{ "cells": [ { "cell_type": "markdown", "metadata": { "tags": [ "hide_input" ] }, "source": [ "$\\newcommand{\\Mn}{M_n(\\mathbb{C})}$\n", "$\\newcommand{\\Mq}{M_2(\\mathbb{C})}$\n", "$\\newcommand{\\Mk}{M_k(\\mathbb{C})}$\n", "$\\newcommand{\\Mm}{M_m(\\mathbb{C})}$\n", "$\\newcommand{\\Mnm}{M_{n \\times m}(\\mathbb{C})}$\n", "$\\newcommand{\\Mnp}{M_n^+(\\mathbb{C})}$\n", "$\\newcommand{\\ra}{\\,\\rightarrow\\,}$\n", "$\\newcommand{\\id}{\\mbox{id} }$\n", "$\\newcommand{\\ot}{ {\\,\\otimes\\,} }$\n", "$\\newcommand{\\Cd}{ {\\mathbb{C}^d} }$\n", "$\\newcommand{\\Rn}{ {\\mathbb{R}^n} }$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This section closely follows Dariusz Chruściński's Lecture Notes presented at the school \"Open Quantum Systems\", Torun, June 20-24, 2012 and published as [*On time-local generators of quantum evolution*, Open Syst. Inf. Dyn. **21**, 1440004 (2014)](https://doi.org/10.1142/S1230161214400046)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.1. The structure of quantum states " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we discussed in **[Chapter 1](introduction.html)**, only pure states can be represented as vectors in Hilbert space, but that does not apply to all physically possible states. As an example, consider the situation depicted in the following figure." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "
" ], "image/svg+xml": "\n\n\n \n \n \n \n 2021-05-10T15:12:34.475844\n image/svg+xml\n \n \n Matplotlib v3.4.2, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", "image/png": 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}, "metadata": {}, "execution_count": 1 } ], "source": [ "from qiskit import QuantumRegister, QuantumCircuit\n", "# Quantum register\n", "q = QuantumRegister(2, name='q')\n", "\n", "# Quantum circuit\n", "bell = QuantumCircuit(q)\n", "\n", "# Create a Bell state\n", "bell.x(q[0])\n", "bell.x(q[1])\n", "bell.h(q[0])\n", "bell.cx(q[0], q[1])\n", "\n", "# Draw circuit\n", "bell.draw(output = 'mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state of the two qubits in the circuit is the Bell state $| \\psi^- \\rangle = \\frac{1}{\\sqrt{2} } \\left( |01\\rangle - |10\\rangle \\right)$, which is maximally entangled. If we were to describe the state of either of the two qubits alone, no single vector in their corresponding Hilbert spaces would faithfully characterize it. Indeed, it is easy to see that, regardless of which single-qubit unitary we apply to e.g. $q_0$, the probability of its measurement yielding zero is $1/2$, contrarily to the predictions for any pure state $\\alpha |0 \\rangle + \\beta | 1 \\rangle$. Instead, these probabilities are consistent with the situation in which one tosses a fair coin and prepares the qubit in states $|0\\rangle$ or $|1\\rangle$ depending on the outcome. In fact, *any* quantum state can be represented in terms of a statistical mixture, as in the previous example.\n", "\n", "Mathematically, statistical mixtures are represented by density operators. From any pure state $| \\psi \\rangle$, one can construct the corresponding projection operator $| \\psi \\rangle \\langle \\psi |$, which promotes the mathematical description of the state from vector to operator, but is otherwise equivalent. The reason why using operators becomes essential is that they admit a *convex sum*, that is, the operator $p_1 | \\psi_1 \\rangle \\langle \\psi_1 | + p_2 | \\psi_2 \\rangle \\langle \\psi_2 |$ results in a physical state if $p_1 + p_2 = 1$ and $| \\psi_1 \\rangle$, $| \\psi_2 \\rangle$ are normalized. Therefore, they can accommodate statistical mixtures of states in a very natural way. As a final remark, one usually finds the terms density matrix and density operator. While density matrix in principle refers to the matrix representing the density operator in some particular basis, it is common to use both terms indistinctly." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let us define the concept formally. Consider a quantum system living in a finite-dimensional Hilbert space $\\mathcal{H}$ isomorphic to $\\mathbb{C}^n$. Fixing an orthonormal basis $\\{e_1,\\ldots,e_n\\}$ in $\\mathcal{H}$ any linear operator in $\\mathcal{H}$ may be identified with an $n \\times n$ complex matrix, i.e. an element from $M_n(\\mathbb{C})$. A mixed state of such system is represented by a density matrix, i.e. a matrix $\\rho$ from $ M_n(\\mathbb{C})$ such that $\\, \\rho \\geq 0$ (that is, it has real non-negative eigenvalues) and ${\\rm Tr}\\, \\rho=1$. The space of states $\\mathfrak{S}_n$ of the $n$-level quantum system defines an $(n^2-1)$-dimensional convex set. Pure states correspond to rank-1 projectors $|\\psi \\rangle \\langle \\psi|$ and define extremal elements of $\\mathfrak{S}_n$. Any mixed state $\\rho$ can be decomposed as\n", "\n", "\\begin{equation}\n", " \\rho = \\sum_k w_k |\\psi_k \\rangle \\langle \\psi_k| \\ ,\n", "\\tag{2.1} \n", "\\end{equation}\n", "\n", "with $w_k > 0$ and $\\sum_k w_k =1$, i.e. $w_k$ provides a probability distribution. It should be stressed that the above decomposition is highly non-unique.\n", "\n", "To illustrate the concept of density operator let us consider the following example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> A 2-level system (qubit) living in $\\mathbb{C}^2$. Any hermitian operator $\\rho$ may be decomposed as follows\n", "> \n", "> \\begin{equation}\n", " \\rho = \\frac 12 ( \\mathbb{I}_2 + \\sum_{k=1}^3 x_k \\sigma_k) \\ ,\n", "\\tag{2.2}\n", "\\end{equation}\n", "> \n", "> where $\\mathbf{x}=(x_1,x_2,x_3) \\in \\mathbb{R}^3$ and $\\{\\sigma_1,\\sigma_2,\\sigma_3\\}$ are Pauli matrices. As usual $\\mathbb{I}_n$ denotes the unit matrix in $M_n(\\mathbb{C})$. It is, therefore, clear that $\\rho$ is entirely characterized by the Bloch vector $\\mathbf{x}$.\n", "This representation already guaranties that ${\\rm Tr}\\, \\rho=1$. Hence, $\\rho$ represents a density operator if and only if the corresponding eigenvalues $\\{\\lambda_-,\\lambda_+\\}$ are non-negative. One easily finds\n", "> \n", "> \\begin{equation}\\label{}\n", " \\lambda_- = \\frac 12 (1 - |\\mathbf{x}|) \\ , \\ \\ \\ \\lambda_+ = \\frac 12 (1 + |\\mathbf{x}|) \\ ,\n", "\\tag{2.3}\n", "\\end{equation}\n", "> \n", "> and hence $\\rho \\geq 0$ if and only if $|\\mathbf{x}|=\\sqrt{x_1^2 + x_2^2 + x_3^2} \\leq 1$. This condition defines a unit ball in $\\mathbb{R}^3$ known as a Bloch ball. A state is pure if $\\rho$ defines a rank-1 projector, i.e. $\\lambda_-=0$ and $\\lambda_+=1$. This shows that pure states belong to Bloch sphere corresponding to $|\\mathbf{x}|=1$. Unfortunately, this simple geometric picture is much more complicated if $n >2$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For any $A \\in M_n(\\mathbb{C})$ we denote by $||A||_1 := {\\rm Tr} |A| = {\\rm Tr}\\sqrt{AA^\\dagger}$ the trace-norm of $A$. If $\\lambda_1,\\ldots\\lambda_n$ are the (necessarily nonnegative) eigenvalues of $AA^\\dagger$, then\n", "$$ ||A||_1 = \\sqrt{\\lambda_1} + \\ldots + \\sqrt{\\lambda_n} \\ . $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The space of states $\\mathfrak{S}_n$ is equipped with a natural metric structure: given two states $\\rho,\\sigma \\in \\mathfrak{S}_n$ one defines the corresponding distance\n", "\n", "\\begin{equation}\n", " D[\\rho,\\sigma] = \\frac 12 \\,||\\rho - \\sigma||_1\\ .\n", "\\tag{2.4}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This quantity measures distinguishability between $\\rho$ and $\\sigma$. It is clear that $D[\\rho,\\sigma] =0$, i.e. $\\rho$ and $\\sigma$ are indistinguishable, if and only if $\\rho=\\sigma$. Note, that if $\\rho$ and $\\sigma$ are orthogonally supported, then\n", "$$ D[\\rho,\\sigma] = \\frac 12 ( ||\\rho||_1 + ||\\sigma||_1) = 1\\ , $$\n", "since $||\\rho||_1=1$ for any density matrix $\\rho$. In this case $\\rho$ and $\\sigma$ are perfectly distinguishable. Hence\n", "\n", "\\begin{equation}\n", " 0 \\leq D[\\rho,\\sigma] \\leq 1\\ .\n", "\\tag{2.5} \n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In particular, if $\\rho$ and $\\sigma$ are two states of a qubit and $\\mathbf{x}$ and $\\mathbf{y}$ are corresponding Bloch vectors then\n", "\n", "\\begin{equation}\n", " D[\\rho,\\sigma] = \\frac 12 \\, |\\mathbf{x} - \\mathbf{y}| \\ ,\n", "\\tag{2.6}\n", "\\end{equation}\n", "\n", "reproduces the standard Euclidean distance in $\\mathbb{R}^3$. For more information about the structure of quantum states see [7,8]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When considering multipartite systems, one often needs to calculate the reduced state of some of its parts. This is done via the so-called partial trace. Suppose that we have a bipartite state, with parts $A$ and $B$, in a joint state $\\rho_{AB}$. The state $\\rho_A$ of part $A$ is obtained by tracing out over $B$'s degrees of freedom,\n", "\\begin{equation}\n", "\\rho_A = \\mathrm{Tr}_{B} \\left(\\rho_{AB}\\right) = \\sum\\limits_{i=1}^{D} \\langle i | \\rho_{AB} | i \\rangle,\n", "\\end{equation}\n", "where $\\left\\lbrace | i \\rangle \\right\\rbrace$ is any orthogonal basis of $B$'s Hilbert space and $D$ is its dimension." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2.1.1 \n", "\n", "Consider the following circuit" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "
" ], "image/svg+xml": "\n\n\n \n \n \n \n 2021-05-10T15:12:39.783209\n image/svg+xml\n \n \n Matplotlib v3.4.2, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", "image/png": "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\n" }, "metadata": {}, "execution_count": 2 } ], "source": [ "# Quantum register\n", "q = QuantumRegister(2, name='q')\n", "\n", "# Quantum circuit\n", "entangled = QuantumCircuit(q)\n", "\n", "# Entangled state\n", "entangled.h(q[0])\n", "entangled.s(q[0])\n", "entangled.cx(q[0], q[1])\n", "entangled.h(q[0])\n", "\n", "# Draw circuit\n", "entangled.draw(output='mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Write the resulting two-qubit quantum state $\\rho_{q_0,q_1} = | \\psi \\rangle \\langle \\psi |$.\n", "2. Compute the partial trace to obtain the reduced density matrix $\\rho_{q_0}$ of $q_0$.\n", "3. Determine the Bloch vector $\\mathbf{x}$ of $\\rho_{q_0}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.2. Positive and completely positive maps " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In many situations, one needs to describe the change of the state of the system, for instance, when studying temporal evolution or to characterize the effect of a measurement. The general (linear) mathematical object used to map operators into operators is called a *map*. However, not all maps map states into states. A map which does is called a *quantum channel*. Notice that a channel need not be a unitary transformation in general, but can map a pure state into a statistical mixture. For example, consider the following circuit, which implements a channel on qubit $q_0$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "
