajj64nPBkaVeP7Tp6/g669noVu397B12zyEtgnC8GFTcf36PWWfZUu3YM2aHZgyZQh++20mLC0l+GxgFKTSfGWfPXuOYew3c9GlSxts2/4D1v86HR9+2KrY+abGfIkjR1crt9DQZlr/GbwJUTlshsAoJoUrV25Djx5h6No1FN7e1REdPRQWFhJs3rxP16WViZDyCCkLwDz6Tkh5hJQFYB5tW7VyO7r3aKvm/PvV9l/zy594u0VjDPysC2rVqoYvv/oE9erVxLq1OwE8WyX85Zc/MHhID7QJbYY6vl6YPmMUkpLSsH//cQBAYaEMU79fijFjBqBX7w/g5eUBb+/q+KDd28XOZ2trDRcXB+UmkZiX3w+DSk3wk8L8/AJcunQTISH+yjaxWIyQkACcOXNNh5WVjZDyCCkLwDz6Tkh5hJQFYJ7yO3+AyvmDQ/xx9sxVtfucPXsVIcH+Km3N326Ms2ef9X/wIBHJyekqmSpVsoafvw/O/n+my5dvITExFSKxGJ07fYkWb/fHoM+mqKw2Pvdt9BI0C/oY3bt9jc2b9kGhULxpbK0Si7S/GQKNJ4ULFixAv379sGHDBgDAmjVrUK9ePfj6+mL8+PEoLCzUepFvIj09CzKZHE5ODirtTk72SElJ11FVZSekPELKAjCPvhNSHiFlAZin/M5vr9Lu7GSPlJQMtfukpGTAyVld/2f1Jic/+//qj/nss//+SwAALFzwKwYP6YnFSybB1s4G/fqOR0ZGtnKfkSP7YN68b7Bi5bdo2zYE0dFLsGbNjjKmJW3S6JU0//vf/zBjxgy0bdsWo0aNwr179zBz5kyMGjUKYrEYc+fOhZmZGaKjo195HKlUCqlUqtImkUggkWgegIiIiHRPLn+22vfF4O4ICwsBAMTEfIlWLcOxe/ff6NXrfQDA0GG9lPvUq1cLubl5WLF8K/r161DxRZfAQBb2tE6jlcJVq1Zh1apV2LRpE3bv3o0JEybghx9+wIQJExAZGYmffvoJ69evf+1xYmJiYGdnp7LFxMSUOcSrODjYwsREjNRU1X+dpaZmwNnZoYS99JeQ8ggpC8A8+k5IeYSUBWCe8jt/hkp7SmoGnF9aDXzO2dkeqSnq+j+r18Xl2f9Xf0zVPt61qis/Nzc3Q7Vq7nj8OLnEev38fZCQkIL8/ILXRaswIpFC65sh0GhS+OjRIzRt2hQA4O/vD7FYjICAAOXnjRs3xqNHxR9Pf1lkZCQyMzNVtsjISM0qLyVzczPUr++N+Pjzyja5XI74+HNo1KhOuZyzPAkpj5CyAMyj74SUR0hZAOYpv/OfUzn/8fjzCGjkq3afgABfxB8/r9J27NhZBAQ861+1qhtcXBxUjvnkyVOcP3cdAf+fqUEDb5ibm+HOnQfKPgUFhXj4MBFVqriUWO/VK3dgZ2cDc3MzzcOSVml0+djd3R2XL19G9erVcePGDchkMly+fBn169cHAFy6dAmurq6vPc6zS8UVd604PLwTxo6diwYNvOHn54PVq7cjNzcPXbqEVlgN2iSkPELKAjCPvhNSHiFlAZhH2waEd8S4sfOKnP+P/z9/GwDA2G/mwtXNEV9/3R8A0LdfB/TrOx4rVmzFO63ews7Yv3Dp4k18++0wAIBIJEK/fh9hyeLf4FmjCjyqumH+D+vg6uqofJ2MjY0VevV6Hz/++CvcK7ugShUXrFi+FQDw/vvPnkA+cOAEUlMz4O9fBxKJGY79fRY//fQ7wj/tXCE/l9Iy1svHGk0KP/74Y/Tr1w8dO3ZEXFwcvvnmG4wePRqpqakQiUT4/vvv0a1bt/KqtczatWuBtLRMzJ+/DsnJ6ahbtyaWLYs2yMsSgLDyCCkLwDz6Tkh5hJQFYJ7yOv+P89crz7902RTl+R89ToaoyCOxjRvXxaxZX2PevHWYO2cNPD2rYMHC8fDxqaHs89mgLsjNzcPkyQuRlZWDJk3qYemyKSqvkxnzTThMTE0w9ps5yMvLh7+/D1at/h52djYAADNTE6xftxMxU5cDUKB69coYO24gevRoWyE/F3o1kUKD58DlcjmmTZuG+Ph4hISEYNy4cdi4cSO++eYbPH36FB06dMCCBQtgbW1dxnIM++31L/hAOFkA5tF3QsojpCwA8+gzIWUBAB8oYHiv7ymJCLq9bSAp7w+tH9PV4iOtH1PbNFopFIvFGD9+vEpbr1690KtXrxL2ICIiIjIsxnr5WPAvryYiIiKi19NopZCIiIhI6Ix1xcxYcxMRERFREVwpJCIiIipCZKQ3FXJSSERERKTCOGeFvHxMREREpIcWLlwIT09PWFhYICgoCCdOnCix76VLl9C1a1d4enpCJBJh3rx5Gp+Pk0IiIiKiIkTl8H+a2rhxIyIiIhAVFYXTp0/D398fYWFhSEpKUtv/6dOnqFmzJqZNmwZ3d/cy5eakkIiIiEjPzJkzB4MGDUJ4eDjq1auHJUuWwMrKCitWrFDb/6233sLMmTPRq1evMn+VMCeFREREREWIRGKtb5rIz8/HqVOnEBr64ruyxWIxQkNDER8fr+24SnzQhIiIiEiF9h80kUqlkEqlKm0SiUTtql5KSgpkMhnc3NxU2t3c3HD16lWt1/YcVwqJiIiIyllMTAzs7OxUtpiYGF2XpYIrhURERERFlOXBkNeJjIxERESESltJ9/45OzvDxMQEiYmJKu2JiYllfoikNLhSSERERFTOJBIJbG1tVbaSJoXm5uZo0qQJ4uLilG1yuRxxcXEIDg4utxq5UkhERESkQvcvr46IiED//v3RtGlTBAYGYt68ecjJyUF4eDgAoF+/fvDw8FBegs7Pz8fly5eV//vhw4c4e/YsbGxs4O3tXapzclJIREREVISmTwuXh549eyI5ORmTJ09GQkICAgICsHv3buXDJ/fv34dY/KLOR48eoVGjRspfz5o1C7NmzUKrVq1w6NChUp1TpFAoFFpNQURERGTAsgr2af2Ytmbvaf2Y2qZnK4XXdV2AlvhAOFkA5tF3QsojpCwA8+gzIWUBhJlHl3R/+VgXdL8+SkREREQ6p2crhURERES6VR6vpDEEnBQSERERFWGsk0JePiYiIiIirhQSERERqTLONTPjTE1EREREKrhSSERERFSESGSc9xRyUkhERESkwjgnhbx8TERERERcKSQiIiIqylhfScNJIREREZEK47yQapypiYiIiEgFVwqJiIiIijDWy8dGs1K4bt1OtG49EA0bdkH37l/j/Pnrui7pjQgpj5CyAMyj74SUR0hZAObRZ0LKQiUziklhbOwRxMQsw7BhvbF16zz4+nph4MDJSE3N0HVpZSKkPELKAjCPvhNSHiFlAZhHnwkpS2mJRCKtb4bAKCaFK1duQ48eYejaNRTe3tURHT0UFhYSbN68T9ellYmQ8ggpC8A8+k5IeYSUBWAefSakLKUnKodN/wl+UpifX4BLl24iJMRf2SYWixESEoAzZ67psLKyEVIeIWUBmEffCSmPkLIAzKPPhJSFXk/jSeHjx48xefJktG7dGnXr1kX9+vXRoUMHLF++HDKZrDxqfCPp6VmQyeRwcnJQaXdyskdKSrqOqio7IeURUhaAefSdkPIIKQvAPPpMSFk0IYJY65sh0KjKkydPom7duoiNjUVBQQFu3LiBJk2awNraGqNHj0bLli2RnZ392uNIpVJkZWWpbFKptMwhiIiIiOjNaDQp/OqrrzBq1CicPHkSR44cwapVq3D9+nVs2LABt2/fxtOnTzFx4sTXHicmJgZ2dnYqW0xMTJlDvIqDgy1MTMRITVX9F01qagacnR1K2Et/CSmPkLIAzKPvhJRHSFkA5tFnQsqiGd5T+FqnT59G3759lb/u06cPTp8+jcTERDg4OGDGjBnYtGnTa48TGRmJzMxMlS0yMlLz6kvB3NwM9et7Iz7+vLJNLpcjPv4cGjWqUy7nLE9CyiOkLADz6Dsh5RFSFoB59JmQsmjCWJ8+1ujl1a6urnj8+DFq1qwJAEhMTERhYSFsbW0BALVr10ZaWtprjyORSCCRSMpQbtmEh3fC2LFz0aCBN/z8fLB69Xbk5uahS5fQCqtBm4SUR0hZAObRd0LKI6QsAPPoMyFloVfTaFLYqVMnDB48GDNnzoREIsF3332HVq1awdLSEgBw7do1eHh4lEuhb6JduxZIS8vE/PnrkJycjrp1a2LZsmiDXfoWUh4hZQGYR98JKY+QsgDMo8+ElKX0DGNlT9tECoVCUdrOT548wcCBA7FlyxbIZDIEBwdj7dq18PLyAgDs3bsXmZmZ6N69exnLEcob0n0gnCwA8+g7IeURUhaAefSZkLIAwsyjO/nyU1o/prm4idaPqW0arRTa2Nhg48aNyMvLQ2FhIWxsbFQ+b9u2rVaLIyIiIqpohvIKGW3TaFL4nIWFhbbrICIiItITxnn52DinwkRERESkokwrhURERERCJeJKIREREREZK64UEhERERVhKC+b1jZOComIiIhUGOeFVONMTUREREQquFJIREREVAQfNCEiIiIio8WVQiIiIiIVxrlSyEkhERERURHG+vQxLx8TERER6aGFCxfC09MTFhYWCAoKwokTJ17Z//fff4evry8sLCzQsGFDxMbGanQ+TgqJiIiIVIjLYdPMxo0bERERgaioKJw+fRr+/v4ICwtDUlKS2v7Hjh1D7969MXDgQJw5cwadOnVCp06dcPHixVKfU6RQKBQaV1puruu6AC3xgXCyAMyj74SUR0hZAObRZ0LKAggzj+4ocE3rxxShjkb9g4KC8NZbb2HBggUAALlcjmrVqmHEiBEYN25csf49e/ZETk4OduzYoWxr1qwZAgICsGTJklKdkyuFREREREWIyuH/pFIpsrKyVDapVKr2/Pn5+Th16hRCQ0OVbWKxGKGhoYiPj1e7T3x8vEp/AAgLCyuxv1oKI5KXl6eIiopS5OXl6bqUNyakLAoF8+gzIWVRKJhHnwkpi0LBPKQqKipKAUBli4qKUtv34cOHCgCKY8eOqbSPGTNGERgYqHYfMzMzxfr161XaFi5cqHB1dS11jXp2+bh8ZWVlwc7ODpmZmbC1tdV1OW9ESFkA5tFnQsoCMI8+E1IWgHlIlVQqLbYyKJFIIJFIivV99OgRPDw8cOzYMQQHByvbv/nmGxw+fBj//PNPsX3Mzc2xevVq9O7dW9m2aNEiREdHIzExsVQ18pU0REREROWspAmgOs7OzjAxMSk2mUtMTIS7u7vafdzd3TXqrw7vKSQiIiLSI+bm5mjSpAni4uKUbXK5HHFxcSorh0UFBwer9AeAffv2ldhfHa4UEhEREemZiIgI9O/fH02bNkVgYCDmzZuHnJwchIeHAwD69esHDw8PxMTEAAC+/PJLtGrVCrNnz0b79u2xYcMGnDx5Ej///HOpz2lUk0KJRIKoqKhSL9/qMyFlAZhHnwkpC8A8+kxIWQDmoTfTs2dPJCcnY/LkyUhISEBAQAB2794NNzc3AMD9+/chFr+44BsSEoL169dj4sSJGD9+PGrXro1t27ahQYMGpT6nUT1oQkRERETq8Z5CIiIiIuKkkIiIiIg4KSQiIiIicFJIRERERDCiSeHChQvh6ekJCwsLBAUF4cSJE7ouqUz++usvdOjQAVWqVIFIJMK2bdt0XdIbiYmJwVtvvYVKlSrB1dUVnTp1wrVr2v8i8oqwePFi+Pn5wdbWFra2tggODsauXbt0XZbWTJs2DSKRCF999ZWuSymTKVOmQCQSqWy+vr66LqvMHj58iE8++QROTk6wtLREw4YNcfLkSV2XVSaenp7FxkYkEmHYsGG6Lq1MZDIZJk2aBC8vL1haWqJWrVr47rvvYKjPdWZnZ+Orr75CjRo1YGlpiZCQEPz777+6LovKgVFMCjdu3IiIiAhERUXh9OnT8Pf3R1hYGJKSknRdmsZycnLg7++PhQsX6roUrTh8+DCGDRuG48ePY9++fSgoKEDbtm2Rk5Oj69I0VrVqVUybNg2nTp3CyZMn0bp1a3Ts2BGXLl3SdWlv7N9//8VPP/0EPz8/XZfyRurXr4/Hjx8rt6NHj+q6pDJJT09H8+bNYWZmhl27duHy5cuYPXs2HBwcdF1amfz7778q47Jv3z4AQPfu3XVcWdlMnz4dixcvxoIFC3DlyhVMnz4dM2bMwI8//qjr0srks88+w759+7BmzRpcuHABbdu2RWhoKB4+fKjr0kjbSv0tyQYsMDBQMWzYMOWvZTKZokqVKoqYmBgdVvXmACi2bt2q6zK0KikpSQFAcfjwYV2XohUODg6KZcuW6bqMN5Kdna2oXbu2Yt++fYpWrVopvvzyS12XVCZRUVEKf39/XZehFWPHjlW8/fbbui6j3Hz55ZeKWrVqKeRyua5LKZP27dsrPv30U5W2Ll26KD7++GMdVVR2T58+VZiYmCh27Nih0t64cWPFhAkTdFQVlRfBrxTm5+fj1KlTCA0NVbaJxWKEhoYiPj5eh5WROpmZmQAAR0dHHVfyZmQyGTZs2ICcnByNvmJIHw0bNgzt27dX+TNkqG7cuIEqVaqgZs2a+Pjjj/+vvfsLaaqP4zj+qRMnxUbRH/VobLSizaxAHYpKV16NkK5qiRen1uUkTRKsLiJCu4uioFrEgmqVVPbvZtUqJSgS64S7KFmFBZURZEujRTu/5+qRx8ceYsc9z+/Z+Lzg3Jyr99jF+Z4fv/2GN2/eyE6y5Pr16/B4PNi4cSMKCwtRUVGBkydPys7KiB8/fuDs2bPw+/2YNWuW7BxL6urqEI1GMTw8DAB49uwZHjx4AK/XK7ksfT9//kQqlUJeXt6U+/n5+Vm70k7/LOf/0eTTp09IpVKTJ4D/qaioCM+fP5dURb9imiba2tpQX1+f1gns/ydDQ0Oora3F9+/fMW/ePPT29mLVqlWysyy7cOECnjx5khP7h2pqanD69Gm4XC68f/8e+/btw7p16xCLxWCz2WTnpeXVq1c4duwY2tvbsXv3bgwMDGD79u1QVRW6rsvOm5GrV69ibGwMW7ZskZ1iWWdnJxKJBNxuNxRFQSqVQldXF5qbm2Wnpc1ms6G2thb79+9HWVkZioqKcP78eTx8+BArVqyQnUcZlvNDIWWPQCCAWCyW1W+fLpcLhmHgy5cvuHTpEnRdR19fX1YOhm/fvkVraytu3749bZUgG/11lWbt2rWoqamBw+FAT08Ptm3bJrEsfaZpwuPxoLu7GwBQUVGBWCyG48ePZ/1QeOrUKXi9XpSUlMhOsaynpwfnzp1DOBxGeXk5DMNAW1sbSkpKsvL7OXPmDPx+P0pLS6EoCiorK9HU1ITBwUHZaZRhOT8ULl68GIqiYHR0dMr90dFRFBcXS6qiv2tpacHNmzfR39+PpUuXys6xTFXVybfnqqoqDAwM4PDhwzhx4oTksvQNDg7i48ePqKysnLyXSqXQ39+Po0ePIplMQlEUiYUzs2DBAqxcuRLxeFx2Sto0TZv2olFWVobLly9LKsqMkZER3LlzB1euXJGdMiMdHR3o7OzE5s2bAQBr1qzByMgIDhw4kJVD4fLly9HX14eJiQkkEglomgafzwen0yk7jTIs5/cUqqqKqqoqRKPRyXumaSIajWb9Xq9cIIRAS0sLent7cffuXSxbtkx2UkaZpolkMik7w5KGhgYMDQ3BMIzJy+PxoLm5GYZhZPVACADj4+N4+fIlNE2TnZK2+vr6aUc3DQ8Pw+FwSCrKjFAohMLCQqxfv152yox8+/YNs2dPfbwqigLTNCUVZUZBQQE0TcPnz58RiUSwYcMG2UmUYTm/UggA7e3t0HUdHo8H1dXVOHToECYmJrB161bZaWkbHx+fsrLx+vVrGIaBhQsXwm63SyyzJhAIIBwO49q1a7DZbPjw4QMAYP78+cjPz5dcl55du3bB6/XCbrfj69evCIfDuH//PiKRiOw0S2w227S9nQUFBVi0aFFW7vncuXMnGhsb4XA48O7dO+zduxeKoqCpqUl2Wtp27NiBuro6dHd3Y9OmTXj8+DGCwSCCwaDsNMtM00QoFIKu65gzJ7sfTY2Njejq6oLdbkd5eTmePn2KgwcPwu/3y06zJBKJQAgBl8uFeDyOjo4OuN3urHyG0m/I/vnzf+XIkSPCbrcLVVVFdXW1ePTokewkS+7duycATLt0XZedZsmvPgsAEQqFZKelze/3C4fDIVRVFUuWLBENDQ3i1q1bsrMyKpuPpPH5fELTNKGqqigtLRU+n0/E43HZWZbduHFDrF69WsydO1e43W4RDAZlJ81IJBIRAMSLFy9kp8xYIpEQra2twm63i7y8POF0OsWePXtEMpmUnWbJxYsXhdPpFKqqiuLiYhEIBMTY2JjsLPoXzBIiS49YJyIiIqKMyfk9hURERET0exwKiYiIiIhDIRERERFxKCQiIiIicCgkIiIiInAoJCIiIiJwKCQiIiIicCgkIiIiInAoJCIiIiJwKCQiIiIicCgkIiIiInAoJCIiIiIAfwATs+QsB1gdsgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 700x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot Ising matrix\n",
