laptopalt.ipynb

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   "source": [
    "# A short Introduction to Open Quantum Systems"
   ]
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    "### From master equations to exact numerical methods\n",
    "\n",
    "Neill Lambert, RIKEN, nwlambert@gmail.com\n",
    "\n",
    "#### Partially based on:\n",
    "- Ahsan Nazir's Lecture Notes on Open quantum systems https://workspace.imperial.ac.uk/people/Public/anazir1/open_systems_notes.pdf\n",
    "\n",
    "- \"The theory of open quantum systems\" by H.-P. Breuer and F. Petruccione.\n",
    "\n",
    "- Robert Johansson's series of Lectures on QuTiP \n",
    "https://github.com/jrjohansson/qutip-lectures\n",
    "\n",
    "- Uses QuTiP\n",
    "http://qutip.org/\n"
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    "\n",
    "\n",
    "# Outline:\n",
    "\n",
    "## Part 1\n",
    "\n",
    "- Motivation:  from quantum optics and physical chemistry to quantum technologies\n",
    "\n",
    "\n",
    "- The Lindblad Master equation; a quick derivation\n"
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    "\n",
    "## Part 2\n",
    "\n",
    "\n",
    "- QuTiP examples and applications\n",
    "\n",
    "    - Direct integration\n",
    "    \n",
    "    - Monte-Carlo simulation\n"
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    "    \n",
    "## Part 3\n",
    "\n",
    "\n",
    "- Beyond the Master Equation: Exact numerical methods for bosonic baths\n",
    "\n",
    "    - The Hierarchy Equations of Motion\n",
    "    \n",
    "    - The Reaction Coordinate\n",
    "    \n",
    "    \n",
    "- Conclusions "
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   "source": [
    "## Motivation"
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    "Every quantum system inevitably interacts with its environment.  \n",
    "\n",
    "In general, it is impossible for us to model the whole dynamics of the system and environment.\n",
    "\n",
    "So the goal of the theory of open quantum systems is to construct minimal solvable models and methods which account for the influence of the environment on the system.\n",
    "\n",
    "\n",
    "<img src=\"sys-env.png\" height=\"400\" width=\"400\"/>\n"
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    "\n",
    "# The motivation for the study of open quantum systems arises from:\n",
    "\n",
    "1. **Describing real experiments** involving quantum degrees of freedom in contact with an environment, and real measurements, e.g.,\n",
    "\n",
    "\n"
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   "source": [
    "## Quantum optics\n",
    "<img src=\"QED.png\" height=\"400\" width=\"400\"/>"
   ]
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   "source": [
    "## Quantum technologies\n",
    "\n",
    "<img src=\"qtech1.png\" height=\"400\" width=\"400\"/>"
   ]
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   "source": [
    "## Physical chemistry and Chemical physics\n",
    "<img src=\"fmo.png\" height=\"600\" width=\"600\"/>"
   ]
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   "source": [
    "## Motivation\n",
    "\n",
    "### 2) **Developing a theory of ``quantum dissipation''** and more recently, quantum thermodynamics.\n",
    "\n",
    "- E.g., the Caldeira-Leggett model allows us to derive classical dissipation/friction from a quantum foundation\n"
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    "\n",
    "### 3) In **quantum technologies and devices** this is typically an unwanted interaction.  \n",
    "\n",
    "- If its unavoidable, or even strong, to what degree can we work around it or mitigate it? \n",
    "\n",
    "(e.g., using feedback, environment engineering, decoherence free spaces, topological protection)\n"
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    "# Part 1: The Lindblad Master equation; a quick derivation\n",
    "\n",
    "\n",
    "Steps:\n",
    "\n",
    "1) A few definitions: density matrix, system and environment (bath) Hamiltonians\n",
    "\n",
    "2) Born - Markov approximations\n",
    "\n",
    "3) The bath correlation function\n",
    "\n",
    "4) An explicit example:  the spin-boson model\n",
    "\n",
    "5) The secular approximation!\n",
    "\n",
    "6) And finally, the Lindblad Master Equation"
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    "## Definitions: The density operator\n",
    "\n",
    "When a quantum system is effectively \"closed\" we describe its dynamics and evolution in terms of a pure state $|\\psi(t)\\rangle$ whose evolution is determined by a Hamiltonian and the Schrodinger equation\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} |\\psi(t)\\rangle = -i H(t) |\\psi(t)\\rangle$$\n",
    "\n",
    "More generally, for open systems it is convenient to use the density operator, which for a pure state, is given by\n",
    "\n",
    "$$\\rho = |\\psi(t)\\rangle \\langle \\psi(t)|$$\n",
    "\n",
    "\n"
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    "When describing one part of a larger composite system, as is the case for open systems \n",
    "<span style=\"color:red\">when we trace out the environment degress of freedom</span>,  the loss of knowledge about the influence of the other systems introduces \n",
    "<span style=\"color:red\">statistical uncertainty</span>. \n",
    "\n",
    "This then gives rise to mixed states, in terms of a statistical ensemble of possible pure states, such that;\n",
    "\n",
    "$$\\rho = \\sum_n p_n |\\psi_n(t)\\rangle \\langle \\psi_n(t)|$$\n",
    "\n",
    "\n",
    "The evolution of the density operator obeys the Liouville-von Neumann equation of motion,\n",
    "\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\rho(t) = -i [H(t), \\rho(t)]$$\n",
    "\n",
    "\n"
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    "\n",
    "\n",
    "\n",
    "The density operator itself has some important properties;\n",
    "\n",
    "-- For pure states $\\rho^2=\\rho$\n",
    "\n",
    "-- It is Hermitian $\\rho^{\\dagger} = \\rho$.\n",
    "\n",
    "-- It has trace one $\\mathrm{Tr}\\rho = 1$.\n",
    "\n",
    "-- Expectation values of system operators can be evaluated as $\\langle A \\rangle =\\mathrm{Tr}(A\\rho)$.\n",
    "\n",
    "\n",
    "\n",
    "\n"
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    "## The system and environment Hamiltonians\n",
    "\n",
    "Ultimately the influence of a large environment on a systems evolution is to induce statistical uncertainty into its dynamical evolution.  \n",
    "\n",
    "This gives rise to dissipation (emission and absorbtion of energy) and dephasing (localization into particular states).\n",
    "\n",
    "The philosophy we will describe here is to start with an \n",
    "<span style=\"color:red\"> explicit Hamiltonian description of the system (**S**) and the full Environment (**E**) </span>, with the Hilbert space\n",
    "\n",
    "$$\\mathcal{H} = \\mathcal{H}_S \\otimes \\mathcal{H}_E$$\n",
    "\n"
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    "and then \n",
    "<span style=\"color:red\"> derive effective models, or equations of motion,</span> for the redused density operator of the system alone, after tracing out the environment degrees of freedom, i.e.,\n",
    "\n",
    "$$\\rho_S(t) = \\mathrm{Tr}_E[\\rho(t)]$$ \n",
    "\n",
    "since $\\rho_S(t)$ descrives all pertinent and accesible information about the system itself.\n"
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    "\n",
    "The full dynamics of the system and environment would in principle be described by the Hamiltonian\n",
    "\n",
    "$$H = H_S + H_E + H_I$$\n"
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    "\n",
    "In general, one can describe the evolution of the whole system and environment, \n",
    "<span style=\"color:red\"> in the interaction picture </span>, as \n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}(t) = -i [\\tilde{H}_I(t), \\tilde{\\rho}(t)]$$\n",
    "\n",
    "where the interaction pictures moves the free evolution of both the system and environment into the operators themselves,\n",
    "such that\n",
    "\n",
    "$$\\tilde{H}_I(t) = e^{i(H_S + H_E)t} H_I e^{-i(H_S + H_E)t}$$\n",
    "\n"
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    "Formally we can solve the equation of motion with\n",
    "\n",
    "$$\\tilde{\\rho}(t) = \\rho(0) - i \\int_0^t ds [\\tilde{H}_I(s),\\tilde{\\rho}(s)]$$\n",
    "\n",
    "Substituting this into the RHS of the original equation of motion, and formally \n",
    "<span style=\"color:red\"> tracing out the environment degrees of freedom </span>, gives,\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) = -i \\mathrm{Tr}_E[\\tilde{H}_I(t), \\tilde{\\rho}(0)]  -  \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho}(s)]$$"
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    "## The Born Approximation\n",
    "\n",
    "This is still an intractable equation of motion.  To make progress we must make a series of \n",
    "<span style=\"color:red\">assumptions</span>:\n",
    "\n"
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    "\n",
    "-- \n",
    "<span style=\"color:red\"> **Factorizable initial conditions** </span>: We assume that at $t=0$ the system and environment are seperable, such that \n",
    "\n",
    "$$\\rho(0) = \\rho_S(0) \\otimes \\rho_E(0)$$\n"
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    "-- <span style=\"color:red\"> **The Born approximation**</span>: In addition, we assume that the density matrix <span style=\"color:red\">factorises</span> at all times, and that the <span style=\"color:red\"> environment state is time-independant</span>,\n",
    "\n",
    "$$\\rho(t) = \\rho_S(t) \\rho_E(0)$$\n",
    "\n",
    "This assumes that the environment is mostly unaffacted by the interaction with the system. (Any excitations emitted by the system quickly decay in the environment)\n",
    "\n",
    "-- Note: We also remove the first term on the RHS (for many examples it is zero, or it can be cancelled with a c-number term in the system Hamiltonian).\n",
    "\n"
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    "Under these assumptions,\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  - \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho_S}(s)\\rho_E]$$\n",
    "\n",
    "This equation of motion assumes weak coupling, as the system and environment remain seperable; \n",
    "\n",
    "... but it still includes some <span style=\"color:red\"> time non-local behavior</span> as the state of the system depends on its history (via the integral over $s$), and thus its past interaction with the bath.\n",
    "\n",
    "\n",
    "\n"
   ]
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   "source": [
    "# The Markov Approximation\n",
    "\n",
    "We can now make what is known as the <span style=\"color:red\"> **Markov** </span> assumption, to eliminate this history. \n"
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    "\n",
    "We assume \n",
    "\n",
    "$$\\tilde{\\rho}_S(s) \\rightarrow \\tilde{\\rho}_S(t)$$\n",
    "\n",
    "in the integral.  \n",
    "\n",
    "This assumptions implies there is a seperation of time scales between environment (**$\\tau_E$**) and system relaxation time (**$\\tau_R$**) and any intrinsic system time scales (**$\\tau_S$**), \n",
    "\n",
    "$$\\tau_E \\ll \\tau_R, \\tau_S$$\n",
    "\n"
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    "I.e., if the environment were to be perturbed by the system, it relaxes back to equilibrium faster than the typical time scale of the evolution (**relaxation** and coherent evolution) of the system. \n",
    "\n",
    "This seems like a consistent assumption to make alongside the **Born approximation**, since that also implies the environment remains in equilibrium.\n"
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    "Now we have\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  - \\int_0^t ds \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(s),\\tilde{\\rho}_S(t)\\rho_E]$$\n",
    "\n",
    "\n",
    "\n",
    "This is sometimes called the Redfield equation; it local in time, but <span style=\"color:red\">not quite completely Markovian</span> (we still have $t$ in the integral limits).\n"
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    "\n",
    "We can simplifiy this further by removing the reference to $t$ in the limits of the integral, by choosing $s=t-\\tau$, and letting the upper limit go to infinity;  \n",
    "\n",
    "In other words, we assume that the integrand  dissappears fast compared to the system time scales.\n"
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    "\n",
    "\n",
    "Thus we arrive at the <span style=\"color:red\">fully Markovian master equation</span>;\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\tilde{ \\rho}_S(t) =  -  \\int_0^{\\infty} d\\tau \\mathrm{Tr}_E [\\tilde{H}_I(t),[\\tilde{H}_I(t-\\tau),\\tilde{\\rho}_S(t)\\rho_E]$$\n"
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    "# Describing the bath with a correlation function\n",
    "\n",
    "The system depends on the environment properties via the two-time bath correlation functions.\n",
    "\n",
    "\n",
    "For example, lets explicitly define the system-environment interaction term as,\n",
    "\n",
    "$$H_I = A \\otimes B$$\n",
    "\n",
    "where $A$ is a Hermitian system operator, and $B$ a Hermitian bath operator.  (An explicit example will soon make this a little clearer).\n",
    "\n"
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    "\n",
    "In the interaction picture \n",
    "\n",
    "$$\\tilde{H} = A(t) \\otimes B(t)$$\n",
    "\n",
    "Our Markovian master equation contains terms like:\n",
    "\n",
    "$$ \\mathrm{Tr_E}[B(t)B(t-\\tau)\\rho_E]$$\n",
    "\n"
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    "If we assume the initial state of the environment is a steady state, i.e., it does not evolve under $H_E$, these terms are <span style=\"color:red\">\"stationary\"</span>, and we can define them as bath correlation functions that just depend on the interval between the two operators\n",
    "\n",
    "$$C(\\tau) = \\mathrm{Tr_E}[B(\\tau)B\\rho_E]$$\n"
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    "Inserting these various terms into our Markovian master equation, and moving back to the Schrodinger picture, one obtains\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] - \\int_0^{\\infty} d\\tau \\left( [A,[A(-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)A(-\\tau),A]C(-\\tau)\\right)$$\n",
    "\n"
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    "In general there may be a sum of interactions in the interaction Hamiltonian, in which case the integral contains a sum of terms for each interaction part, and the correlation functions are generalized\n",
    "\n",
    "$$\\tilde{H} = \\sum_{\\alpha}A_{\\alpha}(t) \\otimes B_{\\alpha}(t)$$\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] - \\sum_{\\alpha,\\beta}\\int_0^{\\infty} d\\tau \\left( [A_{\\alpha},[A_{\\beta}(-\\tau)\\rho_S(t)]C_{\\alpha\\beta}(\\tau) + [\\rho_S(t)A_{\\beta}(-\\tau),A_{\\alpha}]C_{\\beta\\alpha}(-\\tau)\\right)$$\n",
    "\n",
    "This equation in itself is useful, and can be developed and applied to certain problems (see part 3). \n",
    "\n",
    "However, it is still not in the famous <span style=\"color:red\">**Lindblad**</span> form, and does not guarantee positivity of the density matrix as it is evolved. "
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    "\n",
    "\n",
    "Interestingly, there is still not yet any assumption about the timescales $\\tau_S$, due to $H_S$, and the relaxation $\\tau_R$, induced by the bath. \n",
    "\n",
    "If we perform an additional approximation, and <span style=\"color:red\">neglect terms due to system evolution which are very fast compared to the relaxation time scale $\\tau_R$</span>, we can obtain a **Secular master equation** which is in **Lindblad form**. \n",
    "\n",
    "In other words, we will assume, $\\tau_S\\ll \\tau_R$, so that now, the Born-Markov-Secular master equation will be valid when\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n"
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    "\n",
    "\n",
    "It is a little cumbersome to the general derivation of this step, so let us move onto an explicit example.\n",
    "\n",
    "However, one note;  the above **non-secular** form of the master equation is **may be** applicable even if the relaxation time scale and the system time scale are comparable, and thus it is useful in and of itself. (See Chapter 3.6 in Breuer and Pettrucione).\n",
    " \n"
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    "## The spin-boson model\n",
    "\n",
    "The archetypical example of an open quantum system is where the \"system\" is a two-level system, a spin, described by:"
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    "<span style=\"color:red\">Pauli spin matrices</span>\n",
    "\n",
    "\\begin{align}\n",
    "\\sigma_{x} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix},\\quad\n",
    "\\sigma_{y} = \\begin{pmatrix} 0 & -i \\\\ i & 0 \\end{pmatrix}, \\quad\n",
    "\\sigma_{z} = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix},\n",
    "\\end{align}\n",
    "\n",
    "\n"
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    "While the bath is a continuum of <span style=\"color:red\"> boson modes </span>, or harmonic oscillators, described by creation and annihilation operators $b_k$, obeying the commutation relations $[b_k,b_k']=\\delta_{k,k'}$"
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   "source": [
    "\n",
    "This model is important because it can be used to describe the behavior of <span style=\"color:red\">atoms, molecules or a qubits</span>  interacting with the electromagnetic field, vibrational phonons, etc.  E.g, the loss rate $\\gamma$ in a typical cavity QED example could be described by this model\n",
    "\n",
    "<img src=\"QED.png\" width=\"400\" height=\"400\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The total Hamiltonian is then,\n",
    "\n",
    "$$H= H_S + H_E + H_I$$\n",
    "\n",
    "where\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$ H_S = \\frac{\\epsilon}{2} \\sigma_z$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "$$ H_E = \\sum_k \\omega_k b_k^{\\dagger}b_k$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$ H_I = \\sigma_x \\sum_k g_k (b_k^{\\dagger}+b_k)= (\\sigma_+ +\\sigma_-)\\sum_k g_k (b_k^{\\dagger}+b_k)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In the <span style=\"color:red\">interaction picture</span> the interaction Hamiltonian is \n",
    "\n",
    "$$\\tilde{H}_I(t) = e^{i(H_S + H_E)t} H_I e^{-i(H_S + H_E)t}$$\n",
    "\n",
    "   \n",
    "\n",
    "$$ \\tilde{H}_I =  (\\sigma_+e^{i\\epsilon t} +\\sigma_-e^{-i\\epsilon t})\\sum_k g_k (b_k^{\\dagger}e^{i\\omega_k t}+b_ke^{-i\\omega_k t})$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Inserting this into our master equation, we find,\n",
    "\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) =  - \\int_0^{\\infty} d\\tau \\left( [\\sigma_x(t),[\\sigma_x(t-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)\\sigma_x(t-\\tau),\\sigma_x(t)]C(-\\tau)\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "\n",
    "Recall that the bath correlation functions are defined as\n",
    "\n",
    "$$C(\\tau) = \\mathrm{Tr_E}[B(\\tau)B\\rho_E]$$\n",
    "\n",
    "Where\n",
    "\n",
    "$$B(t) = \\sum_k g_k\\{ b_k^{\\dagger}e^{i\\omega_k t}+ b_ke^{-i\\omega_k t}\\}$$\n",
    "\n",
    "$$C(t)=\\mathrm{Tr_E}[ (\\sum_k g_k  \\{b_k^{\\dagger}e^{i\\omega_k t}+ b_ke^{-i\\omega_k t}\\}) (\\sum_{k'} g_{k'}\\{ b_{k'}^{\\dagger}+ b_{k'}\\}) \\rho_E]$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Assuming that the initial state of the environment is a thermal state\n",
    "\n",
    "$$\\rho_E = e^{-H_E / k_B T} / Z$$  \n",
    "\n",
    "$$Z=\\mathrm{Tr}(e^{-H_E / k_B T})$$\n",
    "\n",
    "lets us evaluate this quite easily;\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "The only non-zero terms come from \n",
    "\n",
    "$$\\mathrm{Tr_E}[b_k b_{k'}^{\\dagger}\\rho_E]=\\delta_{kk'}[1+n(\\omega_k)]$$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\mathrm{Tr_E}[ b_{k'}^{\\dagger} b_k\\rho_E]=\\delta_{kk'}n(\\omega_k)$$\n",
    "\n",
    "where $n(\\omega) =(e^{\\omega/k_B T} - 1)^{-1}$.\n",
    "\n",
    "Is the Bose-Einstein occupation number."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Then\n",
    "\n",
    "$$C(t)= \\sum_k \\left(g_k^2 e^{i\\omega_k t}n(\\omega_k)+ g_k^2 e^{-i\\omega_k t}[1+n(\\omega_k)]\\right)$$\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can then move to a continuum representation by turning the sum into an integral, and defining the **spectral density**\n",
    "\n",
    "<span style=\"color:red\">\n",
    "$$J(\\omega) = \\sum_k g_k^2\\delta(\\omega-\\omega_k)$$\n",
    "</span>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "**Note: sometimes it is useful to rewrite this in terms of real and imaginary parts. See part 3!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The secular approximaton\n",
    "\n",
    "Let us return to the master equation, in the interaction picture;\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) =  - \\int_0^{\\infty} d\\tau \\left( [\\sigma_x(t),[\\sigma_x(t-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)\\sigma_x(t-\\tau),\\sigma_x(t)]C(-\\tau)\\right)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We are going to do two things:\n",
    "\n",
    "    \n",
    "    \n",
    "- Neglect terms come from products of system operators that rotate quickly... this is the <span style=\"color:red\">secular approximation!</span>\n",
    "\n",
    "Its equivalent in this case to a <span style=\"color:red\">rotating wave approximation</span>;  and for it be valid, the relaxation rate has to be smaller than the system frequency.  Finally an explicit statement about the system frequency!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "    \n",
    "- Evaluate the integral over $\\tau$ and $\\omega$\n",
    "\n",
    "This is a lot of algebra, so lets just do one term.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## First, the secular approximation:\n",
    "\n",
    "Recall that, in the interaction picture:\n",
    "\n",
    "$$\\sigma_x(t) =(\\sigma_+e^{i\\epsilon t} +\\sigma_-e^{-i\\epsilon t})$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "So the first term in the master equation contains products like\n",
    "\n",
    "$$ \\sigma_x(t)\\sigma_x(t-\\tau)= (\\sigma_+^2e^{2i\\epsilon t}e^{-i\\epsilon \\tau} +\\sigma_-^2e^{-2i\\epsilon t}e^{i\\epsilon \\tau}+\\sigma_+\\sigma_-e^{i\\epsilon \\tau} + \\sigma_-\\sigma_+e^{-i\\epsilon \\tau})$$\n",
    "\n",
    "We neglect terms oscillating with frequency <span style=\"color:red\">$2i\\epsilon$. </span>\n",
    "\n",
    "(Actually in this particular product of operators those terms are zero anyway, because the operators squared are zero, but the equivalent terms in products like  $\\sigma_x(t-\\tau)\\rho_s(t) \\sigma_x(t)$ must be neglected in this way..)\n",
    "\n",
    "Now we see why this is the same as a rotating wave approximation, and that it is valid if \n",
    "\n",
    "$$\\tau_S \\ll \\tau_R$$ \n",
    "\n",
    "i.e., when the relaxation rate is smaller than the system frequencies.  Now we have the seperation of time scales\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Second, some integrals\n",
    "\n",
    "For the remaining terms, that do not rotate at this frequency, we have to evaluate integrals like,\n",
    "\n",
    "$$  \\sigma_+\\sigma_- \\rho_S(t)  \\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau}C(\\tau)$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Using our earlier definition of the correlation function\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "We have to evaluate\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau}C(\\tau) =  \\int_0^{\\infty}d\\omega \\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau} \\{J(\\omega) e^{i\\omega \\tau}n(\\omega)+ J(\\omega) e^{-i\\omega \\tau}[1+n(\\omega)]\\}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can do the $\\tau$ integral first, using the formula,\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{\\pm i\\epsilon \\tau} = \\pi \\delta(\\epsilon) \\pm i \\frac{\\mathcal{P}}{\\epsilon}$$\n",
    "\n",
    "$\\mathcal{P}$ is the Cauchy principal value. The imaginary term leads to environment-induced energy shifts (sometimes called Lamb shifts.  Here we neglect this term, for simplicity.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We see that the delta function lets us then evaluate the frequency integral, and thus,\n",
    "\n",
    "$$\\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau}C(\\tau)= \\pi J(\\epsilon) (n(\\epsilon)+1)$$\n",
    "\n",
    "\n",
    "Thus for this term, the right hand side of the master equation becomes \n",
    "\n",
    "$$  \\sigma_+\\sigma_- \\rho_S(t)  \\left[\\int_0^{\\infty} d\\tau e^{i\\epsilon \\tau}c(\\tau)\\right] =  \\pi J(\\epsilon) (n(\\epsilon)+1) \\sigma_+\\sigma_- \\rho_S(t) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "\n",
    "# The **Lindblad master equation**\n",
    "\n",
    "\n",
    "We are almost there!\n",
    "\n",
    "If we repeat this for each term in the master equation, \n",
    "\n",
    "\n",
    "$$ \\frac{\\partial}{\\partial t} \\rho_S(t) =  - \\int_0^{\\infty} d\\tau \\left( [\\sigma_x(t),[\\sigma_x(t-\\tau)\\rho_S(t)]C(\\tau) + [\\rho_S(t)\\sigma_x(t-\\tau),\\sigma_x(t)]C(-\\tau)\\right)$$\n",
    "\n",
    "\n",
    "and collect terms, and move back to the schrodinger picture, we find a master equation in what is known as the Lindblad master equation \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "<span style=\"color:blue\">\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[\\frac{\\epsilon}{2}\\sigma_z,\\rho(t)] $$</span>\n",
    "<span style=\"color:green\">$$+ \\gamma(\\epsilon) \\left(n(\\epsilon)+1\\right)\\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] $$</span>\n",
    "<span style=\"color:red\">$$+ \\gamma(\\epsilon) n(\\epsilon)\\left[2\\sigma_+ \\rho_S(t)\\sigma_- - \\{\\sigma_-\\sigma_+,\\rho_S\\}\\right]$$\n",
    "</span>\n",
    "\n",
    "\n",
    "\n",
    "Note we have redefined $ \\gamma(\\epsilon)\\equiv \\pi J(\\epsilon)$.  \n",
    "\n",
    "The first part is the \n",
    "<span style=\"color:blue\">coherent system evolution</span>, the second part describes <span style=\"color:green\">spontaneous and stimulated emission</span>, and the third part describes <span style=\"color:red\">absorption</span>.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Why is this so great?\n",
    "\n",
    "- This Lindblad form guarantees positivity:  we will always have a physical density matrix.\n",
    "\n",
    "- It is easy to evaluate, and can be derived for many types of systems.  \n",
    "\n",
    "(see part 2 for more examples).\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "# To recap, it is valid when:\n",
    "\n",
    "- The <span style=\"color:red\">**Born approximation**</span> applies:  the coupling is weak such that we can assume $\\rho(t) = \\rho_S(t)\\otimes\\rho_E$\n",
    "\n",
    "- The <span style=\"color:red\">**Markov approximation**</span> applies:  the bath returns to equilibrium on a time scale $\\tau_E$ which is faster than the relaxation of the system induced by that bath $\\tau_R$. \n",
    "\n",
    "- The <span style=\"color:red\">**secular approximation**</span> applies:  the system time scales are small (i.e., higher frequency) than the relaxation time scales.  In other words, $\\epsilon > \\pi J(\\epsilon) (n(\\epsilon)+1)$.\n",
    "\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "** Two questions (maybe obvious?) **:\n",
    "\n",
    "- Does the secular approximation break at high temperatures?\n",
    "\n",
    "- How valid is the non-secular master equation when the relaxation time becomes of order of the system time scales?   (see part 3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Solution to the Lindblad master equation\n",
    "\n",
    "The spin-boson example is analytically solvable in a few lines.  \n",
    "\n",
    "This is easily done by writing out equations of motion for the matrix elements of the master equation\n",
    "\n",
    "\n",
    "<span style=\"color:blue\">\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[\\frac{\\epsilon}{2}\\sigma_z,\\rho(t)] $$</span>\n",
    "<span style=\"color:green\">$$+ \\gamma(\\epsilon) \\left(n(\\epsilon)+1\\right)\\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] $$</span>\n",
    "<span style=\"color:red\">$$+ \\gamma(\\epsilon) n(\\epsilon)\\left[2\\sigma_+ \\rho_S(t)\\sigma_- - \\{\\sigma_-\\sigma_+,\\rho_S\\}\\right]$$\n",
    "</span>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "which give\n",
    "\n",
    "\n",
    "$$\\dot{\\rho}_{ee}(t) = -2 \\gamma (n+1) \\rho_{ee}(t) + 2\\gamma n \\rho_{gg}(t)$$\n",
    "$$\\dot{\\rho}_{gg}(t) = -2 \\gamma (n) \\rho_{gg}(t) + 2\\gamma (n+1) \\rho_{ee}(t)$$\n",
    "$$\\dot{\\rho}_{eg}(t) = -2 [\\gamma (2n+1) + i\\epsilon] \\rho_{eg}(t)$$\n",
    "$$\\dot{\\rho}_{ge}(t) = -2 [\\gamma (2n+1) - i\\epsilon] \\rho_{ge}(t)$$\n",
    "\n",
    "We an see that the populations are coupled with rates corresponding to the emission and absorption.  The off-diagonal matrix elements decay proportional to the coupling the environment.   This is decoherence!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "The solutions to these equations are very simple for zero temperature ($n=0$), where we see:\n",
    "\n",
    "$$\\rho_{ee}(t) = e^{-2 \\gamma t} \\rho_{ee}(0) $$\n",
    "$$\\rho_{gg}(t) = 1-2 e^{-2 \\gamma t} \\rho_{ee}(0)$$\n",
    "$$\\rho_{eg}(t) = e^{- \\gamma t}e^{ - i\\epsilon t} \\rho_{eg}(0)$$\n",
    "$$\\rho_{ge}(t) = e^{- \\gamma t}e^{  i\\epsilon t} \\rho_{ge}(0)$$\n",
    "\n",
    "The off diagonal terms decay at half the speed of the relaxation terms, leading to the infamous <span style=\"color:red\">$T_1 = 2T_2$</span> relationship.\n",
    "\n",
    "In the general case, it can be tedious to construct and solve such equations of motion.  \n",
    "\n",
    "So... lets use QuTiP to play with some examples.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "## Part 2\n",
    "\n",
    "\n",
    "- QuTiP examples and applications\n",
    "\n",
    "    - Direct integration\n",
    "    \n",
    "    - Monte-Carlo simulation\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# QuTiP:  A brief introduction\n",
    "\n",
    "The Quantum Toolbox in Python was developed primarily by Robert Johansson and Paul Nation.\n",
    "\n",
    "http://qutip.org/devs.html\n",
    "\n",
    "It has a variety of built-in solvers for solving the dynamics via: \n",
    "- the Schrodinger equation, \n",
    "- master equations, \n",
    "- Floquet formalism, \n",
    "- Monte-Carlo quantum trajectories, \n",
    "- stochastic Schrodinger/master equations, \n",
    "- the Hierarchy method, the reaction coordinate method, etc.\n",
    "- supports time-dependance in Hamiltonians, Lindblads, etc.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "It based around a quantum object class which can be used to represent state vectors, operators, and superoperators.\n",
    "\n",
    "It is composed of a numerical matrix, and various properties that define its dimensionality, etc.\n",
    "<img src=\"qobj.png\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Generating comtypes.gen._565783C6_CB41_11D1_8B02_00600806D9B6_0_1_2\n",
      "# Generating comtypes.gen._00020430_0000_0000_C000_000000000046_0_2_0\n",
      "# Generating comtypes.gen.stdole\n",
      "# Generating comtypes.gen.WbemScripting\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from qutip import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Recalling our example of a single two-level system described by the Pauli spin matrices\n",
    "\n",
    "\n",
    "\\begin{align}\n",
    "\\sigma_{x} = \\begin{pmatrix} 0 & 1 \\\\ 1 & 0 \\end{pmatrix},\\quad\n",
    "\\sigma_{y} = \\begin{pmatrix} 0 & -i \\\\ i & 0 \\end{pmatrix}, \\quad\n",
    "\\sigma_{z} = \\begin{pmatrix} 1 & 0 \\\\ 0 & -1 \\end{pmatrix},\n",
    "\\end{align}\n",
    "\n",
    "In QuTiP we can define this manually, or with predefined operators:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.]\n",
       " [ 0. -1.]]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sz = Qobj([[1,0], [0,-1]]) # the sigma-z Pauli operator\n",
    "sz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0 & 0.0\\\\0.0 & -1.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 1.  0.]\n",
       " [ 0. -1.]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sz = sigmaz() # the sigma-z Pauli operator\n",
    "sz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sz.tr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2L, 2L), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & -1.0j\\\\1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2L, 2L), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 0.+0.j  0.-1.j]\n",
       " [ 0.+1.j  0.+0.j]]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy = sigmay()\n",
    "\n",
    "sy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [2]], shape = (2L, 2L), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.0 & 1.0j\\\\-1.0j & 0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [2]], shape = (2L, 2L), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 0.+0.j  0.+1.j]\n",
       " [ 0.-1.j  0.+0.j]]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sy.conj()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Our simple Hamiltonian from before was diagonal in the 'z' basis.\n",
    "\n",
    "We can define and solve the Lindblad Master equation we solved analytically earlier in few lines:\n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[\\frac{\\epsilon}{2}\\sigma_z,\\rho(t)] \\\\\n",
    "+ \\gamma(\\epsilon) \\left(n(\\epsilon)+1\\right)\\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] \\\\\n",
    "+ \\gamma(\\epsilon) n(\\epsilon)\\left[2\\sigma_+ \\rho_S(t)\\sigma_- - \\{\\sigma_-\\sigma_+,\\rho_S\\}\\right]$$\n",
    "\n",
    "QuTiP has several options on how to solve this type of formula.  \n",
    "\n",
    "The default is \"mesolve\" which takes Qobj definitions of the Hamiltonian, and the Lindblad, and converts them into what a set of coupled equations in matrix form, as we did earlier. It then directly solves this set of coupled ODEs.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "First define the Hamiltonian $H_S = \\frac{\\epsilon}{2}\\sigma_z$ \n",
    "\n",
    "and initial condition $psi(t=0) = |1\\rangle$,  $\\rho(0) = |1\\rangle\\langle 1|$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\\begin{equation*}\\left(\\begin{array}{*{11}c}1.0\\\\0.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[2], [1]], shape = (2, 1), type = ket\n",
       "Qobj data =\n",
       "[[ 1.]\n",
       " [ 0.]]"