" ], "image/svg+xml": "\n\n\n \n \n \n \n 2021-05-10T15:12:42.320821\n image/svg+xml\n \n \n Matplotlib v3.4.2, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", "image/png": "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\n" }, "metadata": {}, "execution_count": 3 } ], "source": [ "# Quantum register\n", "q = QuantumRegister(2, name='q')\n", "\n", "# Quantum circuit\n", "channel = QuantumCircuit(q)\n", "\n", "# CNOT gate\n", "channel.cx(q[0], q[1])\n", "\n", "# Draw circuit\n", "channel.draw(output='mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the initial state of $q_0$ is pure and in a coherent superposition of $|0\\rangle$ and $|1\\rangle$, the resulting state will no longer be pure.\n", "\n", "The requirements for a map to be a channel must obviously include the preservation of Hermiticity, positivity and the trace, since a state must have real-valued non-negative eigenvalues adding up to one. However, as we will see in what follows, there is a less obvious requirement that any channel must fulfil: *complete positivity*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a linear map $\\Phi : M_n(\\mathbb{C}) \\rightarrow M_n(\\mathbb{C})$ and let $M_n^+(\\mathbb{C}) = \\{ A \\in M_n(\\mathbb{C})\\, |\\, A\\geq 0 \\} \\subset M_n(\\mathbb{C})$ be a convex subset of positive matrices. One calls a linear map $\\Phi$\n", "\n", "\n", "- Hermicity-preserving iff $\\Phi(A^\\dagger) = [\\Phi(A)]^\\dagger$,\n", "- positive iff $\\Phi(M_n^+(\\mathbb{C}))\\subset M_n^+(\\mathbb{C})$,\n", "- trace-preserving iff ${\\rm Tr}\\, \\Phi(A) = {\\rm Tr}\\, A$,\n", "- unital iff $\\Phi(\\mathbb{I}_n) = \\mathbb{I}_n$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is easy to show that a positive map is necessarily Hermicity-preserving. Moreover, observing that $\\mathfrak{S}_n = \\{ A\\in \\Mnp\\, |\\ {\\rm Tr}\\, A=1\\}$, it is clear that if $\\Phi$ is positive and trace preserving then it maps density matrices into density matrices, i.e. $\\Phi(\\mathfrak{S}_n) \\subset \\mathfrak{S}_n$. If $\\Phi$ is a linear map then one defines a dual map $\\Phi^* : \\Mn \\ra \\Mn$ by\n", "\n", "\\begin{equation}\n", " {\\rm Tr}[A \\Phi^*(B)] = {\\rm Tr}[\\Phi(A)B]\\ ,\n", "\\tag{2.7}\n", "\\end{equation}\n", "\n", "for all $A,B\\in \\Mn$. $\\Phi$ is trace-preserving iff $\\Phi^*$ is unital [[1](#1)-[3](#3)]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Consider a transposition $T_n : M_n(\\mathbb{C})\\ra \\Mn$, i.e. $T_n(\\rho) = \\rho^T$. Since transposition does not affect the spectrum of $A$ it is clear that $A^T \\geq 0$ whenever $A\\geq 0$. Note that $T_n$ is trace-preserving and unital." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Positive trace-preserving maps possess the following fundamental property\n", "\n", "**Proposition 1 ([[1](#1)-[3](#3)])**\n", "\n", "> If $\\Phi$ is positive and trace-preserving, then\n", "> \n", "> \\begin{equation}\n", " || \\Phi(X)||_1 \\leq ||X||_1\\ ,\n", "\\tag{2.8}\n", "\\end{equation}\n", "> \n", "> for all $X \\in \\Mn$, that is, $\\Phi$ is a contraction in trace-norm. Hence\n", "> \n", "> \\begin{equation}\n", " D[\\Phi(\\rho),\\Phi(\\sigma)] \\leq D[\\rho,\\sigma]\\ ,\n", "\\tag{2.9}\n", "\\end{equation}\n", "> \n", "> which means that the distinguishability of $\\rho$ and $\\sigma$ never increases under the action of a positive and trace-preserving map." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It turns out that the positivity property is not sufficient to describe the dynamics of open quantum systems. The reason stems from the properties of composed systems. Composing two systems living in $\\mathcal{H}_1$ and $\\mathcal{H}_2$, respectively, one obtains a system living in $\\mathcal{H}=\\mathcal{H}_1 \\ot \\mathcal{H}_2$. Let ${\\rm dim}\\, \\mathcal{H}_1 = n$, ${\\rm dim}\\, \\mathcal{H}_2 = m$ and consider two linear maps\n", "$$ \\Phi_1 : \\Mn \\ra \\Mn\\ , \\ \\ \\ \\ \\Phi_2 : \\Mm \\ra \\Mm\\ \\ . $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recalling that $\\Mnm = \\Mn \\ot \\Mm$ one defines a tensor product\n", "\n", "$$ \\Phi_1 \\ot \\Phi_2 : \\Mnm \\ra \\Mnm\\ ,$$\n", "\n", "as follows: for a fixed orthonormal basis $\\{e_1,\\ldots,e_n\\}$ in $\\mathcal{H}_1$ let us define $e_{ij} := |e_i \\rangle \\langle e_j| \\in \\Mn$. Elements $\\{e_{ij}\\}$ for $i,j=1,\\ldots,n$ define an orthonormal basis in $\\Mn$ with respect to the standard inner product $(A,B) = {\\rm tr}(A^\\dagger B)$. Now, any matrix $A \\in \\Mnm$ may be represented in the following block form\n", "\\begin{equation}\n", " A = \\sum_{i,j=1}^n e_{ij} \\ot A_{ij}\\ ,\n", "\\tag{2.10}\n", "\\end{equation}\n", "with $A_{ij} \\in \\Mm$. For example if $n=2$ one has\n", "\\begin{equation}\n", " A = \\sum_{i,j=1}^2 e_{ij} \\ot A_{ij} = \\left( \\begin{array}{c|c} A_{11} & A_{12} \\\\ \\hline A_{21} & A_{22} \\end{array} \\right)\\ .\n", "\\tag{2.11}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence the action of $\\Phi_1 \\ot \\Phi_2$ is given by\n", "\\begin{equation}\n", " [\\Phi_1 \\ot \\Phi_2](A) := \\sum_{i,j=1}^n \\Phi_1(e_{ij}) \\ot \\Phi_2(A_{ij})\\ .\n", "\\tag{2.12}\n", "\\end{equation}\n", "\n", "In particular if $n=2$ and $\\Phi_1 = \\mathbb{1}_2$, where $\\mathbb{1}_n : \\Mn \\ra \\Mn$ denotes an identity map defined by $\\mathbb{1}_n(X) = X$, then\n", "\n", "\\begin{equation}\n", " [\\mathbb{1}_2 \\ot \\Phi](A) = \\sum_{i,j=1}^2 e_{ij} \\ot \\Phi(A_{ij}) = \\left( \\begin{array}{c|c} \\Phi(A_{11}) & \\Phi(A_{12}) \\\\ \\hline \\Phi(A_{21}) & \\Phi(A_{22}) \\end{array} \\right) \\ .\n", "\\tag{2.13}\n", "\\end{equation}\n", "\n", "Now comes a surprise: even if $\\Phi_1$ and $\\Phi_2$ are positive $\\Phi_1 \\ot \\Phi_2$ need not be a positive map." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 3 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> Interestingly, the transposition map considered in **Example 2** loses its positivity when tensored with another positive map. This map is evidently positive and trace-preserving. Consider $\\mathbb{1}_2 \\ot T_2$. It turns out that this maps is not positive in $M_4(\\mathbb{C})$. Indeed, let\n", "> \n", "> \\begin{equation}\\label{}\n", " P^+_2 = \\frac 12 \\sum_{i,j=1}^2 e_{ij} \\ot e_{ij} = \\frac 12 \\left( \\begin{array}{cc|cc} 1 & 0 & 0 & 1 \\\\ 0 & 0 & 0 & 0 \\\\ \\hline 0 & 0 & 0 & 0 \\\\ 1 & 0 & 0 & 1 \\end{array} \\right) \\ ,\n", "\\tag{2.14}\n", "\\end{equation}\n", "> \n", "> be a state in $\\mathbb{C}^2 \\ot \\mathbb{C}^2$. Note that $P^+_2 = |\\psi^+_2 \\rangle \\langle \\psi^+_2|$ with $\\psi^+_2 = (e_1 \\ot e_1 + e_2 \\ot e_2)/\\sqrt{2}$ being one of the well-known Bell states of two qubits. One finds\n", "> \n", "> \\begin{equation}\\label{}\n", " [\\mathbb{1}_2 \\ot T_2]( P^+_2) = \\frac 12 \\sum_{i,j=1}^2 e_{ij} \\ot e_{ji} = \\frac 12 \\left( \\begin{array}{cc|cc} 1 & 0 & 0 & 0 \\\\ 0 & 0 & 1 & 0 \\\\ \\hline 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 \\end{array} \\right) \\ ,\n", "\\tag{2.15}\n", "\\end{equation}\n", "> \n", "> Note that $[\\mathbb{1}_2 \\ot T_2]( P^+_2)$ has one negative eigenvalue and hence it is not a positive map." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example proves that quantum physics of composed systems needs a more refined notion of positivity. Consider again a linear map $\\Phi : \\Mn \\ra \\Mn$. One calls $\\Phi$ $k$-positive if\n", "\n", "\\begin{equation}\n", "\\mathbb{1}_k \\ot \\Phi : \\Mk \\ot \\Mn \\ra \\Mk \\ot \\Mn \\ ,\n", "\\tag{2.16}\n", "\\end{equation}\n", "\n", "is positive. Clearly 1-positive is just positive and $k$-positivity implies $\\ell$-positivity for $\\ell < k$. Finally, $\\Phi$ is called **_completely positive (CP)_** if it is $k$-positive for $k=1,2,\\ldots$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Interestingly, one has the following characterization:\n", "\n", "**Proposition 2 (Choi [[4](#4)])**\n", "\n", "> If ${\\rm dim}\\, \\mathcal{H} = n$, then $\\Phi$ is CP if and only if $\\Phi$ is $n$-positive.\n", "\n", "Denoting by $\\mathcal{P}_k$ a convex set of $k$-positive maps one has the following chain of inclusions\n", "\n", "\\begin{equation}\n", " {\\rm CP} \\equiv \\mathcal{P}_n \\subset \\ldots \\subset \\mathcal{P}_2 \\subset \\mathcal{P}_1 \\equiv {\\rm Positive\\ maps} \\ .\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $\\{e_1,\\ldots,e_n\\}$ be a fixed orthonormal basis in $\\mathcal{H}$ and let\n", "\\begin{equation}\n", " |\\psi^+_n \\rangle = \\frac{1}{\\sqrt{n} }\\, \\sum_{k=1}^n e_k \\ot e_k\\ ,\n", "\\tag{2.17}\n", "\\end{equation}\n", "\n", "denote a maximally entangled state in $\\mathcal{H} \\ot \\mathcal{H}$. Moreover, let $P^+_n = |\\psi^+_n \\rangle \\langle \\psi^+_n|$ denote the corresponding rank-1 projector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Proposition 3 (Choi [[4](#4)])**\n", "\n", "> $\\Phi$ is CP if and only if $[\\mathbb{1}_n \\ot \\Phi](P^+_n) \\geq 0$.\n", "\n", "This beautiful result states that in order to prove that $\\Phi$ is CP, or equivalently that $\\mathbb{1}_n \\ot \\Phi$ is positive, it is enough to check whether $\\mathbb{1}_n \\ot \\Phi$ is positive on one particular projector $P^+_n$. Positivity of $[\\mathbb{1}_n \\ot \\Phi](P^+_n)$ guaranties that $[\\mathbb{1}_n \\ot \\Phi](X) \\geq 0$ for all positive $X \\in \\Mn \\ot \\Mn$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Corollary 1**\n", "\n", "> If $\\Phi_1$ and $\\Phi_2$ are CP maps, then $\\Phi_1 \\ot \\Phi_2$ is always CP as well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This analysis shows that the motivation to use CP maps is deeply rooted in physics and it is not just a mathematical trick! The very presence of quantum entangled states enforces us to use maps which are not only positive but also completely positive. The following result provides the most important characterization of CP maps.