    "plt.figure(1, figsize=[7, 5])\n",
    "sns.heatmap(J, annot=True,  linewidths=.5, cmap=\"YlGnBu\", annot_kws = {'alpha': 1})\n",
    "plt.title('Ising distance matrix');\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IMPLEMENTATION OF QAOA WITH BRAKET "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we load a set of useful helper functions that we will explain in detail below. \n",
    "Specifically in ```utils_qaoa.py``` we provide simple building blocks for the core modules of our QAOA algorithm, that is (i) a function called ```circuit``` that defines the parametrized ansatz, (ii) a function called ```objective_function``` that takes a list of variational parameters as input, and returns the cost associated with those parameters and finally (iii) a function ```train``` to run the entire QAOA algorithm for given ansatz. \n",
    "This way we can solve the problem in a clean and modular approach.\n",
    "Here, we show in markdown the definition of the parametrized QAOA circuit. \n",
    "For more details, see the corresponding file ```utils_qaoa.py```. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "from utils_qaoa import circuit, train \n",
    "# auto reload external files, so that we can edit the external .py file and immediately see the changes here\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "# function to implement evolution with driver Hamiltonian\n",
    "def driver(beta, n_qubits):\n",
    "    \"\"\"\n",
    "    Returns circuit for driver Hamiltonian U(Hb, beta)\n",
    "    \"\"\"\n",
    "    # instantiate circuit object\n",
    "    circ = Circuit()\n",
    "    \n",
    "    for qubit in range(n_qubits):\n",
    "        gate = Circuit().rx(qubit, 2*beta)\n",
    "        circ.add(gate)\n",
    "    \n",
    "    return circ\n",
    "\n",
    "\n",
    "# helper function for evolution with cost Hamiltonian\n",
    "def cost_circuit(gamma, n_qubits, ising):\n",
    "    \"\"\"\n",
    "    returns circuit for evolution with cost Hamiltonian\n",
    "    \"\"\"\n",
    "    # instantiate circuit object\n",
    "    circ = Circuit()\n",
    "\n",
    "    # get all non-zero entries (edges) from Ising matrix \n",
    "    idx = ising.nonzero()\n",
    "    edges = list(zip(idx[0], idx[1]))\n",
    "    \n",
    "    for qubit_pair in edges:\n",
    "        # get interaction strength\n",
    "        int_strength = ising[qubit_pair[0], qubit_pair[1]]\n",
    "        # for Rigetti we decompose ZZ using CNOT gates\n",
    "        if 'Aspen' in device.name:\n",
    "            gate = ZZgate(qubit_pair[0], qubit_pair[1], gamma*int_strength)\n",
    "            circ.add(gate)\n",
    "        # classical simulators and IonQ support ZZ gate\n",
    "        else:\n",
    "            gate = Circuit().zz(qubit_pair[0], qubit_pair[1], angle=2*gamma*int_strength)\n",
    "            circ.add(gate)\n",
    "\n",
    "    return circ\n",
    "\n",
    "\n",
    "# function to build the QAOA circuit with depth p\n",
    "def circuit(params, n_qubits, ising):\n",
    "    \"\"\"\n",
    "    function to return full QAOA circuit\n",
    "    \"\"\"\n",
    "\n",
    "    # initialize qaoa circuit with first Hadamard layer: for minimization start in |->\n",
    "    circ = Circuit()\n",
    "    X_on_all = Circuit().x(range(0, n_qubits))\n",
    "    circ.add(X_on_all)\n",
    "    H_on_all = Circuit().h(range(0, n_qubits))\n",
    "    circ.add(H_on_all)\n",
    "\n",
    "    # setup two parameter families\n",
    "    circuit_length = int(len(params) / 2)\n",
    "    gammas = params[:circuit_length]\n",
    "    betas = params[circuit_length:]\n",
    "\n",