      ]
     },
     "execution_count": 323,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "eps = 1.0\n",
    "\n",
    "# Hamiltonian\n",
    "H = 0.5 * eps * sigmaz()\n",
    "\n",
    "\n",
    "# initial state.  \n",
    "N = 2 # number of states in the Hilbert space\n",
    "n = 0 # the state that will be occupied (python counts from zero)\n",
    "\n",
    "psi0 = basis(N, n)     \n",
    "psi0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "We can define our Lindblad master equation by just defining the rates and the operator which goes into master equation.\n",
    "\n",
    "Here we have two operators; one which causes emission, \n",
    "\n",
    "$ \\gamma(\\epsilon) \\left(n(\\epsilon)+1\\right)\\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] $\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 324,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "sm = destroy(2).dag()\n",
    "gamma = 0.1\n",
    "n_th = 0.0\n",
    "\n",
    "#FYI: QuTiPs definition of a Lindblad differs from our derivation by a factor of '2'\n",
    "c_ops\n",
    "c_ops = [np.sqrt(2 * gamma*(n_th + 1)) * sm]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The other absorption:\n",
    "\n",
    "$$ \\gamma(\\epsilon) n(\\epsilon)\\left[2\\sigma_+ \\rho_S(t)\\sigma_- - \\{\\sigma_-\\sigma_+,\\rho_S\\}\\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 325,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "sp = sm.dag()\n",
    "\n",
    "c_ops.append(np.sqrt(2 * gamma * n_th) * sp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Next define the time steps we want to solve the equations for, and run the \"mesolve\" function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 326,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# list of times for which the solver should store the state vector\n",
    "tlist = np.linspace(0, 50, 1000)\n",
    "result = mesolve(H, psi0, tlist, c_ops, [])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Calculate some expectation values, and compare to analytical result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZHGAy8C8zq/PEa2Y22swWmVmxmU03syP3cL1BZlZiZgV1raGhNW8ePHhv1iy4/fawqxER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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17a58c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Since our initial state was the excited state, we can get the probability of being in the excited state\n",
    "#at time t with:\n",
    "Pe = expect(result.states, psi0*psi0.dag())\n",
    "\n",
    "#we can compare this to our analytical result\n",
    "PeAna = [np.exp(-2 * gamma * t) for t in tlist]\n",
    "\n",
    "\n",
    "fig, axes = plt.subplots(1,1, figsize=(6,2))\n",
    "axes.plot(tlist, Pe)\n",
    "axes.plot(tlist, PeAna, color='r',ls='--')\n",
    "axes.set_xlabel(r'$t$', fontsize=20)\n",
    "axes.set_ylabel(r\"$\\rho_{ee}$\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If we assume non-zero temperature, the steady state (the long-time solution) of the master equation predicts a thermal state.\n",
    "\n",
    "Analytically, setting the LHS of our equaitons to zero, and soliving, gives the disribution:\n",
    "\n",
    "$$\\rho_{ee} = \\frac{n}{(1+2n)}$$\n",
    "$$\\rho_{gg} = \\frac{1+n}{(1+2n)}$$\n",
    "\n",
    "Which is equivalent to the thermal distribution:\n",
    "\n",
    "$$ \\rho = e^{H_S/k_B T}/Z $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Lets check this two ways in QuTiP.  First with steadystate() function, then with the thermal_dm() function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 328,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.25  0.  ]\n",
      " [ 0.    0.75]]\n"
     ]
    }
   ],
   "source": [
    "gamma = 0.1\n",
    "n_th = 0.5\n",
    "\n",
    "c_ops = [np.sqrt(2 * gamma * n_th) * sp, np.sqrt(2 * gamma*(n_th + 1)) * sm]\n",
    "\n",
    "rhoss = steadystate(H,c_ops)\n",
    "print(rhoss)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.25\n",
      "0.75\n"
     ]
    }
   ],
   "source": [
    "#Compare to analytical prediction\n",
    "print(n_th / (1+ 2 * n_th))\n",
    "print((1+n_th) / (1+ 2 * n_th))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quantum object: dims = [[2], [2]], shape = (2, 2), type = oper, isherm = True\n",
      "Qobj data =\n",
      "[[ 0.75  0.  ]\n",
      " [ 0.    0.25]]\n"
     ]
    }
   ],
   "source": [
    "#Built in function to calculate thermal state with occupation n_th\n",
    "print(thermal_dm(2, n_th))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let us try a slightly more interesting example, the **Jaynes-Cumming Model** of cavity QED, which describes a single two level system coherently interacting with a single-mode cavity\n",
    "\n",
    "<img src=\"QED.png\" width=400 height=400/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The interaction between the TLS and the cavity is coherent, while the losses are incoherent.\n",
    "\n",
    "Normally, one must fully rederive the master equation, as the Hamiltonian of the system is now different.\n",
    "\n",
    "However, if $g$ is small compared to the cavity and \"atom\" frequencies, we can assume that derivation for uncoupled systems is still valid (i.e., the eigenstates and eigenenergies dont change much).\n",
    "\n",
    "\n",
    "\n",
    "$$H_S = \\frac{\\epsilon}{2} \\sigma_z + \\omega_c a^{\\dagger}a + g(\\sigma_+ a+\\sigma_- a^{\\dagger})$$\n",
    "\n",
    "$$ g \\ll \\epsilon, \\omega_c$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "If we assume both atom and cavity are weakly coupled to independant environments (external EM modes, leaky mirror, etc), we can model this system with the following Lindblad Master Equation \n",
    "\n",
    "$$\\frac{\\partial}{\\partial t} \\rho_S(t) = -i[H_S,\\rho(t)] \\\\\n",
    "+ \\gamma \\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] \\\\\n",
    "+ \\kappa \\left[2a \\rho_S(t)a^{\\dagger} - \\{a^{\\dagger}a,\\rho_S\\}\\right] $$\n",
    "\n",
    "As with the atom, the cavity can decay into its environment even at zero temperature.\n",
    "\n",
    "(Note we assumed zero temperature, for simplicity, and that the rates are \"flat\", so not really dependant on energy)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In QuTiP, we use the tensor function to create operators for composite systems, thus the operators and Hamiltonian of the above example are defined as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# cavity mode operator.  We truncate the Fock states at \"4\"\n",
    "N=4\n",
    "a = tensor(destroy(N), qeye(2))\n",
    "\n",
    "# qubit/atom operators\n",
    "sz = tensor(qeye(N), sigmaz())   # sigma-z operator\n",
    "sm = tensor(qeye(N), destroy(2).dag()) # sigma-minus operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[4, 2], [4, 2]], shape = (8, 8), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}0.500 & 0.0 & 0.0 & 0.050 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & -0.500 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 1.500 & 0.0 & 0.0 & 0.071 & 0.0 & 0.0\\\\0.050 & 0.0 & 0.0 & 0.500 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 2.500 & 0.0 & 0.0 & 0.087\\\\0.0 & 0.0 & 0.071 & 0.0 & 0.0 & 1.500 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 3.500 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.087 & 0.0 & 0.0 & 2.500\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[4, 2], [4, 2]], shape = (8, 8), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 0.5         0.          0.          0.05        0.          0.          0.\n",
       "   0.        ]\n",
       " [ 0.         -0.5         0.          0.          0.          0.          0.\n",
       "   0.        ]\n",
       " [ 0.          0.          1.5         0.          0.          0.07071068\n",
       "   0.          0.        ]\n",
       " [ 0.05        0.          0.          0.5         0.          0.          0.\n",
       "   0.        ]\n",
       " [ 0.          0.          0.          0.          2.5         0.          0.\n",
       "   0.08660254]\n",
       " [ 0.          0.          0.07071068  0.          0.          1.5         0.\n",
       "   0.        ]\n",
       " [ 0.          0.          0.          0.          0.          0.          3.5\n",
       "   0.        ]\n",
       " [ 0.          0.          0.          0.          0.08660254  0.          0.\n",
       "   2.5       ]]"
      ]
     },
     "execution_count": 334,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#We define system paramaters and the Hamiltonian in the same way as before\n",
    "\n",
    "wc = 1.0 # cavity frequency\n",
    "eps = 1.0 # qubit/atom frenqency\n",
    "g = 0.05  # coupling strength\n",
    "\n",
    "# the Jaynes-Cumming Hamiltonian\n",
    "H = wc * a.dag() * a + 0.5 * eps * sz + g * (a * sm.dag() + a.dag() * sm)\n",
    "\n",
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Again, we can create operators that describe the Lindblad master equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "\n",
    "$$\\gamma \\left[2\\sigma_- \\rho_S(t)\\sigma_+ - \\{\\sigma_+\\sigma_-,\\rho_S\\}\\right] \\\\$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "gamma = 0.005\n",
    "c_ops = []\n",
    "c_ops.append(np.sqrt(2 * gamma) * sm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "And for the photon loss:\n",
    "\n",
    "$$\\kappa \\left[2a \\rho_S(t)a^{\\dagger} - \\{a^{\\dagger}a,\\rho_S\\}\\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "kappa = 0.005\n",
    "c_ops.append(np.sqrt(2 * kappa) * a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# intial state, lets start with an excited atom and no photons\n",
    "psi0 = tensor(basis(N,0), basis(2,0))   \n",
    "\n",
    "tlist = np.linspace(0,100,501)\n",
    "output = mesolve(H, psi0, tlist, c_ops, [])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xce5d358>"
      ]
     },
     "execution_count": 340,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ea9us1RFfpZRKwi5dusStW7cIDAzE39/f7jhKJUkP1uC9dOmSFr3uJCBnAOvaruPZuc9S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l1hhODqq8MVgq64QheZkKotNSWVIV2HMKTrEPIL83lh1Qu8kvsKo+eM5kjJEc6qcxaZLTPp2Lgj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\nV0RERERiT0WviIiIiMTe/wPbYBGig9HtGQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18f4db00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_c = expect(output.states, a.dag()*a)\n",
    "n_a = expect(output.states, sm.dag()*sm)\n",
    "\n",
    "fig, axes = plt.subplots(1, 1, figsize=(8,4))\n",
    "\n",
    "axes.plot(tlist, n_c, label=\"Cavity\")\n",
    "axes.plot(tlist, n_a, label=\"Atom excited state\")\n",
    "axes.legend(loc=0)\n",
    "axes.set_xlabel('Time')\n",
    "axes.set_ylabel('Occupation probability')\n",
    "axes.set_title('Vacuum Rabi oscillations')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can plot the Wigner function of the cavity with built in functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dsZgtKqQTLsUF0AqKWEzI1rNzg1TaCwqui5Aio7HGn9tdgVFaAqCgXKU2oAEu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\nLIQQQgghhBDJ9v/slBNhRr2mCAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x20510898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We can plot the Wigner function of the cavity with built in functions\n",
    "\n",
    "import matplotlib as mpl\n",
    "\n",
    "t_idx = np.where([tlist == t for t in [0.0, 25.0, 60, 90]])[1]\n",
    "rho_list = np.array(output.states)[t_idx]\n",
    "\n",
    "fig_grid = (2, len(rho_list)*2)\n",
    "fig = plt.figure(figsize=(2*len(rho_list),4))\n",
    "xvec = np.linspace(-3,3,200)\n",
    "\n",
    "for idx, rho in enumerate(rho_list):\n",
    "    rho_cavity = ptrace(rho, 0)\n",
    "    W = wigner(rho_cavity, xvec, xvec)\n",
    "    ax = plt.subplot2grid(fig_grid, (0, 2*idx), colspan=2)\n",
    "    ax.contourf(xvec, xvec, W, 100, norm=mpl.colors.Normalize(-.25,.25), cmap=plt.get_cmap('RdBu'))\n",
    "    ax.set_title(r\"$t = %.1f$\" % tlist[t_idx][idx], fontsize=16)\n",
    "\n",
    "# plot the cavity occupation probability in the ground state\n",
    "ax = plt.subplot2grid(fig_grid, (1, 1), colspan=(fig_grid[1]-2))\n",
    "ax.plot(tlist, n_c, label=\"Cavity\")\n",
    "ax.plot(tlist, n_a, label=\"Atom excited state\")\n",
    "ax.legend()\n",
    "ax.set_xlabel('Time')\n",
    "ax.set_ylabel('Occupation probability');\n",
    "fig.tight_layout()\n",
    "fig.savefig(\"wigner1.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src=\"wigner1.png\" width=600 height=600/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nnom9Z9OmTViWRXt7OydOnGDTpk2oqsq0adMA+MEPfsCiRYuYOHEizc3NPPDA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\nVNR5Zs6YjlAog5ubGwYGBoyfMBEFBUVmzpvP8dNnGeE1htMnImjZshV29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30nCgoKMDEz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KzI4cOHiYyIoFz58owaNQp9fX3WOzoSHhGhshDIyMjAsndv3rx5g66uLq1atWLmrFk0bpxn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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7808358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_wigner(ptrace(rho_list[1],0), figsize=(6,6),projection='3d', alpha_max=3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Monte-Carlo solutions\n",
    "\n",
    "One downside to solving the master equation in this way is that the size of the matrix of equations we have to construct and solve scales as $N^2$, where $N$ is the number of states in the Hilbert space.\n",
    "\n",
    "Another approach is to \"unravel\" the master equation as a sum of trajectories, and then solve a stochastic equation for the state vector  state $\\left|\\psi(t)\\right>$, instead of the density matrix.  Physically this corresponds to continously monitoring the environment, and conditioning the information about the system we gain.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "For a quantum system that interacts with its environment. The dynamics of the wave function is given by the Schrodinger equation,\n",
    "\n",
    "<center>\n",
    "$\\displaystyle\\frac{d}{dt}\\left|\\psi(t)\\right> = - i H_{\\rm eff} \\left|\\psi(t)\\right>$\n",
    "</center>\n",
    "\n",
    "where the Hamiltonian is an effective Hamiltonian that, in addition to the system Hamiltonian $H_S$, also contains a non-Hermitian contribution due to the interaction with the environment:\n",
    "\n",
    "<center>\n",
    "$\\displaystyle H_{\\rm eff}(t) = H - \\frac{i}{2}\\sum_n c_n^\\dagger c_n$\n",
    "</center>\n",
    "\n",
    "where $c_n$ are the collapse operators that we usually put in the Lindblad Master equation (and by definition we have included the rates in the operators).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "Since the effective Hamiltonian is non-Hermitian, the norm of the wavefunction is decreasing with time, which to first order in a small time step $\\delta t$ is given by $\\langle\\psi(t+\\delta t)|\\psi(t+\\delta t)\\rangle \\approx 1 - \\delta p\\;\\;\\;$, where \n",
    "\n",
    "<center>\n",
    "$\\displaystyle \\delta p = \\delta t \\sum_n \\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>$\n",
    "</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "The decreasing norm is used to determine when so-called quantum jumps are to be imposed on the dynamics.  This corresponds to observing a photon being emitted into the environment, in which case we apply a \"quantum jump\", so that the new wavefunction at $t+\\delta t$ is given by\n",
    "<center>\n",
    "$\\left|\\psi(t+\\delta t)\\right> = c_n \\left|\\psi(t)\\right>/\\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>^{1/2}$ \n",
    "</center>\n",
    "\n",
    "In practise we compare $\\delta p$ to a random number in the range [0, 1]. If the norm has decreased below the randomly chosen number, we apply the quantum jump for a randomly chosen collapse operator $c_n$, weighted so the probability that the collapse being described by the nth collapse operator is given by\n",
    "    \n",
    "<center>\n",
    "$\\displaystyle P_n = \\left<\\psi(t)|c_n^\\dagger c_n|\\psi(t)\\right>/{\\delta p}$ \n",
    "</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.1%. Run time:  16.02s. Est. time left: 00:00:02:23\n",
      "20.0%. Run time:  16.70s. Est. time left: 00:00:01:06\n",
      "30.1%. Run time:  17.63s. Est. time left: 00:00:00:40\n",
      "40.0%. Run time:  18.33s. Est. time left: 00:00:00:27\n",
      "50.0%. Run time:  19.03s. Est. time left: 00:00:00:19\n",
      "60.1%. Run time:  19.80s. Est. time left: 00:00:00:13\n",
      "70.0%. Run time:  20.43s. Est. time left: 00:00:00:08\n",
      "80.1%. Run time:  21.09s. Est. time left: 00:00:00:05\n",
      "90.0%. Run time:  21.75s. Est. time left: 00:00:00:02\n",
      "100.0%. Run time:  22.39s. Est. time left: 00:00:00:00\n",
      "Total run time:  22.50s\n"
     ]
    }
   ],
   "source": [
    "ntraj = [1, 5, 15, 904] # list of number of trajectories to avg. over\n",
    "\n",
    "mc = mcsolve(H, psi0, tlist, c_ops, [a.dag()*a], ntraj)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"monte.png\" width=400 height=400/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NGvHRRx+xcuVKVq5cyTXXXBN2Pxo1asTVV1/NwIEDmTFjBhs3bmTp0qU8/vjj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U9qradinK4pqZSao5R6WSn1ilLqK6A48JzWerq7BxPhfDkOJnFxRivJAw8YwaRYMXj9dWPwtEmT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\nwo3qKwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xbc8b898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.font_manager\n",
    "leg_prop = matplotlib.font_manager.FontProperties(size=10)\n",
    "\n",
    "fig, axes = plt.subplots(4, 1, sharex=True, figsize=(6,8))\n",
    "\n",
    "fig.subplots_adjust(hspace=0.1) # reduce space between plots\n",
    "\n",
    "for idx, n in enumerate(ntraj):\n",
    "\n",
    "    axes[idx].step(tlist, mc.expect[idx][0], 'b', lw=2)\n",
    "    axes[idx].plot(tlist, expect(output.states,a.dag()*a), 'r--', lw=1.5)\n",
    "    \n",
    "    \n",
    "    axes[idx].set_yticks(np.linspace(0, 2, 5))\n",
    "    axes[idx].set_ylim([0, 1.5])\n",
    "    axes[idx].set_ylabel(r'$\\left<N\\right>$', fontsize=14)\n",
    "    \n",
    "    if idx == 0:\n",
    "        axes[idx].set_title(\"Ensemble Averaging of Monte Carlo Trajectories\")\n",
    "        axes[idx].legend(('Single trajectory', 'master equation', 'steady state'), prop=leg_prop)\n",
    "    else:\n",
    "        axes[idx].legend(('%d trajectories' % n, 'master equation', 'steady state'), prop=leg_prop)\n",
    "        \n",
    "\n",
    "axes[3].xaxis.set_major_locator(plt.MaxNLocator(4))\n",
    "axes[3].set_xlabel('Time (sec)',fontsize=14);\n",
    "fig.savefig(\"monte.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Monte Carlo Master Equation: a quick summary\n",
    "\n",
    "- For small systems, its actually slower than a direct solution, but for large systems it can save memory\n",
    "\n",
    "\n",
    "<img src=\"qutipbench.png\" width=400 /> <img src=\"qutipbenchcaption.png\" width=400/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Monte Carlo Master Equation: a quick summary\n",
    "\n",
    "- For small systems, its actually slower than a direct solution, but for large systems it can save memory\n",
    "- Easy to run in parrallel, using multiple cores, etc.\n",
    "- It can give an intuitive picture of measurement.  \n",
    "- Stochastic master equations for arbitrary unravellings are supported in QuTiP.  \n",
    "- These can be used to model continous homodyne and heterodyne measurement, feedback, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Other reasons to use QuTiP\n",
    "\n",
    "- Open source science\n",
    "- Promotes reproducibility\n",
    "- Has even more functionality, including \n",
    "    - Quantum optimal control library (CRAB, GOAT, and other animals)\n",
    "    - QIP library\n",
    "    - functions to calculate spectra, counting statistics, etc\n",
    "    - Supports arbitrary time-dependance, in Hamiltonian and Lindblad collapse operators\n",
    "    - Active development community."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "    \n",
    "## Part 3\n",
    "\n",
    "\n",
    "- Beyond the Master Equation: Exact numerical methods for bosonic baths\n",
    "\n",
    "    - The Hierarchy Equations of Motion, Tanimura and Ueda, (1989)\n",
    "    \n",
    "    - The Reaction Coordinate, Illes-Smith, Lambert and Nazir, PRA, (2014)\n",
    "    \n",
    "    \n",
    "- Conclusions "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Non-Markovian systems\n",
    "\n",
    "In some situations the assumption that $\\tau_E \\ll \\tau_S, \\tau_R$ breaks down. E.g.,\n",
    "\n",
    "- Hyperfine Interaction between electron spins and nuclear spins in quantum dots \n",
    "- Superconducting qubits strongly coupled to open transmission lines\n",
    "- Molecular systems strongly interacting with their environment, e.g., energy transfer in photosynthetic complexes strongly couples to protein \"vibrations\".\n",
    "\n",
    "\n",
    "A recent review:\n",
    "\"Dynamics of non-Markovian open quantum systems\"\n",
    "Inés de Vega and Daniel Alonso\n",
    "Rev. Mod. Phys. 89, 015001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Bosonic environments\n",
    "\n",
    "The choice of a bosonic environment, or in general, a Gaussian environment, simplifies the problem to some degree.\n",
    "\n",
    "Using the fact that the cumulants of a <span style=\"color:red\">Gaussian</span> system truncate at second order, one can show (see Breur and Petruccione, 3.6.4, or Jian Ma et al, PRA 2012) that there is a formal solution (assuming that at $t=0$, $\\rho(0) = \\rho_S(0)\\otimes \\rho_E(0)$ ),\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$ \\tilde{\\rho}_S(t) = \\mathcal{T} \\exp\\left( - \\int_0^t dt_2 \\int_0^{t_2} A^{\\times}(t_2)[C^R(t_2-t_1) A(t_1)^{\\times} + i C^I(t_2-t_1)A(t_1)^{\\circ}]\\right) $$\n",
    "\n",
    "Where, as before $A(t)$ is the system operator which couples to the environment, \n",
    "\n",
    "$C(t)$ is the correlation function of the environment, split into real and imaginary parts, \n",
    "\n",
    "$A^{\\times}B \\equiv [A,B]$ and $A^{\\circ}B = \\{A,B\\}$.  \n",
    "\n",
    "$\\mathcal{T}$ is the time-ordering operator, which means that all terms have to reordered so that time arguments increase from right to left.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Directly solving or using this equation is intractable;  however, by assuming that we can write the correlation functions as a sum of exponentials, and taking repeated time-derivatives, one can derive the <span style=\"color:red\">hierarchy equations of motion.</span>\n",
    "\n",
    "Again assuming that the initial bath state is a thermal state, and recalling that \n",
    "\n",
    "$$J(\\omega) = \\sum_k g_k^2\\delta(\\omega-\\omega_k)$$\n",
    "\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega \\{J(\\omega) e^{i\\omega t}n(\\omega)+ J(\\omega) e^{-i\\omega t}[1+n(\\omega)]\\}$$\n",
    "\n",
    "we can rewrite  this as\n",
    "\n",
    "$$C(t)= \\int_0^{\\infty}d\\omega J(\\omega)\\left[ \\mathrm{coth}\\left(\\frac{\\beta\\omega}{2}\\right)\\cos \\left(\\omega t\\right) - i \\sin \\left(\\omega t)\\right)\\}\\right]$$\n",
    "\n",
    "$\\beta = 1/ k_B T$, the temperature of the initial environment state.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "For some choices of spectral density, this does have the analytical form of a sum of exponentials, e.g. a Lorentzian.  Traditionally, the Drude-Lorentz form is chosen,\n",
    "\n",
    "$$J(\\omega) = \\frac{\\omega}{\\pi} \\frac{2\\lambda \\gamma}{(\\gamma^2 + \\omega^2)} $$\n",
    " \n",