\n", "\n", "**Theorem 1 (Kraus form [[1](#1), [2](#2), [4](#4), [5](#5)])**\n", "\n", "> A map $\\Phi : \\Mn \\ra \\Mn$ is CP if and only if\n", "> \n", "> \\begin{equation} \\label{Kraus}\n", "\\Phi(X) = \\sum_\\alpha\\, K_\\alpha X\\, K_\\alpha^\\dagger\\ ,\n", "\\tag{2.18}\n", "\\end{equation}\n", "> for $X \\in M_n(\\mathbb{C})$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Formula (\\ref{Kraus}) is usually called the **_Kraus_** or **_Operator Sum Representation_** of $\\Phi$ and $K_\\alpha$ are called Kraus operators. Actually, the above formula appeared already in the Sudarshan et. al. paper [[6](#6)]. It should be stressed that the Kraus representation is highly non unique. A completely positive trace preserving map (CPTP) is called a **_quantum channel_**. A CP map possessing a Kraus representation is trace-preserving iff\n", "\n", "\\begin{equation}\n", " \\sum_\\alpha\\, K_\\alpha^\\dagger \\, K_\\alpha = \\mathbb{I}_n\\ .\n", "\\tag{2.19}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following result shows the origin of a genuine quantum channel.\n", "\n", "**Theorem 2 (Unitary dilation)**\n", "\n", "> Any quantum channel $\\Phi$ may be constructed as follows\n", "> \n", "> \\begin{equation}\n", " \\Phi(\\rho) = {\\rm Tr}_E \\big[ U (\\rho \\ot \\omega) U^\\dagger \\big]\\ ,\n", "\\label{200}\n", "\\tag{2.20}\n", "\\end{equation}\n", "> \n", "> where $U$ is a unitary operator in $\\mathcal{H}\\ot \\mathcal{H}_E$, $\\omega$ is a density operator in $\\mathcal{H}_E$, and ${\\rm Tr}_E$ denotes the partial trace over $\\mathcal{H}_E$.\n", "\n", "One usually interprets $\\mathcal{H}_E$ as a Hilbert space of the environment and $\\omega$ as its fixed state.\n", "Let\n", "\n", "$$ \\omega |E_k \\rangle = \\lambda_k |E_k \\rangle\\ , $$\n", "\n", "with $\\lambda_k \\geq 0$. Moreover, let $U = \\sum_{k,l} U_{kl} \\ot |E_k\\rangle \\langle E_l|$. Formula (\\ref{200}) implies\n", "\n", "\\begin{eqnarray*}\n", " \\Phi(\\rho) &=& \\sum_{m,n} \\sum_{i,j} \\sum_k \\lambda_k \\, {\\rm Tr}_E \\big[ (U_{ij} \\ot |E_i \\rangle \\langle E_j|) (\\rho \\ot |E_k \\rangle \\langle E_k|) (U_{mn}^\\dagger \\ot |E_n \\rangle \\langle E_m|) \\big] \\nonumber \\\\ &=& \\sum_{m,n} \\sum_{i,j} \\sum_k \\lambda_k \\, {\\rm Tr} [ |E_i \\rangle \\langle E_j|E_k \\rangle \\langle E_k|E_n \\rangle \\langle E_m|]\\, U_{ij} \\rho U_{mn}^\\dagger \\ .\n", "\\end{eqnarray*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using ${\\rm Tr} [ |E_i \\rangle \\langle E_j|E_k \\rangle \\langle E_k|E_n \\rangle \\langle E_m| ] = \\delta_{im} \\delta_{jk} \\delta_{kn}$ and introducing $K_\\alpha := K_{mn} = \\sqrt{\\lambda_n}\\, U_{mn}$ one arrives at the Kraus representation $\\Phi(\\rho) = \\sum_\\alpha\\, K_\\alpha \\rho\\, K_\\alpha^\\dagger$ which proves that $\\Phi$ defined *via* formula (\\ref{200}) is completely positive. One easily proves that $\\Phi$ is also trace preserving and hence defines a quantum channel." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is worth stressing the importance of this last theorem for the digital simulation of OQS. It implies that *any* quantum channel can be simulated by using auxiliary degrees of freedom living in Hilbert space $\\mathcal{H}_E$, preparing them in the appropriate state, and applying a unitary transformation to the total system. We will often use this strategy in our simulations, given that universal quantum computers are designed to apply only unitary transformations among the qubits." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2.2.1 \n", "\n", "Consider the following circuit implementing a channel on qubit $q_0$ (we assume $q_1$ to be initially in state $| 0 \\rangle$)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "
" ], "image/svg+xml": "\n\n\n \n \n \n \n 2021-05-10T15:12:47.900634\n image/svg+xml\n \n \n Matplotlib v3.4.2, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", "image/png": "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\n" }, "metadata": {}, "execution_count": 4 } ], "source": [ "# Quantum register\n", "q = QuantumRegister(2, name='q')\n", "\n", "# Quantum circuit\n", "channel = QuantumCircuit(q)\n", "\n", "# CNOT gate\n", "channel.h(q[1])\n", "channel.cz(q[0], q[1])\n", "channel.cx(q[1], q[0])\n", "\n", "# Draw circuit\n", "channel.draw(output='mpl')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. Calculate the outcoming state of $q_0$ for the following incoming states: $\\alpha |0\\rangle + \\beta |1\\rangle$ with $|\\alpha|^2 + |\\beta|^2 = 1$, $p_1 |+ \\rangle \\langle +| + p_2 | - \\rangle \\langle - |$ with $p_1 + p_2 = 1$.\n", "2. Verify that the channel is completely positive using proposition 2 (consider a third ancillary qubit $q_2$ maximally entangled with $q_0$).\n", "3. Determine the Kraus representation of the channel." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.3. How to describe quantum evolution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If $\\rho$ is an initial state of an $n$-level quantum system, then by its evolution we mean a trajectory $\\rho_t$ for $t \\geq 0$ starting at $\\rho$. The simplest example of quantum evolution is provided by the von Neumann equation (in units of $\\hbar$)\n", "\n", "\\begin{equation}\\label{v-N}\n", " i\\dot{\\rho}_t = [H,\\rho_t]\\ ,\n", "\\tag{2.21}\n", "\\end{equation}\n", "\n", "with the corresponding solution\n", "\n", "\\begin{equation}\\label{}\n", " \\rho_t = \\mathcal{U}_t (\\rho)\\ ,\n", "\\tag{2.22}\n", "\\end{equation}\n", "\n", "where the map $\\mathcal{U}_t : \\Mn \\ra \\Mn$ is defined by\n", "\\begin{equation}\\label{UUU}\n", " \\mathcal{U}_t(\\rho) := U_t \\rho U_t^\\dagger\\ ,\n", "\\tag{2.23}\n", "\\end{equation}\n", "\n", "with $U_t = e^{-iHt}$. Note that (\\ref{UUU}) defines a family of quantum channels. \n", "\n", "Let us observe that the 1-parameter unitary group $U_t$ implies the following composition law\n", "\n", "\\begin{equation}\\label{U-t-s}\n", " \\mathcal{U}_t \\, \\mathcal{U}_s = \\mathcal{U}_{t+s}\\ ,\n", "\\tag{2.24}\n", "\\end{equation}\n", "\n", "for all $t,s \\in \\mathbb{R}$. Hence $\\mathcal{U}_t$ defines a 1-parameter group of CP maps." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Equation (\\ref{v-N}) may be transformed into the following equation for $\\mathcal{U}_t$\n", "\n", "\\begin{equation}\\label{v-N-U}\n", " \\dot{\\mathcal{U} }_t = L \\,\\mathcal{U}_t\\ , \\ \\ \\ \\mathcal{U}_0 = \\mathbb{1}\\ ,\n", "\\tag{2.25}\n", "\\end{equation}\n", "\n", "where the generator $L : \\Mn \\ra \\Mn$ is defined by\n", "\n", "\\begin{equation}\\label{}\n", "L(X) = -i [H,X]\\ ,\n", "\\tag{2.26}\n", "\\end{equation}\n", "for any $X \\in \\Mn$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now come the natural questions:\n", "\n", "1. how to generalize the unitary evolution defined by (\\ref{UUU}), valid for closed systems, to open quantum systems? \n", "\n", "2. how to generalize the corresponding equation of motion (\\ref{v-N-U})?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Definition 1**\n", "\n", "> By a general quantum evolution we mean a dynamical map, i.e. a family of quantum channels $\\Lambda_t : \\Mn \\ra \\Mn$ for $t \\geq 0$ such that $\\Lambda_0 = \\mathbb{1}_n$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A dynamical map $\\Lambda_t$ maps an initial state $\\rho$ into a current state $\\rho_t := \\Lambda_t(\\rho)$ and hence provides the natural generalization of the unitary evolution $\\rho_t = \\mathcal{U}_t(\\rho)$. Assuming that $\\rho_t$ satisfies a linear equation and that the initial state $\\rho$ provides all necessary information to uniquely determine $\\rho_t$ we expect that $\\rho_t$ satisfies the following equation\n", "\n", "\\begin{equation}\\label{}\n", " \\dot{\\rho}_t = L_t(\\rho_t)\\ ,\n", "\\tag{2.27}\n", "\\end{equation}\n", "\n", "or equivalently\n", "\n", "\\begin{equation}\\label{ME}\n", " \\dot{\\Lambda}_t = L_t\\Lambda_t\\ ,\\ \\ \\ \\Lambda_0 = \\mathbb{1}_n\\ ,\n", "\\tag{2.28}\n", "\\end{equation}\n", "\n", "where $L_t : \\Mn \\ra \\Mn$ denotes a time-dependent generator. This equation provides a natural generalization of (\\ref{v-N-U})." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The formal solution of (\\ref{ME}) may be written as follows\n", "\\begin{equation}\\label{Lambda-t}\n", " \\Lambda_t = {\\rm T} \\exp\\left( \\int_0^t L_\\tau\\, d\\tau\\right)\\ ,\n", "\\tag{2.29}\n", "\\end{equation}\n", "\n", "where T denotes the chronological ordering operator. The above formula is defined by the following Dyson series\n", "\n", "\\begin{equation}\\label{Dyson}\n", " \\Lambda_t = \\mathbb{1}_n + \\int_0^t dt_1\\, L_{t_1} + \\int_0^{t} dt_1 \\int_0^{t_1} dt_2 \\, L_{t_1} \\, L_{t_2} + \\ldots \\ ,\n", "\\tag{2.30}\n", "\\end{equation}\n", "provided that it converges." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2.4. General considerations for circuit implementation and Qiskit tools " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4.1. Circuit design and implementation on IBM Q Experience processors " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section, we will briefly discuss the main aspects to take into account when designing a circuit to be implemented on a real device from the IBM Q Experience in order to reduce the noise in the experiment. As we introduced in **[Chapter 1](introduction.html)** and briefly again in the discussion of the *dilation theorem*, the general strategy consists in using some qubits to play the role of the system and other qubits for the environment and then applying the appropriate unitary gates among them to simulate the dynamics. In fact, we will even use extra ancillary qubits to quantify some dynamical properties of some dynamical evolutions in **[Chapter 8](non-markovian_quantum_dynamics.html)**. In any case, there are many choices for the roles of the qubits, as well as of unitaries, that would be equivalent in principle. However, due to the noisy nature of the current NISQ devices, not all of them yield equally good results.\n", "\n", "Given the large number of experimental runs allowed by the devices ($N = 8192$), the errors due to statistical fluctuations, of order $\\mathcal{O}(1/\\sqrt{N}) \\approx 0.011$, are generally far less significant than other sources of error. The discrepancy between the experimental points and the theoretical predictions, on the other hand, often come from systematic errors induced by various factors in the hardware implementation. First, the qubits undergo relaxation and decoherence due to external noise. This error becomes more relevant when increasing the depth of the circuit. As we add more gates, the circuit takes longer to run, hence being more susceptible to these effects. Second, the gates have errors due to cross-talk and unwanted interactions between qubits when addressing them with pulses. In particular, the error rate of CNOT gates is about 10 times larger than single-qubit unitaries. Finally, there is a readout error affecting the quantum measurement, although this can be mitigated to some extent, as we discuss later on. The error rates and noise parameters on IBM Q devices are characterized on a daily basis using randomized benchmarking techniques. Since there are various, interdependent sources of noise, modeling and predicting the deviations in the experimental data is a non-trivial matter, beyond the scope of this book. Let us discuss some general guidelines targeted at minimising the aforementioned inaccuracies.