    "    # add circuit layers\n",
    "    for mm in range(circuit_length):\n",
    "        circ.add(cost_circuit(gammas[mm], n_qubits, ising))\n",
    "        circ.add(driver(betas[mm], n_qubits))\n",
    "\n",
    "    return circ\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## VISUALIZATION OF THE QAOA ANSATZ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first visualize our parametrized QAOA ansatz for a small number of qubits and fixed (i.e., not optimized) parameters. \n",
    "For convenience, the parameters are displayed in the circuit (up to a factor of $2$ we have added in our ansatz definition). \n",
    "First we prepare the state $|0,0,\\dots\\rangle \\rightarrow |-,-,\\dots\\rangle$, with the superposition state $|-\\rangle = (|0\\rangle -|1\\rangle  )/\\sqrt{2}$. \n",
    "Following the discussion above, we choose to start out with this state as it is the minimal energy state of the simple driver Hamiltonian $H_{B}$. \n",
    "This state preparation is followed by one layer of the QAOA ansatz, consisting of evolution with the cost Hamiltonian by $\\exp(-i\\gamma H_{C})= \\prod_{j,l}\\exp(-i\\gamma J_{j,l}\\sigma_{j}^{z}\\sigma_{l}^{z}) = \\prod_{j,l} ZZ_{j,l}(2\\gamma J_{j,l})$, followed by the single-qubit driving term, $\\exp(-i\\beta H_{B})= \\prod_{j} \\exp(-i\\beta \\sigma_{j}^{x})= \\prod_{j} R_{j}^{(x)}(2\\beta)$.\n",
    "Note that the circuit definition depends on the ```device``` object, as the implementation of the ZZ gate depends on the specific gate set supported by the device.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing test circuit:\n",
      "T  : |0|1|     2     |    3     |\n",
      "                                 \n",
      "q0 : -X-H-ZZ(2*gamma)-Rx(2*beta)-\n",
      "          |                      \n",
      "q1 : -X-H-ZZ(2*gamma)-Rx(2*beta)-\n",
      "\n",
      "T  : |0|1|     2     |    3     |\n",
      "\n",
      "Unassigned parameters: [beta, gamma].\n"
     ]
    }
   ],
   "source": [
    "# create parameters\n",
    "gammas = [FreeParameter('gamma')]\n",
    "betas = [FreeParameter('beta')]\n",
    "params = gammas + betas\n",
    "\n",
    "# for demonstration purposes use small Ising matrix\n",
    "J_sub = np.array([[0, 1], [0, 0]])\n",
    "N = J_sub.shape[0]\n",
    "\n",
    "# get circuit ansatz\n",
    "my_simple_circuit = circuit(params, device, N, J_sub)\n",
    "\n",
    "# print test ansatz circuit\n",
    "print('Printing test circuit:')\n",
    "print(my_simple_circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that our ansatz produces the expected result for shallow QAOA with $p=1$. \n",
    "We run one more sanity check for $p=2$ below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Printing test circuit:\n",
      "T  : |0|1|      2      |     3      |      4      |     5      |\n",
      "                                                                \n",
      "q0 : -X-H-ZZ(2*gamma_1)-Rx(2*beta_1)-ZZ(2*gamma_2)-Rx(2*beta_2)-\n",
      "          |                          |                          \n",
      "q1 : -X-H-ZZ(2*gamma_1)-Rx(2*beta_1)-ZZ(2*gamma_2)-Rx(2*beta_2)-\n",
      "\n",
      "T  : |0|1|      2      |     3      |      4      |     5      |\n",
      "\n",
      "Unassigned parameters: [beta_1, beta_2, gamma_1, gamma_2].\n"
     ]
    }
   ],
   "source": [
    "# set number of qubits and fix parameters\n",
    "gammas = [FreeParameter('gamma_1'), FreeParameter('gamma_2')]\n",
    "betas = [FreeParameter('beta_1'), FreeParameter('beta_2')]\n",
    "params = gammas + betas\n",
    "\n",
    "# for demonstration purposes use small Ising matrix\n",
    "J_sub = np.array([[0, 1], [0, 0]])\n",
    "N = J_sub.shape[0]\n",
    "\n",
    "# get circuit ansatz\n",
    "my_simple_circuit = circuit(params, device, N, J_sub)\n",
    "\n",
    "# print test ansatz circuit\n",
    "print('Printing test circuit:')\n",
    "print(my_simple_circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QAOA SIMULATION ON LOCAL SCHROEDINGER SIMULATOR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are now all set to run some QAOA simulation experiments. \n",