    "Inserting this into $C(\\tau)$ one finds,\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "$$C(\\tau) = \\sum_{k=0}^{\\infty} c_k e^{-v_k|\\tau|}$$\n",
    "\n",
    "\n",
    "Where $v_k = 2 \\pi k/\\beta$ for $k\\geq1$, and $v_0 = \\gamma$, and $c_0 = \\lambda \\gamma [-i + \\mathrm{cot}\\left(\\beta \\gamma /2\\right)]$ and $c_k = (4 \\lambda \\gamma/\\beta) v_k/(v_k^2 - \\gamma^2)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def cot(x):\n",
    "    return 1./np.tan(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "E.g., for $\\gamma = 1.0$, $\\lambda = 1.25$, $\\beta = 0.95$:\n",
    "\n",
    "\n",
    "<img src=\"drude.png\" width=800 /> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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SsSLwS0YXquqhhL/uFJFKwGTg/XTa/ioi3wL1MgsoPDw8WeUacH74+/btm9mlyX2TUDwy\n4RexwHjuORg92hIyY4wrIiMjiYyMTHasMFUBE5EAIAJ4HJjocjjGmDRUq1aNd955J8M23bp149Zb\nb2XBggU8//zzicfr16+frCz9DXFxcSxZsoTx48dnKYa0+kiqXbt2tMukRkDlypVZsWJFquPXr19P\n9vXAgQMZOHBgluIymfPKpExVr4lIFNAZWAUgTureGZibja58gXTL2IiID9AE+CSzjubMmZNqh/Yc\n2b7dKT9fq1bu+/KkkiWdhzHGuCCtD7mio6MJCQlxKaJ89xrwsapuFJGsJWXXruVtRMaYbPPx8WHK\nlCmMGDGCcePGJRtFS8s777xDsWLFCAsLy6cIjVu8stBHgtnAMBEZICK3Aa/j7D+2CEBEXhSRxTca\ni8gIEekqIvUSHkOBMcC7SdpMFJF7RaR2QiGQ94AaJK/OmLe++QZatCgYRT6MMca4TkT6AE2BP2br\nwlNp7Q5jjHFbr169OHXqVKYJGUBYWBgHDx6kaNGi+RCZcZNXjpQBqOoyEQkCnseZtrgDCE1Szr4S\nUD3JJT7Ai0At4FdgPzBWVRcmaRMILEy49iwQBbRS1T15+K38j6qTlA0fni+3M8YYU7CJSDXgZeAe\nVc3e0JclZcYY4zW8NikDUNV5wLx0zg1O8fWrwKuZ9PcM4F41q7g4Z9f5Ll1cC8EYY0yBEoJTMTha\n/rfC3hdoJyJPAsU1nZJo4TNnUuaDD5Idy9FaZ2OMMal4eq2zVydlN53ixZ0Kh8YYY4xjPc7a5qQW\n4VQGnp5eQgYw58EHCZ4+PQ9DM8aYwsvTa50tKTO589//QrVqbkdhjDE3JVW9DOxKekxELgOnVXV3\nhhefPJnhaWOMMQWHNxf6MG6LjIT69eGnn9yOxBhjCpOs7eBqSZkxxngNS8pMzj34IFSoACNGOEVK\njDHG5DlV7ZSwBjpjJUrkQzTGGGM8wZIyk3MBAfDaa7BuHSxb5nY0xhhjknr2WbcjMMYYk0WWlJnc\n6doVHnkEnn4azp1zOxpjjDHGGGO8jiVlJvfmzoXLl2H8eLcjMcYYY4wxxutYUlZQfP89HDrkdhQ5\nU7UqvPACvP46bN3qdjTGGGOMMQXWsmXLKF++PDExMZm2XbBgATVr1uTataztHT9o0CBq166d2xDz\n1KFDh/Dx8WHJkiVuh1KgWFJWUDz1FPzhD25HkXMjRkBICIwZ43YkxhhjjDEFUnx8PJMnT2b06NH4\n+/snHn/xxRdZuXJlqvaDBg0iLi6OBQsWZKl/EcHHp+C/vRcRt0MocAr+v1phoAr//jc0Sbk/qBfx\n9YUlS2DpUrcjMcYYY4wpkFatWsXevXsZNmxYsuPTpk1LMykrXrw4AwcOZPbs2Vnq/80332TPnj0e\niTWv1KxZkytXrvDYY4+5HUqBYklZQXD0KJw9691JGUDDhlCzpttRGGOMMcYUSIsWLaJNmzZUrlw5\ny9f06tWLgwcPsnnz5kzb+vr6UrRo0VxEmD+KFSuW76NlqkpsbGy+3jM7LCkrCHbudP78zW/cjcMY\nY4wxxuTI0aNHGTp0KFWrVsXPz486deowYsQIfv31VwBiY2NZu3Yt99xzT7LrfHx8iImJYdGiRfj4\n+ODj48OQIUMSzwcHB1OuXLk0R9JSSrmm7Mb6rdmzZzNv3jzq1q1LyZIlCQ0N5ciRIwD8+c9/pnr1\n6vj7+9O9e3fOpaimvWrVKrp27Zr4fdWrV4+pU6cSHx+f6v6vvfYadevWxd/fn7vuuosvv/ySDh06\n0KlTp1QxJV1TNmjQIEqVKsXRo0fp3r07pUqV4pZbbmHs2LFoir1wZ82aRZs2bQgKCsLf35/mzZvz\nwQcfpIrFx8eHUaNGsXTpUho3boyfnx9r1qyhdu3aPPzww6nax8bGUqZMGX73u99l+jznhSKu3NUk\nt3cvFCsGBXxhpjHGGC/yyitw/DisXu12JMbc9I4dO0aLFi24cOECYWFhNGjQgCNHjrBixQpiYmIo\nXbo0UVFRxMXFERwcnOzaiIgIhg4dSsuWLRk+fDgAdevWTdYmODiYLVu2ZBqHiKQ5AhUREcG1a9cY\nNWoUZ86cYcaMGfTs2ZNOnTrxz3/+k3HjxvHjjz8yd+5cfv/73/Pmm28mXrto0SJKlSrFmDFjCAgI\nYOPGjTz33HNcvHiRGTNmJLabP38+Tz31FO3bt+eZZ57h4MGDdO/encDAQKpXr55p3PHx8YSGhnLX\nXXfxl7/8hfXr1zN79mzq1atHWFhYYtu5c+fy0EMP0b9/f+Li4vjb3/5Gr169+Mc//sFvf/vbZP1u\n2LCBZcuW8eSTTxIUFESdOnXo378/L730EufOnaNs2bKJbVetWsWlS5fcm1apqvbIxQMIBjQqKkpz\n7MknVRs1yvn1xhhTCEVFRSmgQLAWgNeDgvJIfF0aMkS1WrVcPsvGeM6N39lcvWcqoAYMGKBFihTR\n6OjodNu89dZb6uPjozt37kx1LiAgQAcPHpzutWFhYVqyZMlM4xg0aJDWrl078euDBw+qiGjFihX1\n4sWLicfHjx+vIqLNmjXT69evJx7v16+f+vn5aVxcXOKxq1evprrPE088oQEBAYnt4uLiNCgoSO+6\n665k/S1ZskRFRDt27JgqpsWLFyeL28fHR1944YVk9wkODtYWLVokO5Yynl9//VWbNGmi99xzT7Lj\nIqJFihTRPXv2JDu+d+9eFRFdsGBBsuPdunXTOnXqpPpek8rsZzg3r0s2fbEg+M9/oEEDt6Mwxhhz\nM6lSBY4cgbg4tyMxJseOXTxG9LHodB+7Tu7KtI9dJ3elee2xi8c8EqOqsnLlSrp160azZs3SbXf6\n9GkAAgMDs32PwMBArly5wtWrV3MUY69evQgICEj8umXLlgA89thjyao1tmzZkri4uMSpjeAUG7nh\n0qVLnD59mrvvvpuYmJjEoiLbt2/n9OnTDBs2LFl//fr1y9b3m3REDKBt27b89NNPyY4ljefcuXOc\nPXuWtm3bEh0dnaq/Dh060CDFe+xbb72Vli1b8t577yUeO3v2LGvXrqV///5ZjtXTbPpiQXDwIDz6\nqNtR5J0rV6BECbejMMaYwqV6dae674ED9sGf8VoLohYw5Z9T0j3fqEIjdo7YmWEfPZf3TDN5m9R+\nEpM7TM5tiJw8eZILFy7wmyzWBlDVzBulc01Oi2OknD5YpkwZAKpVq5bm8bNnz1KrVi0Adu3axYQJ\nE9i0aRMXLlxIbCsinD9/HnDWiYlIqmmXvr6+if1kxs/Pj/Llyyc7FhgYyNmzZ5Md+8c//sELL7zA\njh07khXuSGsrgPTuPWDAAJ566il+/vlnqlevzrJly/j1118tKSv0du+GAlwNJldmzID334dt26CI\n/bgZY0y+uVENd+9eS8qM1woLCaNbg27pnvcr4pdpH8t7Lufqr6lHmCoHZL0CoifcSDjOnj1LlSpV\nsnXt2bNn8ff3TzZKlB2+vr7ZOn4jCTx//jzt2rWjbNmyTJ06lTp16uDn50dUVBTjxo1Ls9hHTqUX\nS1JffPEFDz30EB06dGD+/PlUrlyZokWL8vbbbxMZGZmqfYl0BgX69OlDeHg47733HuPGjeO9996j\nefPm3Hrrrbn+PnLK3iUXBL6+kGQDwZtK584wfjzMnQvPPON2NMYYU3gEBUHJkk5SZoyXqlyqMpVL\n5S55alShkYeiSVuFChUoXbo0P/zwQ4btbrvtNlSVAwcOpBpVy2wE7MCBAzRs2DDXsWbX5s2bOXv2\nLCtXrqRNmzaJx/fv35+sXc2aNVFVfvzxR9q3b594/Pr16xw8eJA77rjDI/H8/e9/p0SJEqxbt44i\nST7sf+utt7LVT2BgIA888ADvvfce/fr1Y8uWLcydO9cjMeaUV68pE5GRInJARK6IyFYRaZFB2zYi\n8qWInBKRGBHZLSJPp9GuZ8K5KyLynYj8Nq3+TBY1bw4jR8LEiXD4sNvRGGNM4SEC9etbUmZMHhMR\nunfvzscff5zmuqYbQkJCKFasGNu3b091rmTJkqlK0ScVHR1N69atPRJvdvj6+qKqyUbE4uLimDdv\nXrJ2zZs3p3z58rzxxhvJ2kZERKSafpjbeEQkcZsBgIMHD2Zpu4CUHnvsMXbu3MnYsWMpUqQIvXv3\n9licOeG1SZmI9Ab+AkwCmgHfAetEJCidSy4DrwBtgduAPwNTReTxJH22BpYCbwBNgZXARyKStx+x\n3OymToWyZeHJJ531DcYYY/KHJWXG5Itp06Zxyy230K5dO5555hneeOMNpkyZQpMmTRLXYRUvXpwu\nXbqwfv36VNeHhISwfv165syZw/vvv8+2bdsSz0VFRXHmzBm6d++eL99L0jVvrVu3JjAwkAEDBjBn\nzhzmzJlDq1atUo3sFS1alMmTJ/PNN9/QsWNHXnvtNcaOHcuYMWOoV6+exzaKfuCBB7h8+TKhoaEs\nWLCA559/nrvuuitH0w4feOABypcvz/Lly7n33nsJCkovhcgfXpuUAeHAAlVdoqp7gCeAGGBIWo1V\ndYeqvq+qu1X1sKouBdbhJGk3jALWqOpsVf2Pqj4HRANP5u23cpMrXdrZL+fjj2HFCrejMcaYwmPk\nSHj2WbejMOamV6VKFf71r3/Rs2dPli5dyujRo4mIiKBTp074J1miMmTIELZu3ZqsuiHA7NmzCQkJ\nYeLEifTr14/XX3898dzy5cupWbMmHTp0yFIsKROg9PYuSy9RSnq8XLlyfPLJJ1SpUoWJEycye/Zs\nQkNDmTlzZqrrRo4cydy5c/n5558ZO3Ysn3/+OatWraJMmTL4+SVf+5fTeDp27Mjbb7/N8ePHCQ8P\n5/3332fmzJlpJqzpfd83FC1alN69eyMiDBgwIN12+Sa7NfQLwgMoClwDuqU4vgj4MIt9NAOOAoOT\nHDsEjErRbjLwbQb95H6fssIgPl71kUdUg4JUf/nF7WiMMTcB26fMXpeMd7mZ9ynLquvXr+ttt92m\nEydOzFL72NhYrVy5sr7yyit5HFneiI+P1/Lly+vw4cPdDiVN4eHhWqZMGb1y5UqW2ts+ZakFAb7A\n8RTHjwOVMrpQRH4WkavANuA1VX0nyelKOenTZIEIzJ/v/Bke7nY0xhhjjDH5zsfHhylTpjBv3jxi\nYmIybf/OO+9QrFixVPt3FUSxaVQSX7x4MWfOnKFjx44uRJSx2NhYIiIi6NGjR6qRPDcUxuqLdwMB\nwF3ADBH5UVXfdzmmwuGWW2DZMmfvHGOMMcaYQqhXr1706tUrS23DwsK8IiED2Lp1K+Hh4fTs2ZPy\n5csTFRXF22+/ze23306PHj3cDi/RyZMn+eyzz1ixYgVnzpxh1KhRbocEeG9Sdgq4DlRMcbwi8EtG\nF6rqoYS/7hSRSjjTE28kZb/kpE+A8PDwxA33bujbty99+/ZN/6LvvoOnn4YlSwpPopLF+dDGGJNU\nZGRkqj1obmxaaowxxn21atWiRo0avPLKK5w5c4Zy5coxaNAgXnzxxWTl6922a9cu+vfvT8WKFXnl\nlVe4/fbb3Q4J8NKkTFWviUgU0BlYBSDOSr7OQHY2GfAFku7C93UafdybcDxDc+bMITg4OBu3xtk0\nevNmpxCGMcaYdKX1IVd0dDQhISEuRWSMMSapmjVr8tFHH7kdRqbat2/v0U2vPcVb15QBzAaGicgA\nEbkNeB3wxyn2gYi8KCKLbzQWkREi0lVE6iU8hgJjgHeT9PlX4D4ReUZEGojIZCAEeDVPvoOffoLy\n5SHFCJsxxhhzg4g8kbBv5vmEx1cicp/bcRljjPEcrxwpA1DVZQl7kj2PM8VwBxCqqicTmlQCks4J\n9AFeBGoBvwL7gbGqujBJn1+LSD/ghYTHPuAhVd2VJ9/ETz9BnTp50rUxxpibxs/AszivSQIMAlaK\nSFNV3e1mYMYYYzzDa5MyAFWdB8xL59zgFF+/ShZGvFT1A+ADjwSYGUvKjDHGZEJVP0lx6E8i8juc\nglWZJ2XXr8Obb0LLltC0aV6EaIwxJpe8efqi97Ok7H8OH3Y7AmOMKfBExEdE+uBM1890vTMAPj7w\npz/Bhx/maWzGGGNyzpIyt8TFwc8/W1IG8OmnUK8efJ219xfGGFPYiEhjEbkIxOLMEHlYVfdk8WJn\nlGzr1rx2kbFbAAAgAElEQVQM0RhjTC5YUuaWw4chPt6SMoBOnaB5c+jXD6zEtTHGpGUPcAdwJzAf\nWJJQ5CprWrd2krICWHHMGGOMl68p82olSsCzz0KjRm5H4r4iReC99+COO2DkSIiIcDsiY4wpUFT1\nV+CnhC+/FZE7gdHA79K7Jtn+madOwYUL9J01i75/+ENeh2uMMTc9T++faUmZW6pWhenT3Y6i4Khd\nG+bPh/794b77nD+NMcakx4fk+2ymkmz/zEuXoGxZ52GMMSbXPL1/pk1fNAXH//2fk4yNGOEUQTHG\nGIOITBORtiJSM2Ft2YtAeyDr0woCAuD2223trjF5ZPLkyfj4+HDmzBm3Q3HdoEGDqF27tttheB1L\nykzB8tprUKEC9O4NsbFuR2OMMQXBLcBinHVl64EQoIuqbsxWL61bw5Ytno/OGIOIICJ5eo89e/Zw\n3333UapUKcqXL8+AAQM4depUnt4zJ/LjubgZ2fRFU7CULg3LlkHnzrB9O7Rp43ZExhjjKlV93CMd\nhYY6VX9jY6F4hjMfjTEFzJEjR2jbti2BgYFMnz6dixcv8tJLL/HDDz+wbds2ihSxt/Tezv4FTcET\nEgKHDsGNBerGGGNy78EHnYcxxuu88MILXLlyhR07dlC1alUAWrRowb333suiRYt4/PHsfXajqsTF\nxVHcPqApMGz6oimYLCEzxhhjjBc7dOgQ9erV4/bbb+fkyZO56uvvf/87Xbt2TUzIADp37kz9+vVZ\ntmxZptf7+PgwatQoli5dSuPGjfHz82PdunWAk6C9/PLLNG7cmBIlSlCpUiWeeOIJzp07l6yPVatW\nJcbg5+dHvXr1mDp1KvG21YZH2EiZMcYYY4wxHrR//346depEhQoV+OyzzwgMDATgypUrxMTEZHq9\nr68vZROqpR49epQTJ07QvHnzVO3uvPNO1qxZk6WYNmzYwLJly3jyyScJCgqiVq1aAAwfPpwlS5Yw\nZMgQRo8ezYEDB3jllVfYsWMHW7ZswdfXF4BFixZRqlQpxowZQ0BAABs3buS5557j4sWLzJgxI0sx\nmPRZUuaGEyecef1Nm0LCD7oxxhhjjPF+e/bs4Z577qF69eqsXbv2f/sFAjNnzmTKlCmZ9lGrVi1+\nSqhEfezYMQAqV66cql3lypU5c+YM165do2jRohn2uXfvXn744QcaNGiQeOzLL7/krbfeIjIykt69\neyce79ixI6GhoSxfvpw+ffoAzr5cSac7Dh8+nMDAQObNm8fUqVMzvb/JmCVlbvjHP2DoULh61ZIy\nY4wxxph0HDvmPNLj5weNGmXcx65dzluulCpXdh6e9P3339O7d2/q16/P6tWrCQgISHZ+4MCBtG3b\nNtN+SpQokfj3K1euAKS5/svPzy+xTWZJUYcOHZIlZAArVqygbNmydO7cmdOnTyceb9asGQEBAWza\ntCkxKUt6/0uXLhEbG8vdd9/NwoUL2bNnD02aNMn0+zLps6TMDYcPQ6VKVv0qJ1TByqwaY4wxhcKC\nBZDRwFKjRrBzZ8Z99OzpJGYpTZoEkyfnKrxkVJUHH3yQSpUqsXbtWvz9/VO1qVWrVuK0way6kaDF\nprFV0NWEbDNpEpeetO67b98+zp07xy233JLqnIhw4sSJxK937drFhAkT2LRpExcuXEjW7vz585ne\n32TMkjI3HD4MNWq4HYX3+eEHGDYM/v53z3+0ZYwxxpgCJywMunVL/3zCQFGGli9Pf6TMk0SEHj16\nsHjxYiIiIhg+fHiqNpcvX+bSpUuZ9uXr60tQUFBCnE6gx9IYMjx27BjlypXL0tTBtBK3+Ph4Klas\nyNKlS1HVVOcrVKgAwPnz52nXrh1ly5Zl6tSp1KlTBz8/P6Kiohg3bpwV+/AAS8rcYElZzpQv7zx3\njzwCmzfbSKMxxuRUVBRcvgzt2rkdiTEZ8sQUw8ymN3rSSy+9hK+vLyNGjKB06dKJU/9umDVrVrbX\nlFWpUoUKFSqwffv2VO22bdtG06ZNcxxv3bp12bBhA61bt86wPP7mzZs5e/YsK1eupE2SPWT379+f\n43ub5Cwpc8PPP8Mdd7gdhfepXBk+/NB5EzFyJLzxhk1lNMaYnJg6FY4cgW3b3I7EmJuKiLBw4UIu\nXrzIgAEDCAgIoGvXronnc7KmDODRRx9lyZIlHDlyJLEs/oYNG9i7dy9jxozJcby9evVi3rx5PP/8\n87zwwgvJzl2/fp1Lly5RpkwZfH19UdVkI2JxcXHMmzcvx/c2yVlSlt9UbaQsN+6805lgPmgQBAfD\niBFuR2SMMd6nf3/o0cNZaJOfwwjGFAIiQkREBN27d6dnz56sXr2ajh07AjlbUwYwfvx4VqxYQYcO\nHRg9ejQXL15k1qxZ3HHHHQwaNCjHsbZr146wsDCmT5/Ojh076NKlC0WLFmXv3r2sWLGCuXPn8sgj\nj9C6dWsCAwMZMGAAo0aNAiAiIgKxD8c9xqs3jxaRkSJyQESuiMhWEWmRQduHReRTETkhIudF5CsR\n6ZKizUARiReR6wl/xotI5ptJZMepU87EZkvKcm7gQBg92nls3ux2NMYY430efNCZEr5okduRGHNT\nKlKkCCtWrKBVq1Z0796db775Jlf9VatWjX/+85/Uq1ePP/7xj8yaNYuuXbvy6aefZmk9mYikm0DN\nnz+fhQsXcvLkSSZMmMD48ePZvHkzAwYMSJyqWK5cOT755BOqVKnCxIkTmT17NqGhocycOTPd+5ns\n8dqRMhHpDfwFGA5sA8KBdSJSX1VPpXFJO+BT4I/AOWAI8LGI3Kmq3yVpdx6oD9z4aUq96jE3Dh92\n/rSkLHdmzXLKLT3yCHz9NaQo8WqMMSYDxYpBv37w7rswbRoU8dq3A8YUCJMmTWLSpEnJjvn5+bFx\n40aP3aNhw4ZZ3ig6pevXr2d4fujQoQwdOjTDNnfddRdbtmzJtO933nkn+wEarx4pCwcWqOoSVd0D\nPAHE4CRbqahquKrOUtUoVd2vqhOAfcCDqZvqSVU9kfA46dGog4Od0bLbb/dot4VOkSJOOaXKleHV\nV92OxhhjvM/gwfDLL7BunduRGGNMoeeVSZmIFAVCgA03jqlTx3M90CqLfQhQCjiT4lSAiBwUkcMi\n8pGIeHayvYgzZcR2Pc+9smWd6Ysvv+x2JMYY432aNoVmzcAW6htjjOu8MikDggBf4HiK48eBSlns\nYyxQEliW5Nh/cEbaugH/h/P8fCUiVXIVrck7FSqAr6/bURhjTIGT6awpEWdt7urVsGdPvsRkjDEm\nbYVyErmI9AMmAt2Srj9T1a3A1iTtvgZ2A2HApJT9GGOMMQXV+PFOwdoMtyLr0wd27IA0NpU1xhiT\nf7w1KTsFXAcqpjheEfglowtFpA+wEOihqpsyaquqv4rIt0C9zAIKDw+nTJkyyY717duXvn37Znap\nMcaYTERGRhIZGZns2Pnz512Kxjs0bQrdusEXX0CTJuk0Kl4c5szJ17iMMcak5pVJmapeE5EooDOw\nChLXiHUG5qZ3nYj0Bd4Eeqvq2szuIyI+QBPgk8zazpkzh+Dg4Kx9A8YYY7IlrQ+5oqOjCQkJcSmi\ngm/WLGd24n33wVdfQc2abkdkjDEmPd66pgxgNjBMRAaIyG3A64A/sAhARF4UkcU3GidMWVwMjAG+\nEZGKCY/SSdpMFJF7RaS2iDQD3gNq4CRyxpuowv79bkdhjDGuCQiANWucwbD77oPTp92OyBhjTHq8\nNilT1WXA74HngW+B24HQJCXsKwHVk1wyDKc4yGvA0SSPpKX7AnGmNu7CGR0LAFollNw33uS115yq\nYtHRbkdijDGuqVTJqXh/+rSTmNmMT2OMKZi8NikDUNV5qlpLVUuoaitV3Z7k3GBV7ZTk646q6pvG\nY0iSNs+oau2E/qqo6oOq+m+PBbxnj7Oo+sgRj3Vp0jFoEDRs6LwL2bfP7WiMMcY1t94Kn37qFKtV\ndTsaY4wxafHqpMzr7N0L77/vbHxs8lZAAHzyibMnXJculggbYwq1pk2dyvdly7odiTHGmLRYUpaf\njh51ErIKFdyOpHAICnLm7Vy/Dp07wy8ZFuY0xhgD8N//wu7dbkdhjDGFiiVl+enIEahcGXzsac83\nNWrApk1w8aKTmJ08mfk1xhhTgIjIH0Vkm4hcEJHjIvKhiNTPsxv27u1MAY+Pz7NbGHOzmTx5Mj4+\nPpw5c8btUFw3aNAgateu7XYYXseyg/x09ChUqeJ2FIVP3bqwcaOz0r1bN1tUYYzxNm2BV4CWwD1A\nUeBTEcmbHZ+nTYNt22Dhwjzp3pibkYjg7M6UN7755htGjBhB8+bNKVasGL6+vnl2r9zK6+fiZmVJ\nWX46csSSMrc0aOAkZtOng/1HYYzxIqp6v6q+q6q7VfV7YBDOdi0e26Qt2aBY+/YwbBiMHQuHDnnq\nFsaYXFi9ejVvv/02Pj4+1K1b1+1wTB7wWFImIhVE5B4ReVxExojIeBEZJSKPikhjT93Hqx09ClWr\nuh1F4dWokfNmwxhjvFtZQAGPzJN6+2347W8hJibJwZdecqqCDB9uswuMKQBGjBjB+fPn2bZtG/fc\nc0+u+1NVYmNjPRCZ8ZRcJWUJmyy/ICK7gF+AT3E2cf4jMBKYASwH/i0iZ0XkPREJzW3QXstGyowx\npkDylg8WxZkT9DLwparu8kSftWvDl1/CAw/ApUsJB8uUcaYvfvopzJ/vidsYU+gcOnSIevXqcfvt\nt3Myl2vaK1SoQPHixXN8vY+PD6NGjWLp0qU0btwYPz8/1q1bBzgJ2ssvv0zjxo0pUaIElSpV4okn\nnuDcuXPJ+li1ahVdu3alatWq+Pn5Ua9ePaZOnUq8rT/1iBzVZheRCsAs4EFgI04i9jlwUFXPpWjr\nD1QEWgHtgHkicgkYpar/zEXs3iU+Hh56CFq0cDsSY4wxOB8sAo8DDwMNAAHigXNALFAOKJ7Q9jyw\nGliiqutcCdgxD2gEtPFUhx07OoVq778f7r3X2U2kXDmc4bMnn4RnnoHWrZ26+saYLNm/fz+dOnWi\nQoUKfPbZZwQGBgJw5coVYpINS6fN19eXsh7ew2LDhg0sW7aMJ598kqCgIGrVqgXA8OHDWbJkCUOG\nDGH06NEcOHCAV155hR07drBly5bE9WuLFi2iVKlSjBkzhoCAADZu3Mhzzz3HxYsXmTFjhkdjLYyy\nnZQljHT9BYgE6qRMwlJS1RjgQMJjacKnfD2B2SKyAXhWtRDMjfDxceaIGGOMcZW3frAoIq8C9wNt\nVfVYZu3Dw8MpU6ZMsmN9+/alb9++qdrefTds2ODkYW3bOklatWo40xi//BI+/tiSMmOyaM+ePdxz\nzz1Ur16dtWvXJvs9nDlzJlOmTMm0j1q1avHTTz95NK69e/fyww8/0KBBg8RjX375JW+99RaRkZH0\n7t078XjHjh0JDQ1l+fLl9OnTB4DIyMhko3XDhw8nMDCQefPmMXXqVIoWLerReAu6yMhIIiMjkx07\nf/58jvvLVlImIg8Av8N5QTibkxsmJGDLgGUiMg54CxiSk76M8ZiffgJfX6hZ0+1IjDF5yFs/WExI\nyB4C2qvq4axcM2fOHIKDg7N8jxYtYMsW6NLFGRj79FO47TY/+OILCAjIYeTG5E5s7DHi4tL/DMLH\nx4+SJRtl2Mfly7uIj7+a6nixYpUpXrxyrmNM6vvvv6d3797Ur1+f1atXE5Did2fgwIG0bds2035K\nlPB8cdUOHTokS8gAVqxYQdmyZencuTOnT59OPN6sWTMCAgLYtGlTYlKWNCG7dOkSsbGx3H333Sxc\nuJA9e/bQpEkTj8dckKX1IVd0dDQhITmrwZTdkbKGQDdV9cjkUVWdLiKhItJYVX/wRJ/G5MiwYfDj\nj867kBT/YRljbg7e+sGiiMwD+gLdgMsiUjHh1HlVTf1OMxcaNICvvoLQUGfEbN8+KFvWEjLjnqNH\nF3DoUPojS/7+jbjzzp0Z9rFzZ09iYlIvwaxZcxK1a0/ObYiJVJUHH3yQSpUqsXbtWvz9/VO1qVWr\nVuK0wfyW1n337dvHuXPnuOWWW1KdExFOnDiR+PWuXbuYMGECmzZt4sKFC8na5WaEyDiylZSp6ixP\nB+Dy3HxjHIsXOx8Pt2kDq1fDnXe6HZExxvO89YPFJ3CqLW5OcXwwsMTTN6taFT7/HNavdwowGuOm\nKlXCCArqlu55Hx+/TPv4zW+WpztS5kkiQo8ePVi8eDEREREMHz48VZvLly9zKbGiTvp8fX0JCgry\naHxpjb7Fx8dTsWJFli5dSlqD/hUqVACcaXnt2rWjbNmyTJ06lTp16uDn50dUVBTjxo2zYh8ekKNC\nH2kRkWCgAxADfAdEqWqcp/o3Jk9Vq+asm+ja1Vn1vmKFs7jCGHPT8NYPFlU13/cULVcOevXK77sa\nk1rx4rmfYpjZ9EZPeumll/D19WXEiBGULl06cerfDbNmzXJtTVla6taty4YNG2jdunWG1R03b97M\n2bNnWblyJW3a/K/O0P79+/M8xsLCY0kZsB4oA3wL/BMIE5F4YHGhqrJovFe5cs5Hw717Q7du8NZb\nMGCA21EZY/KBiLRQ1W/cjsMY491EhIULF3Lx4kUGDBhAQEAAXbt2TTzv5pqytPTq1Yt58+bx/PPP\n88ILLyQ7d/36dS5dukSZMmXw9fVFVZONiMXFxTFv3rx8ibMw8GRSNgyoBrxyY2qIiAQB80VkJDBM\nVW3CqSnY/P3hww8hLAwGDoTjx+H3vwcRtyMzxuSt14BU85ZF5GmgJjDZXsNSiIuDs2ehYsXM2xpT\niIgIERERdO/enZ49e7J69Wo6duwI5HxN2eHDh3n33XcB2L59O0BiElWzZk369++fo1jbtWtHWFgY\n06dPZ8eOHXTp0oWiRYuyd+9eVqxYwdy5c3nkkUdo3bo1gYGBDBgwgFGjRgEQERGB2Psjj/FYUqaq\nH6Rx7BTQU0QigU0i0kFVL6S+uhA4fhzKl4cinsyDTZ4oUgTefBMqV3YKf4SH27+bMTcREWmHU/Bj\nC/C5qv4bZ4+yVFT15YT9zF4XkYmq+mM+hlpgqYKMGOGUa9y0CSpVcjskYwqUIkWKsGLFCu6//366\nd+/O+vXraZGLvWoPHDjAxIkTkyVBzz33HADt27fPNCkTkXQTqPnz59O8eXMWLFjAhAkTKFKkCLVq\n1WLAgAGJUxXLlSvHJ598wpgxY5g4cSKBgYE89thjdOrUidDQ0DTvZ7JH8mOLMBEJBH4G3lbVUXl+\nw3yUsJYuKioqKv3Sw6pOOeGpU503+MZ7XLsGhWzfDWO8RZLSwyGqGp3V60SkJfARzv5jCpwHrgEv\n4exXtj1lMRARKY0zE2Sgh8LPM1l6XcqFy5edGd4TBv6XTn9sCaVKwcaNUKWKx+9lbi43fmfz6mfT\nmLyW2c9wTl+XAPJl8XBC6eEo4JH8uF+Bc+kSxMQ4Iy/Gu1hCZsxNR1X/paqVgUZAGPAPIAiYCXwN\nnBORNSIyTkRaiUiRhFke9h8CzqxFHx+4d3A1Zj32HXo5Btq3h59/djs0Y4zxWnmSlIlIuIiMFZH6\nCV8HAvXx7Bo2RGSkiBwQkSsislVE0h0XFpGHReRTETkhIudF5CsR6ZJGu54isjuhz+9EJPcl+H75\nxfnT5t0bY0yBoap7VPVNVR0AROOsHRsMrMB5zZoGfAnEiMgJoLxrwRYggYGwdi2MHQtjZwTR545d\nXIot6iRmVonNGGNyJK9Gyk7jbHS5S0T+BewF/ACPzd0Tkd7AX4BJQDOcMvzrEoqLpKUd8CnwWyAY\n2AR8LCJ3JOmzNbAUeANoCqwEPhKR3NVSPX7c+dPm3BtjTIGlqj+r6hJVHaKqdflfkvY6MA/ok2EH\nhYivL0yfDsuXwyebA2jlv4O9eiu0agXfWBFLY4zJrjxJyhJe1IKBQGAscBV4XVUjPXibcGBBwr32\n4GyuGQMMSSemcFWdpapRqrpfVScA+4AHkzQbBaxR1dmq+h9VfQ7n09MncxXpjZEyS8puLh98AL/+\n6nYUxhjPSLWHWZIkbZSqTk6Yim+S6NEDtm2DOC1GyMk1RJQZCf372/+NxhiTTXm6pkxVL6rq58DD\nwFgRCfNEvyJSFAgBNiS5l+LsldYqi30IUAo4k+Rwq4Q+klqX1T7T9csvUKwYlC2bq25MAbJrl7Of\nWZcucPKk29EYY3JJVd93OwZv1agRbN8O3R/24dXAiVxf9YlVrDXGmGzyWFImIukumFLV7TiFPsZ6\n6HZBgC9wPMXx40BWh6PGAiWBZUmOVcpln2k7ftxZT2blQW8ejRrBhg2wcyeEhDjvSIwxBZqIVBSR\nknnQbwNP9+ltSpWCd9+F9Rt98G1Qz+1wjDHG63hypOz3IvJ8Bi94ZXCmM7pORPoBE4GeCXup5a1f\nfrGpizej9u0hKsqpqnn33fDOO25HZIzJWDzwtoh4rBSuiDwGjPZUf94uIMDtCIwxxjt5cvPosSLS\nFJgpIhdxphYeAsrhrMmqD7zsodudAq7j7DGTVEXgl4wuFJE+wEKgh6puSnH6l5z0CRAeHk6ZMmWS\nHevbty99+/aFCRPg3LnMujDeqFo1+PxzePJJGDLE+furr0JJj38Yb0yhFhkZSWRk8mXJ58+fz1Yf\nqnpSRJ4FlonIO8CilPuRZZWI1ASew/lw8/Gc9GGMMcbc4NFJ36q6AxgpImWBTkB/oAJwFHhAVdd4\n6D7XRCQK6AysgsQ1Yp2BueldJyJ9gTeB3qq6No0mX6fRx70JxzM0Z86c9DdCrFUrs8uNNyteHN54\nwxktGzEC9u2DL76w6arGeFDih1xJJNmkM8tU9WDCViezgXEJydlq4N8Ja5PTlbCB9N041YVDgT+p\n6sJsBVCIXb8OPjuikaZ3OOUbjTHGJMpWUpawbuySql7OqJ2qngP+nvDISr8NVPU/2YkF5wV1UUJy\ntg2nGqM/sCihzxeBKqo6MOHrfgnnRgHfJFkDdyVhU1CAvwKbReQZ4BOcF94QYFg2YzOF0cCB0LIl\n/Pe/lpAZU4Cp6iVguIg0w1lf/BxwTUS+AY4A54DzQDGc2R7lgNpAE+Ak8BbQKF+mv99E/vh0DPvm\n/5cFradxy9/mQpUqbodkXLJ79263QzAmR/LyZze7I2U35uM/rarHPBFAwnz8VsCI7FynqssS9iR7\nHmeK4Q4gVFVvlMKrBFRPcskwnOIgryU8blhMQhl9Vf06IXl7IeGxD3hIVXdl9/syhdRttzkPY0yB\np6rfAv1EpBTOrIhWQEOc5CsAZ5r8OeAgzobSo4AtmY2ombS16uTPooj7+M2WNrzcYAL9Ih9Euj7g\ndlgmHwUFBeHv70///v3dDsWYHPP39ycoKL1tkXMuW0lZQZuPr6rzcDb0TOvc4BRfd8xinx8AH+Qk\nHmOMMQWbiDwMPApsBjYl7Ft5kWzM7jA58/DD0KZNMUaFlaT/R6/z7oNrmd/zWWov/KNtGVNI1KhR\ng927d3PqlA0yG+8VFBREjRo1PN5vtteU2Xx8Y4wx3kpVPxSRhsACABE5AmwCPlLVD10NrhC45Rb4\n24d+PPYPZcTANvxmeTueX/cXnn6vBUW63ud2eCYf1KhRI0/e0Brj7XJU6MPm4xuTQxs2OHvWNW7s\ndiTGFGazgR44FYLX4VT0vZa0gYjcCpxQ1eyVeDRZ8kBXYeehUjz39AWefWs8ux9czFv/2Qv167sd\nmjHGuCJX1RdtPr4x2aAKU6fC11/DtGnw9NPg48mtAo0xWbQU+L2qbsygTVFguohcAiapakz+hFZ4\nBATA7DdL0y9MKbE32BIyY0yhlqOkTETWq+o9N762+fgZ+Pxz2LEDRo1yOxLjNhFYswbGj4cxY+Dv\nf4e33oIGDdyOzJhCQ0TuBg5mkpCRUODpdyLSBHhXRJ70VIErk1zzFgItmrodhjHGuCqnH9OHiEig\nRyO5Wa1eDX/9q9tRmILCzw9mz4bNm+H4cbjjDnjxRbh2LdNLjTEe0Qz4KquNVfV7IAx4VUT88iwq\nY4wxhVpOk7IywH9F5DMRmSAirUXEoxtR3zR++QUqVXI7ClPQtG8P//43jB4Nf/qTs7/Zt9+6HZUx\nhUW2PlRMWP/8Z2BS3oRjMnL5MkRH7IJff3U7FGOMyTO5WdByBeiM80L1BXBWRNaKyDgRaSkitlgG\nnKSsYsXM25nCp0QJmDED/vUvuH4dfvjB7YiMKQwOA9mutKOqO4CaIlLS8yFlTETaisgqETkiIvEi\n0i2/Y3DT26/FEPJYI/qVX8dPb2921ucaY8xNJqeJ00FVDQIa4Wz6vAK4DHQBpuFMDTkrIp+IyO9F\npI5HovVGx4/bSJnJWPPmsH072GaaxuSHzUCPHE5F/AKnqFV+KwnswHm9LXQZye+e8efNPx3kn1fv\n5LahrRlV8yNObLQPsYwxN5ecJmXnAVR1j6q+rqq9VbUS8BvgSZyCH1eB3wIzgb0iMs0TAXsdGykz\nWVG0qFMIxBiTpxJK3G8Bns/B5ceBfP+QUVXXqupzqroSKHT/URQpAkP/XIt9Z4J4/rEfWXzkHmp3\nrs3Y+is58fket8MzxhiPyGlStiitg6q6W1XnqWpPVa2IUxr/KeBr4FkRGZvD+3mn69fh5EkbKTPG\nmILlT8AoEfm/bF5XFYjNg3hMFviXFMYtacRPR0sQ/sA+FvzYidrtq/PdyIVuh2aMMbmWo6RMVbNU\nTlBVd6rqa6raFngcGF+oqjaePu0kZpaUmdz69FP47DO3ozDmpqCqe3FGyhaLyEQR8c3ipb2A/+Rd\nZCYrylcswtR/NOXg0eL8ucd3NO7Z0O2QjDEm1/KtGIeqvgNMxJnSWDhcvgxNmkD16m5HYrzd4sXQ\npQt07Qp7bLqOMbmlqtNwNpGeAnwnIj0yqiIsIhOB2kCG+5v9f3t3Hh9Vef7//3XNZCMJSSBAIhD2\nVVEQRAVlcUGr/OpSV7TVVj/un1pRqxbbaktdPlRFbcXl69ZqS7Vq1bpUxboiiLIoKsiO7CQsAbIn\nc9wtz50AACAASURBVP/+OAOGkJmEkMnJJO/n43EeM3Of+z5znSHMmeuc+9y3NJ32uUlc/8+RBMeO\n8jsUEZED1tTD2L8OnNPE7+mfnj29Yc9FDtSzz8KZZ8JNN8GgQXDVVXD77ZCd7XdkIvHsYrz7xG4A\nngPyzewdvMGq1uLdG90LuAA4FjjXORfyKdb9NnHiRDIzM/cqmzBhAhMmTPApoqbnnG7XFZHYmD59\nOtOnT9+rrLCwsMHbMxfjoWXNbA6QAvwAGBF+zxdi+qZNyMyGAnPnzp3L0KFD/Q5HWrrSUvjTn+AP\nf4BAAH77W7jmGkhK8jsykSY3b948hg0bBjDMOTevodsxsx8AU4H+4aKaB8ZyYKJz7pGGvkdjMbMQ\ncIZz7tUodXRcCvv70+X8+bplXH/hRk6/awSJGW38DklEWrADOS41RffFtnhzwjwGXAH8qwneU6Rl\nSkmBX/4Sli6F88+HG2+E44/XvD0iB8A59x+80YNPAR7Hu1K2BPgYbwThQ/xMyMwszcwGm9mQcFGv\n8Gv1ja9D17aFJAarOGfa8fRst43Jo99h4+dr/Q5LRGQfTdF98TjgPLxh9P/pnKtqgvcUadk6dYKH\nH/aukq1erf45Igco3C3xrfDS3BwBvId3Bc8B94bL/wJc4ldQ8WD0WR354KyOfPHqaqbduo67PxrJ\n5OGJnN31Q665KZ2R1xyOBfT9KSL+i/mVMufcRufcA865p51zRbF+P5FWZdAgGD/e7yhEJIaccx84\n5wLOuWCNRQlZPQ0+rTuPLhzJujWOKWfN4bNN3Tn22qH8ffhUv0MTEQGafqAPEREREV9kdU3nuheO\n5doqxzv3LOCo3of5HZKICNCEQ+LHgpldY2YrzazEzGab2fAodXPN7G9m9q2ZVZnZfbXUudjMQuH1\nofBSHNu9EImxW2+Fzz7zOwoRaWJFRZpSLZJA0Dj55iFknX2i36GIiABxnJSZ2Xl4/epvAw4HvgDe\nMrMOEZokA5uBycCCKJsuBHKrLd0bK2aRJrd1K7z4Ihx5JJxyCsya5XdEItJENm/+h98hxL0Ljv2O\ne8a/x5rZ6/wORURauLhNyoCJwKPOub865xYDVwLFRLjp2Tm32jk30Tn3LLAjynadcy7fObc5vOQ3\nOMLeveGZZxrcXOSAtW8PX38N06fDmjUwciSceCJ8+KHfkYlIjG3d+ibl5QV+hxG3iouhfNsufv3G\nCLqN6MLozC+YNuEj8r9p+M8CEZFI4jIpM7NEYBjw7u4y5024NgNvLrQDkW5mq8zsOzN72cwObtBW\niopgxQoIBg8wHJEDFAx6w+d/+SW88AIUFMCYMTB6NPznP35HJyIxtGHD//M7hLiVmgovfH0wm9dW\n8JfLZ5KWVM61/xjBQYe0Y1y7z5l2znuULF/vd5gi0kLEZVIGdACCwKYa5Zvwuhw21Ld4V9pOAy7E\n+3w+MbPO+72l/PCZtI4dDyAckUYUCMBZZ8H8+fDKK1BZCW+84XdUIhIj2dnjWbv2AaqqdGv0gcjo\n0paLHj2GN/OHs3HRdv78408hGOS2FwYR/Oh9v8MTkRZCoy9W45ybDcze/drMZgGL8Ca9vm2/NrZ5\ns/fYqVOjxSfSKMzgtNO8pbzc72hEJEZycy+houI11q9/mLy8G/wOp0XoMKADVz7TgSuB0k2FJGWc\n6XdIItJCxGtSVgBUATk1ynOAjY31Js65SjObD/Spq+7EiRPJzMz8vmDTJiYAE3SlTJqzpCS/IxCp\nl+nTpzN9+vS9ygoLC32KJj6kpHQhO/unfPfd/9G585UEg2l+h9SipORkRl1fWQkXjlzJ2D5rOeWa\nXvQ4pksTRSYi8SgukzLnXIWZzQVOAF4FMDMLv36wsd7HzALAocDrddWdOnUqQ4cO/b7gqadgzhzo\nEGkwSJE4cM893gTVJ53kdX8U8cmECROYMGHCXmXz5s1j2LBhPkUUH7p1u5WKigIqK7crKWtimzfD\nxu/KuPazo6mcnsiApOX84ODvOP7UNoy+vD+Z3dv5HaKINCPx/CvrPuAyM7vIzAYAjwCpwNMAZnaX\nmf2legMzG2xmQ4B0oGP49cBq639jZuPMrKeZHQ78DegGPL7f0eXnQ7t2uhIh8auyEv75T28o/QED\n4IEHQFcmROJKmzY9GDToXyQn6ypNU+vcGT7YOICCVUW8eMMnjOq1jpe+6sdpdx5N+x4ZDE/7hh0v\nvuN3mCLSTMRtUuacex64Efg9MB84DDi52hD2uUBejWbzgbnAUOACYB57XwVrBzwGfBMuTwdGhIfc\n3z+bN2uQD4lvCQkwezZ8/DEMGwY33ghdusDVV3vD7IuISJ0yu2fxo3tG8tii0awq78LyD9by2E8/\nYUTeGjI6pfgdnog0E3HZfXE359w0YFqEdT+rpSxqEuqcux64vlGCO/10OPzwRtmUiG/M4JhjvOXe\ne+Gxx+CRR+Dhh2HUKJgxQ1eDRUTqyQx6je5Kr9Fd61X/9p+uoitrGXluVwac3J1A0GIcoYj4Ja6T\nsmZt1Ci/IxBpXJ07w+23w6RJ3pD6X36phExEJEaqquCNt4PM3TCC0F+CZNl2RmQvYfiAXRwxOpVh\nP+pO56G5XqYnInEvbrsviohPkpLgnHNg8mS/IxERabGCQZizPo/ta3Yx467PuH7sfJwFmTZzMKfd\neTRdjjiId35wj99hikgj0ZUyEYmNNWvgq69g3Djv/jQREdlvbbtmcsItwznhFu+1CznWfLaBuS+t\nZvioEVHbLlpQRumilQw8tScpmclNEK2INJR+KYlIbLz4IkycCDk5cMEF8JOfwJAh6moj4rNQqIIl\nSy6nfftT6NTpXL/Dkf1kAaPbUQfR7aiD6qx7z28KefK1AQSppG/SCg7N2cyh/co4dFgSh4ztSM8x\n3UhIVTd0keZA3RdFJDZ+8Qv4/HM4/3z4299g6FA47DCYMgXWrfM7OpFWyyyBUKiCRYt+zJYtb/gd\njsTQ/U+05ZNHFzLtwk84sd93bC5M4v7/HsqZU0bQ79Q+XJD+Cuza5XeYIoKulIlIrJh5Q+kPGwZ/\n/CO8/TY88wz89rdwyy1w553eo4g0KTNjwICnqKraxVdf/YhBg14iO/tUv8OSGGjbqQ0jLj+UEZd/\nX+ZCjvVf5rPo3fW03ZYC6ekR2+/YAded9DW9UjfRq38ivQ7PpOfIg+h0cAcsoF4PIo1JSZmIxF5i\nIowf7y2FhfDCCzBokN9RibRagUAihxzyHF9/fS4LF55Gv37T6Nz58robStyzgNFlSEe6DOkIDI5a\nt6AAvlrWhn9vHUzBe9l7ylMpomfyBnq128ZDvysg7/JTYhy1SMunpCwW1q2DxYthzBgNcCBSU2Ym\nXHpp3fWc0/1nIjEUCCQzaNBLLFt2HUuWXMHOnZ/Rp8/9BINpfocmzUSvXjCnoBcAO9bvYuXM9ayc\nu5UVX5ewYqWxYmMqaUWbo27jxce3sfBvX5LXM4G8AWl0HZRF3pBs2nZu2xS7IBI3lDHEwptvwmWX\nQUWF35GIxK9f/AK+/RbOOANOOw26dPE7IpEWxyxInz4Pkp4+hKVLr6W0dA2DB//H77CkGcronM7g\nc/ox+Jyaa46M2m7BrBIe/3AAm97viKs2lEEm2+mcVMD4Tp/xxwUnQXZ2lK2ItHxKymIhPx/at9dV\nMpEDccQR8M038POfw9VXw5FHegnaGWfAgAG6iibSSMyMgw66lIyMY6iq2ul3ONLCTH6iM5OfgPId\npayfu4E1C7ezdmkJa1ZWsmED9AiURb2vraoKerXfRseKDeSm7aRjRhkd2lXSoQN0yEmgQ+ckRpyc\nQaexBzfhXok0PmUNsZCfD506+R2FSHy76CJv2bYNXn8dXn4Z7rgDJk2Cfv3gT3+Ck07yO0qRJmNm\n1wA3ArnAF8DPnXOfNdb209IGNNamRPaRlJFCj+N60uO4mmtGR21XWQk/PWEtGxdvY+P2FJYUtOOT\ntekUVGSy1bUH4I2P7uCUjyMnZbNnOV76+XtkZTqysoNkdUggq1MS7TqnkNU5jXbdM8gd2E4n08VX\n+uuLhc2boWNHv6MQaRnatYMf/9hbSkvh3Xe9BC0nx+/IRJqMmZ0H3AtcDswBJgJvmVk/51xBU8UR\nClUSCOingzSd5GT43UuH1rqusqyKbcu3kp5ySdRtrFxSwSsLe7Ktsi3bQplUkrjX+mwKKHj5dTj9\n9IjbeHTSajbOXE7bDKNtZoD0dom0bZdA2w7JtO2QTJfeKeQc1WO/909kN32zxoKulInERkrK96M4\n1mX7dm9QEXVzlJZhIvCoc+6vAGZ2JTAeuASY0hQBOBfi00/7kJran+zs8WRmjiYtbZCSNPFNQnKQ\njgfXfRJ8wsVJTLi4J+CNIVWytYRtqwrZvnYX29cVUba1CI4+Ouo2Zvw3wMzPDmFnKJVd7DtIyXVJ\nDzG17JqI7fPz4acjviW1ZAupKVWkJodIbeO8Jc1ITTPO+0kSuWeOiLiNkqIQVYW7aNMuhWBKoo5v\nLYy+SWNh82ZvyCIR8c9PfgLz5sEpp8Cpp8KJJ0JGht9Riew3M0sEhgF37i5zzjkzmwFE/gXXyJyr\nIC/verZseY3ly2/EuQoCgTQyMo4kPX0wqakD6dDhTJKS1FNEmi8zSM1uQ2p2G7oMq3+7f87O2/M8\nVOUoLihm54Zd7NxUzM7NJWS3OSpq+6oqSAyGKCxLYcOuBIorkyipTKS4KpniUArFrg2jEv8UNSl7\n8O5ibvmDdxxLpJwUSkm2clKsnORAOb2S1vH2e4nePdgR/PGaVWz6/DtSkr2rkHuWFEhJhsEDyjj8\npnER25eXw7IP15NEOYltEkhMTfz+MS3Je0wJKl9sACVlsaArZSL+u/FGePVVeOMNeOIJCAa9A9WJ\nJ3rL0UdDUpLfUYrURwcgCGyqUb4J6N9UQQQCyXTtei1du15LVVUxO3fOZceOWezYMZstW15n7doH\nycgYETUp27lzASUly0hMbEdCQjuCwXQCgTYEg6kEAm0IBFIwC0RsL9IcBIJGek4a6TlpHFTPNrm5\n8PK3A6NXcjdHXX36WQn02DmL4l0hioscZaWOstIQpSVQVgYZwV2QHf3e0E/nGAu/6EpZKJGyUBKl\nLpkykigjmRBBJqU9EDUpW7UKDhnXOep7zD///xgyPfK+PHbvTv586wYSA5UkWhXBQIiEQIigORIC\nIbql5vP4f/Kizmf6h0tWsOGztQSDEAw6EoIQTIBgwLs1cMwhBRz/0FkR2xcWwku3f0lCUSHBBCMY\nhECCEQwagaARTDBGj29L5shDIm5j3cpy1r23hEDQCCQYgYQgS1evjvrZRKOkrLE55yVluqdMxF9j\nxnjLvffCihXwzjswYwY89BBMngyPPeZNXSEi+y0YTCUraxRZWaP2lIVCZZhF/1mxadOzrF17b8T1\n6elDOeKIuVG3sXDhaZSXb8YsiFlCtSUAeCNJduwY+cdYcfFSVqy4BfBO5ZtZ+Lm3mBl9+jwYNbnc\ntOkfbN36RsT1KSm96Nnz9qj7sWzZRCoqtkRc36nTeWRnR+6qXVKyglWrfhf1PXr3vpekpA4R13v7\n8WbE9SkpPeuxH9fXYz9Ojbje24/fR32P3r3vibofmzc/x5YtkfejTZue9OhxW9T3WLbshnrsR+RJ\nsktKVrB69eSo79Gr1x+j70f+82zdGnlKipSsnpx3/2+jvseyZTdSuTjyfjz6n3Nr3Q/noLI8RMnO\nk1i8+GcR21dWwkd/vYrKLUmUl1RRURaiojT8GF4yzq+Kuo1eA7swZsA4yisDlFcZlVVQGYKqKoOq\nIKnJsKz4PioXu33aFpUX4YBNleP4YOUxVIaCVDmjygWocgkQCuBCQbK3vU3nxa/t076ssoydZTvZ\nuTPAdU8+wY4dh0WMc07gAtq2T96nfEvxFooqivhydl9+ed0jNSOMuL26KClrbGawcyeEQn5HIiK7\n9eoFV1zhLVVVsGABdO/ud1Qi9VUAVAE1R7fJATZGajRx4kQyMzP3KpswYQITJkxo9ADBu5JWl969\np9C9+61UVm6jomIroVARVVXFhEIlhEIlBIN1dzFOSxtEUlI+zlXWWKrCNYJ1bCFEVdXuH05uz+Lc\n7udenWgqK7dSWroq4vpAIKWu3aCsbC3l5TUvflZ/jx1R24dCZZSWroxax7nKqOu9/VgRcX19/k1L\nS7+joiLafmyP2j4UKqW0dHnUOnXtR0VFASUlyyKuDwQSI67brbR0VR3/Htuitg+FSikuXhq1Tlll\nEWUumfKqcsqqyiivKqe8qpy+7ftiZlRUFNS6jV3luyirKqUisJqPd/SioqqCylAllaFKKkIV9Mjq\nwWn9Twvvx8pa92P5tuU451i0fBlLyp7ds42QC1HlqrhhxA2M7TGW8kpXaww7ygpZsW0l4Hi8ZBbb\nEwNUJVQRSg9RFaoi5EIs/flSEoOJrFu3kO2b9t3G0q1LyC/KZ3Ux/PnMO/ZZf3r/03n5/JcB+Oqr\nxykv3nc/Zq2ZiQMWjfgnX/fe9zN+9sxnufCwCykqupBvv718n/VbS7awqGAxAMFf5kBZAoQSwAW8\nJRRk3c8WkeASKA0Oo2DXv/bZxpot35JfXMB7iz+C7n/3Cl34xE55KMq3cnTmfQlJQ5nZUGDu3Llz\nGTp0qN/hiEhjufdemD8fRo/2rrj166ebqpuZefPmMWzYMIBhzrl5fscTS2Y2G/jUOfeL8GsDvgMe\ndM79sUZdHZdEwqpCVZRWllJSWUJJRclez9OT0jmkU+TuaQC/fPuXFFcU75VIVU+obhp5E+N6R+7u\n99qS1/jRcz+iIlQRsU7praUkJ0ROgH/80o/528K/7VOeEEggIZDAaf1P47mzn4u6HyOfGInD7Wmz\newlakGAgyMSjJzK2x9iI7b/Y+AWPfP4IwUBwT5uABfY8D1qQ28beRkKUgX/eWf4Oy7Yu26ft7ud5\nmXkc2+3YqPvx1rK3MDMMI2ABzMKP4df9O/SnU1rkW4gKSwtZtX1VrW13b7dP+z7hK+iRt1FWVbZP\n24AF+GL+F4weMRoacFyK6ytl+zNni5nl4g0nfATQB3jAOXd9LfXOAX4P9ACWALc45yJfExeRlik1\nFZYsgX/8w7u6lpPzfYI2ZgwcfDAEdO+LNJn7gKfNbC7fD4mfCjztZ1AisZJflM+n6z5lV/kuisqL\nvMeKor1eTxs/LWoyc8krl/DUgqcirj+176m8fsHrUeN4d+W7OBzJwWSSgkl7luSEZNKT0qO+P8Ah\nHQ/h/h/cv0/73dtICiZFTWQAHh7/MH865U8kBhP3SqaiJQ41fXLpJ/WuW5vBuYN5+P97+IC2Ma73\nuKgJbH2c3OfkA2qfmZLJ4NzBB7yNSNKS0hq83bhNyhowZ0sysBmYHK5b2zZHAn8HbgZeBy4EXjaz\nw51z3zT+XohIs3XVVd6ycyd88gl88IG3TJwIFRXwy1/ClCYZiVwE59zzZtYB76RhDrAAONk5l+9v\nZCK1e3rB0xQUF1BYWsiOsh0UlhVSWBZ+XlrILcfewtkHnx2x/fyN8/nh9B/ued0moQ1pSWmkJ6WT\nlug9llWVRU2KLh58MaO6jSIlIYU2iW1ok9Bmr+ft2rSrcz/mXXFgF+F7tuvJ1cOvPqBttE3edwh+\naXniNiljP+dscc6tDrfBzC6NsM1rgTedc/eFX//WzMYB/wsc2P8oEYlPbdvCySd7C0BxMcyeXffk\n1c6pu6M0KufcNGCa33FIy7cofxFf53/N1pKte5YtxVvYWuo979OuD0+c/kTUbUx6dxJFFUVkJmeS\nmZJJRnIGmcmZdErrRJ92faJ2MQMY3X00G27YQFpiGqmJqQQDdd0ruK8xPcYwpseY/W4n4oe4TMpi\nOGfLCLyrb9W9BUSe4l1EWpfUVDj++LrrTZ8Ov/oVjBwJI0Z4j4MHQ2LdN5yLiByokAuxpXgLm4s2\n77VsKtrEDSNuiHqV6Mn5T3LPrHswjHZt2tG+TXuy22TTvk178jLy6N+h7pkY1l2/br+619WUkpBC\nbnpug9uLxJu4TMqI3ZwtuRG2qW8FEdk/AwfCOed4XR9fesmbcTMlBYYMgeHDvfvTzo7cdUdEpCG+\nLfiWMU+PIb84n5DbexTJ5GAyOek5XDz44qhJ2a2jb+VXo35FVkoWgQbOG3cgCZlIaxSvSZmISPN2\n+OHeAt6snnPnwqefwmefwZtvwldfKSkTkX3sLNvJ6sLVrN6+mtWFq1m1fRWrC1ezbsc61u9cz4WH\nXsjk4yPPh5WTnsNVR1xFbnouOek5dErrtGdpm9S2XslSVkpWY+6SiNRDvCZlDZqzpR42NnSbe+aD\nWbLEm0q8V6+YzgcjInEkOdnrvjhy5PdlFZGHRwa8ER/vvBMOO8y7utatW6u+R2369OlMnz59r7LC\nwkKfohGJndP/cTrvrXoP8IY8z8vIo3tWd3q268mx3Y5lVPdRUdtnpWRx29joEyWLSPMTl0mZc64i\nPCzwCcCrsGfOlhOABw9g07Nq2ca4cHlUU6dO9eaDGTkS+veHpyIPwSoiUue9ZevXw4MPQkF4MNn2\n7b3kbMgQ7wrckCEwYIB3EqgVqO0kV7V5ykSalZKKEpZvW87SLUtZunUpy7YuY+nWpazevpqlP18a\nddCKO46/g5AL0T2rOwelH9SgAS5EJP7E89E86pwtZnYX0Nk5d/HuBmY2GDAgHegYfl3unFsUrvIA\n8L6ZXY83JP4EvAFFLqt3VFu2QIcOB7ZnIiJ5ebB5M6xb501ivWCB9/ivf8F94QFily6FPn38jVNE\n9pi1ZhbnvnAua3es3VPWNqktfdr3oW92X47JO4ayqjJSA6kRtzEi70DGKxOReBW3SVk95mzJBfJq\nNJsPuPDzocAFwGqgV3ibs8zsAuCO8LIUOH2/5igrKFBSJiKNwwy6dvWWH34/Xw/bt3tJWq9e0du/\n/ro3hP+gQdC3b6u5qibS2AqKC/hq81dkt8nm0JxDI9bLy8zjosMuom92X/q270uf9t7Q7xr0QkTq\nEtdH6GhztjjnflZLWZ1DCDnnXgRebFBAlZWwbZuSMhGJrawsGDu27nqPPQavvuo9T0ryRoQ89FAv\nSTv0UBg6FHI1uKzIbs45VmxbwYKNC1iwcQHzN85nwcYFrNu5DoCrj7iah8Y/FLF914yu3HHCHU0V\nroi0IHGdlDU727Z5E8YqKROR5uCVV7wukF9/DQsXeiM+fvWVV75zJ9x8M9x9t99RijQb5/zzHF5c\n5J2XzUnL4fCDDucnh/2EIblDOCznMPq0V3dhEYkNJWWNafcN+UrKRKS56NTJW4477vsy5+C77+ru\nzrh4MdxxhzegyMCB3mOfPt5VN5E4s2nXJrJTs0kIRP67v/aoa/mfof/DkNwhmrhYRJqUkrLGpKRM\nROKBGXTvXne9wkJYscK7N23bNq8sGITevb9P0iZPrnskSZEmVhWqYuHmhXy4+kNmrpnJp2s/ZXXh\naj6/7HOGdY48Yufo7qObMEoRke8pKWtMGRlw7rmQU3OqMxGROHTUUTBzpndlLT/fu3K2aNH3j2++\nCXfdFX0bq1d7w/m3bds0MUurVVFVwX2z7uPD7z5k5nczKSwrJCmYxPDOwzlr4Fkc1fUoerfv7XeY\nIiK1UlLWmAYPhuee8zsKEZHGZfZ9N8jR+3kl4ayzYO5c72RV375e98e+ffde0tJiE7e0KgmBBJ5a\n8BTds7pz48gbGd19NEd2OZKUhBS/QxMRqZOSMhERiZ3HHvOuqi1d6i1ffw0vv+wN6w9e98df/9rf\nGCUurN+5ns5tO0dcb2YsumaRhp8XkbikpExERGJn6FBvqc452LrVS9LqGpJ/5ky44gpvTrbdS8+e\n3mNJSeziFt8VlRcxY8UM3lj6Bu+seIe1O9ay9eatpCelR2yjhExE4pWSMhERaVpmkJ3tLXXJyoLj\nj/cGHHn7bVi5EkpLvXUDBsQ2Tmly63as47Ulr/HvJf/m3ZXvUlpZSr/sfozvO55xvceRGNCgMiLS\nMikpExGR5uuQQ+DBB79/HQrBxo1ekrZoEVx+uX+xSaPaWrKVbvd3wzBGdR/FHcffwQ/7/ZC+2X39\nDk1EJOaUlImISPwIBKBzZ29JTfU7GmlE7du05/ULXueoLkfRrk07v8MREWlSAb8DEBERkZbNOcc3\n+d/UWe8HfX6ghExEWiUlZY2psNC7gV1ERERYtX0Vf/jwD/T/c38OmXYIK7at8DskEZFmSUlZY6ms\n9G5If/ppvyMRERHxzY6yHTw5/0nGPj2Wng/05O6P72ZE3gj+c+F/yMvI8zs8EZFmSfeUNZbCQu+x\nQwd/4xAREfHJZa9exrMLn6WssowTe53IM2c+w5kDziQtSROEi4hEo6SsseyeCFVJmYiINCIzmwSM\nB4YAZc659j6HFFFuei6/G/s7Ljj0ArpmdPU7HBGRuKGkrLEoKRMRkdhIBJ4HZgGX+BxLVJOPn+x3\nCCIicUlJWWNRUiYiIjHgnPsdgJld7GccxRXFFJUX0TGto59hiIi0SBroo7Fs3+7Nn5OZ6XckIiIi\njWbdjnVMencSeVPzmPTuJL/DERFpkeI6KTOza8xspZmVmNlsMxteR/2xZjbXzErNbEnNs45mdrGZ\nhcysKvwYMrPiegWzfTtkZ3uJmYiISJybu34uP37px/R4oAd/nvNnLjrsIiaNUlImIhILcdt90czO\nA+4FLgfmABOBt8ysn3OuoJb6PYDXgGnABcCJwONmtt459061qoVAP8DCr+s38dj27eq6KCIi9WJm\ndwE3R6nigIHOuSVNFJL3ps7xweoPuOOjO5ixYgY9snow5cQpXDr0UjKSM5oyFBGRViVukzK8JOxR\n59xfAczsSrzRqS4BptRS/ypghXPupvDrb83s2PB2qidlzjmXv9/RnHMOXH31fjcTEZFW6R7gqTrq\nHNBMyxMnTiSzRpf6CRMmMGHChIhtFhcs5ri/HMfgnME8d/ZznDXwLIKB4IGEISLSIk2fPp3p2QZB\nGAAAEGJJREFU06fvVVa4e4qsBojLpMzMEoFhwJ27y5xzzsxmACMiNDsamFGj7C1gao2ydDNbhde1\ncx4wyTn3TZ1BdesGQ4fWK34REWndnHNbgC2xfI+pU6cydD+PSwM7DmTWpbM4qstRmFndDUREWqna\nTnLNmzePYcOGNWh78XoDVAcgCGyqUb4JyI3QJjdC/QwzSw6//hbvSttpwIV4n88nZta5MYIWERHZ\nX2aWZ2aDge5A0MwGh5eYzMh8dNejlZCJiDSxuLxSFivOudnA7N2vzWwWsAi4ArjNr7hERKRV+z1w\nUbXX88KPxwEf7u/GQi5EwOL1nKyISMsUr0lZAVAF5NQozwE2RmizMUL9Hc65stoaOOcqzWw+0Keu\ngBrSd19EROqnsfvuxxPn3M+Anx3oduaun8uk/07i2Lxj+c2Y3zRCZCIi0ljiMilzzlWY2VzgBOBV\nAPP6WpwAPBih2SzglBplJ4XLa2VmAeBQ4PW6YmpI330REamfxu6735qs3bGWSe9O4pkvn2Fgh4EM\nGT7E75BERKSGuEzKwu4Dng4nZ7uHxE8FnoY9ww13ds7tnovsEeAaM/s/4Em8BO5s4NTdGzSz3+B1\nX1wGZAE3Ad2Ax5tgf0RERBpNSUUJt79/O1NmTiE9KZ1Hxj/CpUMvJSEQz4d+EZGWKW6/mZ1zz5tZ\nB7y+9jnAAuDkasPZ5wJ51eqvMrPxeKMtXgusBS51zlUfkbEd8Fi47TZgLjDCObc41vsjIiLSmM58\n7kwK2xdy3VHXMWnUJDJTMutuJCIivojbpAzAOTcNbzLo2tbt0//eOfch3lD6kbZ3PXB9g4J57jno\n3x/SYjIYloiIyH45LOcwHrv8MXq16+V3KCIiUgcNv9RYpkyBykq/oxAREQFgyrgpSshEROKEkrLG\nEgxCRobfUYiIiIiISJxRUtZYMjNBk22KiIiIiMh+UlLWWLKy/I5ARERERETikJKyxqKkTERERERE\nGkBJWWNRUiYiIiIiIg2gpKyxKCkTEREREZEGUFLWWHJz/Y5ARERERETikJKyxnLppX5HICIiIiIi\ncUhJmYiIiIiIiI+UlImIiIiIiPhISZmIiIiIiIiPlJSJiIiIiIj4SEmZiIiIiIiIj5SUiYiIiIiI\n+EhJmYiIiIiIiI+UlImIiIiIiPhISZmIiIiIiIiPlJSJiIiIiIj4KK6TMjO7xsxWmlmJmc02s+F1\n1B9rZnPNrNTMlpjZxbXUOcfMFoW3+YWZnRK7PWjZpk+f7ncIzZI+l8j02dROn0vrZWbdzexxM1th\nZsVmttTMbjezRL9ji1f6/1Q7fS6R6bOpnT6XxhW3SZmZnQfcC9wGHA58AbxlZh0i1O8BvAa8CwwG\nHgAeN7Nx1eqMBP4O/D9gCPAK8LKZHRyzHWnB9J+1dvpcItNnUzt9Lq3aAMCAy4CDgYnAlcAdfgYV\nz/T/qXb6XCLTZ1M7fS6NK26TMrwD06POub865xbjHaSKgUsi1L8KWOGcu8k5961z7iHghfB2drsW\neNM5d1+4zm+BecD/xm43REREauece8s5d6lz7l3n3Crn3GvAPcCP/I5NREQaT1wmZeFuG8PwrnoB\n4JxzwAxgRIRmR4fXV/dWjfoj6lFHRETET1nAVr+DEBGRxhOXSRnQAQgCm2qUbwJyI7TJjVA/w8yS\n66gTaZsiIiJNxsz64PXeeMTvWEREpPEk+B1AC5ACsGjRIr/jaHYKCwuZN2+e32E0O/pcItNnUzt9\nLrWr9r2b4mccDWFmdwE3R6nigIHOuSXV2nQB3gSec849GaWtjktR6P9T7fS5RKbPpnb6XPZ1IMcl\n83r9xZdw98Vi4Czn3KvVyp8GMp1zZ9bS5gNgrnPu+mplPwWmOufahV+vBu51zj1Yrc7twOnOucMj\nxHIB8LdG2C0REWmYC51zf/c7iP1hZtlAdh3VVjjnKsP1OwPvAZ84535Wx7Z1XBIR8dd+H5fi8kqZ\nc67CzOYCJwCvApiZhV8/GKHZLKDm8PYnhcur16m5jXE16tT0FnAhsAoord8eiIhII0gBeuB9D8cV\n59wWYEt96oavkP0X+IzIg1lVp+OSiIg/GnxcissrZQBmdi7wNN6oi3PwRlE8GxjgnMsPdw3p7Jy7\nOFy/B7AQmAY8iZd83Q+c6pybEa4zAngf+BXwOjABuAUY6pz7pol2TUREBNhzhewDYCXwU6Bq9zrn\nXM17oEVEJE7F5ZUyAOfc8+E5yX4P5AALgJOdc/nhKrlAXrX6q8xsPDAVb+j7tcCluxOycJ1Z4W4f\nd4SXpXhdF5WQiYiIH8YBvcLLmnCZ4d1zFvQrKBERaVxxe6VMRERERESkJYjXIfFFRERERERaBCVl\nB8DMrjGzlWZWYmazzWy43zH5zcx+ZWZzzGyHmW0ys3+ZWT+/42puzOwWMwuZ2X1+x+I3M+tsZs+Y\nWYGZFZvZF2Y21O+4/GZmATObbGYrwp/LMjP7td9xNTUzG2Vmr5rZuvD/mdNqqfN7M1sf/pzeCc/l\n1Wrp2LSv+vwdtUY6ZtfOzK4MH4sKw8snZvYDv+NqbvRb5ntmdlv4s6i+7NftT0rKGsjMzgPuBW4D\nDge+AN4K3+fWmo0C/gQcBZwIJAJvm1kbX6NqRsI/kC7H+5tp1cwsC5gJlAEnAwOBG4BtfsbVTNwC\nXAFcDQwAbgJuMrP/9TWqppeGd8/w1Xj3Ue3FzG7Gm0z5cuBIoAjvuzipKYNsLnRsiijq31ErpmN2\n7dbgzSM4FBiGN/rpK2Y20NeomhH9lqnVV3jjXOSGl2P3p7HuKWsgM5sNfOqc+0X4teH9J37QOTfF\n1+CakfAPgc3AaOfcx37H4zczSwfmAlcBvwHmV587r7Uxs7uBEc65MX7H0tyY2b+Bjc65y6qVvQAU\nO+cu8i8y/5hZCDijxvyU64E/Ouemhl9nAJuAi51zz/sTqX90bKpbbX9H4tExOzIz2wLc6Jx7yu9Y\n/KbfMvsys9vwBgdscE8fXSlrgPDk1cOAd3eXOS+7nQGM8CuuZioL76zkVr8DaSYeAv7tnPuv34E0\nEz8EPjez58NdZ+aZ2f/4HVQz8Qlwgpn1BTCzwcAxwBu+RtWMmFlPvLOR1b+LdwCf0gq/i3Vskkag\nY3YN4a7k5wOpRJ+3tjXRb5na9Q13kV5uZs+aWV7dTb4Xt0Pi+6wD3lDENeeI2QT0b/pwmqfwGdr7\ngY81rQCEv9SHAEf4HUsz0gvvTNu9eNNQHAk8aGZlzrlnfI3Mf3cDGcBiM6vCO4l2q3PuH/6G1azk\n4v2ArO27OLfpw/Gdjk3SYDpm783MBuElYSnATuBM59xif6Pyn37LRDQbby7Jb4GDgNuBD81skHOu\nqD4bUFImsTQNOBjv7H6rZmZd8Q52JzrnKvyOpxkJAHOcc78Jv/4ifCC8EmjtSdl5wAXA+cA3eAfB\nB8xsvRJWEYkBHbP3thgYDGQCZwN/NbPRrTkx02+ZyJxzb1V7+ZWZzQFWA+cC9eryqqSsYQqAKryb\n+arLATY2fTjNj5n9GTgVGOWc2+B3PM3AMKAjMC98NhK8M9qjwwM3JLvWeYPnBmBRjbJFwI98iKW5\nmQLc5Zz7Z/j112bWA/gVSlh324g3kXIOe18dygHm+xKRv3RskgbRMXtfzrlKYEX45XwzOxL4BV7v\njtZKv2XqyTlXaGZLgHqPBqx7yhogfHZgLnDC7rLwH+cJePeBtGrhL/fTgeOcc9/5HU8zMQM4FO9q\nx+Dw8jnwLDC4FX+JzWTfblX98c4utXapeD+wqwuh7+09nHMr8ZKN6t/FGXgjybW672Idm6QhdMyu\ntwCQ7HcQPtNvmXoKD4bSB+/kc73oSlnD3Qc8bWZzgTnARLwfUU/7GZTfzGwaMAE4DSgys91nbAud\nc6X+ReavcH/ivfrom1kRsMU5V/NKUWsyFZhpZr8Cnsf7Mf0/wGVRW7UO/wZ+bWZrga/xhmaeCDzu\na1RNzMzS8A5su8/K9goPerLVObcGryvNr81sGbAKmAysBV7xIdzmQMemWtTj76hV0jG7dmZ2J/Am\n8B3QFrgQGAOc5GdcftNvmcjM7I94x+3VQBfgd0AFML2+21BS1kDOuefDQ8f+Hq9ryALgZOdcvr+R\n+e5KvBvv369R/jPgr00eTfPW6s8oOec+N7Mz8Qa1+A2wEviFBrMAvLm3JuONctUJWA88HC5rTY4A\n3sP7/+LwBoUB+AtwiXNuipmlAo/ijRz3EXCKc67cj2D9pmNTRFH/jvwKqhnQMbt2nfD+Ng4CCoEv\ngZM02mCtWv1vmbCuwN+BbCAf+Bg42jm3pb4b0DxlIiIiIiIiPtK9CSIiIiIiIj5SUiYiIiIiIuIj\nJWUiIiIiIiI+UlImIiIiIiLiIyVlIiIiIiIiPlJSJiIiIiIi4iMlZSIiIiIiIj5SUiYiIiIiIuIj\nJWUiIiIiIiI+UlImIiIiIiLiIyVlIiIiIiIiPlJSJiIiIiIi4iMlZSIiIiIiIj5SUiYiIiIizYqZ\n9TKzq/yOQ6SpmHPO7xhERERERPYws0+Ao4B+zrnlfscjEmtKykRERESk2TCzTGALsN0518HveESa\ngrovioiIiEhzcizeb9QP/Q5EpKkoKRMRERGR5mQM4ID3/A5EpKkoKRMRERGR5mR0+PEDX6MQaUJK\nykRaATNLM7O39qP+nWa23cx+FMu4REREzGyImb1nZv81sznAkcBO4P5w+Qwz6+RzmCIxpYE+RFoB\nM3sQeM8596961l8H5AL/ds6dEdPgREREwszsHOA54K/OuZ/6HI5Ik9GVMpEWzsx6AV3rm5CFXRar\neERERKI4Hu9+MnVdlFZFSZlIy3cT8IfaVphZNzNLqFnunHsDeBNYGePYREREqjsu/Pi+n0GINDUl\nZSItmJklAgc75+bVsi4X+AY4KULzDcCsGIYnIiKyh5kdBPQD1jjndFJQWhUlZSIt2xjgkwjrzgDa\nAMsjrB8AzIhFUCIiIrU4Pvz4vp9BiPhBSZlIyzYMWBVh3fHAYufctzVXmNkgoNg5tzWGsYmIiFS3\n+36y932OQ6TJKSkTadkOwrsaVpt+wMM1C80sADwETIthXCIiIjXtcz+ZmSWY2ZX+hCPSdJSUibRs\nQeDEmoVmdjVwGFBYozwReAYIOOdeaZIIRUSk1TOzPKAH3v1kq6qtugDI9CMmkaa0z6hrItKiLAeu\nMbPfAX/BO7BdBVwKbAF+b2YrgDXAMcCtQBdguD/hiohIK5Ubfly4u8DMsoEriTwglUiLocmjRVow\nM+uMd09Z9RMwDi/5KgfuqdFkJ3Cyc252kwQoIiICmFk6sBr4yDl3Rjghexa4zTk3x9/oRGJPSZlI\nC2dm5wJ3A52AL4E7nXOvhecnewQ4G6gA3gZ+65yLNBqjiIhIzJjZKOABYAdQipeQfepvVCJNQ0mZ\niIiIiIiIjzTQh4iIiIiIiI+UlImIiIiIiPhISZmIiIiIiIiPlJSJiIiIiIj4SEmZiIiIiIiIj5SU\niYiIiIiI+EhJmYiIiIiIiI+UlImIiIiIiPhISZmIiIiIiIiPlJSJiIiIiIj4SEmZiIiIiIiIj5SU\niYiIiIiI+EhJmYiIiIiIiI+UlImIiIiIiPhISZmIiIiIiIiP/n97V4yDx3RpggAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2406f0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#A quick plot of the spectral density and environment correlation functions\n",
    "\n",
    "gamma = 1.0\n",
    "\n",
    "lam = 2.5/2.\n",
    "\n",
    "T = 1/0.95\n",
    "\n",
    "wlist = np.linspace(0, 10, 1000)\n",
    "tlist = np.linspace(0, 5, 1000)\n",
    "J = [w * 2 * lam * gamma / (np.pi*(gamma**2 + w**2)) for w in wlist]\n",
    "\n",
    "def c(t):\n",
    "    c_temp =[]\n",
    "    c_temp.append(lam * gamma * (-1.0j + cot(gamma / (2 * T))) * np.exp(-gamma * t))\n",
    "    for k in range(1,5):\n",
    "        vk = 2 * np.pi * k * T\n",
    "        c_temp.append( (4 * lam * gamma * T * vk / (vk**2 - gamma**2))  * np.exp(- vk * t) ) \n",
    "    return c_temp\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, sharex=False, figsize=(10,3))\n",
    "\n",
    "fig.subplots_adjust(hspace=0.1) # reduce space between plots\n",
    "\n",
    "\n",
    "\n",
    "axes[0].plot(wlist, J, color='r',ls='--')\n",
    "axes[0].set_xlabel(r'$\\omega$', fontsize=20)\n",
    "axes[0].set_ylabel(r\"$J(\\omega)$\", fontsize=16);\n",
    "\n",
    "\n",
    "axes[1].plot(tlist, [np.real(sum(c(t))) for t in tlist], color='r',ls='--',label=\"c(t) real\")\n",
    "axes[1].plot(tlist, [np.imag(sum(c(t))) for t in tlist], color='g',ls='--',label=\"c(t) imaginary\")\n",
    "axes[1].plot(tlist, [c(t)[0] for t in tlist], color='b',ls='--',label=\"k=0 real\")\n",
    "axes[1].plot(tlist, [c(t)[1] for t in tlist], color='y',ls='--',label=\"k=1 real\")\n",
    "axes[1].set_xlabel(r'$t$', fontsize=20)\n",
    "axes[1].set_ylabel(r\"$C(t)$\", fontsize=16);\n",
    "\n",
    "axes[1].legend(loc=0)\n",
    "\n",
    "fig.savefig(\"drude.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Given these assumptions (<span style=\"color:red\">seperable initial condition, bosonic environment initially in a thermal state</span>), one can derive the hierachy, which looks like the following\n",
    "\n",
    "$$\\dot{\\rho}^n(t) = -(iH_S^{\\times} + \\sum_{k=0}^M\\, n_k \\,v_k)\\,\\rho^{n}(t)$$\n",
    "$$ - i \\sum_{k=0}^M\\, A^{\\times}\\, \\rho^{n^+_k}(t)$$\n",
    "$$ -i  \\sum_{k=0}^M n_k(c_k\\, A\\,\\rho^{n^-_k}(t) - c_k^*\\,\\rho^{n^-_k}(t)\\, A)$$\n",
    "\n",
    "This is a set of coupled equations for a hierarchy of \"density matrices\" labelled by an index $n$.  \n",
    "\n",
    "In this case $n = \\{n_1,n_2,..n_m,...,n_M\\}$: itcontains M indices, $0$ to $M$, a cut-off in the number of exponentials.  \n",
    "\n",
    "Each element runs from $0$ to $N_c$, an additional cut-off term.\n",
    "\n",
    "$n^+_k$ means one increases the $k$th component of $n_k$ by $1$, while  $n^-_k$ means decrease by $1$.\n",
    "\n",
    "$n= \\{0,0,0,..0\\}$ denotes the physical density matrix. All the rest are \"auxiliary\" non-normalized density matrices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Comparing BMS master equation and the HEOM\n",
    "\n",
    "Lets try and see the breakdown of the BMS master equation as we increase the bath correlation time\n",
    "\n",
    "First try lets try some parameters where BMS should work, $\\gamma=10 \\epsilon$, $\\lambda = 0.05 \\epsilon$, $\\beta = \\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmaz()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmax()\n",
    "\n",
    "\n",
    "gamma = 10.                # Cutoff frequency of DL spectral density\n",
    "lam = 0.05           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 1.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "psi0=(basis(2,0)+basis(2,1))/np.sqrt(2.)  #initial state of system.\n",
    "rho0=psi0*psi0.dag()\n",
    "\n",
    "Ncut = 10\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 515,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "def nbs(energy,Temperature):\n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 516,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "173.546464674\n"
     ]
    }
   ],
   "source": [
    "print 1/(np.pi * J0(1.0) * nbs(1.0,temperature))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 520,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n",
      "0.159154943092\n"
     ]
    }
   ],
   "source": [
    "print 1/gamma\n",
    "print 1/(2 * np.pi * temperature)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so $\\tau_E \\ll \\tau_S \\ll \\tau_R$ for the Born-Markov-Secular approximation seems valid. Let's check.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 521,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True,)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 524,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    " \n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1))*sm,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*sm.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "<img src=\"heom1.png\" width=800 /> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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F0L6z89lvaTLlVVbtfpFf9WwTqDZpyRKGvfgi6zMzPQpURESkZlPisR7yNT01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gCW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\nRERERORxDDwSERERERERERGRx/0/vtAm+y8DvdUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x176adb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P1p=rho0\n",
    "psi01 = (basis(2,0)-basis(2,1))/np.sqrt(2.)\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "import matplotlib.gridspec as gridspec\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "axes1.set_title('$\\lambda=0.05 \\epsilon $, $\\gamma = 10 \\epsilon $, $k_{B}T=\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "fig.savefig(\"heom1.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Next try lets try some parameters where BMS should break, $\\gamma=0.1 \\epsilon$, $\\lambda = 0.2 \\epsilon$, $\\beta = \\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 526,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmaz()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmax()\n",
    "\n",
    "\n",
    "gamma = .1                # Cutoff frequency of DL spectral density\n",
    "lam = 0.2           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 1.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "psi0=(basis(2,0)+basis(2,1))/np.sqrt(2.)  #initial state of system.\n",
    "rho0=psi0*psi0.dag()\n",
    "\n",
    "Ncut = 25\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 527,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "def nbs(energy,Temperature):\n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 528,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "43.3866161686\n"
     ]
    }
   ],
   "source": [
    "print 1/(np.pi*J0(1.0)*nbs(1.0,temperature))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 529,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10.0\n",
      "0.159154943092\n"
     ]
    }
   ],
   "source": [
    "print 1/gamma\n",
    "print 1/(2 * np.pi * temperature)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so $\\tau_S \\ll \\tau_R$ seems ok, but now $\\tau_E > \\tau_S$, so Markov approximation should break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    " \n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1.))*sm,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*sm.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "<img src=\"heom2.png\" width=800 />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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O3QRZSyIbjwCUmUBr3749xxxzDMnJyRGISEREIiE60gFIHWvRM3B4SlHiMS0t\nUtGIiIiIiFRfhytg+3ve8ebZkHxqZOORMk2dOjXSIYiISB3TiMeGpnEyJHQCIDV2O1EUaMSjiIiI\niBzajhgMzj+mQtOtRURE6g0lHhuilqcAEO/bz3ExGWzes4f07OwIByUiIiIiUkWxLSHlPO84bwtk\nfR7ZeKRMldk8Zc2aNYwcOZKjjz6ahIQEmjZtSo8ePXjggQfIysoqs07RGpTnnnsuAHPnzuX888+n\nTZs2REVFFWtvzZo1jBo1in79+tGlSxfi4+NJTEwkNTWVBx98MGQbAB07dgysXZmbm8tDDz1E9+7d\nadasGT6fj82bNxcrn5eXx/jx4+nTpw+tWrUiNjaWdu3a0adPH8aPH8/OnTvL/bwmTZpEr169SExM\npFmzZpxxxhlMmzatVLl169YF1tVcunRpudf8zW9+U+yzEhGpbZpq3RC1PMX7P8E5cNW21XTdlsmq\nzz+n7XnnRToyEREREZGqaX8FbHvHO940C9xvIhuPlFLR5injxo3jT3/6E+YfsRofH8+BAwdYvXo1\nq1atYvLkybz11luceOKJIa9x9913M378eHw+H0lJSaU2xBk0aFAgQdi4cWMSEhLYvXs3K1as4Kuv\nvmLKlCl8+OGHHHXUUSHjz8zMJDU1le+++46YmBji4+Px+YqP6Vm+fDmDBw9m69atOOcC8WRlZZGe\nns6iRYuIjo7mtttuK9VOQUEBgwcP5o033qBRo0bEx8fz008/8dlnn/HZZ5/x3Xff8fDDDwfKH3PM\nMZxzzjksXLiQiRMn0rNnz1LXBPjxxx+ZO3cuzjl++9vfhvwMRURqkkY8NkQtvBGP7IbzN2yga0YG\nP6xYEdmYRERERESqo91g8DXyjtfOgsKCyMbTQFkVp7m/8MIL3HfffSQkJPCXv/yFbdu2kZ2dTV5e\nHkuXLqVfv35s27aNiy++mLy8vDKvsXTpUp588knuv/9+duzYQWZmJrm5uYwYMSJQpk+fPkydOpVN\nmzaRm5tLRkYG+/btY968efTq1Yu0tDSGDRtWbqyjRo0iJyeH//znP+Tk5JCVlcXmzZtp3bo1AFu3\nbmXAgAGkpaXRvn17Zs2aRXZ2NhkZGeTl5QVGXbZq1arM6z/zzDMsXLiQl156iZ9++ondu3ezZcsW\nLrroIgAeeeQRNmzYUKzOLbfcgpkxc+ZMcnNzy7zuyy+/zL59+2jZsiWXXnppue9RRKSmaMRjQ9Qi\nFXCQZLSp7nX4AAAgAElEQVSN9qZY7/juu8jGJCIiIiJSHTHN4eczYOEC2L0NLptf7Uv2nDiR7Tk5\n1Y+tBqU0acLSkSMj1v5hhx1W7vmCgvATvjk5Odx9990455g7dy7nBc3Ecs5x0kkn8e6779KrVy+W\nL1/O888/X+ZIwdzcXO666y7Gjh0beK1Ro0a0a9cu8PPkyZNL1YuOjqZv37588MEHHHnkkSxfvpzF\nixdzxhlnlCprZuzbt4+PP/6Y7t27B15v27Zt4Pj+++8nMzOT5ORkFi9eXOwcwLHHHsuDDz5Y5mdh\nZvz444989NFHnH322cWuP3v2bDp37sy2bduYPXs2999/f+D8pZdeSuvWrcnIyGD69OncdNNNpa79\n/PPP45xj+PDhNGrUqMz2RURqmhKPDVGjppDYFexr2jTOJfqnQrI3b6agsJAonwbBioiIiMghquV5\nsHuBd7z8zWpfbntODmlaC72YitYlrIq5c+eyZ88eUlNTiyUdg/l8PoYOHcqyZct49913y0w8+nw+\n7rnnnirHER8fzznnnMOcOXP4+OOPy0w8OucYMGBAsaRjsLy8PGbPno1zjvvvv79U0rEyevfuXSzp\nWCQmJob+/fszefJkVq5cWexcdHQ0N9xwA3/961+ZOHFiqcTj559/zqpVq3DOlZmUFBGpLUo8NlQt\nToE9XxOVZLTJyuFAro/1mzdzbMeOkY5MRERERKRqzroRpo6CggJYV/4mG5WR0qRJ9WOqYZGOqaIR\njZs2baJTp05hXfOTTz4B4Ouvvy53ROXevXsDbZSlS5cuJCcnV9jeW2+9xcsvv8ySJUvYsWNHqanb\nzjm2bt0asn7v3r1Dnlu6dCn79+/HOcegQYMqjKUk5xy9evUKeb4okblr165S50aOHMljjz3G8uXL\n+eqrr4qthTlx4kTAm2pe1vqVIiK1RYnHhqr5SfDDVGgObaJySTvQjHWrVyvxKCIiIiKHrmYpcGwP\nWLMccsteBzAckZzS3JCkp6cDkJ+fX+GISudcIAFZUtEai6GYGVdffTUzZ84MbHITHR1NixYtiImJ\nAWDPnj3s27cv5DqJFbWzffv2wHGHDh3KjSeUpk2bhjwXHe39Cb9///5S5zp06ED//v155513mDhx\nIs8++ywA2dnZgVGY2lRGROqa5tU2VM17eM9JkBLtrVuzZd26CAYkIiIiIlIDTrs80hFImAoKCnDO\nceWVV1JQUFDho+TGKkVK7mBd0vPPP8/MmTOJjo7m4YcfZv369eTn55OZmUl6ejrp6elcdtllmFm5\nm+SU1055u3bXhaJNZqZPnx5I0E6bNo3c3FxatmzJJZdcEtH4RKThUeKxoQpOPEZ5ices77+PYEAi\nIiIiIjXgnN9CI03sOpSkpKRgZiGnUNeUWbNmBdY4fOihh+jcuXOpMtu3b69W8jAlJSVwXNvvpywX\nXHAB7dq1Izs7m5kzZwIwadIknHOMGDFCm8qISJ1T4rGhimkO8e2hCbROzmNVm9a8HxVFYTn/Z09E\nREREpN5LaAHHh14jT+qfojUTly1bxo4dO2qtnS1btgAUW/swWG5uLp9//nm12ujZs2dg2vZ///vf\nal2rKnw+HyNHjsTMmDhxIl9++SVffvklgDaVEZGIUOKxIWveA3zQ+LwDfNn9MD5p2ZIfdu+OdFQi\nIiIiItVz9jWRjkDCMGTIEJKSkti/fz9//OMfyy1rZuzZs6dK7SQmJgKwYsWKMs+PGTOG7GruYh4X\nF8dVV12FmfHoo4+SlpZWretVxQ033EB0dDRffPEFd955J+BtKtOlS5c6j0VERInHhiypR+CwR6z3\nfxaXb9sWqWhERERERGrGaddBj4RIRyGVlJiYyIQJEzAzZsyYwcCBA/niiy8C6yyaGd988w1PPPEE\n3bp146233qpSOwMGDMDMmDRpEpMmTQps0LJjxw7uvPNOHn/88Urtil2RsWPHkpycTGZmJmeccQZz\n5sxh3759gfOrV6/mnnvuYdq0adVuqywpKSlcfPHFmBkLFy7UpjIiElFKPDZkzQ8mHk+M9XZf+zJo\nFzYRERERkUNSTByc1D/SUUgYrr32Wv71r38RGxvLO++8w2mnnUZ8fDytWrWicePGHHfccfzf//0f\n69atq/IajHfddRddu3blwIED/Pa3vyUuLo4WLVrQtm1b/v73v3PzzTczcODAcjeWqYzDDz+c9957\njyOOOIKtW7dy5ZVX0rRpU1q1akV8fDzdu3fniSeeICsrq1rtlOeWW24BvM1utKmMiESSEo8NWfOD\na5v08CceNeJRRERERH4RDhsQ6Qh+UZxzlU74hVM22MiRI1m3bh133303J554Io0bN2bPnj00bdqU\nU045hdtuu43333+foUOHVqnNxMREFi9ezB133EGnTp2Ijo6mUaNGnHvuucycOZNnn322wmtV9n2d\neOKJrF27lkcffZTTTz+dZs2akZOTQ+vWrenbty9PPvkkw4YNq9S1yoqhojjOPfdcWrRoAaBNZUQk\nolx1/2+O1C/OuVRg2bJly0hNTS2/sBXCnEQ4kMOmA83p+MPttIqPZ8fdd1drJzcREZFD0fLlyzn5\n5JMBTjaz5ZGOR0QOCuse12/5sqWc3PMUwqkj8kuxfPlyevbsiXOOdevWaX1HkQak6J626N+/SN/j\nasRjQ+Z8kHg8AB2id5Pg8snIyyOtmgsqi4iIiIhEnNOfOtJw/f3vfwegX79+SjqKSETpX+OGLvG4\nwGHXmEwAvtR0axERERERkUPS//73P6ZNm4ZzjrvvvjvS4YhIAxcd6QAkwhK7BQ5PIp3M3fGs37AB\njjkmgkGJiIiIiIhIZaWlpdG7d2/27t1LRkYGzjkuvPBCzj///EiHJiINnBKPDV3RiMc0uG7hCtrm\n5ZDdsiVccEFk4xIREREREZFKOXDgAFu2bME5R7t27RgyZAhjxoyJdFgiIko8NnhFIx6bQquoPAB+\n3LQpggGJiIiIiIhIODp06EBBQUGkwxARKUVrPDZ08UdAdBNoAimxewE4sG0b+QcORDgwERERERER\nERE5lCnx2NA550239kGzZntp5AponpfHNzt2RDoyERERERERERE5hCnxKKWmW/vM+Pa77yIbk4iI\niIiIiIiIHNKUeJSDG8w0hVZRuQBsUuJRRERERERERESqQYlHOTjisdnBDWZ2bNwYuXhERERERERE\nROSQp8SjFBvxmBLtJR63b98ewYBERERERERERORQFx3pAKQeiG/v7WzdNIeE842/7DiL/dHRPLV3\nLy3i4iIdnYiIiIiIiIiIHII04lG8na2bdQUftGmxm+hGhQCs0s7WIiIiIiIiIiJSRUo8isc/3dqH\n0TUmE4BVO3dGMiIRERERERERETmEKfEonqJ1HoFjihKPGvEoIiIiIiIiIiJVpMSjeJoeHTg8ulEW\nAGszMyMVjYiIiIiIiIiIHOKUeBRPs2MChyfG/wTAmowMzCxSEYmIiIiIiIiUyefz4fP5WLhwYaRD\nkTL06dMHn8/HmDFjIh2KRJgSj+Jp0hmc1x2Oa7wbgF1795KRlxfJqEREREREJMJGjx4dSPL4fD5m\nz55dYZ2BAwcWq7N58+Y6iLR8U6dOZfTo0UpU1XNPPfUUo0ePZuXKlRWWdc7VQURSFc45fT8