    "First of all, you can play and experiment yourself with the number of qubits $N$. \n",
    "Secondly, you may also experiment with the classical optimizer. \n",
    "Since we are using an off-the-shelf, black-box ```scipy``` minimizer (as described in more detail [here](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html)), you can simply swap between different optimizers by setting the ```OPT_METHOD``` parameter below. \n",
    "Some popular options readily available within this library include *Nelder-Mead*, *BFGS* and *COBYLA*. \n",
    "As a precautionary warning, note that the classical optimization step may get stuck in a local optimum, rather than finding the global minimum for our parametrized QAOA ansatz wavefunction. \n",
    "To address this issue, we may run several optimization loops, starting from different random parameter seeds. \n",
    "While this brute-force approach does not provide any guarantee to find the global optimum, from a pragmatic point of view at least it does increase the odds of finding an acceptable solution, at the expense of potentially having to run many more circuits on the simulator or QPU, respectively.\n",
    "Finally, the optimization loop may require the execution of many individual quantum tasks (i.e., single circuit executions for fixed parameters). \n",
    "For example, when choosing the classical [Powell](https://docs.scipy.org/doc/scipy/reference/optimize.minimize-powell.html#optimize-minimize-powell) optimizer for the graph considered here, we find $\\sim 270$ cycles in the for loop. \n",
    "For the local simulator device chosen here by default this is not an issue, but if you run this algorithm on any QPU you may want to adjust the ```maxfev``` parameter to control the maximum allowed number function evaluations (compare comment in the next code block below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "##################################################################################\n",
    "# set up hyperparameters\n",
    "##################################################################################\n",
    "\n",
    "# User-defined hypers\n",
    "DEPTH = 3  # circuit depth for QAOA\n",
    "SHOTS = 1000  # number measurements to make on circuit\n",
    "OPT_METHOD = 'COBYLA'  # SLSQP, COBYLA, Nelder-Mead, BFGS, Powell, ...\n",
    "\n",
    "# set up the problem\n",
    "n_qubits = J.shape[0]\n",
    "\n",
    "# initialize reference solution (simple guess)\n",
    "bitstring_init = -1 * np.ones([n_qubits])\n",
    "energy_init = np.dot(bitstring_init, np.dot(J, bitstring_init))\n",
    "\n",
    "# set tracker to keep track of results\n",
    "tracker = {\n",
    "    'count': 1,                           # Elapsed optimization steps\n",
    "    'optimal_energy': energy_init,        # Global optimal energy\n",
    "    'opt_energies': [],                   # Optimal energy at each step\n",
    "    'global_energies': [],                # Global optimal energy at each step\n",
    "    'optimal_bitstring': bitstring_init,  # Global optimal bitstring\n",
    "    'opt_bitstrings': [],                 # Optimal bitstring at each step\n",
    "    'costs': [],                          # Cost (average energy) at each step\n",
    "    'res': None,                          # Quantum result object\n",
    "    'params': []                          # Track parameters\n",
    "}\n",
    "\n",
    "# set options for classical optimization\n",
    "options = {'disp': True, 'maxiter': 50}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit depth hyperparameter: 3\n",
      "Problem size: 10\n",
      "Starting the training.\n",
      "====================================================================\n",
      "OPTIMIZATION for circuit depth p=3\n",
      "Param \"verbose\" set to False. Will not print intermediate steps.\n",
      "====================================================================\n",
      "Final average energy (cost):\n",
      "   Return from subroutine COBYLA because the MAXFUN limit has been reached.\n",
      " -0.586455292294228\n",
      "Final angles: [5.78684986 4.70523429 6.47840919 0.25681156 1.2539245  2.7942261 ]\n",
      "Training complete.\n",
      "Code execution time [sec]: 6.3666791915893555\n",
      "Optimal energy: -6.486032631497276\n",
      "Optimal classical bitstring: [-1  1 -1 -1  1 -1  1  1 -1 -1]\n",
      "\n",
      "   NFVALS =   50   F =-5.864553E-01    MAXCV = 0.000000E+00\n",
      "   X = 5.786850E+00   4.705234E+00   6.478409E+00   2.568116E-01   1.253925E+00\n",
      "       2.794226E+00\n"
     ]
    }
   ],
   "source": [
    "##################################################################################\n",
    "# run QAOA optimization on graph \n",
    "##################################################################################\n",
    "\n",
    "print('Circuit depth hyperparameter:', DEPTH)\n",
    "print('Problem size:', n_qubits)\n",
    "\n",
    "# kick off training\n",
    "start = time.time()\n",
    "result_energy, result_angle, tracker = train(\n",
    "    device = device, options=options, p=DEPTH, ising=J, n_qubits=n_qubits, n_shots=SHOTS, \n",
    "    opt_method=OPT_METHOD, tracker=tracker, verbose=verbose)\n",
    "end = time.time()\n",
    "\n",
    "# print execution time\n",
    "print('Code execution time [sec]:', end - start)\n",
    "\n",
    "# print optimized results\n",
    "print('Optimal energy:', tracker['optimal_energy'])\n",
    "print('Optimal classical bitstring:', tracker['optimal_bitstring'])\n",
    "\n",
    "##################################################################################\n",
    "# Compute output and dump to pickle\n",
    "##################################################################################\n",
    "\n",
    "if store_results:\n",
    "    out = {'p': DEPTH, 'N': n_qubits,\n",
    "           'ENERGY_OPTIMAL': tracker['optimal_energy'], 'BITSTRING': tracker['optimal_bitstring'],\n",
    "           'result_energy': result_energy, 'result_angle': result_angle}\n",
    "\n",
    "    # store results: dump output to pickle with timestamp in filename\n",
    "    time_now = datetime.strftime(datetime.now(), '%Y%m%d%H%M%S')\n",
    "    results_file = 'results-'+time_now+'.pkl'\n",
    "    print(f'Writing results to file: {results_file}')\n",
    "    pickle.dump(out, open(results_file, \"wb\"))\n",
    "    \n",
    "    # you can load results as follows\n",
    "    # out = pickle.load(open(results_file, \"rb\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## POSTPROCESSING AND COMPARISON OF OUR QAOA RESULTS WITH CLASSICAL RESULTS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we visualize the results we have found with QAOA. \n",
    "Specifically, we display the results found for the variational parameters $\\beta$ and $\\gamma$ for every layer in our QAOA ansatz. \n",
    "Moreover, we show the solution to our graph coloring problem with every node colored either red or blue (recall that there are just two colors since we solve a _binary_ optimization problem).\n",
    "Finally, we compare these results to results found classically using the open-source ```pyqubo``` package. \n",
    "Ideally, the two results should agree with each other but this is not necessarily the case for several reasons: \n",
    "First of all, for the original small toy problem we have set up there are several degenerate classical solutions with the same optimal quality. \n",
    "The classical and the QAOA approach may find solutions with different coloring configurations but the same quality (that is energy). \n",
    "Secondly, with QAOA we are not guaranteed to find the optimal solutions. \n",
    "Specifically, the deeper the circuit, the harder the classical optimization problem, and we may get stuck in a local rather than global optimum. \n",
    "One brute-force approach is then to just re-run QAOA with different random initial seeds for the parameters $(\\beta, \\gamma)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization on graph with n=10 vertices, m=20 edges, optimized with COBYLA and 1000 shots per call; seed=42.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize the optimization process\n",