CQHSk\nA5B6IioWEjpCzve0dzsAAxxfZ2TQOiEhwsGJiIiIiEikFSURJk+ezBVXXBGy3LZt23jvvfdwzmFm\n9Sb5MGXKFBYsWIBzjrPPPjvS4UgIEyZMYPPmzXTq1Inu3buHLHfMMcfg8/mIj4+vw+hEJFxKPMpB\nTY+BnO9pvHEvv12zlEY5hXzbty99OnaMdGQiIiIiIhJhycnJ5OXlMW/ePNLT02nbtm2Z5aZOnUpB\nQQGdOnXihx9+qOMoy1dfkqBSfWvXro10CCJSCZpqLQc1828w8yOctnsrLfPy2PL995GNSURERERE\n6oWEhASGDBlCYWEhU6ZMCVluypQpOOcYPnx4ncUmIiL1kxKPclDRztZNoKXPW9txRz1Yi0VERERE\nROqHESNGYGYhE4+ffPIJ3377LZ07d65wOvOaNWsYNWoU/fr1o0uXLsTHx5OYmEhqaioPPvggWVlZ\nIesWFBQwceJE+vbtS6tWrYiJiSE5OZljjz2Wq666ihdffDFQdurUqfh8PhYsWICZMWrUqGLrT4Za\ng3Lx4sVcc801dOzYkbi4OJKSkujVqxfjxo0jNze3zLiGDx+Oz+fj+uuvB+D555/nzDPPJDk5GZ/P\nx0svvVTuZ1KSmTFt2jQuuOACUlJSiI2NpXXr1vTv35+ZM2eWW7ewsJCnn36ak08+mSZNmtCyZUv6\n9u3L3LlzgdCbf2zatAmfz0dUVFS5a3N27Ngx5HuqyndbtJbopk2bMLPAZxn8CFbR5jL5+flMmDCB\n3r1706JFC+Li4ujYsSPXXXcdK1asqNT72r9/P48//jg9evSgSZMmJCUl0a9fP959992Q9Suyb98+\n/va3v3HGGWfQokULYmJiaN26Nd26dWP48OG89tprIeuuWbOGkSNHcvTRR5OQkEDTpk3p0aMHDzzw\nQLm/LwB5eXmMHz+ePn360KpVK2JjY2nXrh19+vRh/Pjx7Ny5M+TnEErJ/l5ZO3bs4Omnn2bw4MEc\nd9xxJCUlER8fz1FHHcVNN93E119/Xek2q/s7JrVPU63loKKdrZtASkw+5MOutLTIxiQiIiIiIvXG\nWWedxZFHHsmGDRv4+OOPOfPMM4udf/HFF3HOMWLEiAqvNWjQoEBiq3HjxiQkJLB7925WrFjBV199\nxZQpU/jwww856qijitUrLCzk17/+NfPmzQtMnU5MTCQvL4/169ezfv165syZE0hMxMXFkZKSwq5d\nu9i/fz8JCQk0adIkcD3nHFFRUYGfzYw77riDp59+OnD9Jk2akJeXx9KlS1myZAmTJ0/mvffeo127\ndsViK9pQw8wYMmQIc+fOJSoqisTERKKjw/vze/fu3QwePJhFixYVe59ZWVnMmzeP999/n1mzZjFn\nzpxS1/7555+56KKLAmtt+nw+YmNjWbRoEQsXLuSee+6p9uYf5dWvynfbpEkTUlJSyMjIoLCwkGbN\nmhEXF1esvbJiKEt6ejr9+/dnzZo1OOdo1KgR8fHxbNmyhZdffplp06YxYcIEfv/734d8X9nZ2Zx1\n1lksWbKERo0aERsbS3Z2Nh999BHz58/nhRdeCHtUb05ODmeeeSYrV64MtJOYmMiePXvIysrim2++\nYeHChVx66aWl6o4bN44//elPmBkA8fHxHDhwgNWrV7Nq1SomT57MW2+9xYknnliq7vLlyxk8eDBb\nt24N9IekpCSysrJIT09n0aJFREdHc9ttt5X6HMpT1T503333MXXqVJxzREdH06xZM/bu3cv333/P\nhg0beOWVV5g+fTqXXHJJyDZr4ndM6oZGPMpBQSMeUxrlA+DbtYss7WwtIiIiIiJ+w4cPx8yKjSoE\nb0TVnDlz8Pl8XHfddRVep0+fPkydOpVNmzaRm5tLRkYG+/btY968efTq1Yu0tDSGDRtWqt6MGTOY\nN28ecXFxvPDCC2RnZ7Nr1y7y8vLYsWMHr732Gpdffnmg/BVXXEF6ejqnn346AHfffTfp6emBR1pa\nGocffnig/EMPPcTTTz9NmzZtePbZZ8nKymLPnj3s3buXjz76iNTUVNatW1dmcgi8xOXcuXN54403\nGD9+PLt37yYzM5Mff/yR/v37V+ozLiws5JJLLmHRokWkpqby5ptvkpuby65du8jJyWHq1Km0adOG\nN954g3vvvbdU/fvuu4/33nsPn8/H2LFj2b17N1lZWWzfvp1bbrmFxx57jK+++qpSsVRFVb7bu+66\ni/T0dI444gjA29265PdUGYWFhVx66aWsWbOGpKQkpk2bRk5ODrt27WLDhg1ceOGFFBYWcscdd5Q7\ncvGhhx4iPT2d119/ndzcXPbs2cM333zD6aefjplx++23k52dHdbnMmHCBFauXEnLli157bXX2Lt3\nL1lZWeTn55OWlsZLL73E+eefX6reCy+8wH333UdCQgJ/+ctf2LZtG9nZ2YFkeL9+/di2bRsXX3wx\neSX+ft+6dSsDBgwgLS2N9u3bM2vWLLKzs8nIyCAvLy8wOrVVq1ZhvZciRYnQcBx11FH87W9/Y9Wq\nVezdu5eMjAzy8/NZvXo111xzDfn5+Vx33XVs3749ZJvV/R2TOmRmevyCHkAqYMuWLbOwFRaYzYwz\nexnLvrypPXzOOXbzwIG2aNOm8K8lIiJyiFm2bJkBBqRaPfg3XQ899Dj4qMo9btHvdJXui6WYUaNG\nmXPOOnXqZGZmW7ZssaioKGvatKnl5uYGyr344ovmnLMBAwaYmdn8+fPNOWc+n882hfk3RW5urqWk\npJjP57NPPvmk2Llbb73VfD6f3XzzzWFds0+fPubz+Wz06NEhy2zcuNGio6MtISHBVq1aVWaZnJwc\na9eunfl8Pnv99deLnRs+fHjgPf/jH/8IK75gL730kjnnrFu3bpadnV1mmeXLl5vP57PGjRtbRkZG\n4PX09HRr1KiR+Xw+GzVqVJl1hw0bFoiz5OexcePGSn1vHTt2NJ/PZ1OnTg3rvZX33YZz3aIYFyxY\nUOz1WbNmBc7NmzevVL0DBw7YaaedZj6fz7p3715m+845i4uLs2+//bbU+YyMDIuLizOfz2fTp0+v\n6O0Wc8EFF5jP57NHH3200nWys7MtKSnJfD6fvf/++2WWKSgosJ49e5rP57Onnnqq2LlrrrnGnHPW\nqlUrS0tLq3S7lfkeivr7iBEjSp2rzO9bKIMGDTKfz2djx44N2WZ1f8d+yUr++xfpe1yNeJSDnM8b\n9eiD+IQcfBgt9u7l6xJrPYiIiIiINAjv9IR/H1G/Hu/0jPSnwhFHHMF5551Hbm4us2fPDrw+efJk\nnHNhr/dWlvj4eM455xwAPv7442LnkpKSMLOQo6GqY8qUKRQUFDBgwACOP/74MsskJCQwePBggJAj\n5po3b87IkSOrHMcLL7yAc46bb7652LTwYCeddBLdunXj559/5qOPPgq8/uqrr3LgwAHi4uK46667\nyqw7atSoKsdWXeV9tzVh1qxZAJx++un069ev1PmoqCgefvhhzIzVq1ezZs2aUmWcc1x++eWlpvmD\nt7t70ejZlStXhhVbUd/dtm1bpevMnTuXPXv2cNJJJ3HeeeeVWcbn8zF06FDMrFifzMvLY/bs2Tjn\nuP/++0PuRF/fDBw4EDMrt39U93dM6o4mwEtxzY6GH1fgSzCSovaxqyCODZs2Qc/I3+CIiIiIiNSp\nvdthr9Y8L8uIESN47733ePHFFxk+fHhgzccWLVpw8cUXV/o6b731Fi+//DJLlixhx44dpaaJOufY\nunVrsdcuuOACHn30UV5//XUuuOACrr32Ws455xwOO+ywar+vTz75BPASiuVdLycnBzNj06ZNZZ4/\n5ZRTqrzeXGFhIZ9//jkADz/8MGPHjg1ZdteuXQDF4li6dCkAPXv2DJm0POqoozj88MNJT0+vUoyV\nUZXvtiYsXboU51zIJB1A3759iYqKorCwkKVLl9KtW7dSZXr16hWyflECr+jzr6xBgwYxY8YMnn76\naXbu3MmVV17JmWeeScuWLUPWKeqTX3/9dbl9cu/evUDpvrB//36ccwwaNCisWGvbypUr+de//sUn\nn3zCxo0bA79TwcrrH9X5HZO6pW9Jiita5/Ew2L23Me/6upC8e3dkYxIRERERiYS4lEhHUFo9iemS\nSy6hefPmfPLJJ2zYsCGw3uOwYcOIiYmpsL6ZcfXVVzNz5szA5hTR0dGBXX4B9uzZw759+0rtIN27\nd2/GjRvHAw88wLvvvss777wDHByJee2119KnT58qva/09HScc+Tl5ZVKlJXknAske0pq3bp1ldoH\nL5mVn5+Pc44ff/yxUnWCY925cyfOuWLrVpbliCOOqJXEY3W+25pQtDtzee8/NjaW5ORkdu7cWWo3\n5yJNmzYNWT86OhozY//+/WHFNnToUJYsWcLTTz/NrFmzAjuTd+nShfPPP5/rr7+e1NTUYnWKvqP8\n/PyQsRYp2SeDRwV36NAhrFhr0zPPPMMdd9xBYWFhYLOYpKQkYmNjAS+JumfPnnL7R3V+x6RuKfEo\nxRXtbN0Z9rdoymcZ7Tj8p58iG5OIiIiISCQMWBrpCOqtmJgYhg4dyj//+U8mTZrE9OnTcc5Vepff\n559/npkzZxIdHc0DDzzANddcQ+fOnYuVufbaa3nllVdKjYICbyOSq6++mtmzZ7NgwQIWL15MWloa\nU6ZMYcqUKVx++eXMmDGj2G7VlVFQUADAvffey1/+8pew6gYLt92yYgB45513+NWvflXla0VCdb/b\nX7rx48fz+9//njlz5rBo0SI+/fRTNmzYwLPPPsuzzz7LHXfcwfjx4wPlCwoKcM5x5ZVXMn369LDa\nqs6u5bXlm2++4c4778TMuPLKK7n77rvp0aNHsdGLL774IjfeeGO5/aM6v2NSt7TGoxRXNOIR6Nkk\nB4C07Gz27NsXqYhERERERKQeGjFiBGbGhAkT2Lp1K8cff3yp0VqhzJo1C+ccN910Ew899FCpxBR4\no7XKS5ykpKRw2223MXfuXLZt28bKlSu56aabAG9dvH/+859hv6eUFG9Eaagp1HWhZcuWgSTMxo0b\nw67funVrzKzCXaBDnQ9OAO0r5+/APXv2lPl6TXy31VE0Eq68abr5+flkZWUVK1+XOnfuzL333sub\nb75JVlYWn376KZdccgng7eb95ptvBsqmpKSUO62/PEX9GcLv00X9oKI+EO73+Oqrr1JQUEDXrl2Z\nMWMGJ598cqkp07WxfqtEjhKPUlzTLoHDo2MPDutfm5kZiWhERERERKSeOvnkkznhhBMCa8jdcMMN\nla67ZcsWAE488cQyz+fm5gbWOaysbt268dxzz9G7d28A3n///WLnfT7vz9/yRlH17t0bM2PevHn8\n/PPPYbVfU6Kjozn11FMB+O9//xt2/Z7+9fmXLl0acrr4d999FzIx17x588Bx0fdU0vr160NOA6/u\nd1uZ76k8PXv2xMz44IMPQpb56KOPOHDgAOCtFRhpp556KnPmzKF9+/ZA8b5b1J+XLVvGjh07wrpu\nz549A9Pbw+1LRf0gVB8ws8B6ouEoul6PHj1Clpk3b17Y15X6S4lHKS6mBTRKBOBwlxF4+euMjFA1\nRERERESkgRo3bhx33XVXYOpzZSUmen9zrFixoszzY8aMITs7u8xzFSUE4+LiMLNAAqtIs2bNAMpd\nN/H6668nOjqazMxMHn744XLb2b9/f62sUQgwcuRIzIz//e9/gTUsQ9ldYk3+yy67jKioKPbu3cvf\n/va3MuuMHj065PXi4+M58sgjAW/kaFkeeeSRkPWr891C5b6n8lx11VUAfPrpp2UmsAoKCvjzn/8M\nwAknnMBxxx1XpXaqory+6/P5AknC4L47ZMgQkpKS2L9/P3/84x/Lvb6ZFRuJGhcXx1VXXYWZ8eij\nj1Y4CjZYjx49MDP+/e9/l3l+ypQpVdocqKh/rFq1qszzb7/9NvPnz6+X08SlapR4lOKcgybePzJN\nD+wgGm99ESUeRURERESkpP79+zNu3DjGjRtX7s68JQ0YMAAzY9KkSUyaNCmwSceOHTu48847efzx\nx0lOTi6z7uDBg7nhhht45513iiVZdu/ezSOPPMIHH3xQ5i6+xx9/fCCZF2pTlc6dO/Pggw9iZjz2\n2GNcd911rFmzJnC+oKCAFStWMGbMGLp06VJmcq0mEibXXHMN5513HoWFhQwePJixY8eybdu2wPm8\nvDzmz5/P7373u1JTmdu2bcvvfvc7zIwxY8bw6KOPkpPjLaOVmZnJ73//e6ZNm0ZSUlLI9ocOHYqZ\n8eKLL/LPf/4zMN1269at3HjjjcyZM4eEhIQy61bnu4WD39Orr75apeTjZZddRq9evTAzhgwZwowZ\nMwKjG3/44QcuvfRSPv30U5xzjBs3LuzrF6nK93zqqady++23s2DBgmKjUbdt28Yf/vAHvvvuO8Db\nub1IYmIiEyZMwMyYMWMGAwcO5IsvvgiMCDUzvvnmG5544gm6devGW2+9VazNsWPHkpycTGZmJmec\ncQZz5swpNn169erV3HPPPUybNq1YvaFDhwKwdu1aRo4cGdjBOzs7myeffJJbbrklrN/5IgMGDABg\nzZo1/O53vwskzvPy8njuuecYMmQIycnJ5Y54VVLyEGNmevyCHkAqYMuWLbMqWzTEbBpm07Ajx/7B\nGDXKBk2fXvXriYiIHAKWLVtmgAGpVg/+TddDDz0OPqpyj1v0O12t+2IxM7NRo0aZc846deoUVr35\n8+ebc858Pp9t2rSp2Lkff/zRjjvuOPP5fOacs6ioKGvevLn5fD7z+Xx2yy232PDhw805ZyNGjChW\nt0+fPoF6zjlLTEy0xMTEwM8+n8+uvPLKUvGsX7/e4uLizOfzWVRUlKWkpFjHjh2tY8eOlpaWVqzs\nww8/bFFRUYF24uPjLTk52aKjo4u1s3jx4mL1QsVcFdnZ2XbRRReVeq9Fn1PRa7GxsaXq7tu3z84/\n//xAuejoaGvRokXg873//vsDn+Po0aNL1c/JybHjjz++1PdT1N6sWbOsY8eO5vP5bOrUqcXqVue7\nNTNbuHBhoGx0dLS1bds28D0FK/oOFixYUOoaaWlpdsIJJwRiiI2NDcRf9Hk888wzZX7uod5XsKp+\nz0XXLoq9efPm1qRJk2J96u677y6z7nPPPWeNGzcO1G/cuLElJydbTExMsfrTy/jb/csvv7R27doV\n6w/JyckWFxcXqPfUU0+VqnfdddcV62vNmzcP/F7cfvvt5X4O5fWvYcOGlbpu0e/Wqaeeav/4xz9C\n/jenJn/HfqlK/vsX6XtcjXiU0vwjHgG6NfaGwK/TGo8iIiIiIg2Wc65Ko4xC1UtMTGTx4sXccccd\ndKygiKIAACAASURBVOrUiejoaBo1asS5557LzJkzefbZZ0PWf+aZZ3jssccYOHAgRx/tbY65b98+\nDj/8cC6++GJee+01Zs6cWarNLl26MH/+fC666CJat27Nrl272Lx5M1u2bAmMiCsyatQoVq5cya23\n3spxxx1H9P9n777jo6rSx49/7qRNJiGkASG00KT3Jk0NoKgoCgqL6AqKIIo/F8W17Fdp6iq49hVU\nQNoiIOAuFkQB6QhI6JHeIbT0Xuf8/rgzk0mZkDLJTOR5v17zmjNz7z33mZaceeYUT0+Sk5MJDg6m\nd+/evPzyy+zYsYOePXs67bkqzN/fn9WrV7NmzRpGjBhBo0aNyM7OJiMjg/r16zNw4EDeffddjh49\nWuRYHx8ffvrpJz7++GM6deqEj48PALfffjsrVqy44Yrdfn5+bNu2jRdffJEmTZrg5eWFt7c3w4YN\nY+fOnQwfPtz2WAuryGsL0LdvX9asWcOAAQMICgri2rVrttepMEfPc3h4OHv27OGDDz6gZ8+emEwm\nMjIyaNiwIaNGjSIqKooJEyY4fPylef3K8zovX76cadOmMWDAAJo0aUJOTg65ublERETwyCOPsGHD\nBt57771ijx03bhzHjh3jpZdeomPHjhiNRpKSkqhRowbdunXj+eefZ926dbaeivY6duzIkSNHePfd\nd+nZsycBAQGkpqZSu3ZtIiMj+fDDDxk5cmSR4xYsWGB7D5lMJpRS9O3blxUrVvDRRx+V+3lYsmQJ\nH330ER06dMBoNGI2m2nfvj0zZsxg27Zt+Pn5lVivsz5jompoSt18y9f/mWma1hmIioqKKvWKckWc\nnAu7x4IZPogfwqyT9cnw8eHMu+/iLUvWCyGE+JPau3cvXbp0AeiilNrr6niEEPnK08a1fqYr1C4W\n4k8sMjKSLVu2MGXKFCZPnuzqcIQQTlL4/5+r27ieN95F3HT8LXOExMF9W6NJjo1nZ/36nIqPp1Wt\nWq6NTQghhBBCCCGEEEJUCzLUWhRVwzLU2g+CPTIACM7I4KgMtxZCCCGEEEIIIYQQpSSJR1GUb30w\neIEv+HmkARCUmSmJRyGEEEIIIYQQQghRapJ4FEUZPMCvMWjg46MvLhOUkSELzAghhBBCCCGEEEKI\nUpM5HkXx/JtCynEMphz8Ddmkmr05f+mSq6MSQgghhBBCCOEEGzdudHUIQoibgPR4FMWzm+exgTEP\ngGsXLyKroAshhBBCCCGEEEKI0pDEoyief37isb4xFwCPpCSupaW5MCghhBBCCCGEEEIIUV1I4lEU\nzy7xWMcrG7OmYcrJkQVmhBBCCCGEEEIIIUSpyByPonjWoda1gAdr8/bRPpgNBo7FxXF7RIQrIxNC\nCCGEEEIIIYQQ1YD0eBTF82usX3tBLb94zAb9rSI9HoUQQgghhBBCCCFEaUjiURTP0xd86wHgn33R\ndrckHoUQQgghhBBCCCFEaUjiUThmGW7tkR1LmI++mvWxuDhXRiSEEEIIIYQQQgghqglJPArHrAvM\nAJGheQCcSUggMzfXVREJIYQQQgghhBBCiGpCEo/CMbvEY4+amQAo4GR8vIsCEkIIIYQQQgghhBDV\nhSQehWN2ice2phRbWeZ5FEIIIYQQQgghhBA34unqAIQb829iK0Z4JgB1AUk8/illxkLMj5B0GDxM\nENID6t4JBi9XRyaEEEIIIYQQQohqShKPwjH/CP06F+ruOsJf92eTaDRyrH17l4YlnEiZ4Y8ZEP1P\nyE0tuM0vArp9DuEDXRKaEEIIIYQQQgghqjcZai0c86ml937zAOOJyzRNSKBhUpL0ePyzyM2ArUPh\nwD+KJh0B0s7CprvhyAdgNsP161UeohBCCCGEEEIUx2AwYDAY2LJli6tDETeh0aNHYzAYePLJJ10d\nituTxKNwTNP0Xo8aGLwTCTQaCcrM5Ni1ayilXB2dqAhzHvz2V7i42nKHAZo9DXeshT4roPbt+fvu\nmwRLJsIXX8DJky4JVwghhBBCuM60adNsSR6DwcA333xzw2MGDRpU4Jjz589XQaQlW7hwIdOmTZNE\nlZv7+OOPmTZtGgcPHrzhvpqmVUFEQhSlaZq8/0pJEo+iZH6N9WvfXOqbDHiYzWipqVxOLaaHnKg+\not+GC6v08nkjmKdDt9n6sOqGD0P/jdBumr49Afju35BwDJYtAzdoNAohhBBCiKpn/aI9f/78Eve7\nfPkyv/zyi+1Lubt8OV+wYAHTpk1j06ZNrg5FlOCjjz5i+vTp7N+/v8T9WrRoQcuWLTGZTFUUmRAF\nSYes0pHEoyiZX4R+7Q/1jHkABGVkyHDr6ix2NxyerpcTDRA3DE7mwA8/gPUPp6ZBu8nQ5h9QE6ir\n4OL/IDMFVqwASTwLIYQQQtx0QkNDMZlMrF+/npiYGIf7LVy4kLy8PCIiIqouuFJylySoqLgjR44Q\nHR1N165dXR2KEKIEkngUJbMuMOMHtb1yAPTh1pJ4rJ7MebB7LKg8MAOX7gY/y+rlnp56wtFe+zeh\n3t3QHQhMhctrISUFvv8+P0kphBBCCCFuCn5+fgwbNgyz2cyCBQsc7rdgwQI0TWP06NFVFpsQQgj3\nJIlHUTLrUGsTBHlkAhCYmSk9HqurU3Mh0TJXSkxz8Oysl8PD4a67iu6vGaDHXPAJhB5A5kFIvwjH\njsEff1RZ2EIIIYQQwj088cQTKKUcJh63b9/O8ePHadKkCbfddluJdUVHRzN16lT69+9Ps2bNMJlM\n1KxZk86dO/PGG28QFxfn8Ni8vDy+/PJLIiMjqVWrFt7e3oSGhtKyZUtGjBjBV199Zdt34cKFGAwG\nNm/ejFKKqVOnFph/0tEclDt27OCxxx4jIiICX19fAgMD6dGjBzNnziQtLa3YuAovODF37lz69OlD\naGgoBoOBRYsWlficFKaUYsmSJdx7772EhYXh4+ND7dq1GThwIMuWLSvxWLPZzKeffkqXLl3w9/cn\nJCSEyMhIVq3Sp1y64447MBgMTJ8+vcBx586dw2Aw4OHhUeLcnBEREQ4fU3leW+tcoufOnUMpZXsu\n7S/2brS4TFZWFh999BG9e/cmODgYX19fIiIiGDVqFAcOHCjV48rJyeG9996jQ4cO+Pv7ExgYSP/+\n/fn5558dHn8j9nGnpqby+uuv06pVK0wmE6Ghodx///3s3r27xDrc9bFB2T6bhZ07d46JEyfStm1b\natSogZ+fH61atWLixIlcuHChxPPm5OQwd+5c7rnnHsLCwjAajYSHh9OrVy/efPNNzp49W2B/R+9/\ne9b3ZL9+/cr0HCQmJjJv3jz+8pe/0L59e0JCQmyv0aOPPsquXbtKfc5Vq1Zx1113UadOHTw8PEqM\n1115ujoA4easPR5N4E864K0nHktoBAg3lZcJh6bq5Uwg4Q7w8QCDAQYPBg+P4o8z1YMOb8Ge56AD\ncHAtNB0DP/8Mt9wCXl5VE78QQgghhHC5vn370rRpU06dOsW2bdvo06dPge1fffUVmqbxxBNP3LCu\n++67z5bYMhqN+Pn5kZCQwIEDB9i/fz8LFizg119/pXnz5gWOM5vN3HPPPaxfv942dLpmzZqkp6dz\n4sQJTpw4wYoVK2zJP19fX8LCwoiPjycnJwc/Pz/8/f1t9WmahoddW1gpxcSJE/n0009t9fv7+5Oe\nns6ePXv4/fffmT9/Pr/88gsNGjQoEJt1HkylFMOGDWPVqlV4eHhQs2ZNPD3L9vU7ISGBBx98kK1b\ntxZ4nHFxcaxfv55169axfPlyVqxYUaTu7OxsBg8ebJtr02Aw4OPjw9atW9myZQsvv/xyhRfHKOn4\n8ry2/v7+hIWFcf36dcxmMwEBAfj6+hY4X3ExFCcmJoaBAwcSHR2Npml4eXlhMpm4cOECixcvZsmS\nJXz00Uc899xzDh9XSkoKffv25ffff8fLywsfHx9SUlLYuHEjmzZtYt68eeXu1atpGjExMYwZM4bT\np09jNBrx8PAgISGBH3/8kXXr1vHDDz8wYMCAavXYyvrZtLdkyRKeeuopsrOzAfDx8cFgMHD8+HGO\nHTvG/PnzWblyJXfeeWeRY8+cOcPgwYNtz4mmaQQGBpKSksKuXbvYtWsXCQkJfPDBB0Wei8pgXSDJ\n+rclICAATdO4cOECS5cuZdmyZXz88cfFvkb2XnrpJT744AMMBgOBgYEF/k5VJ27R41HTtIaapg3W\nNO1hTdNkggZ3Yu3x6Aee9c0caNKEo6GhMtS6Ojo9HzKv6OXYnuATrpe7doWwsJKPbfY01GwN9YGa\nlyD1FCQnw4kTlRqyEEII4W6k3SqE3qtPKVWk51J6ejorVqzAYDAwatSoG9Zzxx13sHDhQs6dO0da\nWhrXr18nMzOT9evX06NHDy5dusTIkSOLHLd06VLWr1+Pr68v8+bNIyUlhfj4eNLT07l69Srffvst\nDz/8sG3/4cOHExMTQ8+ePQH9y3xMTIztcunSJerVq2fbf/LkyXz66afUqVOHWbNmERcXR1JSEhkZ\nGWzcuJHOnTtz7Ngxhg4dWuzjUkqxatUqvvvuOz744AMSEhKIjY0lMTGRgQMHluo5NpvNDBkyhK1b\nt9K5c2d++OEH0tLSiI+PJzU1lYULF1KnTh2+++47XnnllSLHv/rqq/zyyy8YDAbefvttEhISiIuL\n48qVKzzzzDPMmDHjhou3VER5XttJkyYRExND/fr1AT15U/h1Kg2z2czQoUOJjo4mMDCQJUuWkJqa\nSnx8PKdOneL+++/HbDYzceLEEnv3TZ48mZiYGFavXk1aWhpJSUkcPXqUnj17opTib3/7GykpKeV+\njiZMmIDRaGTjxo2kpaWRkpLC7t27admyJdnZ2YwbN67aPbayfjat1q1bx6hRozCbzbzyyiucOXOG\n9PR0UlNTOXr0KMOHDyclJYXhw4dz8eLFAsempKTYErHBwcHMmTPH9plLSUnh1KlTvP/++zRq1KjM\nj6e86tWrx9SpU9mzZw/p6enExsaSnp7O6dOnmThxIgAvvvhiib1T9+zZw4cffshrr73G1atXiY2N\nJS0trVQ/6rgdpZRTL0AI+oxw3YFON9i3HvALkFfocgYY7OzYboYL0BlQUVFRyinMZqWW11BqCUqt\nbqZ6zJmjmDpVMXWqSsvOds45ROXLy1HqfxH66zgHpV4br9SUKUq9/bZSqamlq+PcCv342Sj1YnOl\nzp2r1JCFEKKqRUVFKUABnZUb/E+XS5W0m6TdWk0u5WnjWj/TFW4X79ih1PvvO74sWHDjOhYsKLmO\nHTtKPv769dLtV0mmTp2qNE1TjRs3VkopdeHCBeXh4aFq1Kih0tLSbPt99dVXStM0dffddyullNq0\naZPSNE0ZDAZ1roxtx7S0NBUWFqYMBoPavn17gW3PPvusMhgMavz48WWq84477lAGg0FNmzbN4T5n\nz55Vnp6eys/PTx06dKjYfVJTU1WDBg2UwWBQq1evLrBt9OjRtsf82WeflSk+e4sWLVKapqk2bdqo\nlJSUYvfZu3evMhgMymg0quvXr9vuj4mJUV5eXspgMKipU6cWe+zIkSNtcRZ+Ps6ePVuq1y0iIkIZ\nDAa1cOHCMj22kl7bstRrjXHz5s0F7l++fLlt2/r164scl5ubq2699VZlMBhU+/btiz2/pmnK19dX\nHT9+vMj269evK19fX2UwGNTXX399o4frMO46deqo2NjYItsPHTpk22dHoc+8uz+28nw2zWazat68\nuTIYDGru3LkO93vggQeUwWBQL7zwQoH7X3/9ddtjOnDgQKnPW5q/B9a/fZGRkUW2WT/rTzzxRKnP\nafXcc88pg8Ggxo4d6/CcBoNB/f3vfy9z3UoV/f/n6jZuZfR4nAb8Zrn83dFOmqYFAzuA/oBW6NII\n+K+maaMrIT5RFpqWP9w6/RwtQ4Jtm47LcOvq49wySDurl31vgyDLgjI9eoCfX+nqaDAUAlpCANDl\nBBjPVUakQgghRFWSdqu4sawsfaSHo0tq6o3rSE0tuY6srJKPN5tLt18VqV+/PgMGDCAtLY1vvvnG\ndv/8+fPRNK3YYZRlZTKZuP322wHYtm1bgW2BgYEopbhy5UqFz1PYggULyMvL4+6776Zt27bF7uPn\n58eDDz4I4LBXWVBQULE91kpr3rx5aJrG+PHjCwwLt9epUyfatGlDdnY2GzdutN2/cuVKcnNz8fX1\nZdKkScUeO3Xq1HLHVlElvbbOsHz5cgB69uxJ//79i2z38PBgypQpKKU4fPgw0dHRRfbRNI2HH364\nyDB/0Fd3t/aePXjwYLnjHDduHCEhIUXub9u2LY0bNy62fnd/bOX5bG7ZsoWTJ08SGhrKmDFjHO73\n+OOPo5Qq8pmz/t0ZO3Ys7du3L3PMrjBo0CCUUiW+/w0GAy+//HIVRlV5KiPxOBi9EQbwZQn7zQCs\nE2IUXh5XWeqYrWlaE+eGJ8rMOtzanEOXwPy7Zbh1NXL83/nlO9+EF16ABx6A7t1LX4dmgNav5d/+\n413nxSeEEEK4hrRbxY35+EBAgOOLg6RQAf7+Jdfh41Py8QZD6farQtZFZqzDra1zPgYFBfHAAw+U\nup4ff/yRESNG0LRpU/z9/QssJGJNahYeWnnvvfeiaRqrV6/m3nvvZdmyZVy+fNkpj2v79u2AnlCs\nW7euw8v8+fNRSnHuXPE/xnfr1q3Mczpamc1m2+ITU6ZMKTGOY8eOARSIY8+ePQB07drVYdKyefPm\nBYaXV4byvLbOsGfPHjRNK3Z+RKvIyEjbfHnW56uwHj16ODw+PFyftio+Pr7ccZanfnd/bOX5bFo/\nc0lJSSW+18eOHQsUfK+fP3+emJgYQJ9X1J2cOXOGl156ia5duxIUFISnp6ft/X/vvfcCJb//mzVr\nRmhoaFWFW6mcuriMpmnh6LPAKSAZ2OpgvzBgFPkNt0vAu8Bp4HZgEuABeAOvAxX/yUyUn1+ErdjB\nP91WlpWtq4nEQxBnWTUrsAPU6qv3ZO3Uqex1RTwCB9+A9PMQ8xOkngH/xs6NVwghhKgC0m4Vpdaz\np36piFLMd1ii0FB48cWK1eFkQ4YMISgoiO3bt3Pq1ClbAnLkyJF4e3vf8HilFI8++ijLli2zLfDg\n6elJcHCw7fikpCQyMzOLrCDdu3dvZs6cyeuvv87PP//M2rVrgfyemI8//jh33HFHuR5XTEwMmqaR\nnp5Oenp6iftqmkZGRkax22rXrl2u84Oe8MnKykLTNBITE0t1jH2s165dQ9O0GyYW69evb0vaOFNF\nXltnuHbtGkCJj9/Hx4fQ0FCuXbtm27+wGjVqODze09MTpRQ5OTnljvNG9QNF6nflYwsLCyt2MZYR\nI0bw4YcfAuX7bFrfgzk5OQ7jtdI0jczMTNtt+56VVTmH443897//ZeTIkbbPMUBAQABGoxFN08jO\nziY+Pr7E939F/oa4G2f3eGxjV96nlMpzsN9w9KSnBqQAtyqlZiml1iqlXgOeI3/4ykOapt34P5eo\nPHaJpaY+ybbyMRlqXT2cnJtfbvqUnnQsL4MXNH/ackPByTkVCk0IIYRwIWm3ClEB3t7ePPLIIwDM\nmTOHxYsXo2laqVfCnTt3LsuWLcPT05MpU6Zw4sQJsrKyiI2NtS0m8tBDD9nP81nApEmTOHPmDB9+\n+CFDhgyhTp06XLp0iQULFtCvXz+GDx9OXp6jj7Vj1mNeeeUV8vLybnjZsGFDsfVUZPVZ+7jXrl1b\nqjgmT55c7vM5W0VfW+Gerl+/bktm2l+Sk5ML7FfWz6a13KNHj1K913Nzc23HVtaq1BURHx/PE088\nQXZ2NgMGDGDz5s2kp6eTkJDA5cuXiYmJKTBFhSPVdQXr4jg78WifYj5Swn53W64VsEgpVfhnljno\nvyYD+AMdnBOeKBe7Ho911HU8LB9u6fFYDeRlwtnFetnDCI0frXidTZ4EzdJZ+vQ8yMuueJ1CCCFE\n1ZN2qxAVZB1u/dFHH3Hx4kXatm1L586dS3Xs8uXLbfOyTZ48mSZNis5UcOXKlRITC2FhYTz//POs\nWrWKy5cvc/DgQdtwzFWrVjF79uwyP6awsDAAh0Ooq0JISIitx9vZs2fLfHzt2rVRSt1wFWhH2+2H\niNv3LissKSmp2Pud8dpWhLWnWEnDWLOysoizdKSpTj3LXPnYHCUC582bV2Tfsnw2K/KZsx5bnuOt\n7/PyvMdLsmbNGpKTkwkKCuK7776jT58++BSaJqMy5qd1Z85OPNrNAEhCcTtommYA+tjdtbLwPkr/\n2WOT3V2tnRGcKCfr4jKAZ8Z5mgQFAXqPR7P8QuXeLq6GbMtHscEw8A6qeJ2+YdBgiF7OvAYX/1fx\nOoUQQoiqJ+1WISqoS5cutGvXjpycHDRNK3FhiMIuXLgAQMeOHYvdnpaWZpvnsLTatGnDF198Qe/e\nvQFYt25dge0Gg/71t6Redr1790Ypxfr168nOds0P7J6ennS3zMX+/fffl/n4rl27Avr8fo6Gi588\nedJh8iooKP87g/V1KuzEiRMOh4FX9LUtzetUkq5du6KUctgbFWDjxo22nnPdunUr13lcobo+tpI+\nm9b7rly5wt69e8tUb4MGDWzDzsv6WbG+zx29x4Ey/w2yr69FixYYjcZi91m/fn2Z663OnJ14tH9W\nHS251h7912CADGC7g/3O25WLLvUkqo5dj0cSTnOrlxcNEhNJz8nhYqFu1cLNnFueX276hPPqbfZ0\nfvnMIsjOhn37oIRfi4QQQgg3I+1WIZxg5syZTJo0iUmTJvHoo6UfXVOzZk0ADhw4UOz26dOnk5KS\nUuy2GyUEfX19UUrZElhWAQEBACXOm/jkk0/i6elJbGwsU6ZMKfE8OTk5lTJHIegrHiulWLNmjW2e\nPEcSEgr+dvLQQw/h4eFBRkYG//rXv4o9Ztq0aQ7rM5lMNG3aFNB7pxXnrbfecnh8RV5bKN3rVJIR\nI0YA8NtvvxWb4MnLy+PNN98EoF27drRuXX1+L3L3x1aez2ZkZCTNmjVDKcULL7xww3kzC7/fx4wZ\ng1KKuXPnOnzPFadDhw62VbKLm6v1119/5bfffitzz1zr+//48ePFPh/79+/n66+/LlOd1Z2zE4/2\nf3VrOtinl+VaAbtKmE/HvgFYfJpYVA3vQPCydApYdoDHtm9n6BF9RJKsbO3GclIgZo1eNtaBWrc5\nr+46kWCqr5d/XwszpsPq1XD4sPPOIYQQQlQuabcK4QQDBw5k5syZzJw5k5CQ0ufd7777bpRSzJkz\nhzlz5tiSDVevXuWFF17gvffec7ii64MPPsiYMWNYu3ZtgaGQCQkJvPXWW2zYsAFN04qsctu2bVtb\nMs/RoipNmjThjTfeQCnFjBkzGDVqFNHR0bbteXl5HDhwgOnTp9OsWbNiEx3OGEL82GOPMWDAAMxm\nMw8++CBvv/12gdWB09PT2bRpExMmTCgylDk8PJwJEyaglGL69Om8++67pKamAhAbG8tzzz3HkiVL\nCAwMxJFHHnnEtmr57NmzbcNRL168yFNPPcWKFSvw8/Mr9tiKvLaQ/zqtXLmyXMnHhx56iB49eqCU\nYtiwYSxdutTWA/DMmTMMHTrUllCaOXNmmeu3csX8gu7+2Mrz2fTw8ODzzz/H09OTrVu3ctttt/Hr\nr78WmMvxzJkzfP7553Tv3r3IFAovvfQSzZs3JzMzk379+jF37twCie3Tp0/z5ptv8v777xc4bvjw\n4RgMBuLi4hgxYoRt6oHMzEwWLlzI0KFDb/g3rbjn6a677sJgMBAfH8/IkSMLLJ7zzTffMHDgQFty\n/Wbh7MSjfRaqhYN97rQr/1ZCXfYNwOKXChNVx7rAjFcStXyNBGRloZnNMs+jO7v0PZgt34PSboez\n56AcE2wXSzNAI30ycUx5cG2fXj50yDn1CyGEEJVP2q1CuNCkSZNo1aoVubm5PP300/j6+hIcHEx4\neDiffPIJ48ePZ9CgQcUOt83IyGDBggXce++9BAUFERgYSGBgICEhIbZFVoYNG1Zk6PeoUaMwGo2c\nPHmShg0bUrduXRo3bkzjxo0LJCLfeOMNJk+ejMFg4D//+Q/t2rXDz8+PWrVqYTQa6dSpE1OnTuXi\nxYvFJh6csWCKwWDg22+/5f777ycnJ4c33niDevXqERgYSHBwMDVq1KBfv37Mnj272N5aM2bM4M47\n70QpxT/+8Q+CgoIICQmhTp06zJ49m1dffZUOHRxPSfvKK6/Qpk0bcnJymDBhAv7+/gQHB9OwYUP+\n85//sGDBAofJw4q8tqD39tQ0jR07dlCrVi3q1atne51K+9ytWrWKtm3bkpyczKOPPmqLv2nTpnz/\n/fd4eHjwySefcNddd5WqzuK4YmEcd39s5f1s9uvXj5UrVxIQEMDu3bsZMGCA7TPn6+tL06ZNefbZ\nZ4mKiirymfP39+fnn3+mTZs2JCYmMm7cOIKCgggNDcXf359mzZoxderUInOaNm/enNdffx3Qh2k3\naNCAoKAgAgICePLJJxkwYADPPPNMic9FcduaNWvG3//+dwC+/fZb6tevT1BQEP7+/owYMYKAgAA+\n+eSTsj+51ZizE4/W7k4acJumaf72GzVNCwQG2t21pYS67NeHL3lNdVH5rMOtTWZq+5gxKEVAVpYk\nHt2ZdZh1LvBHACxaBLNng7P+QUZYhtIEAuqoXj5/HsoxAa8QQgjhAtJuFaIMNE0rVy8oR8fVrFmT\nHTt2MHHiRBo3boynpydeXl7069ePZcuWMWvWLIfH//vf/2bGjBkMGjSIW265BdB7KdWrV48HHniA\nb7/9lmXLlhU5Z7Nmzdi0aRODBw+mdu3axMfHc/78eS5cuFCgdxXA1KlTOXjwIM8++yytW7fG09OT\n5ORkgoOD6d27Ny+//DI7duygZ8+eTnuuCvP392f16tWsWbOGESNG0KhRI7Kzs8nIyKB+/foMHDiQ\nd999l6NHjxY51sfHh59++omPP/6YTp062Ra3uP3221mxYgX//Oc/Szy3n58f27Zt48UXX6RJ/mtd\nkAAAIABJREFUkyZ4eXnh7e3NsGHD2LlzJ8OHD7c91sIq8toC9O3blzVr1jBgwACCgoK4du2a7XUq\nzNHzHB4ezp49e/jggw/o2bMnJpOJjIwMGjZsyKhRo4iKimLChAkOH39pXr+KvM4VeX+482Mr72cT\nYPDgwZw8eZIpU6bQo0cPatSoQVJSEkajkY4dOzJ27Fj++9//2pJ69iIiIti3bx+zZs0iMjKS4OBg\nUlNTCQoKolevXrz11lu88MILRY6bOnUqixcvpmfPnvj7+2M2m+ncuTNffPEFK1euxMPDo8TnwtG2\nd955h0WLFtGjRw9MJhO5ubm2ROfevXupW7duueqtrjRnZuk1TfMAYgDrTx/zlFLj7LbPA6wTzSUD\ndZRSxc6po2nacaAZ+tCWXkqpss/qeRPSNK0zEBUVFVXqFeVKJepFOPYhHITMrEd5d99FFnTsSLPO\nnVn/+OPOO49wjpxkWFULzNkQVwtinwFNg86dYfBg55xDKVjTDpKi9bVA8/6mD8u/6y7o1euGhwsh\nhLvZu3cvXbp0AeiilCrb7Oai2pF2a/VSnjau9TPt9HaxEH8SkZGRbNmyhSlTpth6owkhqr/C//9c\n3cZ1ao9Hy7w3C9B/OQYYo2naEU3TvtY0LRoYbd0V+LqExls9oKnlppn8X6SFq1iHWpvAaE7F5OVF\nYGam9Hh0V5fX6UlHgIyuetIRoFUr551D0yBipF6uDyTp837KcGshhBDVgbRbhRBCCCEqn7OHWgO8\nBdj3gW4B/AWwz3gkWfZzZAh6I1ABh5RSlbNUmCg9v0b6tQnITiLUZCIwM5NLKSmkZDlaCFK4TMwP\n+rUZSAzTyz4+UMp5UUqtwUP6dQ3A+5RevnwZ4uKcex4hhBCicki7VQghhBCiEjk98aiUSkGfiPsk\n+b8g218nAQ8rpYpfRkz3lF256BrxoupZE49+QE4SIb6+BFpWNjsuSSb3osz5q1nH+4JnuF6+5Rbw\n9HTuuQJaQIDlu1nNU5Cjr5aHZdVzIYQQwp1Ju1UIIYQQonI5OQuhU0od1zStHfovxgOAOkAqsBv4\nSinlcHyupmld0VcGPGe563+VEaMoI7+G+rUJyEkk1GQiICEBgKOxsXQJD3ddbKKguD2QaZnXPqsD\nGCwf85YtK+d8DYZA9BEIBw4fg3aDISCgcs4lhBBCOJm0W4UQQgghKk+lJB4BlFLZwGLLpSzH7QGc\nPB5UVJhXIHjWAFLgDkjq8ByLv/sOQOZ5dDfWYdYAqY31/hoGAzRt6vCQCmkwFKL/Cf7A3Zlw79jK\nOY8QQghRSaTdKoS4GW3cuNHVIQghbgKVMcej+DPSNLtej5dp3rChbcGSYzLU2r1c+lG/NgOd74Na\ntaB+fTAaK+d8QZ3BZHlvJG+GnJTKOY8QQgghhBBCCCGqlUrr8Sj+hEwNISka8jJpbMrFy2Agx2yW\nHo/uJCsOEvbp5eAOcK9l1ens7Mo7p6ZBvfvgxCww58DVX6H+A5V3PiGEEEIIIYQQQlQL0uNRlJ51\ngRnAM+MCzYKDAX1xmTyz2VVRCXvXNqMvqgmE9c+/39u7cs8bfk9+Oeanyj2XEEIIIYQQQgghqgVJ\nPIrSsw61Bkg7T8vQUACy8vI4n5TkoqBEAVc25Jfr9He8n7PViQSDJbl5eS0oVXXnFkIIIYQQQggh\nhFsq01BrTdMa2t9WSp2/0T7OUNx5hAuY7F7a9PO0CGlnu3k0NpbGQUEuCEoUcPVX/VrzgNp9q+68\nnn5Q+za4sh7SzkHyUajZqurOL4QQQhQi7VYhhBBCCNcr6xyPZ7GN40Q5ON5+H2dwdB5R1eyGWpN2\njpahkbabR2Njuad5cxcEJWzSY/SEH0BId/CqUbXnr3uPnngEvdejJB6FEEK41lmk3SqEEEII4VLl\nHWqtWS6l2ccZF+EOHAy1BmSBGXdwdWN+uSqHWVsVnucxMRGiokCG4QshhHAtabcKIYQQQrhIeX6R\nLU2DShpdf0a+4foQXpUHu6Npe3k7D0dHs7JNG47Fxbk6OnHVbn7HsH5Vf/6Alvpw/PTzsHMjbJqp\nz/t4zz3Qo0fVxyOEEEJIu1UAR44ccXUIQgghRJVxt/97ZU08PuGkfUR1ZPAE33p6Yun4JfxSj9At\nKYlVZrP0eHQ1pfIXlkn3gas1wT8N/PyqLgZN03s9nvwCgnLhxFkIuAVOnpTEoxBCCFeQdutNLjQ0\nFJPJxGOPPebqUIQQQogqZTKZCLUbpepKZUo8KqUWOmMfUY35WXq0eaeBOZvavr74Z2dzNS2NxMxM\nAo1GV0d4c0o7o78uAMlt4Nvv9PLw4dC6ddXFUXegnngMANQl4BY4exZycsDLq+riEEIIcdOTdqto\n2LAhR44cIdYdfiDPzoC37oT0DL2P7Yv/gboyH3Z1lGc2s2D/fr6IiiLPbAbA6OnJpF69GNKyJZom\nnaiFEK4XGhpKw4ZOX0OvXGTya1E2fo3g+jYwAdnJhPj6UjMrixSjkWOxsfSoX9/VEd6crm/PL2dE\n5JfDw6s2jtq3AxpoCmpc0O/LyYHz56Fp06qNRQghhBA3vYYNG7rNFy+GPwar50ANQP0CnR91dUSi\nnLp17croe+7hsf/+l+NxcWQCb588yUGDgS/vv58wf39XhyiEEG6jvIvLiJuVydJw8wVykgg1maiZ\nmQnIAjMuZU085gEpNfVyUBAEBlZtHD7BENRRL5vOQG66Xj57tmrjEEIIIYRwN4OnQF9fuBNIWwFZ\nMkd6ddatXj32jhvHuM6dbfd9f/w4bWfNYkV0tAsjE0II9yKJR1E21pWtTUBOop54zMoCJPHoUtbE\nY4IBvMP0ckSEa2KpY1nYpjaQdk4vnznjmliEEEIIIdxFYD3oM1Yfap2XAcdnuToiUUF+3t58cf/9\nrB4xgtqWudXjMjIYvnIlj6xaRXxGhosjFEII13OLxKOmaQ01TRusadrDmqZ1dXU8ogR+jfRrE5Bd\nsMejrGztItmJkGT5VTWzmb6SNECjRq6Jp06kfm0EvK7o5ZgYsCSohRBCiOpM2q2iQlpOBM3yFez4\np5CX6dp4hFMMbtGC6Gef5WG7udWXHT5M21mzWHPihAsjE0II13N64lHTtBBN07pbLp1usG89TdN+\nAc4A/wWWA7s0TTujadpgZ8cmnMBk3+MxiZpGI6E5OYD0eHSZ2J2A0stZEfn3u2o+o9p9QfPQy6Yz\n4O2tz++Ynu6aeIQQQggHpN0qqpx/Y2gwTC9nXYczi10bj3CaUJOJbx5+mCVDh9oW3Lycmsqgr79m\n7HffkSI/wgshblKV0eNxGvCb5fJ3RztpmhYM7AD6ow84sL80Av6radroSohPVIR1qLURCM7C0KED\nuY0bA3AyPp5cy8puogpZh1krIDVEL/v56XM8uoJXAAR308sRF+D5UfDoo66LRwghhHBM2q2i6rV6\nKb985F9gznNdLMKpNE1jZLt2RD/7LPc0a2a7f+6+fbT//HM2ybznQoibUGUkHgejN8IAvixhvxlA\nA0tZFdqmLHXM1jStiXPDExXiVQO8g/RXp08WDB1Kbld9lFGO2cyZhATXxvcndDU1lfWnT7P88GFW\nHz3K4WvXCiZ4Y3fo19lARGfw8IAGDUDTiq2vSliHW3sDsVtdF4cQQghRMmm3iqoX0hVq366XU47D\nxf+5Nh7hdOE1avDjyJF8ed99+Hvr0yCdTUwkcuFCJq5dS4ZlxJgQQtwMPJ1ZmaZp4UB99AZYMlBs\nxkHTtDBgFPkNt0vAu8Bp4HZgEuCBnrZ4HXjSmXGKCjI1hOwESL8I5jxahITYNh2NjaW53W1RPhk5\nOXwZFcVX+/dz8OrVIttDfH15uHVrnunckQ5xu/Q7gxrCgy9Bbi5kuni+oLB+8Mc7evnqrxAxwrXx\nCCGEEIVIu1W4VOtX4dpmvRz9T6g/BAxuMf2+cBJN0xjbpQsDmjThidWr2XxOX3Tx4127WHvyJIuG\nDKF7vXoujlIIISqfs/+7tbEr71NKORo3MBw96akBKcCtSqlZSqm1SqnXgOfIH77ykKZp3k6OU1SE\ndYEZlQuZV2gZGmrbJPM8Vtyyw4dp8e9/M/Hnn4tNOoK+Wt4XUVE8uehNyE3T76zVS7/29AR//yqK\n1oHQXqBZfte4vs21sQghhBDFk3arcJ26AyGgI5wDlu+FXYtcHZGoJI2Dgvh11Cg+HDgQo6fePj4W\nF0fPefN4df16MnNzXRyhEEJULmcnHu2X0T1Swn53W64VsEgpFVNo+xz0X5MB/IEOzglPOIWf3aIl\naecKJB5lZevyS8/JYczq1TyyahUXkpNt93evV49JPXvyrzvvZNoddzCkZUt8LY2WXsYLtv0OmpsV\nqdNlPE0Q3EUvJx+BTElICyGEcDvSbhWuo2lgGgV70NPZ377r6ohEJTJoGhNvvZV9Tz9Nt/BwAMxK\nMWP7djp98QU7L150cYRCCFF5nDrUGgi0Kxc72Z+maQagj91dKwvvo5RSmqZtAh613NUa+N1JMYqK\nMtknHs9zS90utpvS47F8EjIyuGfJEnZdumS7b1Dz5vyzf3/a16lTZP/U7Gzm7t1LvUOrbfc9sf0a\nQ9QW/q9vXzRXzu9oVasPWIeBx+6A+rLgpxBCCLci7VbhWrdNgOX/hNjrcPoY7P8fdHzQ1VGJStQy\nNJQdY8YwY9s2pm/ZQnZeHkdjY+n91Ve8cOutvBkZia+Xl6vDFEIIp3J2j0ejXTnLwT7t0X8NBsgA\ntjvY77xdWSYNdCd+dh0E0s9Rw8eHejVqAHBEEo9lFpeeTv9Fi2xJR5OXF4uHDOGHkSOLTToC+Ht7\nM/HWWxlaJxWALLMHh7Jq88bGjUxYswazKjzvvQvUsvueJsOthRBCuB9ptwrX8vSCQc/k3/72TdfF\nIqqMp8HA/912G3vHjSvQ+/H9336jw+efs+38+RvUIIQQ1YuzE49pduWaDvaxTESHAnaVMJ+OfQPQ\n6GAf4Qp+BXs8ArSqVQuA+IwMrqWlFXeUKEZmbi6Dly1j35UrANT28+O3MWN4rH37Gx+cnYhH6gkA\n4oy3kGPpwDx7zx5eWLsW5erkY63e+eXr28BshsuXITHRdTEJIYQQ+aTdKlzv7lchwPL2i94Lxze5\nNBxRddrUrq33fhwwAB8PDwBOxMdz2/z5/O2nn0jLznZxhEII4RzOTjzad3dr4WCfO+3Kv5VQl30D\nMKPcEQnns+/xmHoO0tLoZjck4I/r110QVPWjlOLJ1avZcUGfpzHM35/No0c77OVYRHyUrRjeqB+L\nhwzBYBli/cnu3UzdtMnZIZeNsRYEWP4MHP0d3nkLvvgC9u93bVxCCCGETtqtwvW8fWHgE/m3V7zh\nulhElfM0GHi5d2/2jx/PrfXrA/qvHJ/s3k37zz9n09mzLo1PCCGcwdmJx8OWaw24TdO0AkvrapoW\nCAy0u2tLCXXVsytfc054wimMdcBgSTR+HQXvvcd9v+dPZRR9TV6u0vho506WHtY/MiYvL34cObLA\nQj03FGd5zhXg3YbH2rVj3uD8eRSnb9nC14cOOTHicrAOtzblQuIZvSzDR4QQQrgHabcK9zB4MphM\nennfdjgXVfL+4k+nZWgo2554gvfvusu28vXphAQiFy5kwo8/kpLlaDYIIYRwf85OPB4ErqOnQvyB\nDwptf5/84ScpwOYS6upsVz7prACFE2gGMDWw3NCHzdYDNLMZkB6PpREVE8Mr69fbbn89dCid69Yt\nWyXxlsRjOrD0MPzrX4xOTOT9u+6y7fLk6tX8brdgTZWzJR4Bg+V72MWLkOdopJoQQghRZaTdKtyD\nKQj6P6KXvRT8/i/XxiNcwsNg4MWePTk4fjx9GuZPbTVrzx7azZ7N+tOnXRidEEKUn1MTj5Z5bxag\n/3IMMEbTtCOapn2taVo0MNq6K/C1UqrYn240TasHNLXcNJP/i7RwF9bh1j6ZkJdJbaMRf8s8JNGS\neCxRek4Oj6xaRY4lUftyr1480LJl2Suy9nhM9gWfELDMrfnCrbfyVKdOAGTl5TF85UqSMjOdEnuZ\nhdrN82i6rF9nZ8PVq66JRwghhLCQdqtwK0OmQycT3APkfgsZl10dkXCR5iEhbB49mo/vvhuTZTqr\nc0lJ3Ll4MeO+/9517XohhCgnZ/d4BHgLuGB3uwXwF6CV3X1Jlv0cGYLeCFTAIaWUrFbibkyWX+FM\nQE4Svl5eNLcMC5AejyV7a8sWTsTHA9AtPJw3+/UreyUZVyHd8jHLbab3QgUID0fTND4bNIheDfRe\nqWcTE3n6hx9cs9hMjWZgrK2XvY+D0pOtMtxaCCGEm5B2q3APNcNh0HPgCZiz4WjhDrjiZmLQNJ7v\n0YOD48dzR0SE7f45e/fSdvZsfjx+3HXBCSFEGTk98aiUSkGfiPsk+b8g218nAQ8rpWJKqOYpu/J6\nh3sJ17H2ePQFspMA6OjrC8D19HSuy8rWxTp09Srv7dgBgLeHB4uGDMHbsopdmcTvyS9n2k0rZRmu\n7e3hwddDh1LTxweA5dHRfLVvX7njLjdNyx9uXTMNMi1JaUk8CiGEcAPSbhVupeULYNDbbpyYDZmx\nJe8v/vSaBgez4fHH+ezee/Gz9H68mJzMfUuXMnLVKvnOJYSoFiqjxyNKqeNAO2AUsBj4BfgWeBVo\nrpT61dGxmqZ1RV8Z8BxwHvhfZcQoKsivYI9HgLbe3rbN0uuxKLNSPP3DD+Rahli/1qdP2RaTsWe/\nsEx6kF6uUUO/WDQKDGSu3WIzf1u7lrOJieU7X0VYE48BQK7le9v58+CKHphCCCFEIdJuFW7DNwya\njdXLuWlw9H3XxiPcgkHTeLZbNw4/+ywDmjSx3b/08GFaffYZiw8ccM3IJiGEKCXPyqpYKZWN3nhb\nXMbj9gCNKyUo4TymoonHFpZf4UCf5/F2u2EBAubv28dvFy8CcEtICK/26VP+yqwLy6QCHrX0cnh4\nkd0ebt2apzp1Yu6+faTl5DDu++/5+bHH0DStyL6Vxpp4NAB+dgnptDTw9y/2EFENpZyCc0vh2hZI\nPw9KA0MjMHaFBg9AWAs9MV6V7z0hhCglabcKt9H6FTj5pT7c+vi/odVL+lze4qYXERjIL489xsID\nB3jx559JyMwkLiODx//3P74+fJjPBw2iUWCgq8MUQogiKi3xKP7krKta2w21bmKXUJAejwWl5+Qw\nedMm2+3ZgwZh9KzAxy8+Sr9ODQAvSwOjmMQjwPsDB7L21CkuJiez7vRpFh44wOiOHct/7rIK7KAP\nGzJnQbMYuP9vEBgoCag/i8zrsO8lOPuf/Dk8Y9DXik07CvwM2jsQ3BVaDIHOPaBHDzCZXBi0EEII\n4aZM9aHpGH2odW4qHP0QOpQ0xai4mWiaxuiOHbmnWTOeX7uWb6KjAVh78iRtZs3in/37M6FbNzwM\nlTKwUQghykX+Iony8bNLPPbxgfHjqfXYY7bNsrJ1QR/t3ElMSgoAg1u0oF/jCnSOyLgCmZZVoXOb\n5CfwHCQeA3x8+HzQINvtF37+mSupqeU/f1l5eENwF73seQ588yTp+GdxdSP82BrOLMpPOgIE+kGG\nXWJdmSFuN/z+Dvy0BD7+GI4dq/p4hRBCiOqg9atgsIwkOvYJZMa5Nh7hdur4+7P84YdZPWIE4Zap\nltJycvjb2rX0mT+f6GvXXByhEELkk8SjKB9PP/AO0qddD4mDsDBCgoOp4+cHSI9He7Hp6czYvh3Q\n52h5p3//ilWYsD+/3C8Sxo+HwYOhfn2Hhwy65RYebdcOgMTMTF5dX8Vz34f0yC/H7arac4vKcXYZ\n/HoXZFkmvvcOhvZvwQNnYUwKjPwG+r8N/YbBLT5QC8hJhtMLIeEPKO/8pkIIIcSfnV9DaPIExAIb\nU+A/L7g6IuGmBrdowR/PPsv4Ll1s9+28eJFOX3zB1E2byMrNdWF0Qgihk8SjKD/rcOuMS7beTq1r\n6fMNXktLIzY93VWRuZW3t2whOSsLgCc7drQ9R+Vmn3gM7QxhYdC5M1hWFXfkw4EDCTQaAVh44AC/\nXbhQsTjKIvTW/LIkHqu/i6vht8dAWRqzde+BQX9A2//TV7zXNHjwQXj2HzDhG3j9ODzUF+4BGuZC\nja8hfbNLH4IQQgjh1ho+D1sNcA3Y+A0kX3Z1RMJN1TQamX3ffWwePZpbQvT5QHPMZqZt3kznL7+s\n2ja/EEIUo8rmeNQ0rSVQHwgCjOh95UpFKbWosuISFWBqAIkHwZyjD/31rUubWrXYePYsoPd6vK1R\nI9fG6GJXUlP5PEqfj9HX05NpkZEVr9Q+8RhU+rkaa/n58WZkJP/vp58AeO6nn9j91FNVMwdMqF2P\nx9idlX8+UXmu/wbbhoPK0283fQq6fQ4Gj4L72Q+n92sI/dbDzlFgWgaYYcej0G8D1OpVZaELIURp\nSbtVuFxYG+jeH3aug8wsWPkaPLnA1VEJN3Zbo0YcGD+eNzdvZuaOHeSazfxx/Tq9v/qK57p35+1+\n/ajh4+PqMIUQN6FKTTxqmtYNmIjez6VmBaqSBpw7svZ4BEi7AL51C/Tmi7527aZPPH7w229kWoY4\nPNO1q20OlgpJtCQeDT4Q0KJMh47v2pUvo6I4dO0aey9fZt6+fYyzG5pRaUwNwRgGmVf0uf6UGTTp\ncF3tZMbC9uH6SpsAEY9C9y9K91p6eEOvJaB5wdnFkJcJWwbD3VF6L0khhHAxabcKtzNiJuzuDGYF\nG5bDwzMgoI6roxJuzOjpydv9+zO8TRvGfPcdUZcvo4BPd+9m9bFjfD5oEPc0b+7qMIUQN5lK+eav\naZqnpmkfAjuBEUAg+i/F9hfb7g4uUIZfl4UL+NklHtP1Lvxtate23XWzz/MYl57OrN9/B8DHw4NJ\nvZzQsys3DZKP6+XAtvkTj5eSp8HAp/fcY7v9jw0bSMjIqHhcN6Jp+b0ec5IgWRYWqXaUgt8eh/SL\n+m1Dd2j/WdkSyJoBesyFsAH67aw42P6I3mtaCCFcRNqtwm016AjdLKNlMjNh1WuujUdUGx3Cwtj5\n1FO8d+ed+HrqfY3OJyVx79dfM3LVqqpdaFIIcdOrrC5HnwPPU7SxpuwuhbfZb6eYbcLdmIomHgv0\neLzJE48f79pFWo6eUBnTqZOTejsewvYRKcMwa3u3R0TwSNu2AMRlZPDOtm0Vj6s0QoqZ5zE3V09o\nCfd3ej5c/slyoxacHghfzIVTp8pWj4c39FkBfpaV3WN/g4NTnBqqEEKUkbRbhfv6y0wwWN5eG5ZB\n6s3dvhal52kw8FKvXhx65hn6NW5su3/p4cO0+uwzvoyKwiztcCFEFXB64lHTtPuBJy03FbAXGAa0\nAszkN8waA+2AAcCrQBT5jbpUYJxlnybOjlE4SYGh1ucBCDWZqC0rW5OSlcUnu/TkmqfBwCt9+jin\n4oR9+eWgTuWu5t0BA/Dx0Ofk+2TXLs4nJVU0shuzn+dx6/cwdy688w5UxblFxWRcgb2T8m8nPwXZ\nBkhJgZ07y5489g6E3ktBs8z2cWQGxP0O8fGwdClYFmMSQojKJu1W4fYadYEud+jljAx9rkchyqBp\ncDDr//pXvho8mGDLYpSJmZk8/cMP9J0/n8PXrrk4QiHEn11l9Hh81a68A+illFqllCowtlIpdU4p\nFa2U+lUpNVMp1Q0YBFwC/IFZQG+l1LlKiFE4g19D/VoBew7AL7/Apk22Xo9X09KIu0lXtp6/fz9J\nluTJX9u3p2HNikwVZaecC8sU1rBmTZ7voScCs/LyeGPjxopGdmPBXfOH5V4+ABcvQl6efi3c294X\nICdRL3s8AFe89bLJBA88UHAhmdIK7QHtp+llZYbVj8Pns+DYMVi3zjlxCyHEjUm7Vbi/Ee/q/2sN\nwOllkJ3o6ohENaNpGk906sTRCRN4vEMH2/07Llyg0xdf8I8NG8jIkalvhBCVw6mJR03TQoGedneN\nV0pll/Z4pdRPQB/gPPrCN19pmtbemTEKJ/Ktp19rwO4TsGMHHDhAG7vh1jdjr8c8s5mPLb0dASb1\n7FnC3mVkTTzGAmuOwIYNcPlyuap6rU8fgoxGABYfOMCBK1ecFKQDXjWgZhu97H0mf4GSS5cq97yi\nYmJ3wrlletkzGC52z982cCD4+5e/7lZ/h0BL4zfvKFzbrpf37IGzZ8tfrxBClIK0W0W1EdEd7r8P\n7gJapsGR910dkaimavn5sfDBB9nw+OM0Dw4GINds5p1t22g7ezY/nzzp4giFEH9Gzu7xaG28KeCA\nUiq6rBVYfikea7npBUx1TmjC6Tx8wGhZWc8rWb9OTqZ1aKhtl5txnscfjh/ndEICAHc2aVJgwZ0K\nMedC4kG9nFEPzlyErVvh6tVyVRfk68v/9e0L6B/YV9avd06cJbHO8xhkhgxLwlR6PLovpWDfS/m3\nc0dDiuU7eaNG0L6C368NXtBjjt4T1g+ovRlyLJOd//ij3iNWCCEqj7RbRfXx0CdQw7Ko4LGPIPPm\na2ML5+nXuDEHn3mGybfdhpdBTwmcTkjg7iVLGLlqFVdl8RkhhBM5O/EYblfeU9KOmqZ5O9qmlFoH\nRKP3pbtX07RA54QnnM46z6NnEqg8yMujg2WOR4BD5UyKVWcf2fV2nHjrrSXsWUYpJyAvUy/nNMy/\nv06dclc5oXt3GlmGgf986hTryrpQSFlZ53n0Abz15CyXL0uCyV1dXA3XLb0QfZrDuRC9rGkwaFD5\nhlgXFtINmo7Ty40yAH0leK5f13s+CiFE5ZF2q6g+/COg6VN6OTcVjsx0aTii+jN6ejItMpID48dz\nW6NGtvuXHj5My88+Y44sPiOEcBJnJx6D7MrFZZzsVwzwvUFdmy3XXkDvigQlKpE18egL5KQA0MY7\nv21+8CabrHj/lStssgwRvSUkhLubNXNe5fbzO2ZZepUaDGA3tL2sjJ6evN2vn+32axs2oCqzgRFi\nt8CMyfJLfW4uVPYwb1F2SsEhu9WmtScgy9LbsVMncFZPXtDnevSsoX9lD98KmZZ/H5uAO/9zAAAg\nAElEQVQ2wU06T6wQokpIu1VUL23+Dzz0aXI4/m9Ij3FtPOJPoVWtWmwcNYp5hRafGffDD9w2fz7R\nN9n3OSGE8zk78WjfbSm3mO3JduXwYrbbiy3DvsJVrIlHE5Cjv7yB2dk0CAgA4ODVq5WbyHIz9nM7\n/q1HDwzO6BFmZU085gEZ+vNLrVrg6Vmhah9p144Oll6TUZcv892xYzc4ogICWoKHSS97n82/X4Zb\nu59L3+cP7Q/pDg+8rC8kExICt9/u3HMZa0Pb/9PLQQr89+rljAzYts255xJCiHzSbhXVi6keNH9W\nL+dlQvQ/XRuP+NMwaBpPWhaf+avdVDrbL1ygo2XxmXRZfEYIUU7OTjwm2JVrFLPd/ueSFjeoy34Z\n4JByRyQql599j8ckvZycTHtLIis5K4vzSUmuia2Kxaan8/WhQwAEGo2MslsxzimsicdkwMfS2yws\nrMLVGjSN6ZGRtttvbNxYecMqDJ4Q3Ekv+8ZArqU3WzkXyBGVRCk4/Fb+7bZvgIeH3tPxuefAWau0\n22vxN/C1fFcP2w3Zlh6xycl6PEII4XzSbhXVT+tXwNMyrdGpLyFNFlIXzlPLz49FQ4aw/q9/pVmh\nxWfazJpVuR0UhBB/Ws5OPNovg1WvmO2H7Mr9b1DXbXbllHJHJCpXMT0eSUqyJR5B7/V4M1iwfz/Z\nlrkKx3TqhJ+3w+mgyifJ8vFJD9CHpUKF5ne0d/8tt9AtXE/6HLp2jZV//OGUeosV3FW/rgm0D4G/\n/AXshnsLN3BlPcRb5loM7ADhg/K3ObMXrz0PI7R+TS+bgCbRMHYsPPxw5Z1TCHGzk3arqH6MtfUf\n6wDMOfD7ZNfGI/6U+jdpwqFnnuENu8VnziYm8sCyZdy/dClnEhJuUIMQQuRzduLxsF25dTHbt1qu\nNeAxTdOKzZpomjYE6GR31xHnhCeczj7xaMqCJk0gONg2dBdujsSjUoovo6Jst8d16eLcE2TF5a8C\nndsoPxHjhB6PAJqm8aZdr8cpmzaRZzY7pe4irIlHD6BNHrRqBZah+cJNHPs4v9zmH1WX+Gv2VH6v\nR9Nm8JU5hYQQlUraraJ6avUS5ATAXmDWYji764aHCFFWRk9PpkdGcvCZZ+jXuLHt/h+OH6f1rFm8\nuXkzmbnFzVIhhBD/n73zDo+qSv/450wy6T2hhoQaQg0QekcQAUEQxS52RBEL1t39WXfdta262MCO\niIKCYkVAeq+hhh4ggTQI6T2ZnN8f904BAyQwLeF8nmeeOXfm3HvfhMlw7ve+7/s9G7sKj1LKLLTF\nlgA6VOPqNx8oByRavtMyIYSlAbcQwkcI8RDwtT4HIBdYb884FXbEVni8Lgzuugt69To74/EKaEi8\n8vhxDmdnA3BVixa0DbdzlVVeonUcEwc9e0J0tN2ER4BrWrdmQLTmln0gK8tSNm53zMIjwBnlWux2\nFByBtEXa2C8Kom5w3rltsx4B9v7TeedWKBRXHGrdqqizeIWCvAmOASYJ3zzt6ogU9Zh2EREsmziR\nuTfeSJOAAABKKyt5cdUqOs+YwZIjRy5yBIVCcaVj74xHgD9sjj3C9g0pZQ7wP7QFngQ6AmuEEPlC\niBNoi7UP0WQs85x3pZS2roIKd8K3CQj9Y1R0wvJyTHg43h4eAOy6AhyLP7bJdpxs72xHgFybpIwu\nA2D0aLjvPvDzs9spzs16fHn1aipMpgvscYkEtQVPbdFCthIe3Y5DH2K5fm77iNaX05m0eQB89YrH\nkz9D/iHnnl+hUFxp1Nt1qxDCKISYKIT4XQhxXAhRIoRIE0KsF0I8JYRwSC9KIYRBCNFZCHGfEOIj\nIcRWIUSZEKJKf6xwxHmvOCa8bl0HJqyDQ6tcGo6ifiOE4NZOnTgwdSrT+vTBQ6+GOZKdzchvvmHC\n999z4grp669QKGqPI4THefqzAO6v5v1XgHVYF2gCCEDrreNl8zrAckDZtbkzBk9raWSxVXj0NBjo\n2FAzQDmcnV2vXdBOFRWxcL9WVdXAz4/x7dvb/yR5NsJjcCf7H19nSIsWDNNLKY7m5PDVrl32P4kw\nQJguzhafgJL6X4pfZ6gogKNfaGMPX2j9gPNj8PCx9q5CwoF3nR+DQqG4kqiX61YhRDtgC/AVMAqI\nQou3EdAXeAtIFEKMsvN5x6HZ4O0CPgMeAroDnmi/J+UWZi8CImDUfdbtOU+5LhbFFUOQtzfvjBjB\njsmTGahXSgH8sH8/7T/8kDfXr7f0vFcoFAozdhcepZTbgFD9MaGa90uAkcBM4HxN5CqAd4HRUkoH\nNZpT2A1zuXXZaTCVWl42l1tXScm+06ddEZlT+HLHDir0foj3du2Kl57paVdybcqeQxwnPAJnZT3+\nc/VqyhzRu8W23Dp7+/nnKZzLsdlWk6jgGyHNRY7SbSZZs2KPzYLSLOfHoFAorgjq47pVCBGJJoLG\noQl9VcBq4AvgV6BYf70hsFAIMcSOpw9BywCV5zxAE2kV9mT8v619shMTYPt818ajuGLo3KgRq++5\nh6+uv56G/prLelFFBc8tW0bXmTNZeeyYiyNUKBTuhCMyHpFS5umP/PO8XyylnIJ29/UBtLuunwLv\noN1tbi6lfEpKWX/T5OoTZuERoPikZXglGMxIKfk0IcGyPckRZdZSWkut/ZqB17ktqOxL36goro2J\nAeBEfj6f2fx8duMs4VGVW7sFUsKRj63b2T3hq6/ggw/A2X1avUKs2ZamUjg84+w4FQqFwo7Uw3Xr\nXKAJmtCXDHSVUg6VUk6SUl4PRKMJkwBGYL4Qwp4ubxLIBH4DXgKuBd6z4/EVZnyDYPwT1u1v/gaO\nMgdUKM5BCMFdXbpwcOpUHunZE4Nefr0/K4uhs2dz+w8/kJpf7deqQqG4wnCI8FhTpJQZUsovpJTP\nSSknSymfllJ+KaWsnypVfeUs4dFabh13BQiP60+cICknB4BhLVvSJizM/icpSYOKXG3swDJrW/45\nZIhl/O+1aymxd6l8uK3BzFb7HltxaWRvt2bWBvaCYwXauKgIQkOdH0/s49b+sYc/gMIcWLMGPvtM\nXVQpFAqXUBfWrUKIa4EB+mYZMEZKaevejZQyG7geOIomToYBz9ophD/QhNimUspxUspXpZRL0Pph\nKhzBtf8HDXWzweSjsPpD18ajuOII8fHhg2uvZeukSfSOjLS8PnfvXmI/+ID/rF2r3K8ViisclwqP\ninqCv7W/h63BTGe9xyPUX+Fxtk0PxHu6dnXMSWyNZRxcZm2me9OmjG/XDoD0wkJmbLNzVmJAazDq\nmZvpWyEhAX77DRzRU1JRM8y9HQHKhoFZbO7SBYxG58cT0AKi9KrH0lPw5YuwYgWkpsIhZTijUCgU\n52GK/iyBWVLKfdVNklIWAy/qmwKYLIS47OsCKeUpKeXJi89U2A1PL7j1BW3cCDg5HaqUyKNwPvFN\nmrDh/vv59LrrCPf1BbTy6/9bsYKOH33EzwcOIFXlikJxRaKER8Xlc27GY1UVlJbSwN+fJgFan7bd\nmZn17j+akooKvk9MBMDfaLQIdXbnLGOZzo45RzW8MmSIpRnTa+vWUVhebr+DC2HNeszLhB/mwLZt\ncPCg/c6hqDmVJXB8rjY2+EKajdFpjx7V7+MM2j5qHQdusI63bHF+LAqFQuHmCCH8gWE2L826yC4/\nAIX6OAwY5ICwFM5g4ENwYw8t19UjCY5+6eqIFFcoBiF4ID6eQ48+ylSb8uujOTlc/913jJgzh/31\nuPe/QqGoHiU8Ki4fs/BYAXz+O7z6KixYAFjLrc+UlJBWUOCiAB3DLwcPkldWBsCEDh3w9/JyzInM\nwmMZcDoAcnKc0ueuc6NG3NJJy7DMKi7m/c2b7XsCc5/HAKBS7yGYmmrfcyhqxsmfrOX8fqMhW/9b\njY6GBg1cF1eD/hDcURsbE8BXN686ehSylOGMQqFQnEM/wFsfFwEX7GUipSwDNtq8NNRBcSkcjcEA\nw6dbt/e8BJXFrotHccUT5uvL+9dey87Jk7mqRQvL638ePUrczJlMW7yY3NLS8x9AoVDUK5wmPAoh\nAoUQQ4UQU4UQLwgh3tCfp+qvBzorFoWdMQuPnkDBGS3jMS8PONtgZlc9K7eevXu3ZXx3ly6OO5G5\n794Z4PftMH06rFrluPPZ8PLgwZY7lW9t2ECePRcIZuHRAPhpnxfy8rSeggrnYltmXdjTOnZU+4Ca\nIgTEPKyPgQibEmt7l/8rFAqFDXV03dpef5bAnho6bNs6yLU/7yyF+9OgHzS7XhuXpMPB6Reer1A4\ngc6NGrH8rrtYcNNNRAcHA1BZVcX/Nm+m7fvv81lCAibVu1uhqPc4XHgUQlwvhFgC5AB/AtOBl4Gn\n9efp+us5QoglQohxjo5JYWd8GoDBSxMGjHqmVF4eSEmXxo0t03ZmZLgmPgeQUVjIkiNHAIgKCmKw\nzZ08u1Jlgjy9PVNFMzDovfaclIUWGxHBxLg4AHJKS3l30yb7HdzWYMbX5rORlma/cyguTnEqZOjm\npr4t4YSeTevpCR06uC4uMy0ngqe/Nvb+E4S+ON25E+xZ/q9QKBTU+XVrrM04uYb7pNiMHdQzRuE0\nuvzHasy273UoO+PaeBQKNPfrGzt04MAjj/DKkCH4enoCcLq4mEm//kqvzz5jfUrKRY6iUCjqMg4T\nHoUQLYUQy9H6x1ytn0ucb7r+/tXAj0KI5UKIlo6KTWFnhAH8mmljD71cs7wcSkuJb9LEMi0hPd0F\nwTmGuXv2YNLLnSfGxVmyAu1O0TEwlWjjiqbW122MexzNi4MH42nQvire2biRM8V2Kt3xiwbvCG1s\nPGItH1fCo3NJ+R4tOQaIug3i4yEwENq1Ax8fl4YGgDEImt+ujQ2F0FDvC1RaCnv2uC4uhUJRr6gn\n61abBr3UtMzEfOfP7G6tqMsEt4dW92njinxI/I9r41EobPA1Gnlx8GAOTJ3KzR07Wl5PSE9nwJdf\ncuePP3IyP9+FESoUCkfhEOFRCNEZ2AQM4a+LNlHN49z3rwI2CiGcY+GruHzM5dZeJWDS+h6Sl0dM\nWBj+uiPu9nokPH5l4758l0PLrG2MZcr06wkPDwgPr36+A2gVGsp9esltQXk5/92w4SJ71BAhrOXW\n/rlQoZdbqz6PzsVsKgMQMxGGD4dp0+Daa10X07mYy60BAtZYRep91Zq1KhQKRa2oR+vWAJtxSQ33\nsZ0XcN5ZirpD55fBQ79xeOgDKDzuymgUir8QHRzMdxMmsPLuuy1+AADf7NlD2/ff56WVK+1raqlQ\nKFyO3YVHIUQ4WgmKbS2oANYDzwEjgK5AjP48AngWWKfPlfqjIfCnEELdfa0LmIVHP7Q7rAB5eXgY\nDHTTsx6P5+baL1vOhezKyLD0q+wdGUlsRITjTmY2lqkCSvV2UuHhmvjoRJ4fNAgv/ZzvbdlCZmHh\nRfaoIRbhEajSzULS0pxinqMACpIgW/ceCO0KwXqVncEAfn6ui+tcwrpBeC9t7LEP4hrC7bfDHXe4\nNi6FQlHnqWfrVts09ZpetZfZjH3tGIvCVfhFQuwT2ri0HH54+MLzFQoXMaRFC7Y/+CAfXXstYb7a\n109JZSX/XLOGtu+/z5c7dqj+jwpFPcERGY9voi2+JNrCbSfQU0o5UEr5lpTyTynlbillkv78p5Ty\nv1LKQUAvfb75bnJD/XgKd+cs4dHGKASIt+nzuKMe9Hn82sZUxqHZjmDNeCwEjLrA6cQyazNRwcFM\n7t4dgOKKCt5Yv94+Bzb3eRRAeCG0aaOV+qpFhnNInmcdN7/VdXHUhNaTrOPo/dC2rSaQKuoPlSWQ\n/ifseh7W3QrLBsPyYbDmBtj1Apz8FUoL4NQpqKhwdbSK+kN9WrfaOsB51XAfb5txTbMkFe5Oh79B\neggsAX5ZDDt/cnVECkW1eBoMPNyzJ4cffZRpffpY2julFxZy3y+/0OPTT1lx7JiLo1QoFJeLpz0P\npjv83Y6lYRjrgFFSyhrZ1EoptwshBgKLgQFoC7nbhRBPSCntlGKlcAj+NsJjhp7xqPfo6N7U2ptw\ne1oaV7dq5eTg7EdlVRXf6H3ljAYDt9j0J3EI+XopaYEHeOtJFC4QHgH+PmAAnyUkUFJZyUdbt/JU\n375EBgVd3kHDulvH3Utg6J2XdzxF7ahLwmP0TbD9Ma3nafK3EP82eHhffD+F+1N4XHNfPToLKnKr\nn3Nyofac7w/bYqDRQIjtofUijYtzj36kijqHu69bhRC9gIkXmTZbSqmnrmN7zppmL9rOU2vt+oJX\nMLR4EDboOvisp+CdseqGncJtCfP15Z0RI3i4Rw+eW7aMhQcOAJo56bDZsxkbG8ubV1/t2EozhULh\nMOwqPKL1uDFfCZYDE2u6eDMjpSwWQkwEDgFG/XjDgJ/tGajCzpgzHoOAfo2gx50W5+XuNgYzdb3P\n459JSWToZcbXxcYS7shy1CoT5B/Sxh5RYPSGykqXCY9NAgN5pGdP/rtxI2UmE/9Zu5YPR4++vIP6\nRoJ3Ayg7DTkJWom1o4x6FGeTu9dayh/RD/ybuzaei+EVDFE3wPFvoDwHUn/RxEhF3aWiEPb+Cw7+\nD6rKrdLPhb4C8osgZ6f2yIiDQ9fAsmXQsycMHKgESEVtcfd1a3vgkYvM2ao/AGwtjBtVM7c6zGUp\nEsiueWiuY9q0aQQHB5/12m233cZtt93moojclHH/gmWz4VQGnDgKy96Ba552dVQKxQWJCQ/nx1tu\nYdXx4zy5ZImlWu6XgwdZdPgwU3r04MXBgx17DaZQ1HHmzp3L3Llzz3otT69GdRX2Fh6j9WcJLJdS\nJl/KQaSUyUKIZcCoc46rcFfMwqMP0MKklczqxEZE4OvpSUllZZ13tp5tW2YdF+fYkxUdgyq99VLP\n7tD/H5CdrTkOu4hn+/dn5vbtFJaX82lCAs/070+LkJBLP6AQEBYP6UugLAuKT1qzZxWO5cQP1nHz\nW1wXR21oda8mPIKWHaeEx7pL1hbYcDsUJmnbBcBOT+gxHIZNhPCe4NsUZBWUZkLODkhbBHkLILoA\nsoDc3ZB/ECJHw/pySEiAkSO1DEh1A0NRM+rCuvVCTY/Pfe+gzbimd5NsYz1Qw31cyrvvvkt8fLyr\nw3B/PL3gjlfh3Qe07e/+A4Mmg4/r1pEKRU0Z0qIF2x58kK937eIfK1aQVlBAZVUV723Zwuzdu3lx\n0CAe6dXL0oNeoVBYqe5mXEJCAt27dz/PHo7H3vn2tuUae887q2bY7q9SGNwdPxuxqPjEWW95Ggx0\n1fs8JuXkkFtaSl0kr7SUn/S0/3BfX0bFxDj4hDaOvUHttfKYiAjwdl15aQN/fx7v3RuAiqoq/rV6\n9eUfNNTm4iEn4fKPp6gZJxZax1E3uC6O2tDoKvDTr5HTF0NxmmvjUVwaRz6DP/tbRcdUI+wdDOFP\nwulBEHEdBLYBTz8wBkBga4ieAH2+gAdSYdIbMDYErgaal0Hqj1r/x6ICWL9e9YhV1Aa3XrdKKb+S\nUnpc4OEppZxts8t+/VkAnYUQNVnn2yp4+887S1E36X8ftO2sjXNzYP4zro1HoagFBiG4u2tXDk2d\nysuDB+NnNAKQW1rKk0uX0vGjj1iwbx9SmVIqFG6PvTMeU23GlZd5LJPNWF1dujteoeDhB6bivwiP\nAPFNmrDx5EkAEtLTGdqypbMjvGwW7NtHaaX2sb69c2fH32HLt1n/B7d37LlqwVN9+/LBli3klZXx\n1a5d/G3AAGLCwy/9gGE21zzZCdBs3OUHWQeQUnIgK4vNqakczMricHY2p4uLyS8ro9xkwtfTkwAv\nLyKDgmgZEkL7iAh6RUbSJiwMcbnZXIXHIHeXNg7oDn9shvb5EBMD+qLOLREGaHW3Vp4rq+D4HOjw\nrKujUtQUKWH3C5D4b30bSG0POVdDuN7D1tcXCgogIKD6YxgDtX/zVvfA9mkQ/C3EAnsTICUbHlgM\nKvtBUXPq27p1A5pLtTfgD/QAtpxvshDCC+hj89IKh0ancD5CwH3vw9+v0r6DF30JI5+FBnW337ri\nysPfy4uXhgzhgfh4nl+5kq927kQCR7KzuWn+fHpHRvLm8OEMau7mbYMUiisYewuPtndKYy/zWG1t\nxvvOO0vhHgihlcjmH4SiE3/p1Wfb57GuCo9f7dplGTvczRogz+bPKch9hMdQX1+e7tePF1auxCQl\nz69cyXcTJlzGAbtZxzk7Lj9AN6akooLFR46wYP9+liYlkVVcXOtjRPj5MapNG8bFxnJN69YEXkoG\nrG22Y0U/2LNHe/Tpo5WqujMtdeERtHLr9s9oGW7HjkHr1qrE1l2REnY8DQfe0beBrLFQFAfeulAY\nFwdjxoBXDcx4fRpC/2+gyXDYOgV6l0DBcdh7E0T8AX6RjvpJFPWLerVulVIWCSGWA9fqL93DBYRH\n4EbAXHebDaxxXHQKlxEzGPqNgPWLobwcFk6DB1XrfEXdIzIoiC/HjePRXr14aulSVh0/DsDm1FQG\nz5rFmLZteX3YMDq6qB++QqE4P3YttZZS7kBbbAlghBAi7FKOo+83Eu3S5KB+XIW7Yy6BNBVr5g82\n2Dpbb0urewmsR3NyWJuSAkD7iIizhFSHkW9TMRV0uddD9uXx3r1poDd1/j4xkU16NuslEdAKjHqT\n+Oz6WWp9MCuLx//4g8Zvv80N33/Pt3v2nFd0NBoMBHh5YTiPgJZVXMzXu3czYf58Gv73v0xcuJC1\nycm1KzM5+ZN1nGtzd7hDh5ofw1UEtoYGA7Vx/n5Y8Q28/TbMmQP636jCDdn1f2eLjsUPQU43ELro\nOGIEjB9fM9HRllb3wLBV4B2hySe5e2DZECjJsFvoivpLPV23fqQ/C+AeIUS1dy6FEL7AK/qmBD6W\nUqo+BfWViR9CqDf0BgJ+1QzmFIo6SnyTJqy46y5+u+02OupmpgC/HTpE3MyZ3P/zz5zMz3dhhAqF\n4lzsnfEI8E9gHuAHfCyEuFnWvvHCx/r+Uj+eoi5wbp9Hb+v6vb2NwcyW1NRqdnZv5tiaynTpcvml\nrhdDSmvGo38LrdeZGxHo7c0rQ4YwZdEiAJ5eupS19957ab8XIbSsx1OroCQVCtOg0ABFRVoGWx1m\n76lTvLRqFT/u/2vbrGBvbwY2b87A6GjiGjWibXg4TQMD8fHUvpallJRUVpKcm8vRnBx2ZGSw6eRJ\nVicnU1heDkBpZSVzdu9mzu7dtI+I4Nn+/bmjc2eMFyo1LT0Fp9dpY9+2kKQLoIGBEFVHjH1a3gmn\n12rjrD+hWM+g3r0bVJmN+3HkU9j3mnW70auwrkIbGwxw/fVatuOlEtELhq+HlSM1U67CI7DyGl2Q\nvCQdSXFlUa/WrVLKRUKItcBAtJLr34QQ10sp95jnCCHCgbmA2QnwDPDm+Y4phGgOHLN56Z5zeksq\n3J0GrWDay7Dr74CEhKfgqsWqSkBRZxFCMLptW0a2acPsXbt4cdUqTubnUyUlX+zcybd79/JE7948\nN2AAIT7KLkKhcDX2NpdBSvk98B7andYbgJ+EEI1rsq8QopEQYiFa6QfAB1LKefaOUeEgLmAwY/Tw\noIee9XgsN5fMwkJnRnZZSCmZrZdZC+BOR7tZgybAVRZoYzfq72jLA/HxxOq9HdefOGEx3rkkzH0e\nJfDGizBzJvxcd8uAknNzuePHH4mbMeMs0dHX05O7u3Rh0e23c+qZZ/j1ttt4tn9/RrZpQ6vQUIvo\nCNqCys9opH2DBoxu25bnBw3it9tvJ+uZZ1h8xx081L07oTYLqf1ZWdz788+0ef99Ptq6lXKTiWo5\n+QsWI9SqQWCe17593bkAiboRDHovSvEnGPXfW2IiVF5umzaFXclYrpVCm+nxAQz7BwwapG2PG3d5\noqOZoLZw9Spr5n3uHlg1CiptMouV6YyiGurpuvV2IF0ftwR2CiFWCCE+FUL8BCSj2TMBVAA3Sylr\nkh4kubDLNgBCiEVCiB22D+Ahmyk9z31ff9To9664RNo9Af76zbmMpZD2u2vjUSjsgIfBwL3dunFo\n6lReHzaMYL0FUWllJa+vX0/r997jnY0bKVPrQ4XCpdhdeASQUj4BTAXKgTHAISHEl0KIG4QQrYUQ\nAUIjQAjRSn/9C+AwMBYoBR6RUj7uiPgUDsJfFx4rgV2bYcMG2Gdtc9SnWTPLeHMdynrccOIESTla\n6fiwVq1oFhTk+JO6aX9HW4weHrxx9dWW7eeWLaPifGLXxTA7WwvAJ1cb5+drWY91iHKTidfXraP9\nhx/y7Z49lquzxgEB/Hf4cFKffJJZ11/PqJiYSzYn8vb0ZESbNswYM4bUJ59kzvjx9LfJVEzJy+OR\nRYvo+NFH/FCd099Jm/6OhTbO7O3aXVI8LsE7HJrovSgr06GJ/rkrLYXDh10Xl+JsCpJg7QSQ+mI/\ndhq0fUQTuIcOhcmTwZ79cv2jYdhy8NG1izNbYOPdmhHRiRMwYwZkZ9vvfIp6Q31bt0opU4GrgJ1Y\nhcIhwP1o8frqr58CxkkpV9Xw0DW9O9Ue6HLOo5HNMfyreT8OqGWvBUWt8PCBbm9Zt7c/AaZS18Wj\nUNgRX6OR5wYMIOmxx3iyTx/LOju7pISnli4l9oMPmLN7N1XKAVuhcAm1Eh6FEKaaPoD30RYQAggA\n7gLmA4eAPDR5Kg9t0TYfuFufJ9BKQz7Qj6VuT9QVzBmP5cAvq2DpUq30UcdWeLysnoBOZratqYwz\nsh0B8nTBtgpYmApffQVr3K/n+9jYWIuD3OHsbD7evv3SDhRmYzDjk2kdp6f/da6bsiU1lW4ff8zf\nly+nRL+rGuHnx3+HDyfpscd4ql8/Qn197XpOX6ORO+LiWHfffay7915Gx1iFxCPZ2UyYP58BX37J\nVrPQX5EPGcu0sXdTSNczwLy9616Jcos7rOOgROt4z56/zlU4H1M5rL8VKvQbCZHXnX3BC+CIXrmB\nbWDoUvDU/TJOLIDF02D2bDh9Gr79VhOoFVcEV/K6VUp5CK2j393AYiAFzfE6EyW5cxoAACAASURB\nVNgEPAN0kFIurukhqUG2YzXza/NQOJqoCdBwiDYuTLL23lUo6gnhfn68PWIEB6dO5c64OMvdkuS8\nPCYuXEj3Tz5h0eHDteuNrlAoLpvaZjwKm+eaPODsxcSlzlXUBczCow9QqVfs5OVZ3q6LwmNpZSXf\nJWqihr/RyA3tnZR9aDaWKQZK/TTHXjcU4YQQ/Hf4cMv2y6tWkV1SUvsDBcaChy7KGW3aSLnhz3wu\nlVVV/Gv1avp9/jn7Tp8GwCAEj/XqxZFHH+Wpfv3wMxodHkf/6Gh+u/12tk6axJAWLSyvbzhxgt6f\nfcbURYsoSvkNqrT+kHgOswowMTFwiRmYLiPyOvD018amJeCnl50fPKiEJXdg1z8ge5s2DoyBft+A\nwUmfsZDO0H8uluVD5ntQpX+vZGXBwoVaH13FlcAVvW6VUlZKKedIKUdLKVtIKX2llE2klP2llO9I\nKWuUAiylTJZSetg8LtjfUUrZ8pz5NXl4SimVQ5ijEQJ6vGc19tr7byiuG2tyhaI2tAgJ4evx40mY\nPJkRNj3jd2ZkMPrbbxk0axZrkpNdGKFCcWVxKaXWtVlQVbdIs8dchTtiFh4NgJdeImsjPDYNDCRK\nL1PekpqKqQ702/r14EHyysoAmNChA/61dVy9VMzCYwHgo7u1RUQ459y1pGdkJLd16gTAmZISXlix\novYHMXhAaFdt7JUKJl28dHPh8WhODoNnzeLFVasw6UJGj6ZN2TppEtNHjSLYBc2sezRtyoq77uLX\n226jvf6ZkcCHW7fy68p3rRPbXQ9XX60ZysS6l2t6jfD0g2bjtbEpH5rovfxMprNaPChcQNofcOBt\nbWzwgv7zwBjo3BgiR0O3/2pjL6DZ92DQv1cOHoSVK50bj8KVqHWrQmFLSGeI0Xvvmoph61OujUeh\ncCBdGzdm8Z13smziROJtKi3WpaQweNYsRs6Zw/a0NBdGqFBcGdTW1foVh0ShqB8YA8AYopXWeeqC\nY3ExVFSAnvHVp1kzTuzbR1FFBYmnTxPXqNEFDuh6vrIts7ZnL7KLYe7xWBam9eQBaNDAeeevJW8O\nH84vBw9SVFHBzO3beSA+nm61LaMMjYesjVrhWmUWeES5tfC4/OhRJsyfT66eXWcQghcGDeL/Bg68\nsKu0ExBCMEZ3+pu+aRMvrlpFSUUZQ7y0z1Wp9Car4QCaxTaEAQNcGutl0eIOOD5HGwckAD0gPBw8\na/tfm8JulOfB5knW7W5vWc2jnE27aZC9FZLngXcBRP0Bx68HYdBaV0RHQ5s2Fz+Ooi6j1q0KRXXE\nvQLHv4UjZ2DR9xBwI3S/2dVRKRQOY1irVmydNIkf9+/nhZUrOZCVBcCSpCSWJCVxY/v2/POqq+jg\nxtdbCkVdplZXZ1JKtYBTXBj/KMjNBY9crZRNCC3rUc+86tOsGfP1bKRNJ0+6tfCYWVjI4iNHAIgK\nCjqrfNWhlGZBmVayS2Wk9XU3zXgEaBYUxAuDBvG35cupkpKpf/zB2nvvxVAbl2SzOGEA/Au0blo5\nOVBSAnbujXi5zNy2jamLFlmyHFuFhjJn/Hj62pi8uAOeBgNP9evHTR07Mn3RBzSWWibykqIW3P3x\nF7w7YgT3dO2KqCtu1ufSeBh4N9D+Xkr/hPvfhWZt6o47d31kxzNQovcUbTAcTnWD1pWuEYOFgF4f\nw5ltUHgEvPdA8/aQorfMWLgQHn4YAgKcH5vCKah1q0JxHrxCIeAx2PqStv3Fk9DlevBU/j6K+otB\nCCZ06MD17doxZ/duXl61imS9Ou+H/ftZeOAAE+PieGnwYFqGhro4WoWifuEQV2vFFYy53Nq3Eir1\ncuv8fMvbZzlbu3mfx7l791qEpYlxcbUT0S6HfBtH6zIbsdGNhUeAaX37EhseDmh9BefYGAvViFAb\ngxlfXXj199eEbDehsqqKx/74g4d//93y2RjTti07Jk92O9HRlujgYN7uZPU7+L0ohryyMu775RfG\nzJ1Lqs3faJ3CYIRoPUNDlkPFeiU6upKM5ZD0qTb2DICye2D5cvj0U83YxRUYg2DA91rJN4D39xCh\nl+UXFcHmza6JS6FQKFzN1X+HpvraJSMVfvo/18ajUDgJT4OBe7p25eDUqXwwahSN/LWe4VVS8tWu\nXcR+8AFTFy0ivaDAxZEqFPUHJTwq7ItFeERz0IWz+jx2a9wYo0H72G0yO+26KbZl1hOdWWZtFh4l\nUKb3RQsOBmf1l7xEvDw8eG/UKMv200uXklVcXPMDBHfUhCSAZmnw5JPw9NOOcb69BPJKSxnz7be8\nv2WL5bVn+vXjp1tuIcjb24WR1ZC0RZahf/NxlvGiw4fpNGMGs3ftqpsOfy1ut46Tv3ddHFc6plLY\nMtm6HfU8JGgZ42RluVYQDusG8bpzqwDCZ4O/EYYNg6uucl1cCoVC4Uo8jXD/dOv2Tx9CtvL3UVw5\neHt68kivXiQ99hivDxtGqN6bvaKqig+3bqX1e+/xt2XLLs04U6FQnIUSHhX2xSw8+gGiGBo2PMst\n19dopGvjxgDsO33abb/Id2VksDMjA4BekZG0c2a2YZ5ujFEGEKKN60i/kWtat2ZChw4AnC4u5vHF\ni2u+s4cXBHfWxqbD4OfhNtlrSdnZ9P38c5YkJQFgNBj4fOxY3hw+HA9DHfgaLT0FZ7Zq45A43r3h\nAX659VYa6yWmuaWl3P3TT4ybN6/u3d2N6GP93sn4E8pqZNKqsDcH3oFC7e+DiAGwNxTMBmIDB7o+\nYztmCjTRb4zITOidqMVVF/5+FQqFwlF0HQ89BmvjkhKYNfnC8xWKeoi/lxfPDRjA0ccf5/mBA/HX\nvQlKKit5Y/16Wk6fzj9XryZP7+uuUChqj1pxK+yLWQBoDNzbE6ZMgbi4s6YMiI62jNcmJzsxuJpj\nm+14jzOzHcFqLGMAbrwT+vUDXcyrC7w/apTljuG3e/bw68GDNd/ZYkIhIWfXBac6i9XHj9Prs8/Y\nrzehDvf1Zdldd3Fft24X2dONSPsDLYUWaDoagOtiY0mcMoU7One2TPv10CE6fvQR3+7ZU3eyH4UB\nom/SxrISTv7k2niuRIpPwt5/a2PhAcZHIFV3iIyIcA8DIyGg96eaARrAyblwYqFrY1IoFAp34P5P\nrVU16xfDnt9cG49C4SJCfHz419ChHH38cZ7o3RsvPXkmv6yMl1atouX06by6Zg35ZWUujlShqHso\n4VFhX/x14VEAxSeqnTK4eXPLeLUbCo8VJpOlP6GXhwe3durk3ADMpdb+IdDnarjmGoh3kSvsJdA4\nIID/jRxp2X7o998tzs8Xxdb9NjvBzpHVns8TEhj+9deWzNz2ERFsfuABBtl8husENmXWNL3WMgzz\n9WXODTfw480301Dvb5NTWsodP/7IhPnzOVVU5OxIL41oGyfOFFVu7XR2PAsmva1C9IOw1aZUb8wY\n93EZ94uEHu9Zt7dM1sy8FAqF4kqmYQxc96B1+5MpUFnuungUChfT0N+fd0eO5PCjj/JAt2546BVY\nOaWlvLByJS2nT+c/a9dSoARIhaLGKOFRYV/8bAw2ziM8DmzeHHMBrTsKj4uPHOG03pvw+nbtCHWm\no3JFgfX3FtzebUqNa8vEuDhGtWkDQFpBAdOWLKnZjqE2wmPODgdEVjNMVVU8vXQpD/z6KxV6ueiI\n1q3ZeP/9tA4Lc1lcl0RVBaTrv39jCKxK1Qw1zpyxTBnfvj2JU6ZwS8eOltd+3L+fjh99xPzERGdH\nXHvCe4GfnkmdsQzKzlx4vsJ+nFoLyXO1sXc45AwFc2/Xzp2hRQuXhVYtLe6EZnqP07LTsONp18aj\nUCgU7sBNb0HjpuANND0BR2a4OiKFwuVEBwfz6dixHJw6lXu6drUYjWaXlPB/K1bQcvp03li3jsJy\nJdQrFBdDCY8K++Jnda0+n/AY5utL50aNANiZkeF2/TJm2ZRZ3+3sMuuCQ9ZxUHvnntuOCCH4eMwY\nAvXSnVk7dzJv796L7xjSWSudBchxTcZjflkZ4+bN4+2NGy2vPd67N7/dfjvBegl5nSJrM1ToBk9e\ng2HffvjjD1i69KxpEX5+zJswge8nTCDCz0/btbiYmxcs4NYFC2pnFORshIDmZndrk1ZCW1oKO3dC\nbd3VFTVHVsH2J6zbnV6F5ExtbDTC1Ve7Jq4LIQT0nAnGYG372FeQudK1MSkUCoWrMfrAo5/ANUBz\nYPcLUJzm6qgUCregdVgYX44bx4FHHmFiXJxFgDxTUsLfli+n5fTpvLV+PUVKgFQozosSHhX2xcMH\nfBpq4/MIj2Att66SknUp7uOgl1VcbOlJ2DgggGtat3ZuAPk2/RCDYp17bjsTFRzM+zYu15N/+41j\nOTkX3snTzyq45u4Fk3NLGI7n5tL/iy/4/fBhLRyDgZmjR/O/kSPxrKsmFBk2AmOpTa9QPSP1XG7q\n2JHEKVO4ob1V+P4uMZGOH33Ewv37HRXl5WNbbn1kLrz9Nvz0E6xeDXWlX2VdI2W+9QZBSBeImQST\nJ2vtIYYMgeBgl4Z3XnwbQ9c3rNtbHtJcuQFMJtfEpFAoFK6m3Whof782riyAhCddG49C4WbEhIcz\ne/x49uk90s11aVnFxTy7bBmt3nuPdzZupLiiwqVxKhTuSB29kla4NeZy65I0qKqsdoptn8dVx487\nIaiaMXfPHktp7cS4OOeLTfk2GY+BbZ17bgdwV5cuFvOS/LIybv3hB8oqq/9MWDCXW8tKyNOzJM3u\nuA5kfUoKvT79lL2nTgFag+kld97J5B49HH5uh5JuIzzm2Lijn0d4BK23zYKbbmLujTcSprcaOFVU\nxA3ff89tP/zgns7XYT3Av4U2zlkNDYO08ZkzkJnpsrDqLVUVsOt563bXN8DgofVz7NcP+vd3XWw1\noc0kiOirjQsOQeLrcOKEJlYrFArFlUrXN7S2GQAp30H6n66NR6FwQ2IjIphzww3se+QRbuvUySJA\nnioq4qmlS2k1fTr/27SJEiVAKhQWlPCosD9m4VFWQUl6tVMGuanBzFeuLLOGc0qt63bGI2gl1x+N\nHk2r0FAAtqSmMnXRogs7JtsazCz5Dj75BF57DRz4n/fXu3YxdPZsS2/PmLAwNj/wAENbtnTYOZ1C\neQ5kb9XGvu3hlC4YhoeD/m9yPoQQ3NqpE4lTpjA21vpZnLd3L+0+/JD3Nm+m0gmCcI0Rwpr1KE0Q\nbvPdU5MyfydQYTKRXVJCWkHBWY9TRUUUV1TUHSdxgKQvoPCINm44BJpc49Jwao0wQK+PQejGN/te\ngyObYOhQ18alUCgUrsQ7HLq+Zd3eOsWaEa5QKM6iXUQE3954I3sefpibO3a0CJCZRUVMW7LEkgGp\nSrAVCnATq0lFvcJs8gBQnKI5XUt5llFKA39/OjZoQOLp0ySkp1NQVkagt7cLgrWyJzOT7emaWNGj\naVM6Nmzo/CDMpdbCAAGtnH9+BxDk7c13EyYw4IsvKDOZ+GzHDro0bszUXr2q38FWeEzdA4Vav0Ey\nM6FZs+r3uUQqq6r427JlZ/VzHNayJfNvusm5pkKOImOFdgMAwNTTmjl6gWzHc2kcEMBPt9zCnN27\neWLJErJLSsgvK+PxxYv5cudOZoweTR87/7tcMs1vhv1vamOvjSCGaN89iYkwbJjDzJqklJwqKuJA\nVhYHz5zheG4uqbqomJqfT1ZxMQXl5ZReJNvXQwgCvb0J8fGhSUAAkUFBRAYGEhkYSPOQENpFRBAT\nFoav0eiQn6PGVBbD3les211fr5tGWCGdof3TsO91qCqHqhkQ8tbF91MoFIr6TKu74egXcHqddoNp\n3xvQ+SVXR6VQuC0dGzbkuwkTeGHQIF5ZvZoF+/YBkFFYyFNLl/LaunU82acPj/TqRZCLr3cVCleh\nhEeF/fHXMx7zgM9mgXEjdOkCw4efNW1w8+Yknj6NSe/zOComxumh2mKb7XiPK7IdpbRmPOZHwv7D\n0KABRESAh4fz47EjPZo25fOxY7lz4UIAnli8mDZhYYysTgAL7Wode50AemvjtDS7Co85JSXc+sMP\nLE1Ksrz2UPfuvDdqFMY6/vu2YNvfsdAme7MWwiNo2Y8Tu3RhVEwMf1+2jM92aI7jOzMy6Pv559zR\nuTP/uuoqWl4ki9LhhMZrgn3hUShYA1ETIOU05ORon5/IyMs+RYXJxL7Tp9malsa2tDR2ZWZyICuL\nXDuYZJmkJLe0lNzSUo7n5lY7RwDNQ0KIDQ+nS6NGxDdpQnyTJrQOC7M0O3c4h963ZrM3Gw8RvZ1z\nXkfQ6QVI/g6KjmkmM6WqrFChUFzhCAP0nAF/dNPa3iS+Bi3ugMDarR0UiiuNTg0bMv+mm9idmckr\nq1fzo94bPau4mH+sWMFbGzbweO/ePNa7d/1IcFAoaoESHhX2x5zx6AGcPA4NIiEv7y/TrmrZko+2\nbQPgz6NHXSo8lptMfK273xoNBm7t1Mn5QZRmQGWhNj4RBgsWaOMnnoCQEOfHY2fuiItjd2Ymb27Y\ngElKbvjuO5ZOnMiA6OizJxqDIKCNdpfd84iWsScMkF592f6lsO/0acbNm8eR7GxAM5F5f9QoHqrr\n/RxtkdLa31EYIcsXKNF68LVocUmHjPDz49OxY7mvWzemLFrEzowMAL7Zs4fvExN5uEcPnh80iAb+\n/vb5GWqLudx63+va5yYsFVI0Z3X27r0k4TG7pIQ1ycmsPn6cTamp7MzIuGjmoi2+np409Pcn2MeH\nQC8vgry98fH0RNiIhBUmEwXl5eSXlVFQVsaZkhKyS0qqPZ5EM0E6npvLEhvRPNDLi66NG9OzaVP6\nR0fTPyqKRgEBtf55L0pFIezXswKFAbq8av9zOBNPP+j+P1gzTtve/45r41EoFAp3IKQTtJsG+96C\nE2Xw7o3w/A6oq0Z7CoUTiWvUiB9uvpnEU6f499q1fJeYSJWU5JSW8vLq1by9cSNTe/ViWp8+rlsz\nKxRORgmPCvtj7vHoC1TogmM1wuOwli0xCEGVlCw+coR3RoxwXozn8POBA5wqKgJgXLt2hPv5OT8I\nW0frshDtr9NodF9n2EvgP8OGkZSTww/791NSWcnob79l5d13E9+kydkTw+I14TGgDE6cAe8GdhMe\nv9q5k0cWLaJI7xnZwM+PBTfffFbf0XpBYRIUHdfGEQOg3TVwRO/Jd5mlun2jotg6aRIztm7lldWr\nOVNSQkVVFe9t2cIXO3cytWdPHuvdmyaBgZf3M1wKzW/RhEcAr/VgGKaVmCcmam7LF8kKzCoutgiN\nq5KT2ZOZycU6L0YHB9MuIoJ24eG0i4igdViYViIdFESwt/dZImNNKa2stPSAPJmfT1J2NgfPnOHg\nmTMcyMoiv+xsx/eC8nLWpqSwNiWFdzZtAqB1aKhFhOwXFUWHBg0uPyvy8AwoO6P/4LdZXejrMpHX\nQdNrIW0RlJ12dTQKhULhHnR+CRbMggOngd2w6FUY86Kro1Io6gwdGzbk2xtv5OUhQ3ht3Tq+3rUL\nk5QUlJfz2rp1TN+8mYd79OCpvn1ds2ZWKJyIEh4V9sdcau0BeGhiXnXCY6ivL70jI9l48iT7s7JI\nycsj2kUi28fbt1vGk7t3d0kMljJrE1DmD/5oZdZ1sXfaefAwGPjmhhsomDePpUlJ5JeVcdVXX/Hz\nrbcyxDYLLyweUr7XvqF8C6GqAZw6BZWVWsbeJVBQVsaURYuYo2e2AnRt3JifbrmF5vUgo/Qv2LpZ\nN70GOnaDbt3sdnhPg4FHe/fmri5deGvDBt7ZuJGSykoKy8t5ff163tm0ibvi4niqXz/aRUTY7bwX\nJaQLBMZAwWHIWwfRt4D0hU6dNAHynDL600VFrElOZpUuNJpdzc9Hm7AwejRtSo8mTegZGUm3xo0d\n0p/Wx9OTVqGhFmMmW6SUpBcWsiM9nYT0dBIyMkhITyflnO/ZpJwcknJymK23kQj18aF/dDQDoqIY\n2Lw53Zs0wbs2f0+VxXDgv/qGgKob4YsvNEOWumzEJATE/w8ylgGqAbxCoVAA4OkPI1+FA5O17Xmv\nQ9+JEF6Hv+8VChfQNjycL8eN48VBg3hj/Xq+2LGDiqoqiisqeHvjRj7YsoVJ8fE8278/UfUo4USh\nsEUJjwr749MEhIfmLGvUXXQLCsBk+stF/8g2bdh48iQAS44cYZILRL8j2dksP3YM0DKEXOZknK8L\nj0WAV7g2Dg93TSwOxNvTkx9vvpmR33zDupQU8svKGDFnDnPGj+emjh21SaE2BjN+2Vp/wqoqTXxs\n2rTW5/wzKYnJv/3GMZu+efd368Z7o0bh52qjDkeRYdOrzoGOw8E+Prw6dCiP9OzJP1ev5nN9MVWu\nGwl9tmMHA6Kjub9bN27q0AF/Ly+HxQJYy60T/62VW/epgnb3Wt7OKCxk9fHjrE5OZnVyMvtOnz/D\nzSAEXRs3ZnDz5gxp0YIB0dGEuUFPHiEETQMDaRoYyOi2bS2vny4qYuPJk6xPSWHDyZNsTU2lzGSy\nvJ9TWspvhw7x2yHtu8bH05NekZEMjI5mQHQ0/aKiLtz0/MgnUKoLs5ETICFF65/51VcweTKcm7lc\nlwiK0Yxmkv7j6kgUCoXCfRj4IKz5GhLWQUkJzLwL/m+tq6NSKOokLUNDmTlmDM8PGsRb69fzSUIC\npZWVlJlMfLB1Kx9v3849XbvyXP/+tA4Lc3W4CoVdUcKjwv4YPMA3UnO09tSFHik18fGczLIRrVvz\n0qpVACxJSnKJ8PipTbbjg927O8+g4VzMpdaFWIVHZ2aKORF/Ly8W33EHtyxYwO+HD1NuMnHzggU8\nk5bGv4cOxRhqk5nndRLQPxfp6bUSHs8UF/PU0qVnGQcFennxyXXXuaaPp7OoqoDMFdrYO+Jswx4H\n0SQwkBljxvDC4MFM37SJmdu3W8qB16WksC4lhUf/+IMxbdtyfWwso2JiHOfsZxYegaKj3/JD2UDW\np6SwOjmZg2fOnHc3gxDEN2nCkObNGawLjSE+Po6J0QE08PdnbGwsY2NjASirrCQhPZ31J06w/sQJ\n1qWkkFVcbJlfWlnJmuRk1iQnA9rPH9eoEQOjoy1ipKX0x1RqdQwHMNwMOXu1catWdVt0NNPxH7Dr\nAPCjqyNRKBQK9+Gh2fB4R014TFgHaz/RBEmFQnFJNAsKYvqoUfx94EDe3rCBGdu2UVRRQUVVFZ8m\nJPD5jh3c1KEDz/XvT7f6sL5SKHBD4VEIMQLIklJuv+hk+5zPCNyqPzoCjYAc4Bja1ccsKeX5r1Rr\nf767gS9rudtnUsq69T+8f7QmPBoLNBHEYIT8/L8Ijz2aNiXM15fskhL+PHqUCpPJqY7C5SYTX+7c\nCWimMvd0dbxAc17MpdZF3prBCtTLjEcz/l5eLLzlFh787Tdm6f8Gb23YwPJjx/j0uuuI94uC4hPg\nexgGDYSmkRAVVaNjF1dU8N7mzby+bh15Nr3wBjdvzudjx9b/u4hntkBFvjZufLVmAuIkmgYG8sbw\n4fxj4EA+37GDzxIS2J+VBUBheTnz9u5l3t69eBoM9GjalEHR0fSPjqZLo0ZEBwdfUj9EgLzSUkv/\nw8TMTB6RjYkWGfjmbOS5hK/JMP21d46HEPRo2pTBNkKjw8RQF+Dt6UnfqCj6RkXxNFqJ9sEzZ1in\n94Jcl5LC0Zwcy/wqKdmZkcHOjAze37IF0LLAB0RH82DgJvrZOlnvzrSeaPBgJ/5UDsTTHzr9H0p4\nVNQGZ69bFQqnE94SbvsHfPGCtv3lc9DtBgionzfHFQpn0TgggLeuuYbnBgzgf5s28f6WLeSXlVEl\nJd8lJvJdYiIjWrfmbwMGMLh580teIysU7oBbCY9CiJeBF4EqIcQ4KeXvNu91B+KAuVLKUjudrx0w\nF+iiv2T2EGgENAb6As8IIe6VUv5hj3PacDG/grqN2WDGDyjNB+/wavs8ehgMXNO6NfP27iW/rIy1\nKSlOLXVeuH8/p/UMoBvat6ehq5zFqiqg8Kg2rmwCHvp/LPVYeAQwenjwxdixdG3UiGf+/JOKqioS\n0tPp+emnbI1tQjwnwL8IekRrpZAXIaOwkJnbtjFz2zYydbMggGBvb94aPpz74+Ndl9HqTNJtyqwb\nO67M+kIE+/jwZN++TOvTh82pqXyekMCC/fvJLdW+viurqth08iSbTp6EDRsALRs1NiJCM2YJDCTC\nzw9foxEfT0+8PTwoM5koqaiguKKCMyUlpBcWklZQwIm8PNILC886v39YW14Mz8Ag4MaAfXyY1xtP\ng4FekZGa0Ni8Of2iohzSn9FdEUJoJjgRETwQr7UzSM3Pt2Skrk1JYfc5ZjpJOTmcyD3Nv5rPAL0r\nwQvrIxmQuJEmgYGEx8bSKCrKvRYTCoWTcPa6VaFwGaP+AevmwaFEyMuFz++Dx39xdVQKRb0gws+P\nV4cO5el+/ZixdSv/27zZYnq6JCmJJUlJ9I6M5G8DBjA2NvbKuJZR1Dvc7VphEPA5cD/Q5pz39gF9\ngBVCiEcv986yECISWI4mMEr9sQZIAhoAV6P5MjcEFgohRkopV13OOavhgB7Dxdhg5/M6HrPwGAE0\naQmthp43W21s27bM26uV7C3cv9+pwuPMc8qsXUbhMZCV2tg/EqQ3lJXVe+ERNDHk8T596BcVxX2/\n/MLeU6eokpKFp/yJ13/8ZdvmExX3IG3CwvAwWLP3Kquq2Hf6NGuTk/np4EFWHT9OZVWV5X2DENzb\ntSv/vOoqml5JbnEZNsYyTYa7Lg60f98+zZrRp1kzPho9mrUpKSzcv58/jx79S9lzQXk529LS2GaH\n884v7MiL4WsAeDYqlfFjJ9KnWTPH95isY0QGBXFLp07corceyCstZYNelr02JYUtqanc6reDKKOW\nQftrQQyZG46zsUDr3/uN0cjJ116jbXg4seZHRASx4eG0DQ8n2I1L1StMJnJKS8ktLSWnpITc0lJ2\nmJ3fFYqa4bR1q0LhUgwGmDIHnukFogKKf4XTG6FBX1dHplDUG0J8fPj7Ek0AMgAAIABJREFUwIE8\n0acPs3bu5K0NGyz96TenpjL+u+9oFxHBc/37c3vnzng5sUpQobhc3E14NEgpJwkhZgA7bd+QUpYA\nHwoh5gNzhRBPSSl3VnuUmjEXMDdNOA6MlVLuNb8phAgD5qEJkEZgvhCitZQy/zLOeS6bpZSP2fF4\n7oN/tPYcCnQJhdbnL2G+NiYGo8FARVUVPx08yHujRjkllXxXRgarjh8HNLexq2xdlZ2NucwaYNRV\nEPc3KC6GKygbq2dkJAkPPsi7mzbx+rp1JJRae5ok7Pud4Wsr8PLwoElAAN6enhSVl5NZVHSW0GjG\nQwhuaN+el4cMoUODBs78MVxPeS6c2ayNg9qDXzPXxmOD0cODoS1bWm4uZBYWsi4lhe3p6ew9dYo9\np06RnJtbq3RwATT09ycmPJz2ejZf+4gIujZqBGtWQv4Bosv2EN3YB5ToeFGCfXwYFRPDqBgtw7is\nooLK37uA3hryt9Q+NC1IASAjIIAjYWFQWcnuzEx2Z2b+5XiBXl40CwqyPMyZrGG+voT6+mrPPj74\ne3nh7eGBt57d6u3pedYd/SopMVVVYZKSKikp0x3UiyoqKNKfC8vLKSovp7C8nFyzoHjusy4w5pSW\nUlxR8ddfQFqa/X+pivqMM9etCoVrieoKdz8F6a+DD7DlARi5AzzU/60KhT3xNRp5uGdPJnXvzveJ\niby+bh17Tmnmfgeysrj35595YeVKnurblwfi4wlQ61tFHcDdhMe9QojrpJS/nm+ClPKUEGIiMBMY\neyknEUJcCwzQN8uAMVLKfeecJ1sIcT2wG2gFhAHPAs9fyjmvOPxsshuLT1xwarCPD8NatWLxkSOc\nzM9nW1oaPSMjHRwgTN+82TJ+vHdv1/bNMBvLAAS11Zx5XVX27UKMHh48278/k7t35+vNiyH1WwDi\nfbTecuUmE8nVlOybaRESwq0dO/Jwz55EBwc7JWa3I3OV5uYMIPrAihXQsqWWcezpXl/5jQICuLFD\nB27s0MHyWmVVFRmFhaTm55NbWkpJZSUlFRWUmUz4eHriZzTi6+lJiI8PTQMDaejvf/6+sNE3w95/\nAhJO/ACxjzrnB6tHeJ9Zi3fxfm0jvBcfj36EQn4nIzeXVT17ku3jw67MTI7m5FR7E6CgvJz9WVmW\nPp+1wdNgQEqJSdbvziSKOo1T1q0Khdsw4l+wdBlkb4O8fZqRW9wrro5KoaiXeBoM3N65M7d16sQf\nR47w+rp1rE3Rbv6ezM9n2pIl/GvNGh7t1YupvXoR4efn4ogVivPjXleh8CTwpRBiLDAL2CSlNJ07\nSUqZJoS4nLrJKeZDoZnH7KtukpSyWAjxIjAHLbFmshDiRSnlX6+uFGdjzngEzWTmIoxv147Feonb\nwgMHHC48nioq4ps9ewAtrf2uLl0usoeDsc14DGzrujjchGAfH6YOvh65sAmiJJ3+AVmMa9uWpNxc\nMgsLqaiqwsfTk0b+/rRv0ID4xo25pnVr4ho1Uo2XM1dax3ktYOsaWLMGJkyAOuDk7WkwWLLjLhuL\n8AikfA8N74TERDhyBCZOBFWicnEOvGMdt3sSmvcmoGNH2uzcSZt+/XhAb31QYTJxLDeXg1lZHDxz\nhoNZWSTl5HAyP5+T+fmUVFbW+tTVCZmXi6+nJ6G+voT4+BDq46M9+/oS4u1NqK8vhcnJvPvJJ3Y/\nr6Le4qx1q0LhHhg8ofdnsLiH1iIo8T/Q7HoI6+bqyBSKeosQgmtjYrg2Job1KSm8sX49vx7Srh2z\nS0p4ZfVq3ly/nnu7dmVa3760qe8mmoo6ibsJjz5oXQGHA/cBRUKINcAKYLmUcheAECIKuKTmd0II\nf2CYzUuzLrLLD2h3qQPQsh4HAasu5dxXFLYZj0UXzngEGBcby0O//YYEFuzbx7+HDnWogDRz2zbK\nTdq1wSR3SFHPtxEeg5TwaEaExkPJ7/hWFfDT2D4Q4Lz+n3WWzBXaszBAThCg9YbBib1T3YaQjhDc\nQcvKOL0O/pgPh/RS2qQkaKv+1i5I/kFI070y/KIg6kZtHBAAAwacNdXo4UFbva/jdeccRkpJbmmp\nRYTMLikhRy97No+L9azWsspKSisrLWODEHgYDNqzPvYQAm9PT/yNRvy9vAjQn/2NRgK8vPD38iJE\nFxVtBcYQHx+8L5L1m5CQwLt2+vUprggcvm5VKNyO0C7Q8R/ajT1ZCZvugRFbVcm1QuEE+kdH80t0\nNHtPneLN9ev5ds8eTFJSUlnJR9u2MWPbNq5v146n/p+9+w6PssoeOP696T2kQEJNQg+9SFea2F0V\nRcW+llV0UUFd9ecWd13Xtgjq2mUt2FFhRVawgIgiTbp0CC2UUJKQ3u/vj/sOM7iUEGbmnXI+z5Nn\nzpuZyRwQ8M6Ze84dMICBLVvKhgzhM3yt8PgvzMLsJcyQ7v7AhcAFAEqpEiAXyASeauBrDAQcg/NK\ngaUnerDWulIptRCzqAQYjhQeTy4iGUKjobb8pK3WYFouB2dk8P2OHWzOz2fpnj309dCux4qaGl5e\nav6zhyrF2L59PfI6p6TYarWObAwRSfbm4kuSezkLH/nLpPB4MhX74bA1qjamB2yy2tLT0oKydR8w\nux7X/NXEjbYD1hujtWul8HgyG593xh3uMTtdGkApRZI107FrWpqbkhPCJ3hj3SqE7+n8R8j9HApX\nQeFqWPs4dHvM7qyECBpdmjRhysiR/H3YMCYuXMi/V6ygtLoajekenL5hA/1btOD+AQMY2bHjUYdz\nCmEHX/sT2AXor7W+W2t9AWYxNwD4C/ADpmCYDfxLa/33Br5GtnWrgTX1bJtefoznu0MjpdQopdSj\nSqmJSqm/KqVuV0p1deNr2EMpZ7t12U6ox4yuG7p1OxK/u2qVpzLjrRUryCstBWBkdrb9swCri6Hc\nzDCU3Y6/kuxy0vi2BbBsGXzxBeTn25eTL8ub54xrezr/3gXjbkeHVlc6YzXPeWDThg3QgPbfoFF5\nCHLeNnFYLLS5zdZ0hPBR3li3CuF7QiNgwNugrA+k1j4B+ctP+BQhhPtlNGrE8xdcwK7x43nq7LNp\nFu+c6rEoN5crP/mE9i++yL8WL6akqsrGTEWw87XCY5HW+sg7Qa11ndZ6sdb6H1rroZhW59uAs5RS\nDd0O18El3lHP57gOKezYwNc9lsuAqcCjwDjMQvVVYJVSaqNS6hY3vpb3Odqta0qhuvCkDx/VqRNR\nVhvcR2vXUl37P2OSTlt1bS1PLVhw5PrhQYPc/hqnrHizM47vcPzHBaOkXs541U+m6LhsGew6+S7a\noOQ637HUZc5q69bez8VXJHaCxM4mLlgImakmrqw0sx7FsW153exYB2h9C0Q0sjcfIXyTN9atQvim\npB5m5yPA7lp44lKoKrM3JyGCVFJ0NA+deSbb7r2Xdy67jK5Nmhy5L6eggHtmz6bVpEk8MmcOe4uL\nbcxUBCtfKzyuV0qdebw7tdZlWus3MXN0Xmjga7jO2Mmr53P2WbcKs4h0F32Cr3bAZKXUDKVUtBtf\n03tirMJHFbBhEaxeDfv2HffhiVFRXNrBFN4OlpUdOWzGnd5dvZqd1qnIF7RtS+9mzdz+GqfMcaK1\nBuLb2ZqKz4lpAZFWoShss3MH35499uXky47MdwyDgjgTh4RARoZ9OfmCVlc546RtznjtWu/n4g9q\nq2DTi9aFgg732pqOED7MG+tWIXxX50cgty0sBLblwju3252REEEtIjSUG7t3Z9WYMXx9/fWc26bN\nkfsKKip48scfyXjuOW7+/HN+2b/fxkxFsPG1wuMjwD+UUmcc606lVKpSajzmtISGbr+Ic4nL6/kc\n18fFHfdR9bcDmICZA9QSM5w8FrMb8y5gA84C5MXAB254Te9z7HjMB95+F6ZNg/XrT/gU13brN5a7\nt2Wjpq6OJ3/88cj1nwcPduvPbzDHidZlwLtr4Y03YNEiW1PyGUo5261jCqC6yMRSePxfZbudf5ai\ne0O+9XvVrJmzvThYubZb6+8g2vosZ+NGqK62JydftnMqlFt/x1pcCvFtTvx4IYKXN9atQviu0Ai4\n5FXzISfA1x/AL7PszUkIgVKKc9q04avrr2fVmDHc1L074dbf0+q6Ot5euZKur7zCue++y383baKu\nHmPRhDgdPlV41FoXApcDDymlpiilfr1N5xZMwW46ZvdhQ0S5xPUddFDpEp/u7sPpWussrfVDWuuv\ntNZ7tNbVWusKrfUWrfVrQHfgLZy/xkuUUtee5ut6X6xVeIwGqq1DLqzdhsdzXtu2tEhIAGDmpk1s\ndeMsvw/WrGGL9fPOzspiQMuWJ3mGlzhOtC4BSIDdu0G2wDs52q0jgEjr92XfPqirz3jWIOLaZp16\nFvTtC6mpwd1m7ZCYDY2s0bkFiyDT2vheVQWbNx//ecFIa9jgcq5z7W9gxgyQT8WF+B9eWrcK4ds6\nng0X3mTiOg0v3wqVpfbmJIQ4oltaGm9fdhnbx43j4UGDaBTlLId8k5PDxR9+SEdrDmRxZeUJfpIQ\nDedThUcArfUhrfWVwNOYHX+uZmL2z51Bw1tWKlziiHo+x3W7UH13SR6T1rqoHo+pAX6HGUzu8NDp\nvK4tHK3Wp1B4DAsJ4fd9+gDmP/6LS5a4JZXy6mr+NHfukWuf2e0IzhOtS3CeaJ2SctyHBx3XA2Zi\nrVmh1dVw8KA9+fgq18Jj2wvgwgth7FgYOtS2lHyKa7t18jbo0gWuvhrayXiDoxz4AQqs3eZJvWBt\nGSxfDi+/LH/nhDgGL6xbhfB9178MzawP9PP2wpv+PaZeiEDULD6eJ0eMYNf48bxw/vlkNXJuxN+c\nn889s2fTYtIkxs+eTU5BgY2ZikDkc4VHB631Wq31zl99bx3QHEjVWv+ngT+6xCWu7+5F18eVHPdR\nbqS11sDfrEsFdFFK+cBAwlPgaLWOgCO/bScpPAL8rlevI4fMvLlypVs+eXlh8WJ2FZma7wVt2zIk\nM/O0f6ZbaO3c8VidBiHW6YBSeHRKdjlgJtKlxVrarY/mmO8YEgmpA5zfD/HZf+a9y7Xdum4OjBoF\n2dkQHm5fTr5ow0RnHHWts9jYqpXZQSuEOCYPrluF8H3hUTD2HQgNNdffToWlH9mbkxDimOIiIri7\nXz823303n48ezfCsrCP3FVVW8tzixbR94QUu/egj5uTkoKUNW7hBmKdfQCkVorV2W0+k1rqK+rdI\nH8shlzitns9Jd7w85pNrb5kPVAOOd8bZQL2qLePHjycxMfGo711zzTVcc801bk3whGJdWpnDrcJj\nUZEptqnjdxylxMRwfdeuTF6xgqLKSl5aupSHzzzu7PaTyisp4QlrtmOIUjxzzjkN/lluV5EHNVb7\ncHUT595aKTw6xWaanaBVBRC2BTjXfH/vXujRw87MfEfJNijdbuLGAyHMP8+j8qiEDtCoOxSugkOL\noWQ7xGXanZVvKd4CuTNMHN0MdiYD1r9PAwYc92n+6sMPP+TDDz886nuH6/HhmAhsPrhuFcI/dBgG\nl9wB018216/cCdlnQ1xje/MSQhxTaEgIl3TowCUdOrAmL48XFi/mvTVrqKipQQMzNm5kxsaNdGnS\nhHv69uW6bt2IkQ/sRQN5vPAIrFZKlQAD3bmQOw0bXeL6HvXayiXe4MZcTkhrXaOUOgg0tb5V7+0m\nkyZNolevXid/oCeFxUJEMlTlQ7j1Zq6mBkpLIe7EZ/TcP3Agb65cSZ3WPL1gAWPOOOOoeRSnYtxX\nX1Fk7Zq8pUcPujRp0qCf4xFFLn8cKxuZwmNUFMTG2paSz1HKtHzmzYHoAxCloVUHSE8/+XODhWub\ndZNh9uXh6zKuMoVHgF2fQvYD9ubjaza+wJFO0ZSbYdUOEyclQYcOtqXlKcf6MG758uX07t37OM8Q\nQcLX1q1C+I/Rz8GqObBzI7QthFX3waB37c5KCHESXdPSeOOSS3hyxAjeWLaMl5YuZbd15sAv+/dz\n+8yZPDxnDrf36sVdffrQ8lcbnIQ4GW/04HUC+gBZJ3uglziOVVZAV6VUfX4PXCt4Jz6W2f1cK1D+\nN6nZ0W4dVgCO9XvRScdc0jE1lRu7dwegsKKCfy5Y0KCX/3LzZj765RcAkqOjeeLssxv0czzGcQpx\nDVATb+KUlBPuCA1KyS4HzNzQF669Fnr2tDUln5LnnF9K+nD78vB1LV3arXdMtS8PX1RVCDlvmjg0\nBvZ3dN7Xv7+07Itg4mvrViH8R1g4jP8ELoiHTGDHe7DzE7uzEkLUU2pMDP931llsu/dePrriCga6\nHMaaX17OUwsWkPX881z5ySfM275d2rBFvXnznUSoF1/rRH7CeUp1LGbg93EppSKA/i7fmnu8x7qb\nUioLSHD5lv8NtYu1NotG1kJNKcTEQEXFiZ9jeXTIEMKtN7vPLV7M9sLCU3rpg2Vl3DFz5pHrieee\nS2Nf20noKDyWAhFWe7W0Wf+vJJfaf/5y+/LwRVo7dzyGxkByH3vz8WUJ7SDJas/PX2pa1IWx5Q3z\nbzRA+rWwYbuJo6KkyC+Cla+sW4XwL826wpCXnNdLxkCZ/72FESKYhYeGcnWXLiy45RaW3HYb13fr\nduR9ea3WfLpuHcPeeYcur7zCS0uWHOkuFOJ4gm4Lg9a6FJjj8q3fnuQpVwDWVjTyMXMXveVWl/gw\nsNKLr+0ejh2PbYGxl8ODD0Lr1vV6amajRtxlnXBdVl3NHTNn1vtTlTqtuXH6dHKt3ZVnZ2Ud2UHp\nUxyt1tHAVTeYE4g7dbIzI9/kerJ1wTL78vBFxZug3FrQNzkLQiPszcfXuZ5uvfNT+/LwJXU1sOlf\nzuuQi8xYDIDevSFC/kwJIYQ4BZnXOw91q8qHRTc7O5+EEH6lT/PmvDtyJDvGjeMvgwfTxGUjz7oD\nBxg7axbNJ07krv/+l1/277cxU+HLgq7waLGmHqOA3yqlso/1IKVUNM6TpTXw2unM+1FK1Xu7nVJq\nIHCf9boa+NAvZw05djyGA9Wn/mnnY8OG0Tze1H2/3rqV5xcvrtfz/jpvHrO2bAGgcUwMU0aORPli\n+7Jjx2N0NPQ52xQeO3Y84VOCUnwbCLPq/7Lj8Wiu8x2ru8PatVBWZl8+vs71dOudLu3WdXVQW+v9\nfHzBrs+gbJeJm10MZ10GY8aYw5v69rU3NyGEEP5HKejzCkRbY+r3fQ2bXjrxc4QQPq1pfDx/GzaM\nXePH8+EVV3BmK+cxGCVVVbzy8890feUVhrz9Nh//8gtVwbquFsfkzcJjc6XUE0qp5UqpIqVUqVJq\nq1JqhlLqDqVUsrcS0Vp/CfxgXUYCM5VSXV0fo5RKAT7H7NUDcxr2M8f6eUqpDKVUncvXjcd56VFK\nqcVKqRuUUgnHeoBSKlIpdQ/wjZWbAgqBx07hl+g7YlxOti7ddcpPT4iM5PXf/ObI9QNff82szZtP\n+JyJCxfy9/lmY6oCPrjiCprFx5/wObaoq4HirSaObwf1GjcapFQIJFvtnmW7oOKAvfn4Etf5jtvj\n4ZNP4Jln4OBB+3LyZfFtna37+T/DzuUwaxZMmgSrVtmbmx20hg0Tndcdx5vb9HS47DKQ4eEiePnM\nulUIvxSZAv3ecl6vfBAK19qXjxDCLSJCQxndpQs/3Hwzq8aM4Y7evYl1Oe16/o4djP7sMzKee46/\nfPfdkQ5EEdy8Wen4CngI6AHEYZpLs4CLMDsQt1sLPG8N4bsW2GvFWcBKpdRcpdQbSqn/ADuAEdb9\n1cBVWuuT/a1x7E48kT7AO8BBpdRqpdRUpdRrSqnJSqlZQB7wHOb3RwFlwCVa67xT/QX6BNfCY9mp\nFx4BLmzXjocHDQLMTImRH3985MAYVxU1NYybPZv7v/76yPcmnnceI+rZ2u11JdtAW+2M8e3tzcUf\nJLm0W8uuR0PXQd48E4fGw0FrV29MjMwKPZEMl3brLZ/C4sVQXGx2iwabgwvh0BITN+oOaXIquhAW\nX1u3CuF/mp0H7ceauLYC5lwJ5VKEECJQdEtL49WLL2b3fffxwvnn0zE19ch9+0pK+Pv8+WQ+9xxX\nTJ3K3G3b5DCaIBZmw2utw5wMHQk0BToDUZhF3UPA5Uqp0Vprj84z1FrvVkoNAz7ELCoBhlpf4Cwi\nHgB+q7WeV48fqzh54dFxfyjQxfr69f2Oxyy2XntTPV7bN8U6t2BTtrPBP+bx4cPJKSxk6tq1VNbW\ncs1nn/HBmjXc1L07jWNjWb53Ly8uWcLWgoIjz/nrkCGM69//BD/VZsUu/1kTOtiXh79IdjlgpmC5\nWcwGu8NrodLa/RnaD6qqTZyVJSejn0irK2HlwyaumAWNboLCQti2DUpLwdcOofKkDZOcccfx8udG\nCCefWrcK4bd6PAP7v4dNa2DpetgxGu770u6shBBulBgVxd39+jG2b1++276dl5cu5T8bNlCrNbVa\nM239eqatX0/7lBRu79WLm3r0IDUmxu60hRd5s/BYCYzWWn/u+k2lVBQwGLgSuAFoD8xTSp2nta7f\nQL8G0lpvUkr1A0YD12AWk2mY1uYc4DPgba11fn1+XD0e8wGwERiIOSm7DZAKpGB2nx4GtgGLgE+1\n1j+d0i/IF0U340g9tgGt1g6hISG8N3IkMeHhvL3SrO2/2LSJLzb9b002IjSUF84/nzvOOOGB5fZz\nHCwDsuOxPlwLj/nLzOEX+/ebgy9cPl0LKq7zHStcZoNmZXk/F38S1xqSzzCt1oUrIXMsrCw0cx7X\nrYM+QXIyeMk2yJ1m4qg0yBhtbz5C+BafW7cK4ZfCoqHnWzClP1TXwIJZ0O05GDHO7syEEG6mlGJ4\nVhbDs7LILSrijWXLeH35cvaVlACw6dAhHvjmGx6ZO5crsrO5vXdvhmRk+OZZDMKtvNlq/cyvF28A\nWusKrfXXWuvfYVpYXgMSgC+VUhmeTkprXaO1fk9rfZHWOlNrHa21bqq1HqS1nlifoqPWeofWOtTl\na8pxHlettV5k/dyrtNa9tdYZWus4rXWM9boDtdb3BUTRESAk3Co+clo7HgHCQ0N585JLeOeyy2iR\ncMwRmQzPymLZ7bf7ftERfrXjUQqPJxXfAUKtT8Y2L4Enn4TXX4clS+zNy06u8x2L05yxr44X8CWZ\n1zvj+DXOOJjmPG78l/OU0fZjITTS3nyE8C0+uW4Vwi817Q2jH3Jev/V/sHu1ffkIITyuRUICfxs2\njB3jxvHxqFEMzcw8cl9VbS0f/vILw955hw4vvsiEn37iQGmpfckKj/PGjkfHTsC5J3wUoLXeC9yp\nlJoLTAZeB6Sf0t/FtITy3VCRB7WVp/XmVinFjd27c3XnznyTk8Pi3FzKqqtplZjI2a1b06VJEzcm\n7mGuhUfZ8XhyIaGQ1AMO/gQhu6CqBEKjYc+pn5YeEOpqIe97E4clw0Hrn9rEREhKsi8vf5FxNay4\nzxTeSj6HJg/A/gOQmwuHDgX+jMzqItg62cShUdB2jL35COE7ZN0qhCdc8hismQMrF0FFBUy8Ap5e\nC2ERdmcmhPCgiNBQrurcmas6d2bjwYNMXr6ct1et4mBZGQCb8/P5wzff8MicOVyenc0dvXszNDNT\ndkEGGG/seHQc4HK4vk/QWn8CXAwMUUoN9khWwntirQNmDgBTXoFXXzXtjKchMiyMi9u35+/Dh/Ps\needxb//+/lV0BGerdX4SrNsBO3ea9mFxfMnWATMRQKT1qdi+faZFNtgUroTqQuuiL9TWmlDmO9ZP\ndDqkn2Pi0u3QyuX3bHUQ7MLY+m+oKTZxk9GwZB1YC0AhgpysW4XwhJAQuHc6NLI+HN2+Bd661d6c\nhBBe1SE1lX+eey6548fz4RVXMMxlF2R1XR0fr13L8ClT6PDii/xzwQL2yy7IgOGNwuMG6zb7VJ6k\ntf4BeAm4xe0ZCe+KsQ6YqQLWrjSFokOHbE3JdtUlUG7t1NvTGD7/HN5805ysK47Pdc5jrPWesKYG\nDhywJx87uc53TBkArVqZRb20Wdefa7t1zDJnwTY31558vKWuFja+4LwuPgvmzoVJk2D9evvyEsI3\nyLpVCE9JSIe734QQ6/+3s9+DJR/am5MQwusiw8IY3aULc2+6iY1jx/LAgAFHHTazOT+fB7/9lhYT\nJzL600+Zk5NDnZyI7de8UXh8H3O6yI0NeO6/gX7uTUd4XYy14zEGqLaKRYfrvZEgMBVvdsZVyeY2\nLMy0yYrjS3IpPEbtdcbB2G69z6UL8Iwr4ZZb4OGHIfuU3isHtxaXOeeG5v8HRgyHW2+F668/8fP8\nXe5/zC5PgMbnwoaDJq6thebNbUtLCB8h61YhPKnHZfCb25zXn4+FioP25SOEsFX7lJQjuyA/uuIK\nhrsckunYBTni3Xdp+8IL/P3779kZ7HUEP+WNwuNHwG7gXKXUTaf43C1AS/enJLwq1trxGI0UHh0c\nbdZ1QGWciZOTzY41cXyJncw8OoAwl+Lt3r3HfnygqquGAz+YOCodEqwTrSMiIDzcvrz8TXicKT4C\nVOVDRgG0bBn4reobJjrj2kucLdZdusBxDu4SIojIulUIT7v2JejQCXoAnfJh4Y3Ow86EEEEpMiyM\nq7t0Yc6NN7Jp7Fj+MHDgUbsgtxUW8pd588h87jnOe+89Pv7lFypkTJnf8HiVQ2tdDtyO+fR4slLq\noZM8xVUTQHpP/Z1jx2MkUFdi4mAvPDoOlinHHAwCgX+YhTuEhEFSTxOH74SachMH247HQz9DjfV3\nKW1Y4BfKPCnLZXfj9vfsy8NbDi4xBzQBJHSGTbXO+/r3tycnIXyIrFuF8IKwcPjj19CpsfmbtncW\nrH3S7qyEED6iXUoKz5xzDrnjx/PxqFGc26YNjnc7Gvh661ZGf/YZzZ59lru//JIVwbYJxQ95ZXuV\n1noW8BcgFHhCKfV1PYdvPwwEwZT/AOcoPCog3BoQK4VH6xaItAqOUnisn+Q+5jYCiLTe35WWQjDN\n/chzabNOG25fHoEg/RyIbGzi3V9AVYD/27RxkjOOugby802cmQk/5m2QAAAgAElEQVTNmtmSkhC+\nRtatQnhBbHMY9AE4yglr/gL75tiakhDCt0SGhXFV5858df31bB83jseGDiWrUaMj9xdUVPDi0qX0\nev11er72Gv9avJhDcliiT/JaX6fW+nHMIg7gbOA7pdRypdQ/lFJnK6UylFJRSqkkpdQQpdRM4E7g\nNW/lKDwkqjGERJo43HpTX1kJFRX25WQ3R6t1MRBh7XhMTbUtHb+S0tcZD4qD+++He+8Nrl1/rgfL\npA2zL49AEBIGGaNNXFsBu6bZm48nle6CnZ+YOLIx7GzivG/AAHtyEsJHybpVCC9IHwFd/2ZiXQc/\nXQtlu+3NSQjhk1olJvLnIUPYcs89zL3xRq7v1o2osLAj96/ct497Zs+m2cSJXP3pp3y1ZQu1dTLC\nwVd4daCctYg7H8jDfLzVHfPp8NdADlAKHATmAhcCH2qtA/hdYJBQIRDTwsShBc7vFxXZk4/dtHbu\neKxJM4UPkB2P9ZXSxxmHboT4ePtysUNtJRxcYOKYlhAnp1iftswgabfe+Dxoq7U66UbYab25S0mB\n9u3ty0sIHyXrViG8oMsfoel5Jq7YDwtGm1nWQghxDCFKMSwri3dHjmTf/ffz6kUX0dflcMSq2lqm\nrl3L+e+/T+bzz/OnuXPZeFAOsLKb10+y0Fp/A7QBHsG5kPv1Vx3wNPBbb+cnPMRxwExKGfTsDCNG\nQHS0vTnZpWI/VFtF1/gWzsKZFB7rJ74thFtb7A8tCa4Wa4CDi8zOPID0s4Nrp6enpPSB+HYmzvsO\nSnfYm48nVB2GLa+bOCQS+j8Ao0dDRoaZ7Sh/joQ4Jlm3CuFhKgQGvOcczXTgR1j1iL05CSH8QmJU\nFHeccQaLb7uNNXfeyX39+9PY5UCa3KIi/vHDD3R86SX6T57My0uXSiu2TcJO/hD3swZ3P6WUehoY\nZH21AKqBzcA0rXWeHbkJD3EsJloBQzpBo862pmOr4o3OePhAOON+03oeGWlfTv5EhUDKGbDvW6jY\nB+W7nTtqg4HrfMeqLnDwoClaS+Go4ZSC1r+FVX8ENOS8DV0fNX8vN2+Gzp39//d362SosWaitr4J\nYtKhYzp07Bh8xXshTpGsW4XwsKhUOHMqfDsYKqvhrQlQ0AqG3213ZkIIP9GlSROePe88nhwxgv9u\n2sSbK1fy5ebN1Fnr3MW7d7N4927GzZ7Nxe3bc0O3blzUvj0RoaE2Zx4cbCk8OmitNfCj9SUCmaPw\nCFC2K7gLj0WbnHFCB3MrRcdTk9zHFB4BDi0N3sLjklKY+yIkJcHdd0OI1zexB46sG2H1n82MqZy3\noHAY/PAjVFVBcrJ/H7xSVw0bn3Nedxh/9P3+XlQVwktk3SqEB6X2hw5PwHN/gBJg8h+gzUDI6G13\nZkIIPxIRGsrI7GxGZmezr6SED9asYcqqVazKM58PVtfVMX3DBqZv2EBydDSjO3fmxu7d6du8OUrW\nxB4j71KFdzharQHKdtqXhy8odik8xstctQZxPWDm0BL78vC2mlI4tNjEKgtKrIHJCQlSdDxdMS0g\n3ZoxVboDyteaoiPA8uX25eUOOz+BslwTN7sYEjvam48QQghxLN3vg7bWYWeVlfDPS6H8sL05CSH8\nVnpcHPcNGMDKMWNYeccd3D9gAOlxcUfuzy8v5+Wff6b/v/9Nx5de4h/z57OjsNDGjAOXvFMV3uG6\n47F0l315+IIil1brBCk8NojrATOHltqXh7cdWOAcuF7b0/n9rCx78gk0bW51xuHfQUSEidescRYh\n/Y3WsH6C8zr7AftyEUIIIU4kJATGz4DGTcz13t0w8WKQk2mFEKepe3o6E849l13jxzP7uuu4tmtX\nol1Oxd506BB/+u47Mp9/nmHvvMNbK1ZQVFlpY8aBRQqPwjuOarWWHY8AhEYd/fsi6i+mOURbra/5\nS017LAT+wjTvO2dcmumMpfDoHs1/A5GpJs6bAR0yTFxZCevW2ZfX6dg/DwpWmDi5NzQZbGs6Qggh\nxAnFpcIfPnN++Lf8R/joHntzEkIEjLCQEM5r25b3L7+cfQ88wJuXXMLQzMyjHjNv+3ZumTGDtAkT\nuOqTT/jPhg1U1tTYk3CAkMKj8A7XVuvSIC481tVAyVYTx7czB6WIhnHseqwugulvwmuvwYsv2puT\npznmO2qgMMHE4eHQIohmXHpSaARk3mDiukpovM15n7+2W7vuduz4gMxzFEII4fvanAm/c/n/17SX\nYeE79uUjhAhICZGR3NyzJ9/ddBPb7r2Xx4cNo31KypH7K2pq+GTdOkZ+/DFpEyZw24wZzN22jdpA\n3+ziAVL1EN4RngDhjUxcusPeXOxUut3ZKivzHU+P65zHLYth717Iz4eSEvty8qSqw5D/s4lVByi3\nTiJu1QrkNDb3aXOLMy7+BBo3NvHOnXDggD05NdThdbDnSxNHtYSijlBba29OQgghRH0MvxsusD4M\n1BreuguKt9qbkxAiYGU2asQfBw9mw+9/z6Jbb+WuM84gNSbmyP2HKyv594oVnD1lCi0nTeK+r75i\n6e7daOvUbHFiUngU3hNrtS0W74QD+yEnB0pL7c3J2xwnWmsgTgqPpyXZZc5jrEtBaPdu7+fiDQd+\ncLaUV3d3fr91a3vyCVSNukBKPxMfXg2tw533LfWzeaJrn3TGEdfAtP/A88/D+vX25SSEEELU1y1v\nQXZPSAH6l8EPI81Be0II4SFKKfq1aMFLF13EnvvuY9Z113FDt27EOcY/AHtLSpi0aBF9J0+m/Ysv\n8uh337Hx4EEbs/Z9UngU3uMoPG6uheeegilTYPt2W1PyumLrYJlK4N2N8PLLMH++rSn5rZQznHF4\njjMO1MLjvrnOOL47REWZWOY7ul+7u5xx5FzTzt6ypX/9XpfkwI4PTRyeBLuam7ioyDk3SwghhPBl\nIaHw0Gy4sB1EAYVrYNEtZgekEEJ4WHhoKOe3bcuUkSPJe+ABPh41iks7dCA8xFlG25Kfz2Pz59Px\npZfo/frrPPvTT+QWFdmYtW8KO/lDhHATR+ExGjhUaNqvg+0vpWPHYzEQlgT79wffrk93iUgyczKL\nN0PYRqirNQvU3Fy7M/MMx3xHFFw0Bi5rZNrL09NtTSsgZVwFK+6HyoOwfxrc9jiktbU7q1Oz7mnQ\nVlt17E2wNt/ETZvKLlkhhBD+I74JDPscvuoHNcWwcyok94JOD9mdmRAiiMSEh3NV585c1bkzBeXl\nfLZ+PR+sWcO87dtxfBSyfO9elu/dyx+++YbBGRlc3bkzl2dnkxYXZ2vuvkB2PArvcS08Vh828eHD\ntqVjC8eJ1iVAhDW4NjXVtnT8nmPOY2QVhBWbeM+ewPskvPIQFK4ycVJPiEyGkBBo3tzcCvcKjYI2\nt5q4rhoOfGxvPqeqbDfkvG3i0DjIdSk0nnmmHDAjhBDCvyRmw8D3nNcr/w92f2lfPkKIoJYUHc1t\nvXox96ab2DV+PM+eey69mzY9cr8Gvt+xg7u+/JJmEydy9pQpvPrzz+wP4g1H8o5VeI+j8BgDVBWa\nONgKj0VWq3VFPIRFm9jl5CxxihxzHhUQbxUeKyrg0CHbUvKIvHnOOG2YbWkElbZ3YP5gAVteNSfS\n+4v1E6CuysSx18Me6+9DaipkZ9uXlxBCCNFQLS6Brn+1LjQsGA2Fv9iZkRBC0DwhgfsGDODn229n\n49ix/HXIkKNOxq7TmrnbtnHnf/9L02efZcSUKby+bBkHy8pszNr7pPAovMd1x2NNEO54rC6Bcmv+\nYI1Le6wUHhvO9WTr6L3OONDmPOa5zHdMG25fHsEkLguaXWTislzY/YW9+dRXxQHY8rqJQ6Jgdwfn\nfUOGyA5ZIYQQ/qvLn6HlFSauKYbvL4byPHtzEkIIS/uUFB4dOpQNv/89K++4g0fOPJM2SUlH7q/T\nmjnbtnHHzJmkT5jAue++y+TlyzkUBEVImfEovMdReAwBwkpMHEyFx5ItzrgqGSIxh1YkJNiWkt9L\n6gEqDHQNxG6FIX8w7cctW9qdmXvlfWduVSg0OcveXIJJ+9/Dnpkm3vgCtBxpbz71sfF5qLUWL1FX\nwwZrd3njxtC5s315CSGEEKdLhcCAd6B0O+Qvg3U74Mcz4fEVECkz1IQQvkEpRff0dLqnp/P48OGs\n3LePqWvXMnXdOnIKCgCo1ZpvcnL4JieHMTNnMqJ1a67q3JnLOnYkOTra5l+B+8nWB+E9kY0h1PpL\nFGYdKlNaCjV+1MJ4Ohxt1nVApbU4SkmReWunIywaGnUzcehmGNQL2reHQPrHunwvFK03cXIfCI+3\nN59g0vRciG9v4v3zzJscX1ZxwBQeAULCYfhf4aKLzIcbsttRCCFEIAiLhcGfw45U+BnI2QLPXgh1\ndXZnJoQQ/0MpRc+mTXlyxAi23H03P//udzw4cCCZjRodeUyt1ny1dSu3zphB2oQJXPj++7y5YkVA\ntWPLuxDhPUpBbCsThx4yB4AoBcXF9ublLY4TrUuBcKu9WtqsT1/qACvQcGixral4hGO3I0C6tFl7\nlQqBjvc5r9f90xnX1kJVlfdzOpF1T0ONtZu89a2QkAl9+sA990CnTramJoQQQrhNTHO49D3TOQSw\n7AeYcru9OQkhxEkopejdrBlPn3MOOffcw5LbbuMPAweSkZh45DE1dXXM2rKFW2fMIH3CBM6eMoWX\nlixhd1GRjZmfPik8Cu+KsdqtO1XBmBvgT38Cl7kHAc1xonUUcO31cO650LWrrSkFhMYDnfHBhfbl\n4SmuhUe6mYKX8J6sG81ubYBdn0DBJli8GF54Ab7/3t7cXJXtgc0vmTg0yszBcggLk92OQgghAkun\n8+D2Cc7rL/4N306yLx8hhDgFSin6NG/OM+ecw7Z772Xxbbdx/4ABtHQZw1ZrHUwzdtYsWkyaxIB/\n/5t/LljA1vx8GzNvGK/MeFRKKSATaATEceSo0PrRWs/3QFrCDo45j7FA5GEIDbU1Ha9ytFqHK+g5\nwnmqtTg9R3Y8Agd+si8PT3EcLFMTDtPWwH+3Qs+ecMEF9uYVLMKiocM9sPrPoOtg9USY39wUgH/+\nGc46C6Ki7M4S1j4OtRUmbvd7iGlmbz5C+DFZtwrhJ4bfA7m/wOdvmOvJD0J6R+giayQhhP9QStG3\neXP6WoXIJbt3M339ej5bv56t1kxIgEW5uSzKzeXBb7+le1oal2dnc3l2Np0bN0b5+Pg2jxUelVIR\nwPXADUAfzFnGDaGRQ3ACh6PwCFCyHZJ725aKV2nt3PEYmyFFR3eKzYSodKjYB4cWmeKQCpDdXSXb\noSTHxDXdzUE6VVUyF9Tb2t0Ja580h7bsexc6vQprtkJlJSxZAoMH25tfSQ5ssd50hcVBp4ftzUcI\nPyTrViH81PWvwp7NsHQeVNfAP6+CfyyAFt3szkwIIU5ZiFL0b9GC/i1a8NSIEazZv59p69czbf16\n1uzff+Rxq/LyWJWXx6Pz5tEuOZnLs7O5IjubM5o188kipEfenSulugIrgDeAwUAM5tPiU/niV7EI\nBK6Fx9Id9uXhbZUHoNo6wdtxWIVwD6Wcux6ri+DwOnvzcad93zjjio7OuHVr7+cSzCJToO3vTFxb\nBimLncXfn36Cigr7cgNY/RdzsjuYmZRRqfbmI4SfkXWrEH4sJATGz4TMtua6pASmXQKV/teKKIQQ\nrpRSdEtL469Dh7L6zjvZNHYsT48YQd/mzY963Ob8fJ5esIC+kyeT8dxz3DtrFt9t20aNDx265fbC\no1KqNTAH6MjpLb5k4RaIgrXw6GizBkiQwqPbBeqcx33fOuOiJuY2JAQyMo79eOE52Q+a2YkAeW9C\nR+ugrIoKWGjjn7mDS2D7+yaOSD76MBwhxEnJulWIABAZC3+aC+lp0A9I3QHzL3GOIBFCiADQLiWF\nBwcNYvFtt7Fz3DheOP98hmZmEuKyw3FXUREvLFnC8ClTSJswgRunT2fa+vWUV1fbmLlnWkEmAqmY\nVhOAKmAGMB/YjjnTVx/zmSLwuRYey4Ko8OhoswaI72BfHoHKdc7jzu/hcC/YtQvat/ff03x1HeTN\nMXF1ApTHmre1zZtDZKStqQWlmGbQdgxsfA5qy6HZEtjUzMx6XLgQ+vaF2Fjv5qQ1LB/nvK64AXL2\nQocEaccXov5k3SpEIEhqCU8ugG8HQUUeHFgAP90AZ34cOCN4hBDC0jIxkbv79ePufv04UFrKjI0b\nmbZhA99s3Uq1tdMxv7ycd1ev5t3Vq4lwadO2g1sLj0qpdOASnAu01cBIrfU2d76O8GPRzUCFgq4N\nsh2PLoVH2fHofsm9ISQc6qph+0LY2dZ5n78WHgtWQOUhE9ee4Vw0S5u1fTo9BFteM4XHvLeh82uw\nOsfM3VywwJxU7007Pnbu8K1pCzkJsOUj6NwZRo2S4qMQJyHrViECTEIbGPpf+HYI1JTCrk9h+QPQ\ne6LdmQkhhMc0jo3l1l69uLVXLw5XVPDl5s18vnEjX27eTHFVFQBVNTW25ujuj3+GWLcKKAculsWb\nOEpIGMS0MHEwFR6LXVqtZcaj+4VGQVIvE4fngK408a5d9uV0uva6zHcsb+OMpfBon+h0aP97E9dW\nQOK3EBYGiYnQsqV3c6kugZUPmlgDBy7myP/SmzaVoqMQ9SPrViECTXJvOPMTs9EBYOMk2DDJ3pyE\nEMJLEqOiuKZrVz4aNYoDf/gDs6+7jjG9e5Pq7c6sX3F34bGpdauB2VrrXDf/fBEIHO3Wuwpg+lR4\n913Yu9fenDzNMeMxLwJ+2Qtbt5pdUsJ9Uq05j6FAXKmJDx2CsjLbUjotrvMdQ6zCY3g4tGhhTz7C\nyH4IwhNNnPceXNgNxo6F7Gzv5rHmUSizCuulA6HYyik1FQYMOP7zhBCuZN0qRCBqdgH0fc15vfx+\n2PmJffkIIYQNIsPCOK9tW165+GJmXXedrbm4u/Do2rq93s0/WwSKGKvwWAgsnmeKcAcP2pmRZ9XV\nQMlWEx9Ih9lfmWJrUZG9eQWaxi7FlrgDztgfdz3WlMOBH00cmwFjHoRx4+DKKyE01N7cgl1UKnT5\ni3WhIf9Zs+vRm/KXm1mTAJWRsNflcKULL5Q/I0LUn6xbhQhUbW49+v/X866DlVNtTUkIIewSYnM3\nlLsLj67v8L38Tkz4DceOx1igqtDEhYW2peNxpdvN7EGAqhRzGxICSUm2pRSQXA+YidjqjP2x8Hjg\nB6iz2sXTzzFts40amcNyhP3aj4U4a47o/vmw6zPvvXZdDSy53Rw+pIH9l4C2Wie6dZNWfCFOjaxb\nhQhkXf8KrX8LFcC8anj6Blg72+akhBAi+Li78LjSJW5z3EeJ4OZaeKw+bOJALjw62qw1UJFg4qQk\n2ZXkbjEtnH+2wlabAg3ADj+cJeraZp1+jn15iGMLjYBezzqvl42DqsPeee11T0P+MhMfag2lHUwc\nHw8XXOCdHIQIHLJuFSKQKQV9X4e8PnAYM+boqSsgZ6HdmQkhRFBxa+FRa70RWIwZ0n22UirGnT9f\nBAhHcSiG4Njx6Cg8lgOh1i7HlBTb0glojQeb2/BKiLbmPO7Z43/zNPc5DpZRkDbc1lTEcTT/DTQ9\n38Tlu2HlQ55/zYNLzGxHMKecD3gK4uLN9W9+A9HRns9BiAAi61YhgkBIOIz7FjLbmeuyMnj8Qtiz\n1t68hBAiiLh7xyPAw0At0Ah41AM/X/i72ExzGwHoYhMXFNiVjec5TrQuASKtgqMUHj0jbYgzTjls\nWpOHD4e6OvtyOlUV+6HA2oST1NPMFBS+Ryno+yqEWW3OW16DfXM893rVJfDTtaBrzXWnR6DPlXDH\nHXDOOdKGL0TDybpViEAXnQCPzoemzc314UJ47GzI32lvXkIIESTcXnjUWn8P/Anz6fEDSikvbAMR\nfiW2pblVQIRVeDx8GLS2LSWPKtpkbotxFh5TpZjkEY4djwDt9sC118KgQRAVZV9Op8q1eNVU2qx9\nWmwGdH/Keb3wBlM41hoWLYKZM93zOlrDkjuch1Sl9IOu1sD8xETzZ1wI0SCybhUiSCSkm+JjsrUG\nP5AHfxsMJQF8wKUQQvgIT+x4RGv9NHALUA08oZT6WSl1i1KqrVJKesGCXWgURKWbOMJqsa6theJi\n+3LyJMeOx4oECLX++MuOR8+IbwvRTU18YIFzzqM/2fuVM04fYV8eon7a3+X871S+FxbeBNOnwezZ\n8PPPsGLF6b/G+gmw4wMTh8XBwPdM65gQwi1k3SpEkGjcGv7yDcRbM9dzd8Ck4VBbYW9eQggR4Nxe\neFRK1SqlaoF/A+GYT5B7AW8AG4ESx2Pq+eWHlQNxUo45jwmF0KEtDBhgWhcDTXWRKUYANGoFycnm\nRGvZ8egZSjl3PdaUQIEbij7epOtgr3XaYm00xPa2Nx9xcioEBrwLUU3M9d7ZUP2F8/4vvoCtW4/9\n3PrY9Z+j50cOeMcU2IUQbiHrViGCTMse8McZZi5yI6D5GvjxKqj1s3ngQgjhRzyx41H96lZbX+o0\nvkSgcRQe2wMX94fzzjOnsgYaR5s1wOB+cM898Mc/QmysfTkFuiYu7db759uXR0MUrISKPBOXnQET\nX4DJk/3zZO5gEp0OA98HZZ1UX/sONLdat+rqYOpUyM099Z+771tYcDXmf6FAl0eh5eVuSVkIcYSs\nW4UINu2GwP99AkOjIQrY/QX8dJ1/dsoIIYQf8EirNUcv4mQRJv6Xo/AIULLNvjw8rdil8BhvHf4Q\nGhqYuzt9RROXA2b8rfC4Z5YzLmtrZvvl5kJEhH05ifpJHwFn/Mt5Hf0SNNpt4spKmDIFtp3Cv3W7\n/wvfX2J2YGwFwi9zznUUQribrFuFCDadL4JzZpoRUAC7PjXjUupq7c1LCCECUJgHfubfPPAzRaCJ\ny3LGpQFceCza6IwTOtiXRzBJzDaH+FQeggM/mPZl5anPWNxsr1V4rAMKU8xb37g4SE+3MytRX+3u\nNB+krP+n+VgveTKUXQGVnaGqCt57Dy69FLp1O/7P0NqckP3zWKiuhRVAYQdQvWBXLrRq5a1fjRDB\nQtatQgSr9OFw1nSYfynUVZl5yqFR0O8N/1k7CiGEH3B74VFrLQs4cXKxLoXHQN7x6Fp4jJfCo1eo\nEDPnMXc6VBVA4S+QdIJCj6+oKoCDC01c0RqU1Y7fpo3skPUnPZ4GtDkQJgxo+Rls3gY1QyE8+cRF\n5Ir9sPT3sONTyAV+ASI6QcuRUFNrdkxK4VEIt5J1qxBBrtn5cOZU+GEU6BrIeRNCI+GMl2T9JYQQ\nbiIf5Qh7xAVJ4dHRaq1CIa61vbkEE9c5j/vmwe7dsGAB5OXZltJJ7f3G7M4EqOju/H5bOUjErygF\nPZ6Bbo8DCkKB9stBvQxtt0NM2f8+pyQHVv0Z3sqCLz+Fr4ClQEw/aDkKomJg1CgYMuR/nyuEEEKI\n09PiUhj0gXOX4+ZX4Os7zJxmIYQQp80TrdZCnFxsBqaPVAduq7XWzsJjbBaEypw+r3EtPC6aATvy\nTVxdDWlp9uR0Mo42aw0UWLviQkKk8OiPlIIuf4Tk3rDwetP236kCaifDjMmQkG19EKGhZKtzZ/Re\nYBOmzavVJWZsQLt2cMEFkJxs4y9ICCGECHCtrjRzlRfeADs1THsDthXB7R+Y9ZgQQogGk8KjsEdo\nFEQ3g/LdgbvjsXw31JSaWOY7elej7hCRZNqXQ34GPdB8ir1tGwwdand2/0vXwZ7ZJi6Lhupksx+9\nVSuIjrY1NXEamp0PF2+E1Y/ClldBWwPri9abr19LDYXknpA2FDr1hH79oHVrafUSQgghvCHrOsg/\nBNPuNR8Ef/Ox2Uhwx4dSfBRCiNMghUdhn7gsU5yrPAAlh6C0BuLjISbG7szcw3W+Y0w7+/IIRiGh\nkDYcdn0G4YchuhwqYmHXLnPCcGSk3RkerWAVVOwzcVhfCI+E2lpo397evMTpi0yBPi9Cp4dg+3uw\naxoUroK6anN/SCQk9TBzHJuNgr1VpuAcG2tv3kIIIUQw6n0PXLsX3n/KXH87FWpr4K5PpPgohBAN\ndEqFR6XUUVPttdY7T/YYdzjW64gAEJsFB36EHODxP0NUE7jsMujRw+7M3MPRZl0JvLcFfnoOunSB\nESNsTStopI8whUeAxAOm8FhXB9u3Qwcf24G6e6YzPvNqaHULbN0KzZvbl5Nwr9iW0Pn/zFddjdmN\nq0IgPBFCXP5X3Mi+FIUINLJuFUI0yOVPAgref9JcfzcNakfC3dOl+CiEEA1wqjset2M2nmPdHuv5\nro9xh+O9jvB3jgNmooD8AlN4LCy0NSW3cux4LAEiUsyvrbLS1pSCSvo5zjh6A5Bp4q1bfbDw+Lkz\nbnaR2ZHZqZN9+QjPCgmDqMZ2ZyFEMNiOrFuFEA1x+RMQGgZT/m6u58+Aut/AvTNMZ40QQoh6a+hH\nNsr6qs9j3PElApGj8BgLVFkFx0AsPBZj2i0BUlJsSyfoxLWG2EwThy4HrPl6W7faldGxleVC/jIT\nJ/WEWLdvvhFCiGAn61YhxKm79DG4+W/O6x+/hM+vN7O5hRBC1FtDCo/1WVDJokucXKxVeIzBtB0C\nFBTYlo7bOQqPZVEQFmdiKTx6j1Km3RogtBoSy0x86JBvFbhzZzjjFpfal4cQQgQmWbcKIRru4r/A\nrf8w68ouQPlHsPh3UFdrd2ZCCOE3TrUV5GY3PUYI547HcCCk2MS+VBA6HbWVULrdiptCmPWeJjXV\ntpSCUvo5sHWyieN3Q10faNPGzHr0FbkubdZSeBRCCHeSdasQ4vRd+AikpcKmu0DXQs6bUFsOA96B\nkHC7sxNCCJ93SoVHrfU77niMEABENzf/s66rNicPAxQVmdN8Q/18dkrxFo6MjKpMgUjMrykx0c6s\ngk/acMxGFg3pG+DWD80n1r6i6jDs/87EsRnQqLu9+QghRACRdasQwm163w6Nk2DBNab4uONDqC6G\nM6dCWLTd2QkhhE+TY7mEfUJCISbDxGGHQGvzVVRkb17uUCufQTMAACAASURBVGy1WdcBVfEmTkmR\nk/C8LSrVzE0EKFoFFfvszefX9swyhXeA5pf6VlFUCCGEEEI4tboSzpoOIZHmes9MmHehKUAKIYQ4\nLqmCCHs52q0jK0zLAgTGnEfHfMdSICzZxNJmbY9mFzjjPbPsy+NYHKdZ1wFhg0zhXQghhBBC+KYW\nv4Fhs5zz2/fPgzlnQ+UhW9MSQghfJoVHYS9H4TELuHIwPPAAZGXZmpJbFG8yt9HAb2+Giy6CHj1s\nTSloNb/YGe+eaV8ev1ZbBXu+NPHheJi+Bp5/HlatsjcvIYQQQghxfGnDYPgciEgy1/uXwuM9Yf9m\ne/MSQggfJYVHYS/HydbxQFI5xMUFRrupY8djGNB5CPTpA+3b25pS0EruA5HWbtN935iDf3zB/nlQ\nbY0VKO8NKtQcruTv802FEEIIIQJdal8YMR/C02AhsG4X/HEA7Fppd2ZCCOFzpPAo7BXnsruxJMe+\nPNzNUXiMbg7hcfbmEuxCQqHZhSauKYH98+3Nx2HnVHNbBxS0NHFYGLRrZ1tKQgghhBCinhp1gYGz\nocra+Zh/CP40GDZ8a29eQgjhY6TwKOwV61p43GZfHu5UeQiq8k2c0MHeXITha+3WtVWwa5qJD0dD\nqFV4bNsWIiPty0sIIYQQQtRf8x7wjwXQJM1clxTD3y6Cxe/am5cQQvgQKTwKe8UFYOHRsdsRpPDo\nK9LPBRVm4j0zoaoKNm2Cn36yJ59930KVdYhSeV8ICTdxdrY9+QghhBBCiIZJz4YnlkJGa3NdVQXP\n/hZmP2VrWkII4Suk8CjsFZkKYbEmLg2UwuN6ZxwvhUefEJEITc4ycUkOvPQEfPABfPstlJd7P5+d\nH5vbOqAw08RhYdBB/rwIIYQQQvidpJbwj+XQuZe5rq2DN/4Ppt1nb15CCOEDpPAo7KWUs926dAfo\nOnvzcYeiDc44UXaw+YxmLu3WsTvNbV0dbNx47Md7Sm0l5P7HxPmxENLCxO3bQ1SUd3MRQgghhBDu\nEZ0If1kIA88z1zFAwSRYdl9gvMcRQogGksKjsF+c1ZZQVwXle+zNxR0Ou+x4TJDCo89oebkzjl7s\njH/5xbt57P3KeZp18nBItAaSd+vm3TyEEEIIIYR7hUXA+C/h0lthEBANbJwEC641Hz4LIUQQCrM7\nASGIa2Nuy4DZnwKtoHVr6NHDzqwaztFqvTsalm+HxqXm1xMRYWtaQS8uE5L7QP5SCFkHUdVQEQ45\nOVBWBjEx3sljx4fOeNgYaHo+bN8OGRneeX0hhBBCCOE5ISFw42TYOgCW3AG61ozZqdgLZ02DyBS7\nMxRCCK+SHY/CfvFtzW01MG8urF4N2/x03mNNufOQnLw0mDMHPvoIqqvtzUsYGVeZWwWk7DVxXR2s\nX3/cp7hVVaGzzToyBdJHmMVp69YQGuqdHIQQQgghhOe1uRUGfw6h0eZ6/3z4qj8UbbI3LyGE8DIp\nPAr7OXY8xgJV+SYuKLAtndNSvAnQJq6yPs2MjvbebjpxYi1HOePoJc547VrvvP6Oj6G2wsQZ10Go\n7IIVQgghhAhYzS+Cs+dBVJq5LtkCX/eHvHl2ZiWEEF4lhUdhP8eOxzAgxJp9l59vWzqnxTHfsRqo\nSTRxaqo5REfYz9FuDaDWQkytibdtg5ISz79+zlvOuPVvPf96QgghhBDCXql94bwl0Kirua4qgLdH\nwIxH7c1LCCG8RAqPwn6xGaCscaMRhea2pASqquzLqaEc8x1LgMhUE6em2paOOIaj2q33QJMmMGyY\naXn2pMPr4ZB1qE2j7pDc07OvJ4QQQgghfENsKzjnR2h2IRwEfq6Fdx6DV0dDXa3d2QkhhEdJ4VHY\nLyTMFB8Bwg6AtlqV/bHd2lF4LAYiG5u4cWPb0hHH4NpunboA7rwTBg/2fDt8ztvOWHY7CiGEEEIE\nl/AEM/MxYiTUWd/75mN4bCCUH7Y1NSGE8CQpPArf4Gi3jqqA2jIT+2Ph0dFqXRwCkUkmlh2PviUu\nE5oMNnHpRucuRE+qq4ZtU0yswiDzOs+/phBCCCGE8C0hYTBmGlzzgHMU05ol8GBX2L3a3tyEEMJD\npPAofEOcVXiMAyqt+Y7+NuexrsY6XAaoaQrKOqVYCo++p/XNzth17qKn5P4HKvaZeG8/yDkAtdJW\nI4QQQggRlEb9E8ZPhgjroME9u+DhAbD0I3vzEkIID5DCo/ANjh2P8UCyhm7d/K9gV7od6qy5lGmZ\nkJ5uTrRu1MjOrMSxtBwFYbEm3vER1JR59vU2vWhui4E9rWHqVHjnHc++phBCCLdTSoUopVorpfoo\npY67UFFKtVRKxXszNyGEnxl0Czz2DSRb/5SUlcEz18LSZ5yjp4QQIgD4beFRKXWx3TkIN4prY26T\ngItawuWXQ/v2tqZ0yhxt1gBnD4UxY+DBBz1/aIk4deFx0OpKE1cXwc5PPfdaBath/3wT724BsVkm\n7tDBc68phBDC7ZRSvwO2A5uBRcA+pdSXSqkux3j4OcAspdRm6zHPeDFVIYS/aDcYJqyCDtaJ1x01\nbH4IFt8GtRX25iaEEG7izxWRR+xOQLiRY8cjQPEW+/I4HUUuhceEbHPrmN0ifE+b25zxphc898ny\npn+Z2wqgqIf5MxERAb17e+b1hBBCuJ1S6h/Aq0ALQFlfIcD5wBKl1DWuj9dav6m1PhO40XrM/d7N\nWAjhNxKbwWPL4KqboaP1vZw34duhULbbzsyEEMIt/Lnw2MTuBIQbxWVh1vBASQAUHhOz7ctD1E/q\nQEjqaeL8ZXBwkYm1hqoq97xG2R7noTLboyHe2hTTuzdERbnnNYQQQniUUmoA8DBQDrwPjAPGABOA\nTUAUMEUpde0xnu5nA6uFELYIC4er34RBH0JotPneocUw+ww4sMDe3IQQ4jT5ZeFRKdUByLQ7D+FG\noVEQ09LE/rrj0bXVOkHaaH2eUtDhHuf1hudhzRp44w2YPt09r7Fxkpn7WQ0c7guhkab1vn9/9/x8\nIYQQ3nAnsBJor7W+QWv9gtb6da31g1rrjsAoYB/wllLqHFszFUL4t8zRcO5PEJthriv2mZ2PGybJ\n3EchhN+ypfColNqvlKpt6BewjiPb40TAiLfmPFblQ1WBvbmcKq2dOx5jM5wHlwjfljEaIhubeOen\nMPNj2LMHNmyAAwdO72dX5sPmV0y8NRzizjBx166QmHh6P1sIIYQ3DQSu0FrvOdadWutpQDfgv8Cn\nSqke3kxOCBFgknrAef/P3n2HR1Xlfxx/n0knISQQAqGHSK8CggpRikgRERVZwQYogm3XxZ8F3XUB\nuyK66mJXUIoFcUVstEgQEFaRIr2GFjokhAQImfP7404aBBIgySTh83qe88zJmXPv/c4khJvvnPIb\nVOnkfG1PwtLh8ENvSN7j3dhERM6Dt0Y83gCcJHuNnPMpUtaE5FzncZP34jgfaYnOJiUAoQ3P3ldK\nDp9AqHefUzcZEPGnU7cWfv75ws69diycPApuILWts6GNywVXX31h5xURkeJ2wFq79WwdrLWHrLU3\nAW8BPxpjLjlbfxGRswqMgE4zofEI5+uTwNQZ8EhTWDvHq6GJiJwrryQerbWLgHHAc0D0eZQexR+1\nFLnSvMFMXhvLSOnQ4G/gW96pB30Hfp71HVetgt27z++cqbucxCM4a/Y8+SF06QJXXAEVK154zCIi\nUpxSCtrRWvsUMBqYZYypVXQhiUiZ5/KFls/D1d/CmmBIAg7uh391h+kjvR2diEiBeXONx/FAI2tt\nwnmUn4AdXoxdikKuxOMGSEmBvXu9F8+5yFzf8STgV9erocg5CqjoJB8BXCeh6urs5+bMOb/1dFb+\nCzLSnHq9+6FiA4iNha5a+ktEpBRabozpkvmFMaaSMeZGY0xIXp2tteOA4cD3QLViilFEyqrqveD+\nX6C657OMkydhwih4+RpIS/ZubCIiBeC1xKO1djlQ5QJOkec6O1KKhcRk1z+YDmPGwJQp3ovnXGSO\neNwNfLoUXnkF/vjDqyHJOWj49+xRjwHTwdczuGXDBme9x3NxaBls/sip+4VCk38UXpwiIuINzwNj\njTGZM27mAlOBr850gLX2a5ydr98p+vBEpMyr2RJeWQ0dema3LZ4DjzSEDfHei0tEpAC8vav1vAs4\n9uNCi0JKhpyJR+PZXObwYedTvZIuM/F4BGezkqNHwd/fqyHJOQioCE2ecOouC1XmZo90/OEHOH68\nYOdxn4RfB4N1O183HuGs0SMiIqWWtXY/0A94yRjzG9AUZ73xyHyO+wW4Ec3SEZHCEBAMf/8OhrwA\nfn5O255E+EcXiH9Bu16LSInl1cSjtfa8hwJZa98rzFikBPALgcCqnvoB59FaOFQKdrhOWuU8poaC\nbzmnHnnWv0ekpGn4CJSv59TL/QGhuyAgANq3z765y8+aMXDIM9K1QlNoOLxoYhURkWJlrV0HtMRZ\nv/FVnE1k+hfguNXAFcAHRRqgiFw8uj8Bz8VB1erO1+VPwrYn4Ze+cPygd2MTEcmDt0c8iuSWuc5j\nwGHI8IwyO3DAe/EUxLF9cMyzFmW6J3Hq46NNREobnwBo/aZTN0ClKXBnd2jXztmNOj/7f4WVT3uO\nd0G7D8FHo15FRMoKa63bWjvdWvuYtfav1toCrcVhrd1prR1a1PGJyEUkpj2MXQsdr4e2OH/Vb58G\nP7SEvfO9HZ2ISC5KPErJUr6+8xgCnPAkHEt64jFztKMbOOFJNlaq5CQfpXSp1g2i73Lq/kdh+UBI\nL8Ci3Ue3w/y+cCId/gRi/g4RbYsyUhERERG5mAWEwEPToec34O/5GyR1O8zpCCtHOUsAiYiUAKU2\n8WiM6eXtGKQIhDZwHssDx0tJ4vHwn85jCuDvWc+vcmWvhSMXqM1b2VOuD6+A+D6QnnLm/qk7IO5a\nOLAT4oHtNWFZPUhLK5ZwRUSk5NN9q4gUmRq9oedyiLza+dq6YeVImH01HNno1dBERKAUJx6BJ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0dur+u8B90qkn5rlmedE5mGNjmczEo9Z3FBERkZKhQY56QgGP2Zaj3rAQYzkrY0xNnBGWmaMe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\nMmrUKFasWFEk5///9u49Ourq3P/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x2477dc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "P1p=rho0\n",
    "psi01 = (basis(2,0)-basis(2,1))/np.sqrt(2.)\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "import matplotlib.gridspec as gridspec\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_title('$\\lambda=0.2 \\epsilon$, $\\gamma = 0.1 \\epsilon$, $k_{B}T=\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "\n",
    "fig.savefig(\"heom2.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Next try lets try some parameters where secular approximation should break, but Born-Markov is ok $\\gamma=10 \\epsilon$, $\\lambda = 0.5 \\epsilon$, $\\beta = 0.25\\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 530,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "eps = 1.0    # Tunnelling term\n",
    "Hsys =  0.5 * eps * sigmaz()\n",
    "#Coupling operator to the bath:\n",
    "sm = destroy(2).dag()\n",
    "Q = sigmax()\n",
    "\n",
    "\n",
    "gamma = 10.                # Cutoff frequency of DL spectral density\n",
    "lam = .5           # Coupling strength of DL spectral density\n",
    "\n",
    "temperature = 4.     # Temperature of environment\n",
    "\n",
    "tlist = np.linspace(0, 20, 800) #time steps\n",
    "\n",
    "psi0=(basis(2,0)+basis(2,1))/np.sqrt(2.)  #initial state of system.\n",
    "#psi0=basis(2,0)  #initial state of system.\n",
    "rho0=psi0*psi0.dag()\n",
    "\n",
    "Ncut = 20\n",
    "#K is the matsubara terms; if temperature < system energy,  N>1\n",
    "Nk=3\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 531,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def J0(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma * (energy)/(np.pi * ((energy**2) + (gamma**2)))\n",
    "def nbs(energy,Temperature):\n",
    "    beta=1./Temperature\n",
    "    \n",
    "    return 1./(np.exp(energy*beta) - 1.)\n",
    "\n",
    "#spectral density/w at w=0\n",
    "def J02(energy):\n",
    "    #underdamped brownian oscillator\n",
    "    return 2 * lam * gamma /(np.pi * ((gamma**2)))\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The relaxation time is roughly \n",
    "$\\tau_R \\approx 1/\\pi J(\\epsilon)n(\\epsilon)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 532,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.23411209098\n"
     ]
    }
   ],
   "source": [
    "print 1/(np.pi*J0(1.0)*(nbs(1.0,temperature)+1.))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest environment correlation times are\n",
    "$\\tau_E \\approx 1/\\gamma,  1/2 \\pi k_B T $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 533,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1\n",
      "0.039788735773\n"
     ]
    }
   ],
   "source": [
    "print 1/gamma\n",
    "print 1/(2 * np.pi * temperature)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system time scale is $\\tau_S \\approx 1/\\epsilon$, so now $\\tau_R \\approx \\tau_S$, so Secular appoximation should break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 535,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Configure the solver\n",
    "from qutip.nonmarkov.heom import HSolverDL\n",
    "hsolver = HSolverDL(Hsys, Q, lam, temperature, Ncut, Nk, gamma, stats=True)\n",
    "resultHEOM = hsolver.run(rho0, tlist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 539,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#lets compare to the BMS solution,\n",
    " \n",
    "resultMEsec = mesolve(Hsys, rho0, tlist, [np.sqrt(2*np.pi*J0(1.0)*(nbs(1.0,temperature)+1.))*sm,np.sqrt(2*np.pi*J0(1.0)*nbs(1.0,temperature))*sm.dag()], [])\n",
    "resultMEnonsec = Lnonsec(Hsys, Q, tlist, rho0, temperature, [])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "<img src=\"heom4.png\" width=800 />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 541,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7oG0/58+eTWkIdMbIo42N+Y5QkiSl2ONxvCophcr6pDxI4vHqRYtoqqwEYOO+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\nQ5bv2rWrunbtqr/+9a+aNGmS7r33Xi1btkzdunULm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      "text/plain": [
       "<matplotlib.figure.Figure at 0x24c80780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "P1p=rho0\n",
    "psi01 = (basis(2,0)-basis(2,1))/np.sqrt(2.)\n",
    "\n",
    "P12p=psi0*psi01.dag()\n",
    "\n",
    "P1HEOM=expect(resultHEOM.states,P1p)\n",
    "P12HEOM=expect(resultHEOM.states,P12p)\n",
    "\n",
    "\n",
    "P1ME=expect(resultMEsec.states,P1p)\n",
    "P12ME=expect(resultMEsec.states,P12p)\n",
    "\n",
    "\n",
    "P1MENS=expect(resultMEnonsec.states,P1p)\n",
    "P12MENS=expect(resultMEnonsec.states,P12p)\n",
    "\n",
    "import matplotlib.gridspec as gridspec\n",
    "fig = plt.figure(figsize=(15,6))\n",
    "\n",
    "gs1 = gridspec.GridSpec(1, 2)\n",
    "gs1.update(wspace=.5, hspace=1.3) # set the spacing between axes. \n",
    "########################################################################\n",
    "axes1 = plt.subplot(gs1[0])\n",
    "\n",
    "axes1.plot(tlist, P1HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes1.plot(tlist , P1ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation secular\")\n",
    "axes1.plot(tlist , P1MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation nonsecular \")\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_ylabel(r'$\\rho_{11}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "axes1.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "\n",
    "ticks = [0,0.5,1.0]\n",
    "axes1.set_yticks(ticks)\n",
    "axes1.set_yticklabels([\"0\",\"0.5\",\"1.0\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes1.set_xticks(ticks)\n",
    "axes1.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "axes1.legend(loc=4, fontsize=12)\n",
    "\n",
    "\n",
    "\n",
    "axes1.set_title('$\\lambda=0.5 \\epsilon$, $\\gamma = 10 \\epsilon$, $k_{B}T=4\\epsilon $ ',fontsize=24,y=1.05,x=1.0)\n",
    "\n",
    "\n",
    "\n",
    "axes2 = plt.subplot(gs1[1])\n",
    "\n",
    "\n",
    "axes2.plot(tlist, P12HEOM,  color=\"teal\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Hierarchy\")\n",
    "axes2.plot(tlist , P12ME,  color=\"orange\", ls=\"-\", alpha=1, linewidth=2.0,label=\"Master equation Secular\")\n",
    "axes2.plot(tlist , P12MENS,  color=\"red\", ls=\"--\", alpha=0.5, linewidth=2.0,label=\"Master equation non-secular\")\n",
    "\n",
    "axes2.set_xlabel(r'$\\epsilon t$', fontsize=28)\n",
    "axes2.set_ylabel(r'$\\rho_{12}$ in $\\sigma_x$ basis', fontsize=28)\n",
    "\n",
    "ticks = [0,-.1,-.2]\n",
    "axes2.set_yticks(ticks)\n",
    "axes2.set_yticklabels([\"0\",\"-0.1\",\"-0.2\"], fontsize=24);\n",
    "\n",
    "ticks = [.0,10.,20.]\n",
    "axes2.set_xticks(ticks)\n",
    "axes2.set_xticklabels([\"0\",\"10\",\"20\"], fontsize=24);\n",
    "\n",
    "#axes1.set_xlim(-1.2, 1.2);\n",
    "axes2.set_ylim(-0.25,0.);\n",
    "\n",
    "axes2.legend(loc=0, fontsize=18)\n",
    "\n",
    "\n",
    "\n",
    "fig.savefig(\"heom4.png\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The HEOM and FMO\n",
    "\n",
    "The HEOM method became slightly more famous after being applied to the Fenna-Matthews-Olsen complex (Ishizaki and Fleming, PNAS, 2009).\n",
    "\n",
    "<img src=\"fmo.png\" width=600/>\n",
    "\n",
    "Figure adapted from N. Lambert et al., Nat. Phys. (2013)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The HEOM and FMO\n",
    "\n",
    "In a minimal model, we can write the Hamiltonian of the $7$ sites as,\n",
    "\n",
    "$$ H = \\sum_{j=1}^7 \\epsilon_j |j\\rangle\\langle j| + \\sum_{j,j'} J_{j,j'} \\left(|j\\rangle \\langle j'| + c.c \\right)$$\n",
    "\n",
    "This can be reconstructed via a combination of ab initio model and spectroscopy to be, e.g., \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "Quantum object: dims = [[7], [7]], shape = (7, 7), type = oper, isherm = True\\begin{equation*}\\left(\\begin{array}{*{11}c}200.0 & -87.700 & 5.500 & -5.900 & 6.700 & -13.700 & -9.900\\\\-87.700 & 320.0 & 30.800 & 8.200 & 0.700 & 11.800 & 4.300\\\\5.500 & 30.800 & 0.0 & -53.500 & -2.200 & -9.600 & 6.0\\\\-5.900 & 8.200 & -53.500 & 110.0 & -70.700 & -17.0 & -63.300\\\\6.700 & 0.700 & -2.200 & -70.700 & 270.0 & 81.100 & -1.300\\\\-13.700 & 11.800 & -9.600 & -17.0 & 81.100 & 420.0 & 39.700\\\\-9.900 & 4.300 & 6.0 & -63.300 & -1.300 & 39.700 & 230.0\\\\\\end{array}\\right)\\end{equation*}"
      ],
      "text/plain": [
       "Quantum object: dims = [[7], [7]], shape = (7, 7), type = oper, isherm = True\n",
       "Qobj data =\n",
       "[[ 200.   -87.7    5.5   -5.9    6.7  -13.7   -9.9]\n",
       " [ -87.7  320.    30.8    8.2    0.7   11.8    4.3]\n",
       " [   5.5   30.8    0.   -53.5   -2.2   -9.6    6. ]\n",
       " [  -5.9    8.2  -53.5  110.   -70.7  -17.   -63.3]\n",
       " [   6.7    0.7   -2.2  -70.7  270.    81.1   -1.3]\n",
       " [ -13.7   11.8   -9.6  -17.    81.1  420.    39.7]\n",
       " [  -9.9    4.3    6.   -63.3   -1.3   39.7  230. ]]"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Multiple by h*c*100 to get joules from inverse centimeters\n",
    "idFMO = Qobj([[200, -87.7, 5.5, -5.9, 6.7, -13.7, -9.9],\n",
    "                    [-87.7, 320, 30.8, 8.2, 0.7, 11.8, 4.3],\n",
    "                    [5.5, 30.8, 0, -53.5, -2.2, -9.6, 6.0],\n",
    "                    [-5.9, 8.2, -53.5, 110, -70.7, -17.0, -63.3],\n",
    "                    [6.7, 0.7, -2.2, -70.7, 270, 81.1, -1.3],\n",
    "                    [-13.7,11.8, -9.6, -17.0 ,81.1, 420, 39.7],\n",
    "                    [-9.9, 4.3, 6.0, -63.3, -1.3, 39.7, 230]])\n",
    "idFMO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Using the HEOM, and assuming the Drude-Lorentz spectral density describes the $7$ independant baths, one finds, e.g., (T = 300 K, $1/\\gamma = 166$ fs, $1/\\lambda=6.6$ ps)\n",
    "\n",
    "from A. fruchtman, N. Lambert, E. Gauger, Scientific Reports 2016:\n",
    "\n",
    "<img src=\"fmo2.png\" />\n",
    "\n",
    "Dashed lines: HEOM, solid lines: quasi-non-Markov master equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Generalizing the spectral density\n",
    "\n",
    "The Drude-Lorentz spectral density is convenient because we can <span style=\"color:red\">analytically expand it as exponentials </span>.\n",
    "\n",
    "In other cases, we can <span style=\"color:red\">numerically calculate</span> the correlation functions, and then <span style=\"color:red\">numerically fit</span> them to a sum of exponentials.\n",
    "\n",
    "As a simple example, we can bench-mark against the analytically solvable \"pure dephasing model\", i.e., we set the coupling operator equal to the system Hamiltonian \n",
    "\n",
    "(see A. fruchtman, N. Lambert, E. Gauger, Scientific Reports 2016 for more interesting examples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"ohmic.png\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"superohmic.png\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Conclusions\n",
    "\n",
    "The study of open quantum systems lets us model how a system interacts with it environment in various limits:\n",
    "\n",
    "- Weak coupling, no bath memory (Markov), and weak damping gives us the Lindblad Born-Markov-Secular master equation\n",
    "$$\\tau_E \\ll \\tau_S \\ll \\tau_R$$\n",
    "- We can still solve the non-secular case if need be\n",
    "$$\\tau_E \\ll \\tau_S, \\tau_R$$\n",
    "- Exact methods (HEOM, reaction coordinate, etc) give insight into strongly correlated system-bath problems\n",
    "\n",
    "$$\\tau_E \\approx \\tau_S \\approx \\tau_R$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "#Calculates  generic non-secular master equation\n",
    "\n",
    "\n",
    "import time\n",
    "import warnings\n",
    "import numpy as np\n",
    "import scipy.sparse as sp\n",
    "from numpy import matrix\n",
    "from numpy import linalg\n",
    "from qutip import spre, spost, sprepost, thermal_dm, mesolve, Odeoptions\n",
    "from qutip import tensor, identity, destroy, sigmax, sigmaz, basis, qeye, dims\n",
    "from qutip.ui.progressbar import BaseProgressBar, TextProgressBar\n",
    "def Lnonsec(Hsys, Q, tlist, initial_state, Temperature,\n",
    "            return_vals, eigen_sparse=False, options=None,progress_bar=None):\n",
    "    \n",
    "\n",
    "    if progress_bar is None:\n",
    "        progress_bar = BaseProgressBar()\n",
    "    elif progress_bar is True:\n",
    "        progress_bar = TextProgressBar()\n",
    "        \n",
    "    if options is None:\n",
    "        options = Options()\n",
    "    output = None\n",
    "    \n",
    "    dot_energy, dot_state = Hsys.eigenstates(sparse=eigen_sparse)\n",
    "    deltaE = dot_energy[1] - dot_energy[0]\n",
    "    \n",
    "    \n",
    "    #Reaction coordinate hamiltonian/operators\n",
    "    \n",
    "    dimensions = dims(Q)\n",
    "    Nmax = dimensions[1][0]        #hilbert space \n",
    "    #Nmax = 2       #hilbert space \n",
    "    \n",
    "    H = Hsys\n",
    "    L=0\n",
    "    PsipreEta=0\n",
    "    PsipreX=0\n",
    "\n",
    "    all_energy, all_state = H.eigenstates(sparse=eigen_sparse)\n",
    "    Apre = spre(Q)\n",
    "    Apost = spost(Q)\n",
    "    for j in range(Nmax):\n",
    "        for k in range(Nmax):\n",
    "            A = Q.matrix_element(all_state[j].dag(), all_state[k])\n",
    "            #A = sh.matrix_element(all_state[j].dag(), all_state[k])\n",
    "            delE = (all_energy[j] - all_energy[k])\n",
    "            if np.absolute(A) > 0.0:\n",
    "                if abs(delE) > 0.0:\n",
    "                    #X = (0.5 * np.pi * gamma*(all_energy[j] - all_energy[k])\n",
    "                    X = (0.5  * np.pi * J0(all_energy[j] - all_energy[k])\n",
    "                         * (np.cosh((all_energy[j] - all_energy[k]) /\n",
    "                            (2 * Temperature))\n",
    "                         / (np.sinh((all_energy[j] - all_energy[k]) /\n",
    "                            (2 * Temperature)))) * A)\n",
    "                    #eta = (0.5 * np.pi * gamma *\n",
    "                    eta = (0.5 *  np.pi *\n",
    "                           J0(all_energy[j] - all_energy[k]) * A)\n",
    "                    PsipreX = PsipreX + X * all_state[j]*all_state[k].dag()\n",
    "                    PsipreEta = PsipreEta + (eta * all_state[j]\n",
    "                                             * all_state[k].dag())\n",
    "                else:\n",
    "                    #X =0.5  * np.pi* J0(0.) * A * 2 * Temperature\n",
    "                    X =0.5  * np.pi* J02(0.)* A  * 2 * Temperature\n",
    "                    #X =0.5 * np.pi * gamma * A * 2 * Temperature\n",
    "                    PsipreX=PsipreX+X*all_state[j]*all_state[k].dag()\n",
    "\n",
    "    A = Q\n",
    "    L = ((-spre(A * PsipreX)) + (sprepost(A, PsipreX))\n",
    "         +(sprepost(PsipreX, A)) + (-spost(PsipreX * A))\n",
    "         +(spre(A * PsipreEta)) + (sprepost(A, PsipreEta))\n",
    "         +(-sprepost(PsipreEta, A)) + (-spost(PsipreEta * A)))           \n",
    "\n",
    "    #Setup the operators and the Hamiltonian and the master equation \n",
    "    #and solve for time steps in tlist\n",
    "    psi0 = ( initial_state)\n",
    "    output = mesolve(H, psi0, tlist, [L], return_vals, options=options,progress_bar=progress_bar)\n",
    "    \n",
    "    return output\n",
    "              "
   ]
  }
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