    "cycles = np.arange(1, tracker['count'])\n",
    "optim_classical = tracker['global_energies']\n",
    "\n",
    "# print information\n",
    "info = 'Optimization on graph with n={} vertices, m={} edges, optimized with {} and {} shots per call; seed={}.'\n",
    "print(info.format(n, m, OPT_METHOD, SHOTS, seed))\n",
    "\n",
    "plt.plot(cycles, optim_classical)\n",
    "plt.xlabel('optimization cycle')\n",
    "plt.ylabel('best classical minimum')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal energy found with QAOA: -6.486032631497276\n",
      "Optimal bit-string found with QAOA: [-1  1 -1 -1  1 -1  1  1 -1 -1]\n"
     ]
    }
   ],
   "source": [
    "# print the optimal energy found with QAOA \n",
    "print('Optimal energy found with QAOA:', tracker['optimal_energy'])\n",
    "# print the corresponding bitstring\n",
    "print('Optimal bit-string found with QAOA:', tracker['optimal_bitstring'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# get results for variational angles\n",
    "gamma = result_angle[:DEPTH]\n",
    "beta = result_angle[DEPTH:]\n",
    "# get array [1, 2, ..., p]\n",
    "pa = np.arange(1, DEPTH + 1)\n",
    "\n",
    "plt.figure(2)\n",
    "plt.plot(pa, gamma / np.pi, '-o', label='gamma')\n",
    "plt.plot(pa, beta / np.pi, '-s', label='beta')\n",
    "plt.xlabel('circuit depth (layer) p')\n",
    "plt.ylabel('optimal angles [pi]')\n",
    "plt.xticks(pa)\n",
    "plt.legend(title='Variational QAOA angles:', loc='upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Minimal energy found with QAOA: -6.486032631497276\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualize solution\n",
    "colorlist = tracker['optimal_bitstring']\n",
    "colorlist[colorlist == -1] = 0\n",
    "\n",
    "# plot_colored_graph(J, N, colorlist, pos)\n",
    "plot_colored_graph_simple(G, colorlist, pos)\n",
    "print('Minimal energy found with QAOA:', tracker['optimal_energy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Classical solution: {'s0': -1, 's1': 1, 's2': -1, 's3': -1, 's4': 1, 's5': -1, 's6': 1, 's7': 1, 's8': -1, 's9': -1}\n",
      "Minimal energy found classically: -6.486032631497276\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# validate quantum results with classical algorithm\n",
    "solution, energy_min, colors_classical = solve_classical_ising(J, n_qubits, pos)\n",
    "# plot classical solution\n",
    "plot_colored_graph_simple(G, colors_classical, pos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that QAOA may arrive at a different solution than our classical benchmark code. \n",
    "First of all, the classical optimization routine may get stuck in a local rather than global optimum. \n",
    "To avoid this, more sophisticated optimization strategies may be employed (as proposed for example in Ref.[4]), going beyond the scope of this introductory notebook tutorial. \n",
    "Secondly, even if QAOA arrives at the same classical energy as our classical approach, the coloring may differ since the solution space may be degenerate for the specific example shown here (this means, two different classical bitstrings have the same energy).\n",
    "At minimum, you may find an inverted coloring (by swapping red and blue colors), because of the underlying $\\mathbb{Z}_{2}$ symmetry. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SUMMARY"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we have gone through an end-to-end demo on QAOA and its implementation on Amazon Braket. \n",
    "We have built modular core building blocks that may easily adapted to other problems. \n",
    "The QAOA routine is tailored towards solving combinatorial optimization problems such as _Maximum Cut_ [4] and arguably one of the most prominent examples of the emerging class of hybrid, variational algorithms and still very much a field of active research today. \n",
    "For example, as we increase the circuit depth of QAOA, the classical optimization step becomes increasingly difficult (because of the curse of dimensionality as well known in classical machine learning) and may easily get stuck in local sub-optimal solutions. \n",
    "To address this issue some heuristics have already been developed, for example in Ref.[4], but further improvements will arguably be necessary to fully unlock the potential of this approach. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## REFERENCES"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[1] E. Farhi, J. Goldstone, and S. Gutmann, \"A Quantum Approximate Optimization Algorithm\", arXiv: 1411.4028 (2014).\n",
    "\n",
    "[2] Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferova, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. Sawaya, et al., \"Quantum Chemistry in the Age of Quantum Computing\", Chemical reviews 119, 10856 (2019).\n",
    "\n",
    "[3] A. Smith, M. Kim, F. Pollmann, and J. Knolle, \"Simulating quantum many-body dynamics on a current digital quantum computer\", npj Quantum Information 5, 1 (2019).\n",
    "\n",
    "[4] L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, \"Quantum Approximate Optimization Algorithm: Performance, Mechanism,and Implementation on Near-Term Devices\", arXiv: 1812.01041 (2018). \n",
    "\n",
    "[5] F. Glover, G. Kochenberger, \"A Tutorial on Formulating and Using QUBO Models\", arXiv:1811.11538 (2018).\n",
    "\n",
    "[6] P. Vikstal, M. Groenkvist, M. Svensson, M. Andersson, G. Johansson, and G. Ferrini, \"Applying the Quantum Approximate Optimization Algorithm to the Tail Assignment Problem\", arXiv:1912.10499 (2019). \n",
    "\n",
    "[7] L. Li, M. Fan, M. Coram, P. Riley, and S. Leichenauer, \"Quantum optimization with a novel gibbs objective function and ansatz architecture search\", arXiv:1909.07621 (2019). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## APPENDIX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Version: 1.35.4.post0\n",
      "Version: 1.11.5.post0\n"
     ]
    }
   ],
   "source": [
    "# Check SDK version\n",
    "!pip show amazon-braket-sdk | grep Version\n",
    "!pip show amazon-braket-default-simulator | grep Version\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### APPENDIX: Example for Ising Matrix Syntax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this appendix we provide a small code example to showcase how we obtain all edges with corresponding weights. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ising matrix:\n",
      " [[0 1 0]\n",
      " [0 0 3]\n",
      " [0 0 0]]\n",
      "Edges: [(0, 1), (1, 2)]\n",
      "Interaction strength: 1\n",
      "Interaction strength: 3\n",
      "All interactions: [1 3]\n"
     ]
    }
   ],
   "source": [
    "# example Ising matrix with edges between qubit 0 and qubit 1 (weight=1) and qubit 1 and qubit 2 (weight=3)\n",
    "ising = np.array([[0, 1, 0], [0, 0, 3], [0, 0, 0]])\n",
    "print('Ising matrix:\\n', ising)\n",
    "\n",
    "# get all non-zero entries (edges) from Ising matrix \n",
    "idx = ising.nonzero()\n",
    "edges = list(zip(idx[0], idx[1]))\n",
    "print('Edges:', edges)\n",
    "\n",
    "# for every edge print interaction strength\n",
    "for qubit_pair in edges:\n",
    "    # get interaction strength\n",
    "    int_strength = ising[qubit_pair[0], qubit_pair[1]]\n",
    "    print('Interaction strength:', int_strength)\n",
    "\n",
    "# get all non-zero entries from Ising, with proper order\n",
    "interactions = np.array([ising[q[0], q[1]] for q in edges])\n",
    "print('All interactions:', interactions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Task Summary\n",
      "{}\n",
      "Estimated cost to run this example with SV1: 0 USD\n"
     ]
    }
   ],
   "source": [
    "print(\"Quantum Task Summary\")\n",
    "print(t.quantum_tasks_statistics())\n",
    "print(f\"Estimated cost to run this example with SV1: {t.qpu_tasks_cost() + t.simulator_tasks_cost()} USD\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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