\n", "\n", "Since the IBM Q Experience devices are universal quantum computers, they enable the implementation of any unitary transformation of their constituent qubits; once a quantum circuit is provided for its execution, it is compiled into an equivalent circuit involving only the machine's basis gates (that is, those realisable experimentally). However, if the circuit requires a multi-qubit gate among qubits that are not physically connected [[1](#1)], the corresponding gate will be replaced with a longer circuit in which the states are swapped to neighbouring qubits in the compiled circuit. Since every swap gate includes a minimum of three CNOT gates, and these introduce considerable noise to the execution, it is crucial to assign the relevant qubits involved in the simulation (e.g. system, environment and ancillae) to the machine's qubits so that the number of CNOT gates between\n", "disconnected qubits is minimised. Furthermore, the devices are calibrated daily and the errors of the basis gates are reported. This information can also be taken into account in the qubit assignment, as using the CNOT gates with smaller errors is preferable. The figure below shows the connectivity layout and gate errors of `ibmq_16_melbourne`, IBM Q's 14-qubit device." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to the gate errors, the qubits' readout errors characterising the discrepancies between the qubit state and the measurement outcome probabilities are also provided. In the IBM Q Experience devices, there are considerable differences in the readout errors of the different qubits, so this information should also be taken into account in the qubit-assignment process: if possible, it is preferable to assign the system (and any auxiliary ancillae whose measurement is required) to low readout-error qubits, while qubits with large readout errors can still be used to simulate the environment or other ancillae that need not be measured. In any case, Qiskit provides post-processing error-mitigation tools that generally improve the experimental\n", "results under the package `ignis`. We will explain how to use it in the next subsection. \n", "\n", " [1]: The basis gates for the IBM Q Experience devices include any single-qubit rotation, whereas the only\n", "multi-qubit gates are CNOTs. Two qubits are connected in a given device if there is a basis CNOT between them. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4.2 Noise mitigation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we prepare a qubit in state e.g. $|0\\rangle$ and measure it in a NISQ device, we will not obtain the outcome 0 with probability one due to imperfections in the measurement process. Nevertheless, Qiskit's `Ignis` provides a tool to mitigate these errors that is very easy to use.\n", "\n", "The working principle is the following. We first prepare all possible computational-basis states $| 0\\cdots 0 \\rangle, | 0\\cdots 1 \\rangle, \\ldots, | 1\\cdots 1 \\rangle$ and measure their corresponding outcome probabilities (notice that it is only necessary to include the qubits whose measurement outcomes are needed). Once these are known, they can be used to correct any other experimental result by finding, via likelihood maximization, the experimental outcome that is most congruent with the observed measurement deviations. All the data shown in the book have been mitigated as described above.\n", "\n", "We now illustrate how to use the noise mitigation tool in what follows." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "from qiskit import IBMQ, execute\n", "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n", "from qiskit.tools.visualization import plot_histogram, plot_state_city" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "IBMQ.load_account()" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "backend = IBMQ.get_provider().get_backend('ibmqx2')" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "State labels: ['00', '01', '10', '11']\n" ] }, { 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# qiskit-ignis provides tools for noise mitigation\n", "from qiskit.ignis.mitigation.measurement import complete_meas_cal, CompleteMeasFitter, MeasurementFilter\n", "\n", "# For visualizing the circuits\n", "import matplotlib.pyplot as plt\n", "\n", "# Suppose we have a 5-qubit quantum computer, and we want to perform measurements on qubits 0 and 2\n", "\n", "# We first initialize a 5-qubit quantum register\n", "q = QuantumRegister(5)\n", "\n", "# Next, we generate the calibration circuits\n", "meas_calibs, state_labels = complete_meas_cal(qubit_list=[0,2], qr=q)\n", "\n", "# We can plot them \n", "fig, axes = plt.subplots(1, 4)\n", "for i, circuit in enumerate(meas_calibs):\n", " circuit.draw(output='mpl', ax=axes[i], scale=2)\n", " \n", "print(\"State labels:\",state_labels)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "# We now perform the calibration on the real device\n", "job_calibration = execute(meas_calibs, backend=backend)\n", "cal_results = job_calibration.result()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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7mQ2izPfhDTgwIn4zsBMRyyW9ocCYzKykumHSYmAZ9n9N9z8M3FdcSGZWVp3epc2S8D4OfIZkMQFIlnq/uLCIzKyU2t1dzaJpwouIZyR9D1gUEataEJOZlVSnJ7ymHW5JJwD3Aj9N9w+R1Fd0YGZWPt0wafFVkq9MuxUgIu7N+q1l1tjmzZvbHUJhxo4d2+4QCvHYY4+1O4RCJGtpvnyd3sLL9EXcEfFk3YXk89sxs64xsABoJ8uS8FZIOhUYnX7T95nAr4oNy8zKqNNbeFnS8RkkX9f4LPAj4Eng80UGZWblVOoxPEmjgfMj4kvA2a0JyczKqtNbeM3Ww9sm6S2tCsbMyq3UCS91T3obyjXA84t/RsS/FxaVmZVOu7urWWRJeGOAx4F31JQF4IRnZi9S+lnaiPh4KwIxs/IrfQtP0g8Z5L67iPhEIRGZWWmVPuEBN9ZsjwFOBB4uJhwzK6uuGMOLiOtq9yUtBP6nsIjMrLRKn/AGMRXYK+9AzKz8Sj9pIWkTLx7DexT4cmERmVlplb6FFxG7tSIQMyu3MozhZVkP7yhJu6bbH5H0bUn7FR+amZVNpz9Lm6XDfTHwtKQ3AV8EfgdcUWhUZlZK3ZDwtkayOuBM4LsRMR9wN9fMXqLTE16WWdpNkr4CfAR4q6RRwCuKDcvMyqYMC4Bmie5kkrXwZkfEo8AE4JuFRmVmpZRnC0/SDEmrJPVLmtfguA9ICkk9zerMMkv7KPDtmv0/4DE8MxtEXt3VdC3O+cBxwFpgiaS+iFhZd9xuJF8he1eWerPM0h4haYmkzZK2SNom6cnhX4KZdbscW3iHAf0RsToitgBXkcwj1PsH4ALgmSyVZunSfheYBTwA7Ax8EviXLJWbWbUMI+GNk7S05jWnrqp9gYdq9temZbXnmg5MjIifZI0v06NlEdEvaXREbAN+KOke4CtZT2Jm3W+YM7AbIqLpmFuDc40iGWo7fTify5Lwnpa0I3CvpG8Aj5CtK7wAeA+wPiIOSsteDVwNTAbWAB+KiCeGE7CZda4cZ2nXARNr9iekZQN2Aw4Cbk2T7GuAPkknRMTSIePLcOKPpsfNJVnifSLwgQyfuwyYUVc2D7g5IqYCN6f7ZtYlchzDWwJMlTQlbXCdAvQNvBkRT0bEuIiYHBGTgTuBhskOss3SPihpZ2CfiPhalkjTz90maXJd8Uzg6HT7cuBWvBCBWdfIa5Y2IrZKmgssBkYDCyJihaTzgaUR0de4hsFlWS3lvcA/ATsCUyQdQvLVjSeM4Hx7R8Qj6fajwN4NzjsHmAMwadKkEZzKzFop76coImIRsKiu7Nwhjj06S51ZurTnkUwRb0wrvheYkqXyRtLH1V6ydHzN+70R0RMRPePHj3+5pzOzFuiGR8uei4gn64IcMlE18ZikfSLiEUn7AOtHWI+ZdaBueLRshaRTgdGSpkr6DvCrEZ6vDzgt3T4NuGGE9ZhZh8naumtnCy9LwjsDeCPJ87QLgf8DPt/sQ0q+++IO4EBJayXNBr4OHCfpAeDYdN/MukSnJ7wss7RPA2enr8wiYtYQbx0znHrMrDzamcyyGDLhSWo47TvCWVoz62KlTXjAkSTPsi0kWYmgs6/EzNquzAnvNSRLs8wCTgV+AiyMiBWtCMzMykVlXgA0IrZFxE8j4jTgCKCf5Lm1uS2LzsxKpdSTFpJ2At5N0sqbDFwEXF98WGZWRqXt0kq6gmQ1gkXA1yJiecuiMrNSKm3CI/nSnqdIlk8+s+ZCRPJk2NiCYzOzEml3dzWLIRNeRHT26KOZdZxOn7TItOKxmVkWpW3hmZkNlxOemVVCqcfwzMyGywnPzCrDCc/MKsOztGZWCR7DM7NKccIzs8pwwjOzynDCM7PKcMIzs0oowwKgTnhmlhu38HLS6f/nGInt27e3O4TCbNy4sd0hFGLPPfdsdwiF2LRpUy71OOGZWWU44ZlZJfjGYzOrlE4fenLCM7PcuIVnZpXhhGdmleAxPDOrlE5PeJ09wmhmpTLQymv2yljXDEmrJPVLmjfI+2dJWinpPkk3S9qvWZ1OeGaWm1GjRmV6NSNpNDAfOB6YBsySNK3usHuAnog4GLgW+EbT+IZ9RWZmg8jausvYwjsM6I+I1RGxBbgKmFl7QETcEhFPp7t3AhOaVeoxPDPLzTDG8MZJWlqz3xsRvTX7+wIP1eyvBQ5vUN9s4L+andQJz8xyM4yEtyEienI650eAHuBtzY51wjOz3OQ4S7sOmFizPyEtqz/fscDZwNsi4tlmlTrhmVluckx4S4CpkqaQJLpTgFPrzvVm4PvAjIhYn6VSJzwzy0WeC4BGxFZJc4HFwGhgQUSskHQ+sDQi+oBvAq8ErkkT7R8i4oRG9TrhmVlu8rzxOCIWAYvqys6t2T52uHU64ZlZbjr9SQsnPDPLjROemVWCFw8ws0rxAqBmVhlu4ZlZZTjhmVkllGEMr7AOt6QFktZLWl5T9kFJKyRtl5TLc3Rm1jnyXA+vCEWOMF4GzKgrWw68H7itwPOaWZt0esIrrEsbEbdJmlxXdj90fj/fzEbGs7RmVgntbr1l0bEJT9IcYA7ApEmT2hyNmWXR6QmvY9ufEdEbET0R0TN+/Ph2h2NmGVR2DM/MqqeyLTxJC4E7gAMlrZU0W9KJktYCRwI/kbS4qPObWetVtoUXEbOGeOv6os5pZu2T5wKgRXGX1sxy0+ldWic8M8uNE56ZVYYTnplVQrsnJLJwwjOz3HjSwswqwy08M6sMJzwzqwSP4ZlZpTjhmVllOOGZWSX40TIzqxS38MysMpzwzKwynPDMrDKc8MysEnwfnplVimdpzawy3MIzs8ro9ITX2e1PMyuNrF/gkzUpSpohaZWkfknzBnl/J0lXp+/fJWlyszqd8MwsN3klPEmjgfnA8cA0YJakaXWHzQaeiIj9gQuBC5rV64RnZrkZNWpUplcGhwH9EbE6IrYAVwEz646ZCVyebl8LHKMm2bQUY3jLli3bIOnBFp1uHLChRedqpW69Lujea2vlde33citYtmzZYknjMh4+RtLSmv3eiOit2d8XeKhmfy1weF0dzx8TEVslPQnsSYPfWSkSXkSMb9W5JC2NiJ5Wna9VuvW6oHuvrWzXFREz2h1DM+7SmlknWgdMrNmfkJYNeoykHYDdgccbVeqEZ2adaAkwVdIUSTsCpwB9dcf0Aael2ycBv4iIaFRpKbq0Ldbb/JBS6tbrgu69tm69rqbSMbm5wGJgNLAgIlZIOh9YGhF9wKXAlZL6gT+RJMWG1CQhmpl1DXdpzawynPDMrDKc8MysMpzwzKwynPDMrDKc8MysMpzwzKwy/h9p9aeteYjlXAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# We now calculate the calibration matrix from the outcomes\n", "meas_fitter = CompleteMeasFitter(cal_results, state_labels)\n", "meas_fitter.plot_calibration()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The element $(i, j)$ of the calibration matrix is the probability that the prepared state $j$ (columns) is measured to be in $i$ (rows). In a perfect, noiseless situation, it would be equal to the identity matrix.\n", "\n", "In the real devices, we can see that, for example, there is a certain probability that the state $|01\\rangle$ is actually measured to be $|00\\rangle$." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Average Measurement Fidelity: 0.953369\n" ] } ], "source": [ "# What is the measurement fidelity?\n", "print(\"Average Measurement Fidelity: %f\" % meas_fitter.readout_fidelity())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The calibration matrix is used for mitigating the measurement counts. Let's see it in action in an example where we generate a Bell state." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "
" ], "image/svg+xml": "\n\n\n \n \n \n \n 2021-05-10T15:14:04.238184\n image/svg+xml\n \n \n Matplotlib v3.4.2, https://matplotlib.org/\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n", "image/png": 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\n" }, "metadata": {}, "execution_count": 9 } ], "source": [ "# Make a 2Q Bell state between Q0 and Q2\n", "c = ClassicalRegister(2)\n", "bell = QuantumCircuit(q)\n", "\n", "bell.x(q[0])\n", "bell.x(q[2])\n", "bell.h(q[0])\n", "bell.cx(q[0], q[2])\n", "\n", "meas = QuantumCircuit(q, c)\n", "meas.measure(q[0],c[0])\n", "meas.measure(q[2],c[1])\n", "qc = bell + meas\n", "\n", "qc.draw(output='mpl')" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "# We execute the circuit\n", "job = execute(qc, backend=backend, shots=5000)\n", "results = job.result()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# We also simulate the circuit in a noiseless case\n", "from qiskit import Aer\n", "simjob = execute(qc, backend=Aer.get_backend('qasm_simulator'), shots=10000)\n", "simresults = simjob.result()" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "# We get the raw counts\n", "raw_counts = results.get_counts()\n", "sim_counts = simresults.get_counts()\n", "\n", "# ... and the mitigated counts\n", "# First we need to get the measurement filter object\n", "meas_filter = meas_fitter.filter\n", "# and then we apply it to the results\n", "mitigated_results = meas_filter.apply(results)\n", "mitigated_counts = mitigated_results.get_counts(0)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_histogram([sim_counts, raw_counts, mitigated_counts], legend=['simulated', 'raw', 'mitigated'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that, thanks to mitigation, spurious counts for the '00' and '11' states are filtered out. The counts for '01' and '10' are still deviating from the expected ones because of other sources of noise other than measurements (gate errors, decoherence...)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For more detailed information, please refer to the `qiskit` documentation and to the Ignis [measurement mitigation tutorial notebook](https://github.com/Qiskit/qiskit-iqx-tutorials/blob/master/qiskit/advanced/ignis/4_measurement_error_mitigation.ipynb)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4.3 Quantum state tomography " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "State tomography is the process of reconstructing the density operator of a quantum system by performing a set of measurements on identical preparations of its state. To be able to uniquely identify the state, the measurements must be **_tomographically complete_**, meaning that the measurement operators must form an operator basis on the Hilbert space of the system, so that full information of the state can be obtained.\n", "\n", "State tomography is very useful for the characterization of devices, in particular for determining the actual state of qubits under the action of noise.\n", "\n", "### How does it work?\n", "Since the Pauli matrices form a tomographically complete set of measurements, and they are natural choice of measurement operators for a digital quantum computer, we will focus on those.\n", "\n", "Given a qubit in the state $\\rho$, the expectation values of the Pauli matrices are given by\n", "\n", "$$ \\langle \\sigma_i \\rangle = \\text{Tr}[\\rho \\sigma_i], \\qquad i=1,2,3 $$\n", "\n", "where we identify $\\sigma_0 = \\mathbb{I}$, $\\sigma_1 = \\sigma_x$, $\\sigma_2 =\\sigma_y$, and $\\sigma_3 = \\sigma_z$. \n", "By performing a large number of measurements of $\\sigma_x$, $\\sigma_y$, $\\sigma_z$, one obtains an *estimate* of the expectation values of the operators, (let us call them σ_i) allowing us to write the density operator of the system as\n", "\n", "$$ \\rho = \\frac 12 \\left(\\mathbb{I} + \\sum_{i=1}^3 \\overline{\\sigma_i} \\sigma_i \\right).$$\n", "\n", "This method would work if $\\overline{\\sigma_i} = \\langle \\sigma_i \\rangle$, but, since this is not the case with a finite number of measurement shots, the equation above can give states that are not physical.\n", "\n", "In order to obtain a physical density operator, a **_maximum-likelihood method_** is employed: among all possible density operators, the one that maximizes the probability to give $\\overline{\\sigma_i}$ as expectation values is chosen as the result of the tomography process.\n", "\n", "For reconstructing a state of $n$ qubits, all possible combinations of the Pauli matrices $\\sigma_{i_1} \\otimes \\ldots \\otimes \\sigma_{i_n}$ are needed, with $i_{j} = 0,\\ldots,3$, meaning $3^n-1$ measurement (the case $\\sigma_0 ^{\\otimes n}$ does not need to be measured). \n", "\n", "`qiskit` implements the maximum-likelihood state tomography in the `qiskit-ignis` package. \n", "Here we will see an example with the Bell state prepared above" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "# We import the required classes from ignis.\n", "from qiskit.ignis.verification.tomography import state_tomography_circuits, StateTomographyFitter\n", "\n", "from qiskit.tools.qi.qi import partial_trace" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "job_state_vec = execute(bell, Aer.get_backend('statevector_simulator'))\n", "state_vec = partial_trace(job_state_vec.result().get_statevector(), [1, 3, 4])\n", "plot_state_city(state_vec)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The bar plot above shows the real (left) and imaginary (right) parts of the density matrix of the Bell state. \n", "Now let's perform a two-qubit tomography on the real device" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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76VC75OkR3zyvTnv0qsFpnRveeb8DcK/BrEODbXl5Hdi3a/OTgKmwdu3aRhNcqRbWcxS/HO20adP2mtw65ZRTeOeddzj11FMZMWIEt9xyC5dddlmdBJeIiIiItI2ZfYGg6PxtqT6Xu28AmrccoUiSTZgw4ZWwY5BwZUyCixxe0rYtS9mmexnbpqYutHXJ02SOTolEOY9gxF0iNb0OP3Guu6d06GxTy9TOmjVr4ujRoxNOK0nGErWNPU9hLEvbkuVoEyW3XnvtNd59911uvPFGTj31VI444gheeeWVVsUikmqxzpgrCXrCjwW6AIPdfW0j+48ArgKOIxhV/DrwP+6u4uGyVyNGjGjNamciInXEZqw07BUWyTEFBQUTkz21X7JLepfga5qWtK0n05axzYQlT+MsAP5JUGA+Xk2s7ZZ0BpMpwnyOhgwJRoctWNCweCc0ntwC+Ne//sVjjwVTdY877riUxSiSBIcD3wG2AfWn09dhZhcBjxF0towFzgLuIkiKiezVlClT2l2Cy8zo3bs3X/3qV+nXrx/77LNPg32+9rWvMXDgwBCiExERkUyWSQmu+CVtzzOzAjMrBy6MbW+wpG1sWdv4JW3HmtmeZFZsadvaJW0vN7NCMysjWNK2NJOXtG1qGVs++ghflf7pxZmw5GmtshI+BQppuCrLDmBsWQl/S2tA9cyfP/+eMM4b5nO0fv16Fi1axIsvJi6Vd//99ydMbtV69tlnqaio4L333ktpnCJttMrde7r76cD9je1kZv2AOcAUd/+Buy929yXuPsvdo2mLtoX8k0/YNe5calb96fO2nTvZHflvdv+sNC2dK7d//1DWLr+9blzulE/4IusrH2rkp3JTUVHR+HSfM6zff/fu3Zk8eTKvvvoq//znP3nllVfYuHEjW7Zs4ZZbbuGoo44CguTWk08+yYoVK+jXr1/K4hEREZHskzFTFLWkbV3WP/OWsc2EJU/jlZXwt0iUQcBpwB9jzb3LSmi4bF+arVmz5uD8/Py30n3eMJ+j+fPnM3/+/Ea3/+pXv2LQoEGMHj26QXILYNasWcyalagEn0h6mFke8CPgEqAvwcq7PwDmASvdfaK7NzfDcxHgBPewrGFdupA39myqo/diQ0+Gmhqqr/8FdOpEh6lXYo0sN50sOz54h6ptm+iRf2yd9o/e28Bnn/6LngNS35kSiTKaYJWwgQSL3NxcVsIfUn7iBKqqqtK6ZHJYv//x48czd+5cunYNHu6HH37Ie++9R9euXenbty+XX345l19+ORUVFZx88sl0796d5cuXs2nTppTEIyIi2WnQoEFpf/8lmSWTRnDh7uvc/VR338/d+7n7tcBgGlnStpGPw+rtt8PdI+7e2907u/sR9ZJbuPtWoHZJW7SkbfYoK6G6rITH4r4PPbkFMGfOnJFhx5BpVq5cyZFHHpkwuSWSIe4AriXoaBlFMBX6PmAALZ8mPxT4O3COmb1mZrvN7E0zuyqWSMtYeUVnwAcf4k89TXXZHHzrVjpMvw7r3Cnl5968oRLL68BBfY6u0771rRfoun9Puh3UN6Xnj0SJAI8S1ODsB5wCPByJ8pOUnjhDhPH7v/TSS7n77rvp2rUrixcvpqioiIMPPnjPFMWjjz6aW2+9lU8++YTRo0fTvXt3HnroIc4991x27dqV9HhERCR7lZeXPx52DBKujBnB1QQtaSuSI6qr65dME8kMZlYMnA+c4u61tbWWm9nXCEYCP9/CQx4a+5gFTCMYDTYaKAX2B6YmIeyU2FPv8VczofsBdCy7CdsvPQOJNm+opHuvQXTsvG+d9i1vvcAhKZ5mHYnSHfhF7Nu8ep+vj0S5s6xkT73QtOjVq1daz5fu3/+wYcO45ZagZOYPf/hDbr755gb7vPzyy8yfP5/vfve7dOkSlK97++23ldwSkUZ9VjgqIxcpKishI+PKJZMmTRqZ6iRXJj+PzV2ga+qMeXUWLLtxysSMfUwtldEJLi1pKyIiaXI18HhccqvWemAXDafJ700e0A0Y5+4PxtqWx1btjZjZ9bFVrTCzwwim5PcGdhJMo29TocXa1U0T6bT4scY21fXpp3T4zjlY9+5tOl99P7yn8V03b6hk2+b1zL304Drtu3buYMgZVyXl/I05/Piz+fYPH2xsc+fHb/2vLTb+vraepoHJkyc3uq24uJiKioqJ9dsLCgoatDVXJv3+r7zySjp06MCMGTMSJrfg85pbX/ziF1m+fDnDhg3j4osvZvr06XzwwQdtOr/snVYzFpFssm7dOhVnbOcyOsGlJW0lWxUXF6d/FQARaRUz6wMcTTDaqr5+wMv1VtltjvcJajg9Ua/9CeA84EjguVjbXOB+d78tNkX+ATPrH9Yo4ponl1Fz/wLstBFUP/QHbNRpmKXnPe7mN/7MiWOmc8Q3z6vTHr1qcBoWM2k6R+J72Z4KS5YsobCwMG3nS+fvf8CAAYwcOZJPP/2UX/7ylwn3qU1ude/enYULF3Luuefy8MMPc/rpp3PBBRdw0003JTUmERERyW4ZneASyVYTJkx4JewYRKTZ+sQ+vxvfaGZdgGHAolYc8yXg601sr4md42Dgm0ARgLuvNrN/EtSAqp8ca7amRl10XrKo0UxNzXOVVN9yKx1+Nh0bOJDd512Ar3oKG9b0AOeWjPKIRBNnira9u56dVR+Sf8xpdDuoT932j7fRc8DxSTl/E3EdAGwC9k2weeeoy+/70qur73u/reepb9myZXMb2zZr1qyJs2fPnle/febMmZe09nxh//5rR1v913/9F3l5edx///17RmLFS5Tc2rVrF+Xl5Zx++ul897vf3ZPg0igjERERgQwrMi+SK9oyfURE0q62ztGgeu1XEkwbbGmBeYCHYp9H1WsfBVQBL8e+7wdsrjdC7A0gvxXnbJOal/9G9Q030uEn/03eMYM/r8V1z314TXMXj2y9zRsq6bhPV3r0+7c67ZteW80XDupL1/0PSen5y0rYRvCcQywBGefqshKSntzKJOn+/R966KEAPPfccw22NZbcit+/9udFRERqLV26tEGnkLQvSnCJiEh7t4GgxtbVZnaemRWYWTlwYWx7nQSXmY01s7EEi6AAFMba9iSz3H0RsASYa2aXm1mhmZUBJUBp/ZWBw+ZvvEn1ddPpcMnF5J180p72vKLR8NFH+KrUz7revKGSnv2PJ69D3cHlm9Y/k4bpiYGyEuYApwOL45rPKCthZloCCFG6f/8/+clPOOyww7j33nsbbDviiCPYf//9GyS3ALZu3cqgQYM48sgjkx6TiIhkt9tvv/2IsGOQcGmKYgbIpJU+MnlVCPlcJj1PzZkaUrtSx41TJlr816mOTaQ53L3GzMYR1MIqJ6if9RvgVuAGGhaYf6De97XJj43AYXHtY4DrgWuAg4DXCQrI/zpun7eAnma2T9worv6xY6WN9T+MTr9f0LB9333ptKBhAiIVvjU+cQ5p+AXlaTl/rbISFgGLaqfylZVQkdYA4syfP/+edJ0r3b//qqoqqqqqEm6LRqO8++67rFq1qsFqiTU1Nbz22mspiUlERLLb6tWrD1epmPZNCS6RFBg0aNBbYccgIs3n7usI6l7tYWZ3A3+rP9qqufV+YgulRGIfje2z1cyeBi4CaovMfwlY3rJHILlozZo1B+fn57fL+8nSpUvDDkFERLLMxo0be4cdg4RLUxRFUqC8vPzxsGMQkTYbQuvqb7XUpcC5ZrYOmAcUh7WComSWOXPmjAw7BhEREZFsoQSXSApMmjRJb0pEspiZfYGg6PzzqT6Xu29w92+5+yB3P9rdV6b6nCIiIiIiuUZTFEVSYN26df3CjkFEWi82vbBD2HGIiIiISPOUlpYuDDsGCZdGcImIiIhkoOLi4tQvXykiIiKSIzSCSyQF8vPzN4Udg4hIImGv3JtJq8BmulSsBBX2778lK+/W0qq7IiLSHNOmTRuzdOnSeWHHIeHRCC6RFNAKHiIi0lYFBQUTw45BREREJFsowSUiIiIiIiIiIllNCS4RERERERERyWojRoz4S9gxSLiU4BJJAa3gISIibTVo0KC3wo5BREQkW0yZMkUJrnZOCS4RERGRDFReXv542DGIiIhki6KiovFhxyDhUoJLJAWmTZs2JuwYREQku02dOnVo2DGISG4zsz5mdrOZrTazj83MzezoJvYfYWbLzWy7me0wsxfMTP/3SkaoqqrqGnYMEi4luEREREQyUGVl5RFhxyAiOe9w4DvANmBlUzua2UXAY8BLwFjgLOAuoEtqQxQRaZ6OYQcgIiIiIiIioVjl7j0BzOx8YGSincysHzAHmOLuN8VtWpLyCEWaqVevXlvDjkHCpRFcIimgFTxEREREJExmlmdmPzaz18zs09h0wmFm9qqZzQNw95pmHu4iwIFbUxawSBtFo1Et9NXOKcElkgJawUNERNpKK/KKSBvdAVwLzAVGAQuA+4ABQEv/Vx0K/B04J5Yw221mb5rZVWam95SSEVS7UrLyYqRiiJLptIKHiIiIiITFzIqB84Eid/+Vuy9391LgGYIyNc+38JCHAgOBWcBNQCHwe6AUuCFZcYu0hWpXSrbW4KothvgXgmKICeeKw55iiHOB24BfEAytPRoVQ5QU0goeIiLSVtOmTRuzdOnSeWHHISJZ6WrgcXevXzh+PbALeLGFx8sDugHj3P3BWNtyMzsYiJjZ9e6+A8DMfgacS/Ce7Zy4/ZPCzDyZx5Pm++E9wa8+rOdg8uTJe92noqJiYqL2goKChO3t0ZQb59b5PhP/ptzdWvNz2ZrgUjFEERERERGResysD0GH/qwEm/sBL7v7zhYe9n2CEVxP1Gt/AjgPOBJ4Ltb2OMHqivNbeA4RkTbJuARXbA73j4BLgL7Aq8APgHnASnefqGKIkum0goeIiIiIhKRP7PO78Y1m1gUYBixqxTFfAr7exPY978/cfXXsfK04zd61dmSHtF0kikN4z8GyZcvmNrV98ODBXfPz8z9OtG3mzJmXpCaq7DN1xrw6I7Zy6W8qE2twqRiiZD2t4CGSm1QDUtJJK/KKSCvVdrQOqtd+JdCblr+nAngo9nlUvfZRQBXwciuOKZJUa9asOTjsGCRcGZXkUTFEyRVawUMkZ9XWgNxGUAOyUbEakI8R9HqPBc4imLKhGpDSLFqRV0RaaQNBja2rzew8Mysws3Lgwtj2OtcWMxtrZmOBIbGmwljbnmSWuy8iKPMy18wuN7NCMysDSoBSd/8k1Q9KZG/mzJnTaG1uaR8ybYpiThZDzMSibbkmjIKHTRU5rKyspKKiIuEqHu2xwGFtIUMz8/ivw4wpE+XS8OAcphqQkjZFRUXjH3nkkXvCjkNEsou715jZOIIZMeUE9bN+Q1C25QYavqd6oN73M2OfNwKHxbWPAa4HrgEOAl4HLnP3XyczfhGR1sqYEVxxxRDrX2ChbcUQIXExxH0IiiHWepzgjcqqFp5DRERygJnlmdmPY1PaP41NJxxmZq+a2TwI3jQ083CqASltphV5RaS13H2du5/q7vu5ez93vxYYDPyt/mgrd7dGPg6rt98Od4+4e2937+zuRyi5JSKZJJNGcOVsMUSNyki9MAoeNlXkcNasWRNHjx6dcGn39ljgsLaQobtb/NfhRiXSwB0EvdM/J5i+cRJBDcgefN6b3VzxNSCvBfoDbxP0ps9oQaJMREQkWYYAz6b6JGb2c+ACgvvn4NhUxmHu/nqqzy3tW3Fx8VNhxyDhypgRXKgYouSQ+fPna0qJSBZRDUjJRFqRV0SSxcy+QPA+q6X3sxZz92vdvY+77+PuB8W+VnJLUm7ChAmvhB2DhCuTRnDFF0P8AHiHoCjv6bHtDYohxr6ML4b4VaAqVgQRd19kZrXFEHsA64BvExRDnKZiiJIqa9asOTg/P/+tsOMQkWbLqRqQqnHXdumq7dhUPcfi4mIqKioa1G3M9VqOtbUaa+n1HB6Nts4dsXtOh7DjEEmlgoKCiUuXLk04i0bah4wZwRWbrjGOYFRVOXAnwaiuW4FqEhdDfAC4PPb9zNj35fX2G0NQVPEa4I/AaQTFEH+R/EchEtAKHiLZQzUgJVMtWaI1CURERESaK5NGcOHu64BT49vM7G4aKYbYzGPuAEoNzocAACAASURBVCKxDxERkfpyrgakRl20XbpqO+6tnuPs2bMb9ETnei3H2lqNtfR6FhERkebImBFcTRhC6+pvtYiZ/dzM3ga+QTCl8W0z+3KqzysiIqFTDUgRERGRLDdo0CCViGnnMmoEV31xxRBvS/W5YkvnXpvq80j7oBU8RLKKakCKiIiIZLny8vLHw45BwpXRI7jcfYe7d3D3OWHHItISWsFDJHuoBqRkKq3IKyIi0nyTJk1SHeR2LqMTXCLZKtdXuBLJNe6+zt1Pdff93L1fbFTvYBqpAdnIx2H19tvh7hF37+3und39CHf/dRoflmS5NWvWHBx2DCIiItli3bp1/cKOQcKlBJeIiEhiqgEpodKKvCIiIiLNpwSXiIhIPXE1IJ9P9bnc/Vp37+Pu+7j7QbGvX0/1eUVEREREcklGF5kXyVZawUMku7n7DqBD2HGIiIiISPMsXbp0XtgxSLg0gkskBbSCh4iItJVW5BUREWm+22+//YiwY5BwKcElkgJawUNERNpKK/KKiIg033333Tc07BgkXEpwiaSAVvAQEZG20oq8IiIizZefn78p7BgkXEpwiYiIiIiIiEhW27hxY++wY5BwKcElkgLqPRARERERERFJHyW4RFJAvQciItJWWpFXREREpPmU4BIRERHJQFqRV0REpPlKS0sXhh2DhEsJLhEREZEMNHXqVK0GJSIiItJMHcMOQCQXqfdARETaqrKy8gjgqbDjEBHJJp2XLPJUHv+zwlGWyuNL602bNm3M0qVL56XyHGaW0tcXgLvrNdZKGsElIiIiIiIiIiJZTSO4MkAqexnUwxCOVPceRKKk7DVTVkLWvmZS2aOinhQREREREYhEsbKS1L0fEWktJbhEREREMpCmu4uISNgiUfoBE4Hz4po/i0R5A7gDmF9WwpZQgqtnxIgRfwk7BgmXElyS1SJRugB94r7fv6yEj0IMSUREREREJKtFouQDs4EzaFjaqCMwELgR+Fkkyu+AyWUlfJDeKOuaMmWKElztnBJckpUiUb4CXApcAOwft2lLJMqDwG3A02ENnVXvgYhkqlRMi9d0+NRIxXT3VExxz6ap7WE//lRMpdcUehFJtkiUY4FFQK9m7N6ZYHTXiZEop5WVsDGlwTWhqKho/COPPHJPWOeX8KnIvGSVSJSukSj3An8HItRNbgF0AooJVp36f5EofdMcIqDeAxGRbBWJsk8kyoD478OMR0Qklcysj5ndbGarzexjM3MzO7qJ/UeY2XIz225mO8zsBTMbk86YJbVi98DFNC+5Fe8rwOJIlIOSH1XzVFVVdQ3r3PUdeOCBDB06lKKiIkaNGsXxxx9Phw4dGuzXuXNnrrnmGvbdd98Qosw9WZvg0sW4/YlE+QLwJEECqzmOB56NRDk8dVElVlRUND7d55Tk6tKlS9ghiEgaRaL0j0SZAbwDvB636Z+RKP8bifLlkEITEUmlw4HvANuAlU3taGYXAY8BLwFjgbOAuwD905QjIlEM+B3QI9H2spLgowmDgF8nP7LsccIJJ3DXXXfxzjvvsGrVKv7whz/w2GOP8dxzz/HGG28wbdo0evbsCQTJrQcffJCf//znzJ8/P+TIc0PWJrjQxbhdiUTJI7jYfiPR9iYutocCiyJRDkxddA1lUu+BfO5LX/oS06dP59FHH2XVqlU88cQT3HHHHXzrW9+qs1/fvn156aWXuPTSS0OKVDKVOldyTySKRaJcT5DUuhIa9DwfCPwYWB+JMiN2P0qLTJruvn3Lmyyee37YYYhI8q1y957ufjpwf2M7mVk/YA4wxd1/4O6L3X2Ju89y92jaok0C/+QTdo07l5pVf/q8bedOdkf+m90/K8VrakKMLnQnEgwSaIsxkejnNZLTqVevXlvDOC9Ajx49WLFiBf/v//0/vve979G5c2eee+45KioqeOKJJ9iwYQN9+/bl+uuv5x//+AelpaU8+OCDnHHGGbz//vvceOONYYWeU7I5wdUuLsa6AO8xHPh2K3/2cGBSEmPJeLd//1DWLr+9Tpu7Uz7hi6yvfCikqMLz7//+7zz44IO8+eab/PSnP2X06NEMHTqUESNGcOGFF7Jy5UrWrl3LxRdfTN++fVmxYgVf/vKXOf/88xMOJZZ2TZ0rOSTWU30LMA2aVUfpSmBu7OdSTtPd269u3brRuXPnhNsOOeQQBg4cmOaIJBuZWZ6Z/djMXjOzT2OdLMPM7FUzmwfg7s19M3ER4MCtKQs4TaxLF/LGnk119F7cHa+upvr6X0CnTnSYeiWWl81vkdssGe+Z8oCLk3CcFotGo6GsPty3b1+effZZhg0bxvvvv88vf/lLBg4cyIknnsgZZ5zByJEjOfzwwyksLGThwoXk5eVx9dVX70luDR8+nBdffDGM0HNORv716mL8OV2A97isjT9/SSSavkUVwuw92PHBO1Rt20SP/GPrtH/03gY++/Rf9BwwJKTIwnHmmWfy9NNPc/bZZ+Pu3H///Zx99tkMGzaMkSNH8rOf/YxNmzZx1FFHMW/ePF5++WUGDBjAc889x2mnnUZ1dXXYD0EyS053rrTDTpVLaOT+0sTI4AnAFSmMaY9Mme6+4jdXsOiWc9n44uM8eP0pbH4jd/NuYXUQ5eXlMXr0aB577DF27drF9u3b2blzJ5s2baK0tJR+/foBQXJr+fLlrFixQkkuaY47gGuBucAoYAFwHzAAaOkf8lCCGrjnxN6j7TazN83sKjPLujckeUVnwAcf4k89TXXZHHzrVjpMvw7r3Cns0EITiXIAQSdeMkxMV2dQvKlTpw5N9zn3339/Fi1axIABA6isrOTII49kypQpbNiwoc5+7s6TTz5JcXExlZWVe9orKiqU3EqiTL0Y6WIcp71fgGNDXP+zjYfpC4xOQjjNElbvAcDmDZVYXgcO6lN31tTWt16g6/496XZQKHX3Q1FYWMiCBQvo0qULd955J/n5+Zx77rksXLhwzxTFn/70p+Tn5zN58mRqamro1q0bW7ZsYcSIEXz00UdhPwRJI3WutK9OlUiUDgQjslrjx+noNEnXdPd/rnuah//3dP7v8t7cdtEXuHPyAFY/cM2e7ad8bw6jvv878o8ZydhrVtCz/3HpCCvtwuogOv7441m/fj2PPvooo0aNomPHjuzYsYNdu3bRq1cvrr76at544w3uvvtuVqxYwZFHHsn777/Ptm3bUhKP5AYzKwbOB4rc/VfuvtzdS4FngI7A8y085KHAQGAWcBNQCPweKAVuSFbc6WJd9iVv3NlU/2om/uKLdLzh59h+7b7CSD9I2sIqvYBuSTpWs1VWVh6R7nNOmTKFo446irVr11JYWMh7773X6L61Nbe+/vWvs337dnbt2sX3vvc9jjnmmDRGnNvSNqKlueIuxqe4e+30j+Vm9jVgDK27GB9KcDGeBrxKkOgoJViBb2oSwk6p+Asw3Q+gY9lN7e0CfBLJScYOBR5OwnH2aurUqUNvvPHGp9Jxrvo2b6ike69BdOxcdyWOLW+9wCH928/orW7durFgwQI6derE//7v/3LllY2/j+3VqxdXXHEFeXl5VFdX06NHD4qKirj77rvTGLFkgDsI7jM/J+hMOYmgc6UHMLOFx4rvXLkW6A+8TdBxM6MFibK0yys6g5oHF+JPPU1N5Z/xrVvp+Ktf5mKnymkEz0tr9CWYNv+H5IUTjjdfeJxFc86hYML/8eXJwS1y61svsn1raKu8hyaMDqJhw4bx2GOP0bVrV9avX095eTl33XUXH3zwAQDf+MY3uOyyyzjnnHMYPz4Y0Ld27VoKCgrYsmVL0uORnHI18Hjc+6la64FdQEuHjOQRJCzGufuDsbblZnYwEDGz6919h5l1B+4mKDb+CbAZuMzd17f2gdRnZt7U9k6LH2v+wT79lA7fOQfr3j1p589Wh37lm4y79vO3L00Vk0+0LVJvfPodP+j70ezxbycpusDkyZP3uk9FRcXERO0FBQUJ29uic+fOTJgwAYCJEyc22Tlem9yKn5Y4YcIErrjiCiZNmsSkSZ/PDk31a2zKjXPrfJ+Jr2l3b9UIwIxLcJGDF+OkXYTb6QX46FMvpuCieXu+b8nFNv5C+/KKO35k4yf8KFlxNXWBrayspKKiImEPQjIurj+8p/GndfOGSrZtXs/cSw+u075r5w6GnHHVXo+ditdM7UXUzDz+62SfJ953v/tdDjjgAP70pz8xZcqURverrblVOy0xGo0ye/ZsrrjiijoJrnT8LbX2Qi5tp86Vz7WjTpW2Tv8bT4oTXOmY7v7ik7dy2LHfZtDXP5+V0nPAkHY3nR3S30HUv39/Hn74Ybp27cpdd93FxRdfzO7du+vs88wzz/D6669z0kknMWDAAACef/55JbekSWbWBzia4B5UXz/gZXff2cLDvk8wguuJeu1PAOcBRwLPEYxeLnP3J2Ox/AC4k6DjJ2PUPLmMmvsXYKeNoPqhP2CjTsOsff8btnvnx0k93q6dVUk9XiYaO3YsPXr0YM2aNTzzzDON7pcoufXiiy9SXl7OFVdcwfjx45kyZQrbt29PY/S5KaMSXLoYJ9beL8DVuz/LqONkus1v/JkTx0zniG+eV6c9etVgerajEVyXXRaU1Zk9ezbuiXNT9ZNbI0aMYOfOnVx33XUcf/zxDBkyhD//+c/pDFvCk1OdK00lZFPRqZKNnSljrl5G3yNPBVrXcfLPV/801mxomx93U50lxcXFCXui29JRUr+DpEu3Hmx4/hHWPD6b/MEjOPBLLZ/dkeznP5U9y6noIGptfD/84Q854IADqKio4KKLLqImQY272ppbAwYMYP369fTr14+SkhKuueYa/vGPf7Tp/M2hjpesVbuC3bvxjWbWBRgGLGrFMV8Cvt7E9hoAd98GPBnXvprWTwdPaG+vy85LFjX5N1HzXCXVt9xKh59NxwYOZPd5F+CrnsKGfaupH2v2+bNVJMqhwDtx3zdQe09MtK2eTy+d+8EXykpIajHbZcuWzW1q++DBg7vm5+cnzNTNnDnzkmTEEH/NLSkJfiHl5eWN7t9YcgvglVdeYcWKFZxyyin853/+557O9VS/xqbOmFfnbySXXtMZleAiRy/GbbkI6wIMkSijCFYiq/2+geZcbI/5j0n/s+zOSdOTFVdTF9hZs2ZNHD169LxE25JxcY1ESfia2fbuenZWfUj+MafR7aA+dds/3kbPAXtf9TcVr5nai6i7W/zXyT5P7Q3n2GOP5aijjmLTpk08/HDiWamJklu1w4rvvPNOfvzjHzN+/Pg9Ca5c+FuSxNS5Uld76VTJy2vbCqnWxp9vjiVLllBYWJjScwz77my+2KM/f1t1J6uik+l2YF9OHDOdo4ZdUGe/Dp32pXvvr6Y0lrCls4Ooa9eunH/++QBcc801TSa3jjzySF566SUKCgqYPXs2xcXFTJw4kWuvvTapMUlOqR39OYi4/6EJ3tv0puU1jQEeIlgZr7Y+cq1RQBXwciM/FyFNJUKao+blv1F9w410+Ml/k3fMYIBg1PI992FDv5lTtSZbqqyEf0airABOScLhfpfs5FZzrFmz5uD8/Py30nW+3r17AzTaId5UcqvWn//8Z0455RR69eqV8njbg0xLcOliHEcX4D2WAVsI6uC0xe+SEEuzzJ8//550nSve5g2VdNynKz36/Vud9k2vreYLB/Wl6/6HhBFW2tXebF544YUG0z2g6eQWfH6Tqj2O5Lyc61xpKiGbik6VbEwAR6I8BJwZ+7qBvXWc9B74jT+6e5sXL9lbZ8ns2bMbdJa0paOkfgdJ5y7dOPGsaznxrGv5+KP3eHbhdJbePoF+RxfW6SjZ74BeHF+UeGZtsp//VPYsp6KDqCXx1XbEnHXWWey///6sXr2aF154ocF+iZJbW7Zs4bbbbqO4uJgLL7xwT4IrG//+JOU2EIw8vtrMPiAYlTMWOD22vc57KjMbG/uyNpNbaGZfBarcfRGAuy8ysyXAXDPrAawjqEVYAkxz90/qB2FmPwUOB4Yn88G1lr/xJtXXTafDJReTd/JJe9rzikYHtSdXPYWdMizECDPCbSQnwXVbEo7RYnPmzBl55plnJhxkkApTp06lT58+vPHGGwm3f/vb324yuQVw//3388ILL2jWSJJkWoJLF+MYXYA/V1bCzkiU24G9F5Bq3LKyEv6erJj2Jt29B7U2b6ikZ//jyetQ90970/pn2tX0xNWrV/PNb36TTz5p8OcNwBlnnNFocgtgxYoVFBQU8NZbaX8KJRzqXKFddqo8TCzB1Yafzyld9z+EgSeM5aWl5ez+LLm1WDJdujuI8vPzAVi1alWDbY0ltwCefvppqqurOfTQQ+nYsWPCThwRd68xs3EEC5uUE4wq/g3Byr430HDa/QP1vq9dWGUjcFhc+xjgeuAa4CDgdYJp9b+uH4OZXUNQe7LQ3TPigmL9D6PT7xc0bN93XzotuDft8WSohwk6/NoynOjPZSVUJimejLZ48eImtz/00EN8//vf56mnnkqY3IKgY13JreTJqASXLsZxcfTXBbieucBPaP1r9pYkxrJX6e49qPWt8YkXeht+QePzwnPRRx99xNNPP93o9ttuu42PP/6Yhx56KOFqJ5s3b2bz5s2pDFEyS7vvXGmnnSoLCP5vOLAVP/sRwQqbWa3ykV9wSP8h9B74DTp17sqWjX/lT7+7kvzBp9G996Cww0urdHcQ3X777SxbtizhvWbo0KF89atfbZDcAnB3hg8fzvbt2xNOaxSp5e7rgFPj28zsbuBv9e9BzR0F6O47CDpiIk3tF7ufnU7wfmpbS+KWcJWVsCsS5WKCRVRa07P1MXBZcqPKbrfeemvYIbQrGZXgAl2MJbGyEjZGolwC3JFo+14KHc4lB3vapW3uuuuusEOQDKHOlfbZqVJWwieRKHNp3ejg/ysrIeXLQ6V6uvvunR/zVHQy/9r6FuTl0e2gfhxx8nf5txFXpPK0GSndHUTvvfce7733XsJtv//97xk3bhxPPfVUwtUSE436EmmmIcCzqTyBmR0FTCe4562oreHo7sem8rySPGUlVESiTATmUS/JtZf3XJ8C48IcvVVcXPxUWOeWzJBxCa5G6GIslJUwPxJlP2A20Nx6E3cB3y8rSVxzQ0QE1LnSjk0HTgAK6m9o4p/4VQRJy5RL9XT3b4z7Od8Y9/NUHV7aYOHChWGHIDnGzL5AMBU/pbWR3P1lmv9/umSoshLuiETZQvBeau/LKQej38eVlfBMSgPbiwkTJrwS5vklfBlfUCPuYvx8Ks/j7i+7u7n74e5+bO1HKs8pLVdWwhyCN4J/2suurwGTgAvLSkh7gQr1HojkhCG0rv5Ws8V1rhxE0LnyVzP7ayrPKZ8rK+Ez4D+Bimb+yCLg22UltHRVzVaZM2fOyHScR0Ryn7vvcPcO7j4n7FgkO5SV8AjwJeACaHRU1jKCsg79w05uARQUFEwMOwYJV8aP4Ir1gKd+LW7JGmUlPA48HolyDHApMBjYn6Bw85vAfGBpWQmhFadQ74FIdlNPd/tRVkJVJMqZBFNELwNGJNjtSYLXwqNhdJqIiIiEoayETwhGcd0ViXIEQcKrG0EtyjfLStgQYngiDWR8gkukMWUlvEiGFjEsKCiYuHTp0rQXmReR5FDnSvtSVkI1QUHdP0SiHA4cA3wR+BfwUlkJ68KMT0REJGxlJbwCqBNfMpoSXCIiIiIxZSWsB9aHHQdouruIiEhLDBo0KGV1KyU7KMGVAT4rHKXpKdIiZSWa0pRIc4t/T50xr86iAzdOmajfp4hkHE13FxFpOb23ar/Ky8sfT/U5mvt+A/SeIwxKcImkgHoPRCRT6R//7JGK6e7tvYMk7MffnDdGekMkItI6kyZNGpmOJJdkroxfRVEkG+nCKiIiIiIikj7r1q3rF3YMEi4luERSYNKkSVraXURERERERCRNlOASSQH1HoiISFtpuruIiIhI8ynBJSIiIpKBNN1dRESk+ZJdt1KyjxJcIimQn5+/KewYREQku02dOnVo2DGIiIhki9tvv/2IsGOQcCnBJZICGzdu7B12DCIikt0qKyv1j7qIiEgzrV69+vCwY5BwKcElIiIiIiIiIllNgwxECS4REREREREREclqSnCJpEBpaenCsGMQEZHspnuJiIiISPMpwSUiIiIiIiIiWU0dQ6IEl0gKTJs2bUzYMYiISHbTvURERESk+ZTgEhEREREREZGspo4hUYJLRERERERERESymhJcIikwYsSIv4Qdg4gkn5n1MbObzWy1mX1sZm5mRzex/wgzW25m281sh5m9YGbqXZRm0b1EREREpPmU4BJJgSlTpuhNiUhuOhz4DrANWNnUjmZ2EfAY8BIwFjgLuAvoktoQJVfoXiIiItJ86hiSrExwqQddMl1RUdH4sGMQkZRY5e493f104P7GdjKzfsAcYIq7/8DdF7v7Enef5e7RtEUrWU33EhERkeZTx5BkZYIL9aBLhquqquoadgwi0jJmlmdmPzaz18zs01hnyDAze9XM5gG4e00zD3cR4MCtKQtYcp7uJSIiIs2njiHJ1gSXetBFRCTZ7gCuBeYCo4AFwH3AAKClPYJDgb8D58QSZrvN7E0zu8rMsvXeKyIiOUSzYiTXqGNIMu6fbPWgSy7o1avX1rBjEJHmM7Ni4HygyN1/5e7L3b0UeAboCDzfwkMeCgwEZgE3AYXA74FS4IZkxS25TfcSEUkxzYoRkZzSMewAErgDGAP8nKDH/CSCHvQewMwWHiu+B/1aoD/wNkHv/IwWJMpEWiQajS4MOwYRaZGrgcfdvf4/+OuBXcCLLTxeHtANGOfuD8balpvZwUDEzK539x0AZvYwwSix6ti5rnb3J1v5OIgd09vy85I+kydPbnRbcXExFRUVE+u3FxQUNGjLJVNunFvn+/b2es6kx+/uFta5JS1WuXtPADM7HxiZaKd6s2Juitu0JOURirSAOoYko0ZwqQddcsXUqVOHhh2DiDSPmfUBjgYeSLC5H/Cyu+9s4WHfj31+ol77E8A+wJFxbee7+zHu/u/AJcDvzaxDC88nOWjJEr13FJHW0awYaY80yEAybQRXTvWg12pvPY/tRVO97pWVlVRUVByRaFuu97wnUtsbbWYe/3XY8dTKlL9R9ZSHpk/s87vxjWbWBRgGLGrFMV8Cvt7E9j1vKtx9W1z7/gRvItr0WtBrKXssW7ZsbmPbZs2aNXH27Nnz6rfPnDnzktRGFa6pM+bVuSa3t9dze3/8kjSaFSPtztSpU4feeOONT4Udh4QnY0ZwqQddRERCUjucfVC99iuB3rS8wDzAQ7HPo+q1jwKqgJfjG83sVjPbQDDK+Gx3392Kc4qIiGhWjLRblZWVCQcYSPuRSSO4cq4HPe7Y6nnLQXvrdR89enSDXnfI/Z73RGp7o93d4r8OO55a+htt9zYQjBC+2sw+AN4hKKB7emx7nQSXmY2NfTkk9rnQzL4KVLn7IgB3X2RmS4C5ZtYDWAd8GygBprn7J/HHdPfLY8ceBswys2/VjjAWERFpoZycFVMrU0beS/o1NYOmVqLalRDOLJpMnTWSqXHFa+37s4wZwYV60CWHzJ8//56wYxCR5olNrRhHcE8oB+4kuCfdSvAPev03Ag/EPi6PfT8z9n15vf3GAL8BrgH+CJwGXObuv2gilpUEnS8nt/4RSa7QvUREWkqzYkSkPcukEVzqQZecsWbNmoPz8/PfCjsOEWked18HnBrfZmZ3A39LcK9oVo9S7P4RiX0kZGZfAA5y942x7/8d+DLwSosegOQk3UtEpBVydlZM3Dk08r6damoGDcDgwYO75ufnf5xoWxizaDJ11kimxpUMGTOCSz3okkvmzJmTcJllEckqQ2jd6OGW2A+438zWmtlfCe5h491dSQ3RvUREWkOzYqTdWrNmzcFhxyDhyqQRXOpBFxGRjBC7LwwCbkvledx9M033iouIiLSEZsVIuzVnzpyRZ555ZsI6yNI+ZFSCqxFDgGdTfI7aHvQvALuBT1EPuohIuxX7R1w1Q0REJKu4e42ZjQPmEowKfp9gNsutBCseJpoVE29m7PNG4LC49jHA9QSzYg4CXieYFfPrJmJZaWa1s2Lq1+8SEUm6jE5wqQddslVxcfFTYccgIiLZTfcSEWkNzYoRkfYqoxNc6kGXbDVhwgTdyEVEpE10LxGRJNKsGMl56hiSjCkyL5JLCgoKJoYdg4iIZDfdS0QkGeJmxTyfyvO4+2Z3/7q7H+3ux8a+/mMqzykSTx1DogSXiIiIiIhIjnL3He7ewd3nhB2LSCqpY0iU4BIRERERERERkaymBJdICgwaNEi1BkREpE10LxERERFpPiW4RFKgvLz88bBjEBGR7KZ7iYiISPOpY0iU4BJJgUmTJo0MOwYREcluU6dOHRp2DCIiItlCHUOiBJdICqxbt65f2DGIiEh2q6ysPCLsGERERLKFBhmIElwiIiIiIiIiktU0yECU4BIRERERERERkaymBJdICowYMeIvYccgIiLZrbS0dGHYMYiIiIhkCyW4RFJg8eLFx4Udg4iIiIiISHuxdOnSeWHHIOFSgktEREQkA02bNm1M2DGIiIhki9tvv12Ls7RzSnCJiIiIiIiISFZbvXr14WHHIOFSgkskBVQ3RUREREREJH02btzYO+wYJFxKcImIiDSTmfUxs5vNbLWZfWxmbmZHN7H/CDNbbmbbzWyHmb1gZpp2Js2iBUtEREREmk8JLpEUUN0UkZx1OPAdYBuwsqkdzewi4DHgJWAscBZwF9AltSFKrpgyZYoSXCIiIiLNpASXiIhI861y957ufjpwf2M7mVk/YA4wxd1/4O6L3X2Ju89y92jaopWsVlRUND7sGERERLKFysSIElwiIiKAmeWZ2Y/N7DUz+zQ2nXCYmb1qZvMA3L2mmYe7CHDg1pQFLDmvqqqqa9gxiIiIiGQLtgIMjgAAIABJREFUJbhEUkB1U0Sy0h3AtcBcYBSwALgPGAC09G96KPB34JxYwmy3mb1pZleZme69IiIiIkmmMjGSlf9kq8ivZDrVTRHJLmZWDJwPFLn7r9x9ubuXAs8AHYHnW3jIQ4GBwCzgJqAQ+D1QCtyQrLglt/Xq1Wtr2DGIiIiIZIuOYQfQSrVFfv9CUOR3ZGM7xor8zgVuA35BMGXkaFTkV1KoqKho/COPPHJP2HGISLNdDTzu7vULx68HdgEvtvB4eUA3YJy7PxhrW25mBwMRM7ve3XfE/4CZTSS4X8X/TKuYmbfl5yV9Jk+e3Oi24uJiKioqJtZvLygoaNCWS6bcOLfO9+3t9ZxJj9/dLaxzi4iItFRWjuBCRX4lw6luikj2MLM+BB0fDyTY3A942d13tvCw78c+P1Gv/QlgH+DIejEMBC4Anm3heSSHLVmyJOwQREREsobKxEjGjeCK1Sb5EXAJ0Bd4FfgBMA9Y6e4TVeRXRESSqE/s87vxjWbWBRgGLGrFMV8Cvt7E9j33MTPrCMwHJgFlrThXAxp1kT2WLVs2t7Fts2bNmjh79ux59dtnzpx5SWqjCtfUGfPqjFhqb6/n9v74RURaS2ViJBNHcKnIr2Q91U0RySq1f6+D6rVfCfSm5fcegIdin0fVax8FVAEvx7VdCyxy97+24jwiIiIiQlAmJuwYJFwZNYIrrsjvKXF1UJab2deAMbSuyO+hBEV+pxGMBhtNUOR3f2BqEsIWaSAajS4MOwYRabYNBDW2rjazD4B3gLHA6bHtdRJcZjY29uWQ2OdCM/sqUOXuiwDcfZGZLQHmmlkPYB3wbaAEmObun8SOdSIwHDglRY9NREQkodgU/SsJ7mfHEtQoHuzuaxvZfwRwFXAcwUCJ14H/cXf93ysZQWViJKMSXORYkd+4Y7ar4qjtRVOFgZcsWUJhYWHCbbleHDiR2oK5ZubxX4cdT61M+RvVNJRwuHuNmY0juPaXE9TP+g3B9PYbaHjvqV+ra2bs80bgsLj2McD1wDXAQQRvBC5z91/H7XMq8GXgdTMD6AUcaWb57n5T2x6ZZLv58+drsRIRSSUt3CUiOSVjpumpyK/kkrVrE3Z8iUiGcvd17n6qu+/n7v3c/VpgMPC32tFWcftaIx+H1dtvh7tH3L23u3d29yPqJbdw9xvd/VB3Pyz2888SJMGU3BLWrFlzcNgxiEhO08JdklNUJkYyaQRXzhX5raVRGblpb4WB/z97dx5eVXktfvy7AoKoOCEOLYJzpQ71XuG2dRauqK11xhbRKoooTjfaXhNFW3+OoU5YVAStU41eJ6oWhaqAdaitaLFataVK1Xqdr6UqIAi8vz/2CYZwAgRypuT7eR6ek+y9z94r5CQ5a+33Xe8BBxywVGNgaPvNgfNpaJibUorGH5c6ngb+jKoZffCGh0po9OjR+x188MF5/5ZI0rK4cJfaI9vEqGxGcGGTX0lSmYiItcj+HrW09+MqSSnt1VrT4yVJ7ZoLd6ndqa2t3b3UMai0ymkEl01+1WbYN0WqbLn+jB1KHYckSS3lwl1qr6ZNm9YbeLLUcah0yqbAZZNftSXTp0/foFevXm+VOg5JUuUaNGiQb9IlrYw2uXBXo3OXxeJAKr5lLfLVYMKECXkX9CrFQl/lurBVucbV2Mq2kCmrIaU2+VVbMXr06GZXoZEkaUUMHTr01VLHIKmyuHCXpPasbEZwLYNNfiVJUrvTv3//YZMnT7bJvKSWaLMLdzVwcaD2a1mLfAHssMMOa/Tq1WtOvn2lWOirXBe2Kte4WkNZjeBqyia/kiRJkrTCXLhL7db06dM3KHUMKq2yHsFlk19VKvumSJIkqQRcuEvt1ujRo/c7+OCDHfncjpV1gUuqVPZNkSStqm222cbFSiS1iAt3SWrPynqKolSpSrFKhySpbRkzZsykUscgqfK4cJek9soRXJIkSSXSr1+/ZpveRsTOKaWV6ZcjSU25cJfaPNvEyAKXJElSGbK4Jak1NFq467piXjeltFcxryfZJkZOUZQKwL4pkiRJKge56YUdUkqjSx2LVEi2iZEFLqkA7JsiSZIkSVLxWOCSCmD48OH7lToGSconIjaNiMkR8WpEvBwRl5Y6JmllRcReudfxaxFxY0R0KHVMxRQRV0fE2xGxoNSxSJJUaha4pAKYMWNGz1LHIEnNWADUpJR6A/8G7BYRB5U4JqnFIqIKuBEYmFLaClgbOKq0URXdPWTNwyWp3bNNjCxwSZLUjqSU3k0pPZf7eD4wHbAor0rUF3gnpfRK7vNfAIeVMJ6iSyk9lVJ6r9RxSFI5sE2MXEVRWknLWtodeLdfv37nFysWSVoZEbE+cDAwoNSxSCuhB/CPRp+/BWxaolgkSSU2fPjw/SxytW8WuKQCSCmdX+oYJBVWRHwVGAh8B9gW2Bj4GHga+FlK6Q/NPC+AQ4DTcs9bhyxJfxwYmVKaWfDgszg6AfcCV6eU/lKMa0rNqR05bjVgtWb2rQGkupphc5vsioIHViS1I8d1BDo1s28NgLqaYXOKGpQkVRjbxMgpipIkrZzTgKuALYBHgCuAp4CDgN9FxBHNPO9y4D7ga8D9wGjg78AJwAsRsX2B4ybXiPsO4IWU0hWFvp60Ar4BzM79a2o2cF6e7f9gyRFbPYG3Wz+0ouhBViBv7usfU9xwJEmqPBa4JElaOc8Ce6SUtkopDU0pnZ1SOhzYG1gIjImIzo2fEBEbA9XAm0DvlNLwlFJNSmk/4EdAV+DMIsQ+Dvg0d02p5Opqhj0H3NLM7veAfKt9Pgf0iIiv5z4/Hhjf+tEVXl3NsDfIiuT5zAHOLl40kiRVJgtckiQ1IyIOiogJEfFBRMyLiDcj4o6I2CGlND6l9GTT5+S2TQXWB3Zosnszsr+9T6WU/tVk34TcY/dW/jKWEBG7AseRrbw2PSJeiIjTC3lNaQWNIP8IpnPqaoZ92nRjSmkhMBS4NyJeBz4DflnYEAuqjqyY19SldTXD3sn3hIgYGxFvAx0i4u2IuLagEUpSGZs8efK4Useg0rLAVWIRsWlETI6IVyPi5YjId4dSanciYq/cz8RrEXFjbkpVqWK5Opc4LChVDCquiOgYEfVkUwh3IBsVcjXZioOHAV9dzikWNHls8DdgPrBrRHRtsu87ucfJKxv3ikgpPZ1SipTSDimlnWrqxp5dUzd279qR4zYs5HWl5ckVcZq+D5oO3Nrcc1JKU1JKX08pbZlSOi6lVLG/p3NFvHOabH6L5kd2kVI6MaXUI/cz3SOldEpBg5SkMnbjjTf2LnUMKi2bzJfeAqAmpfRcruHv5Ig4KKX0QKkDk0olIqqAG4EDU0qvRMTdwFEsI8kpsHvIkq5K7e2ilhsNHAlcA5zROGmOiB5A09FXNNrfE+gPvAu81HhfSun/ImIEcBnwakQ8SDZVcAfgP4Hrc9csitqR4wI4H9gQmFWs60rLcCVZP7peuc+r62qGLSphPMV2K3Aq8O+5z8/K01xfktql5axiT//+/c+/4447zi9SOCpDFrhKLKX0LlkSREppfkRMJ2uSKrVnfYF3Ukqv5D7/BXAKJSpwpZSeAsgWv1NbFxG7AycBk4DTU0qp8f6UUrOFzohYjWyKVGeymxcLmx6TUro8N6VoHDC80a6ngNtbYwRK7chxaflHLWVe7UhH9qvs/Ladvy7/p3bkuP8p1cXraob5h09SxXAlezlFsYxExPrAwcCjpY5FKrEeZKtjNXiLJVfKkgqpOvdY27S4tSy5kYc3AXsAN6SU8vYCyo3gug24hOx13RXYHVgdeDwiDlyF2CVJkqR2yRFcZSI3PfFe4OqU0l9KHY+0qmpHjusMDGmy7aQmH88Gbq+rGda0iNDqd4xrR447lGwaVr59DXHdVVcz7J+tfW1VnAHAGymlP63oEyIb3ncD2VTa28lGgOU7rh9wEXBVSqmu0a6nIuJ7wEzgcuDBlYxdkiRJapfaxAiuiPhqRFRHxCMR8VZEzI+I9yLivoj45jKeFxFxaERMjYh3I2JORPw1tyLNFkWMvwNwB/BCSqnZRqJSJamrGTYP2BMY02hz04975SluQTZ6q/GIrZ6sev+rdXPXHJNn3xhgEPYgavciYl1gLeCNFjynimwa7XHAncCxKaXmegZ9N/c4temOlNJ7wF+ArSNirRaELUmSJLV7bWUE12lADfA68AjwIbA12XS/gyNiUErp7jzPuxw4k6wH1v3AJ8A3yJqbDoqIXVJKfy5C/OPImgz/qAjXkoqphuzncPU8+5a1MtRzQI+I+HquD9fxZKvYrYqGxr3/lmdfImtkvDJ9i9S2NIweXKEVBRstiDAEuAs4Ol/frUY65R67N7O/O7AI+GJFrt+c5fXNqR05bn/gYeCEupphN67KtSRJkqRy0CZGcAHPAnuklLZKKQ1NKZ2dUjoc2BtYCIyJiM6NnxARG5P1WXkT6J1SGp5Sqkkp7UdWaOpKVvwqqIjYleyufx9gekS8EBGnF/q6UjHU1Qx7i2y1uHyaXRkqVyAYCtwbEa8Dn5E17l6VWBbyZW+lpm6qqxk2vbnn5kZ1vg10iIi3I+LaVYlF5Sul9E+yaYK9I+I/m+6PiK81+rhh5NYQspU2j1pOcQvg6dzjmRGxTpNzn0TWf+6ZlNK8lf8qVsiZZKPUbivwdSRJKpqI2DQiJkfEqxHxckRcWuqYpJaIiKtz+cYqLzrUmiJir9zP1GsRcWNuFlrZqZgCV0QcFBETIuKDiJgXEW9GxB0RsUNKaXxK6cmmz8ltmwqsT7YEe2ObkX39T6WUmi73PiH32Nwd9laTUno6pRQppR1SSjullHaqqRv7UO3IcRNqR47bqtDXl4rgZ8A7Tbb9Dsg3qnKxlNKUlNLXU0pbppSOa42V5epqhj1B1uuusc+Ac5cTy4kppR65n9UeKaVTVjUWlbWzyUZyTYyIeyNiZETcHBF/BRr3zfoJcCzZa2gGcG5EnN/k305Nzn0P8ASwHTAjIm6IiMsiYjLZVNm5FOHmCnAEMLCuZtj8IlxLkqRiWUC2inFvslH7u0XEQSWOSWqJe8gGv5SNRjMWBqaUtgLWJus7W3bKfopiRHQkm1p0JNmUpvFkUwm3AQ4ju/v80jJOsaDJY4O/AfOBXSOia0rp00b7vpN7nLxq0a+0EUB/sgbcUkWrqxn2We3IcWeT/Rw3KOV0wLOA7wENozovrqsZ9l6JYlEZSindHRH/Av4b2Ifs9fIB2WjhUY0O3Sz3uBbZ7+183gBeaHTuhRExADiDrMh0JNm0xffJmtNfklJ6tbW+lubkFlN4rtDXkSSpmFJK75K1nyGlND8ippP1cpUqQkrpKYBs/aKy0Rd4J9c6BrIZDKewZH5XFqIFK6CXRESMIVuN6hrgjMajOCKiB/CvJsWpxs/tSXZX/WNg06ZTRyLix2TTp/6XbMWqT8lGev0n2TfttNYYNVI7clx5/ydLKgvL65skSZKkFRMR65PdZBrgKvUqhaZ1gJa814+IBSmlggxIamlcEXEYcGhKaXDu897AHSmlfL2NS6qsR3BFxO5kxa1JwOmpSTUupdTsqmoRsRpZz57OZMNUl+qLklK6PNdXZxwwvNGup4DbW6O4JUmSJEkqnojoRNaW4mqLWyqW2pHjViPr+Zu3P1XtyHG1uQ9frasZ9kDRAsuufRzNLKLUKK5/1tUMG5vnkIq5CV/WBS6+bAhd27S4tSy5OaI3AXsAN6SU8janjogRwE/J+qjcDswCdgKuAh6PiMNSSg+uQvzAildqa0eO2xL4KzC6rmbYGat6Xanc1I4c9626mmG/L3UckMUC/MGVEyVJkiAivgoMJGvXsi2wMdlMmKeBn6WU/tDM8wI4hGxl+22BdYB/AI8DI1NKMwse/JLxdADuAF5IKTW3YrfU6upqhn1RO3Lc5iw5eKaxhkUP9ixSSI11aHT9phq2N7cg1z+ATRt93hNodrBRKZX1FMWI+BT4KKW0eQueE2QN0I4jK1odk1JalOe4fmQ9tq5KKZ3ZZN/GZKtovZ1S2mYVvgTAKYqSVoxTFCVJUqlERB1QA7xOVpz6ENgaOJhsBMeglNJSiwRFxBVkC6S8CzxA1i/5G8AAsoVYdkkp/bkIX0JDPL8gW0zsuJYMkpBaQ+3Icd3J+n2v08wh99bVDBu4vPO09hTF2pHjOgDPk/1s5vNXYIe6mmFf5ImlA9nXdEBK6ZWIuBuYmFK6ubXiay1lu4piRKxL1rj3jRY8p2HJ9uOAO4Fj8xW3cr6be5zadEdK6T3gL8DWEbFWC8KWJEmSpEr0LLBHSmmrlNLQlNLZKaXDgb2BhcCYiOjc+Am5gQHVwJtA75TS8JRSTUppP+BHQFeKszpwQzy7kuWCfYDpEfFCRJxerOtLdTXDPgT+XzO755EteNWsiBiba6PUISLejohrWymuhWSLHDXnzHzFLcgWSQKGAvdGxOtkheu8s+RKrZynKDaMZMg7T3Spg79cunIIcBdwdL6+W410yj12b2Z/d2ARkPeb3BIrMiqjduS4m4BBwBZ1NcPeXdVrSpIkSVJjEXEQcALwH2QjTN4jm4J4aUppfL7npJSejIipZCOydmDJVXg3Ixs08VRK6V9NnjoBuJLm861Wl1J6mjz9gmpHjvsu8EZdzbCXixWL2rVryaYpbt1k+5V1NcP+vqwnppROLFRQdTXDptaOHPcrsinFjf0GmLicuKYAXy9UbK2lbEdwpZT+STZNsHdE/GfT/RHxtUYfN4zcGgLcAxy1nOIWZL/IAc6MiCWGD0bESUAP4JmU0ryV/ypWTO3IcR2BbYDrLW5JkiRJak0R0TEi6oH7yYpU44GrgenAYcBXl3OKBU0eG/wNmA/sGhFdm+z7Tu5x8srG3RpqR45bk6w/85WljEPtR13NsPlkIxgbe5/me2AV03+T/cw2WAj8qK30JS7nEVwAZ5ONxpoYEQ+QzQffENgFeIUvK48/AY4lGyo3Azg3a8W1hPtTSi80+vwesqrqHsCMiHiQrMn8vwP9gLkUaThtXc2wBbUjx+1OtuKjJEmSJLWm0cCRwDXAGY1Xi4+IHkDT0Vc02t8T6E/WY+ulxvtSSv+XW7jrMuDVXE71KVkR7T+B63PXLKWTyHLIC0och9qXCcBjZD8HAOfU1Qz7tITxAFBXM+z12pHjRvHlVMnr29LIxrJuMg8QEfuSVRn7AqsDH5DNDx+VUnoyd8wtwDHLOdWQlNItTc7dmWwe6hHA18imLb5P1pfrkpTSq632hUiSJElSkUXE7sATwCTgOy1cnX41siR9D+CHy1id/gfAOLKeWw2eAmpz0wZbjQt4SW3fyi6+Ve4juEgp/YZsTuiyjjmWbARXS889D6jL/ZMkSZKktqY691jbwuJWFdnUvj2AG5ZR3BoB/JRsVs3tZLNidgKuAh6PiMNSSg+uQvyStELKtgeXJEmSJGmVDQDeSCn9aUWfEFm/lxuAo8iKVic1c1w/4CLgmpRSXUrp7ZTSZymlp4DvkS3YdfmqfgGStCIscEmSJElSGxQR6wJrAW+04DkNC3gdB9wJHJtSWtTM4d/NPU5tuiOl9B7wF2DriFirBWFL0kop+ymKkiRJkqSV0tDHZsMVOjgrbt1Itjr9XcDRy1mdvlPusXsz+7sDi8hGcrWKFenNk1s5cSbwp7qaYQNa69qSypsjuCRJkiSpDUop/ZOs0NM7Iv6z6f6I+FqjjxtGbg0hW3H+qOUUtwAaGsifGRHrNDn3SUAP4Jlc7+Nialg58f8V+bqSSsgRXJIkSZLUdp1NNhprYkQ8ALxOVvzZBXgFOCR33E/IFu76DJgBnJu14lrC/SmlFxp9fg8wnKwR/YyIeJCsyfy/A/2AucCZrf8lLddawK/raoa16gqOkspbtGAhDUmSJElShYmIfYH/BvoCqwMfAM8Co1JKT+aOuQU4ZjmnGpJSuqXJuTsDZwBHAF8jm7b4PllfrktSSq+22hfSArUjx0VdzTCTXakdscAlSZIkSZKkimYPLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRbPAJUmSJEmSpIpmgUuSJEmSJEkVzQKXJEmSJEmSKpoFLkmSJEmSJFU0C1ySJEmSJEmqaBa4JEmSJEmSVNEscEmSJEmSJKmiWeCSJEmSJElSRetY6gCkSjVlypSxze0bOXLkzjU1Nc/n29evX78TCxeVJEmSJJWWuZJKwRFcUgE88sgjO5c6BkmSJEkqN+ZKKhQLXJIkSZIkSapoFrgkSZIkSZJU0SxwSQVw8cUXjy91DJIkSZJUbsyVVCgWuCRJkiRJklTRXEWxDHR6dGIq1Lnn77N/tOT46noKFsuowbQolko2YsSIQydPnjyuUOcvp+9TOcUSEQWLJaXUbl6/kiRJ5cJcqe0xVypNLO0hV3IElyRJkiRJkiqaBS5JkiRJkiRVNKcoSgUwYMCA50sdgySp/E2ZMmVsc/tGjhy5c01NzVJ/T/r163diYaOSJKlwzJVUKI7gkgogX0JSLj758A0eGXtsqcOQJC3HI488snOpY5AkqbWZK6lQKrLAFRE9IuLnEfG7iJgTESkitl/G8QMiYmpEfBIRn0XEnyLi0GLGrPblwAMPPKrUMWjVfO1rXyOiLHolSpIkrTBzJZU7c6XKt+WWW9KxY/lNCKzIAhewFfB9YBbw22UdGBHHAw8DLwGHA4cAtwBdChui2rPZs2evUeoY8nn81tOYeM0PePPFSdx70V68//eyvXnS6qqqqvjud7/LQw89xHvvvcfcuXP5+OOPefHFF/nRj37E+uuvv/jY3Xbbjeeee46xY8da5JIkSZXGXEllzVypPPXr1497772Xd955hzlz5jBr1ixeffVVzj33XDbaaKPFx+2444784Q9/4K677iq7Ild5RbPinkgpbQQQEccC++U7KCJ6AqOBmpTSFY12PVrwCFtJmjuXBT8cQofTTqVqj92ybfPmsbDmHFh/fTqcezZRVdw65Y2nfoVvHXYB2+899Ms4U+L6E9ZhnxNvZau+hxQtlup61gUGA9sC7wG/HDWYt4oWQJl5Z8bTPPvAxXz4xnS++PxTuqy9IV/b5Uh2GXgRAHsdM5pPPnyD348/nwEn3lK0uEr9mjn66KO54IIL2GyzzZbYvvrqq7Peeutx+eWXc9FFF/HLX/6Se+65h/Hjx7PWWmvRuXNnIoKUCrairiQ16+KLLx5f6hgkVSRzJXMlAKrrWRMYBHwD+BioHzWYGUULoMyYK+V30EEHUVdXx7bbbrvE9i5durDOOutw4YUX8pOf/IR77rmHMWPGcP/999OtWzc6depEVZF/vpanvKIBIqIqIn4cEX+LiM9zQ2T3jIi/RsQ4gJTSohU83fFAAq4tWMAFFl26UHX4YSysv4OUEmnhQhZedCmsthodas8q+i/szz7+X2bPepfuvXZaYvu/PpjJ/M8/ZaMt+hQtlup69gDeAq4BTgYuAv5eXc/JRQuiGRtvvPFHxb7mG3+axAM/25+v734Mx139JieO/ZjvnHY33Xv9W7FDWUKpXzPnn38+t912G5ttthmvv/46P/7xj+nZsydrrLEG3bp143vf+x4PP/wwnTp14oQTTmDixImstdZa3HbbbQwZMoRFi1b0140kSVJhmSstyVypedX1/Bvwd+AGslzpJ8Bfq+s5t2hBNMNc6Uulfs2ceuqpjB8/nm233ZZ//OMfnHfeeWy55ZasueaarLfeeuyzzz7cd999RARHHnkkjz/+ON26dWPChAkcdthhzJ8/v6DxtVQ5juD6BXAocCHwPLALcCfQHbiyhefaHfgLcEREnAdsDrwNjAVGtuCXf0lVHfg9Ft07nvTk0yya9hzpo4/oePnPiE6rFT2W92dOI6o60K3HktP4P3rrT6yxzkZ07bZpUeKormcd4NfAmrlNVY0er62u5/lRg/lDUYLJo76+vuh33V987Fo22+nJxy9QAAAgAElEQVS7bPOt7y/ettEWfYr6hzSfUr5mTj/9dH7605+yYMECTjvtNMaOHbvEaKy5c+cyYcIEJkyYwFFHHcWtt95Khw4d+OCDDxg+fLjFLbVJnR6d2OpDEufvs/8Kz+WtrqfVrz9qMG1yLvGIESMOnTx58rjWPGep//9Lff2IaPXrp5Ta5OtPZctcqQlzpaVV19MJmAA09OBoXOm7sLqe6aMG81BRgsnDXOlLpXzNHHnkkYwePRqAs88+m8suu4yFCxcu3j9nzhwee+wxHnvsMfbff38efPBBOnbsyCeffMJxxx1XdsUtKLMRXBExCDgWODCldHlKaWpK6WLgGbJi3B9beMqvAFsDVwFXAPsA9wEXA5e0VtyFFl1Wp2rgYSy8/ErSiy/S8ZILiTVLM235/ZnTWG/jbejYafUltn/41p/YcPOi/nI4Elib/K/hRVDaUVy1tbW7F/uaXbp2560/P8r0SVfz8f++WuzLN6tUr5mvfvWrXHFFNtr+mGOO4frrr292quFuu+3GmDFjqKqq4rPPPmPDDTfk1FNPLVhskiRJLWWulJ+5Ul4Hkn1/O+TZtxA4rZjBNGWu9KVSvWbWXnttxo4dC8B//dd/UVdXt0Rxq7Edd9yRX/7yl3Ts2JFPP/2Utddem7POOqtgsa2KchvBdQ4wKaXUtBnia8AXwIstPF8V0BUYmFK6N7dtakRsAFRHxEUppc8AImIz4FZgE2AecHJK6cmV+iqaWN7dwtUeeXjFTvT553T4/hHEeuu12rWb+q/bl334+zOnMev91xh70gZLbP9i3mf0+d7ZrRrLsuxx9Ci+sc+pVFXl+51N1XuvP/vDiG/+sLWul88ZZ5zR7L5p06YxYcKE3vn29e/ff9iqXjvf92nPo69m7e6b88oTN/NE/Rl0XX9Tvnno+Wy355Aljuuw2uqst8m2Sz2/QVt5zZxwwgl07NiRu+++mzvuuKPZ43bbbbclpiXec889/PrXv+akk07i8ssvXzyKqxB3/ZtyFIAkSVqGNpkr5c7f7Pssc6WW63vQiMV9pfLo8MlHb+4bsVlB39uaKzUfS2Oles0cffTRrLXWWjz++OP8/Oc/b/a4HXfckSlTpiyelnjppZfy9NNPc9xxx3Heeefx+eefr3IsK2pFcqWyKXBFRA9ge7I7CE31BF5OKc1r4Wn/j+yuxG+abP8N8EPg68CzuW1jgbtSStdFxC7APRGxeUqp5OPuFj02hUV33U3sO4CFv3qA2H/fkq3s9v7fn+Obh55P792WrB3Vn70DGxXxrsScWe82V9xi0aIFzP7nO0WLpVx06tKVbx5yHt885Dzm/OsDfj/+fCbfOJSe2+9D1249Fh+35rob0/fA2qLFVYrXTMeOHRk2LPvbeO21zbeVaFrcGjIk+wM3c+ZMtthiC/bbbz8efngF31SpXcj9rToL6APsRLbK1A4ppT83c/wA4GxgZ7JE4nXg/6WUbB6u5RowYEDZLN9Uiqa7kr5krtQ8c6WlzZn1brP7Fi1ayOxZ5krtOVcCOPnkbMLTsnKlpsWthp5b06ZNo2/fvnz/+9/n1ltvLViMK6NsClxAw6vqvcYbI6ILsCcwcSXO+RLwrWXsX5S7xgbAbmRDOUkp/S4i3gH2Zulf+C22vErjsvqhLHp2GguvuZYOF5xPbL01C344hPTEk8See7TKtZtaVm+MWe+9xrzZ/6TXjvsu8Utg1nuvMW/OLDbaom+rxrKcOHsAb5AljEuct6qqI1v2OfiQlNL9rXW9fKZMmTK2uX1XXXXVsAMOOCBv35Qrr7zyxFW99vJ6mKyxzoZs/R+H89LkMSyYP6dF567k10zDnYO+ffuyySabMGPGDJ544om8x+YrbjWM1rrxxhu55JJLOPjggxcXuBxdpZyGpdefJ1t6Pe/KVLB46fWxwHXApWSNfLfHpde1gmpqasqmwKUvde7cmaqqKubOnVvqUNS+tNlcKXfOZt9nmSu1XK5f8bvA6iyVK3Vgk62+PSyldENrXS8fc6Xlx1KqXGmrrbbi61//Oh9++CH3358/ZW6uuAUwbtw4+vbty8EHH7y4wFUuuVI59eBqWElhmybbzyIbCrsyb/J+lXvcv8n2/YHZwMu5z3sC7ze56/F3oNdKXLPVLHr5FRZeUkeH//4RVTvu8OX88tvvJJWg+fX7M6fRsfMadO/5jSW2v/u337FWt01ZY50NixbLqMG8DQzPfdr0P+MG4IGiBZPHTTfddHsxrzftwUt586VHmf/5Z6RFi/jg73/kqf85i1477Mt6mzT9kSqeUr1m1l8/66c5Y0b+VZCXVdxq/LyG80iNPJFS2iil9B3gruYOarL0+ukppUdSSo+mlK5KKdUXLdoWSnPn8sXAH7Doiae+3DZvHguqf8SCCy4uyt+eG0/9Cn+eeuOScaXEmKFr89q0XzXzrLbpwAMPPKrUMQA8futpTLzmB7z54iTuvWgv3v974epupfz+9+jRgwsuuIAnn3ySl156iWnTpnHXXXcxYMCAxaNBOnfuzP3338+DDz5Ily7WqlVU5kpNmCs1b9Rg/gUcTZYnNS2w3AfcXLRg8jBXypQ6V5o5cyYLFixYav+yiltQ3rlSOY3gmkk2b/yciPgY+F/gcOA7uf1L/NKOiMNzHzaM29snIrYFZqeUJgKklCZGxKPA2IjoDswAvgsMBkaklMr21lv6+xss/Mn5dDjxBKp23WXx9qoDD8hWCXniSWKvPYsa0/szp7HR5n2p6rDky+bd154p6pDbBqMGc0N1PdPJGso3TJ4+EJgwanDrr9LUEtOnT9+gV69ebxXregvmzeHJ+jP49KO3oKqKrt160nvXo/nGgJL2jyzZa+ahhx6ic+fOdO7cOe/+tddem9VWWy1vcQtgwoQJrL322nz66acFi1HlJyKqgDOBE4FNgb8CpwPjgN+mlIa19aXXGy+3HrvvCosWFXW59VIvlQ1QXU9XYBCwJdl7kztHDeaTgl84j9mzZxelS/I7M57m2Qcu5sM3pvPF55/SZe0N+douRy7u37LXMaOLMkWxVN//TTbZhGuuuYaDDjqIDh2WbH/Qp08fjjjiCF577TUuuOACjjzySPbbbz8++OADevTowd/+9reCxCTlYa7UiLnS8o0azH3V9XwDOBU4Kbf5+8B9owaTv5t4kZgrZUr1mnn22Wfp1KkTa6yR/21G165d6dy5c97iFsAzzzzDOuusU5a5UtkUuFJKiyJiINl0jjFkc8JvJUsOLmHppon3NPm8YVncN4HNGm0/FLgIOBfoRtb/5OSU0vWNjnkL2CgiOje6M7F57lwlEZtvxmr33b309tVXZ7W7m2+YXUh7HJV/5eF+Q8YUOZIvjRrMc8Bx1fVZgWvUYH5dsmAaGT169H4HH3xwqy7tvizfHngh3x54YbEut8JK+ZqZP39+s0vXPvzww+yyyy688MILSxW3AObNm8e8eS1tY6E2wKXXKe1y66VeXr26np2BR8iWVU9k0zrqquvZd9TgxX1o2pQ3/jSJiaOPoP/QG9jyjGyawkdvvcgnHxX/LVApvv9bb701jz32GD179uSLL77gnnvu4bbbbuPtt9+mS5cu9O/fn5NOOomtttqK2267DYAPPviAfv36WdxSUZkrLSk2N1daEaMG8zIwvLo+K3CNGszS/2klYK6UKeVr5osvvuBf//pX3n1PP/00u+66K3/5y1/y5lNffPEFX3zxRaFDXCllU+ACSCnNIJvLvVhE/BJ4pekdhBWd45lb+aM696+5Yz6KiKfJ7rg3NE78KjC1ZV+BpErxxz+2dCVttWWNll7fq9HqVFMj4t/J3vyvzNLrXyFrBjyCbDTYAWRLr68DFK97aQs1Xm6d9dal46grirbceimXV6+upwPZtI11c5sa3md0BX5VXU+vUYNZehx/AW288cYfLf+oVfPiY9ey2U7fZZtvfX/xto226FOU0XJNFfv7v8EGGzBp0iR69uzJ008/zRFHHME77yzZePnZZ59l1KhRPP/88/TunS349fOf/5yXX3453ymlgjJXklQsL77Y0kVZy0NZFbia0Qf4fRGucxJwS0RUA/OBQeWwKogkqSja1NLrxV5uvSVLQy9rueyVXSq7NZam3nS7fhx69uR8uzoAX7n/Z/t/cfVRk1b1MktZ1jLqgwYNYsKECUstl74qS6g3/f/v0rU7M//4INMnXU2vHQaw/lfzrtq+TJX6/T/jjDPYYosteO655xgwYABz5izdaLhz586MHz+e3r1788knn7D22mtzxhlncMUVVxR1afRSKZemwVomcyVJyinrAldErEXWSPG6Ql8rpTQTWLHlNqTlGDRo0Colp5KKx6XXl1TK5dZLubx6l7WX3ci1mM2BGzz66KPss88+Bb3GnkdfzdrdN+eVJ27mifoz6Lr+pnzz0PPZbs8hSxzXYbXVWW+TbQsaSzG//506dWLo0KEAnH766c0Wt+6///7FPbf69evHLbfcsrgvV8OURalUzJVUqcyVVChlXeDK3d3usNwDpTIzdOjQV0sdg6QV1uaWXi/2custGeXR3HLZq7JUdmuMMqmuZ1ug2d/dA068dcdXnrj1pVW9TlPLW0b96quvXqpHyaosod70/79Tl65885Dz+OYh5zHnXx/w+/HnM/nGofTcfp8lvg9rrrsxfQ/MP7O2kr7/DaOtDjnkEDbccENeeOEFnnnmmaWOy1fcevnll7nuuuu46aabGD58+OICl6OcVCrmSqpU5koqlMIuhyS1U6syfURS0bn0OqVfbr3Uy6uPGsxfgPF5diWy1XlbvbhVbtZYZ0O2/o/DSWkRC+YvPaKpkIr9/d9++6yR/QMPPLDUvuaKWwD335814t9uu+1aNR5Jak/MlVQoZT2CS5KkImj3S6+Xw3LrZbK8+g+BWcDRQMOykbeRLbHe5kx78FI23LwPm2z9bVbrtAYfvvkCT/3PWfTaYV/W26Rpvbewiv39f/jhh5k1axZPP/30UvtOPvnkvMUtgFmzZnHuuefy8ccft3pMkiRp1VjgKgPz99m/bIa2jxpM2cSi5pXT96mcYlnRaSK1I8ctMUWmrmZY2XwNKj6XXi+P5dbLYXn1UYOZDRxfXc9/k70OGDWYY4sWQBM33XTT7YU8/4J5c3iy/gw+/egtqKqia7ee9N71aL4x4LRCXjavYn//n3nmmbxTEwGuvvpqevXqxQ033LDUaokpJS6++OKCxCQpP3MltVQ5fZ/KKZb2kCtZ4JIKYJtttnmr1DFIWnEuva7GRg3m4+r6UkcB06dP36BXr14F+3vy7YEX8u2BFxbq9BVr0aJFVFc3+2MrSVpF5koqFHtwSQUwZsyY1l9LXlKx9WHl+m+11EnADyJiBjAOl15XzujRo/crdQySJLU2cyUVigUuqQCGDx9uUiJVsEZLr/+x0NdKKc1MKe2RUtompbR9Sum3hb6mJElSqZgrqVCcoigVwIwZM3qWOgZJK8+l1yVJkgrDXEmF4gguSZKkMjRo0KAnSx2DJElSpbDAJRVAr1693i11DJKkyjZ06NBXSx2DJEmtzVxJheIURakA3nzzzU1KHYMk5VPq5dbLabnscte/f/9hkydPHtea5yz1/3+pr78iq6BW8vLoklQJzJVUKI7gkiRJkiRJUkWzwCVJkiRJkqSKZoFLKoCLL754fKljkCRVtm222eatUscgSVJrM1dSoVjgkiRJKkNjxoyZVOoYJEmSKoUFLqkARowYcWipY5AkVbba2trdSx2DJEmtzVxJhWKBS5IkqQxNmzatd6ljkCRJqhQWuCRJkiRJklTRLHBJBTBgwIDnSx2DJEmSJJUbcyUVigUuqQBqamr8pS1JWiWuMiVJaovMlVQoFVngiogeEfHziPhdRMyJiBQR2y/j+AERMTUiPomIzyLiTxFhYzsVzIEHHnhUqWOQJElS+2S+pHJmrqRCqcgCF7AV8H1gFvDbZR0YEccDDwMvAYcDhwC3AF0KG6Las9mzZ69R6hgkSZXNVaYkrQLzJZUtcyUVSsdSB7CSnkgpbQQQEccC++U7KCJ6AqOBmpTSFY12PVrwCCVJkiSpNMyXJLU7ZTeCKyKqIuLHEfG3iPg8Nzx2z4j4a0SMA0gpLVrB0x0PJODaggUs5bHxxht/VOoYJEmS1PaYL6nSmSupUMquwAX8AjgPGAvsD9wN3AlsAbS0Gd3uwF+AI3J/ABZExBsRcXZElOPXrjaivr7exsBSG2RPExWTq0xJaob5kiqauZIKpax+aUXEIOBY4MCU0uUppakppYuBZ8imU/6xhaf8CrA1cBVwBbAPcB9wMXBJa8UtNVVbW7t7qWOQVBD2NFHRuMqUpKbMl9QWmCupUMqtB9c5wKSUUtOk4TXgC+DFFp6vCugKDEwp3ZvbNjUiNgCqI+KilNJnABFxAfADsuTliEbHr7KISK11LuX3X7dn/8XF/L8+44wzmt03bdo0JkyY0Dvfvv79+w8rWFBaITV1Y5f4vFx+RlNKUeoYtFz2NFHRHHjggUc9+OCDt5c6DkllxXxJLWaupJao5FypbEZwRUQPYHvgnjy7ewIvp5TmtfC0/5d7/E2T7b8BOgNfb7RtElmi8kQLryFJagPsaaJy4ypTkhozX5KkZSunEVw9co/vNd4YEV2APYGJK3HOl4BvLWP/4kQlpfS73PVW4jLL5qiMwquuJ0Fx/6+nTJkytrl9V1111bADDjhgXL59V1555YmFi0oronbkuCXuQvgzqpxfAIcCF5L1MNmFrKdJd+DKFp6rcU+T84DNgbfJ+qWMbEGhTJKkBuZLWinmSmqJSs6VymYEF9CwksI2TbafBWxCyxsmAvwq97h/k+37A7OBl1finNJy3XTTTU4pkSqIPU1UjlxlSlIT5ktqE8yVVCjlNIJrJtmc8XMi4mPgf8ma8n4nt3+JX9gRcXjuwz65x30iYltgdkppIkBKaWJEPAqMjYjuwAzgu8BgYERKaW4hvyC1X9OnT9+gV69eb5U6DkkrrE31NCmXXgmVrFj9SpbVo2TQoEFMmDBhqV4k9icprHLtPVIKlXTXvp0wX1KbYK6kQimbEVy56RoDye4SjAFuJrtLcS2wkKWTi3ty/07JfX5l7vMxTY47FLgVOBd4CNgXODmldGnrfxVSZvTo0XkbT0sqP/Y0Ubl69FHXJJD0JfMltRXmSiqUchrBRUppBrB3420R8UvglaZ3D1b0jlLuDnl17p8kSU21uZ4mjrpYdcXqV7K8HiVXX331Uj1K7E9SWJXce0Rtn/mSJDWvbEZwLUMfVm4+eYtExIUR8TbwbbIhum9HxJaFvq4kqeTsaSJJqmTmS5JEmY3gaioi1iJLOK4r9LVSSucB5xX6OmofBg0a9GSpY5C0wuxpIkmqSOZLqkTmSiqUsi5w5YbLdih1HFJLDR069NVSxyBpxaSUFkXEQGAsWV+S/yPrRXIt2YqH+XqaNHZl7vFNYLNG2w8FLiLradINeJ2sp8n1rRm/2i5XmZK0POZLqkTmSiqUSpiiKFUcV7iSKktKaUZKae+U0poppZ65u9Q70ExPk2b+bdbkuM9SStUppU1SSp1SSr0tbqklpk+fvkGpY5AkqbWZK6lQLHBJkpSfPU1UUq4yJUmStOIscEmS1ESjniZ/LPS1UkrnpZR6pJQ6p5S65T5+vdDXlSRJktqSsu7BJVWqbbbZ5q1SxyBp5dnTRJIkqTDMlVQojuCSCmDMmDGTSh2DJKmyucqUJKktMldSoVjgkgpg+PDh9k2RJK0SV5mSJLVF5koqFAtcUgHMmDGjZ6ljkCRVNleZkiS1ReZKKhQLXJIkSZIkSapoFrgkSZIkSZJU0SxwSQUwYMCA50sdgySpsrnKlCSpLTJXUqFY4JIK4JFHHtm51DFIkiqbq0xJktoicyUVigUuSZKkMlRbW7t7qWOQJEmqFBa4JEmSytC0adN6lzoGSZKkSmGBSyqAiy++eHypY5AkSZKkcmOupEKxwCVJkiRJkqSK1rHUAQg6PToxFerc8/fZPwp1bjVvxIgRh06ePHlcoc5fXU/BXjOjBtOi10xEFCyWlJKvX0ntlne4JclcqS0qdK5kftJ+OYJLkiRJkiRJFc0RXKpI1fUEsAswHNih0faHgF8AD44azIIShSdJZasQd8K9A14YhbjDXYgRwC0Z+Vvq65daIUYVOJpAUj7V9exMliv1abTtEeBW4N5Rg5lXqtikQrHApYpTXc9hwE+AHfPs/k7u3/9W1/Nz4PJRg1lUzPgABgwY8HyxrylJkiSpfauuZ1/gAuA/8uzeJ/dvVHU9Y4ALRw3mi2LGB+ZKKpyKnaIYET0i4ucR8buImBMRKSK2X8bxAyJiakR8EhGfRcSfIuLQYsasVVddzznAveQvbjX2VWAkcFd1PZ0LHlgTNTU1/tKWpApTXU+f6np+UV3P84223Vxdz3/kRg5LUkUwV2qfqus5EXiY/MWtxjYAzgMeqq5nrYIH1oS5kgqlYgtcwFbA94FZwG+XdWBEHE/2g/4ScDhwCHAL0KWwIao1VddzOnBxC592OPCLYicmBx544FHFvF45iwj23ntvjjvuOE477TSOOeYY+vTps9RxG264ITfccANrrrlmCaKUVowJQ9tUXc+3qut5FpgGHAf8e6PdxwJ/AKZV17NbMeMqpzvcn3z4Bo+MPbbUYUhaceZK7Ux1PYOA62lZjr8PcHd1fXFndpU6V+rcuTMHHHAAJ5xwAqeeeipHHXUUW2211VLH7bjjjlxxxRVEeI+rUlTyFMUnUkobAUTEscB++Q6KiJ7AaKAmpXRFo12PFjzCVpDmzmXBD4fQ4bRTqdoje1+d5s1jYc05sP76dDj3bKKqkuuUK6a6ni2BUc3tHzV48XH5DAYmAP/T+pHlN3v27DWKda18bjz1K3zrsAvYfu+hi7ellLj+hHXY58Rb2arvIQWPYf311+e4447jpJNOYsstt1xq//PPP891113HnXfeSdeuXZkyZQrbbbcdKSWGDRtW8PikldSQMDxPljDk/dsDixOGscB1wKVAArbHhKGsVNdzAHAPsPpyDt0ZeKy6nh+MGsz9hY/MO9zKLyLo0KEDCxbYalTLZK7UvnKlDYCbmtu/nFxpf7JeXaNbP7L8SpUrbbbZZpx44okcf/zxdO/efan9v/nNbxgzZgwTJkxgu+22Y8qUKXTr1o2ZM2dy7bXXliBitVRZ/rRHRFVE/Dgi/hYRn+fueO8ZEX+NiHEAKaUV7at0PFlSUZGvyOjSharDD2Nh/R2klEgLF7LwokthtdXoUHtWu/iFnXMSrNIorJNbK5By99nH/8vsWe/SvddOS2z/1wczmf/5p2y0xdKjp1rb7rvvzt/+9jcuu+wyttxyS9544w1uvvlmrrnmGm6//XY++ugjdt55Z37xi1/w8ssv89RTT7Hddtvx5z//mREjRhQ8PmkVPJFS2iil9B3gruYOapIwnJ5SeiSl9GhK6aqUUv63l2UgzZ3LFwN/wKInnvpy27x5LKj+EQsuuJi0qOgtDQuqup7/oJni1qjBXyYEjXQG/qe6nl0KH13p73A3ePzW05h4zQ9488VJ3HvRXrz/98LV3W489Sv8eeqNS2xLKTFm6Nq8Nu1XBbtuOejSpQtDhgzhzjvvZNKkSTzwwAP8/Oc/Z6edvvx7HhFce+213Hfffay22moljFalZK70JXOlxYaw/Bs1y3JyW5+Kf+yxxzJjxgxqa2vp3r0706dP54YbbuDaa6/l3nvvZc6cOey7777cf//9/P73v2fq1Kl069aNX//619xwww2lDl8rqFxHcP0COBS4kOwu+S7AnUB34MoWnmt34C/AERFxHrA58DbZXfWRLfjlXzJVB36PRfeOJz35NIumPUf66CM6Xv4zolP7eGNTXU8Xsikjq2L36np2GDWYl1ojpuXZeOONPyrGdfJ5f+Y0oqoD3XosOWvqo7f+xBrrbETXbpsW9Pp77703EydOpHPnzjz++ONcdtllTJo0iUWNEuPOnTszcOBAzjnnHHr37g3AjBkz6NevHx9++GFB45OaExFVwJnAicCmwF+B04FxwG9TSsPaesLQOFGI3XeFRYvaeqJwKS1PCDoDdcAerR/Okop1h/udGU/z7AMX8+Eb0/ni80/psvaGfG2XI9ll4EUA7HXMaD758A1+P/58Bpx4S8HiKIcbNKWwxhprcMEFF3Dcccex3nrrLbX/tNNO45lnnuHCCy/ke9/7HsOHD2fu3LnsuOOOPP+8g/zaKXOlRsyVqCIbgbUqtgX2AqauckAroNi50vDhw7nuuusAuPPOOxk1ahTPPvvsEsesu+66HHPMMYwYMWJxO5WJEydy+OGHM3/+/GKGq1VQdgWuiBhE1u9ir5RSw3zxqRHx72S/yP/YwlN+JffvKmAEWcJyAFkvp3WA2lYIu6Ciy+pUDTyMhZdfCeutS8dRVxBrlnQGXLH1A9ZvhfMcAcUpcNXX148vxnXyeX/mNNbbeBs6dloyZ/vwrT+x4eaFTQ569erF+PHj6dy5M9dffz2nnHLKEoWtBvPmzeORRx7hnHPOWbytU6dOfPbZZwWNT1oOEwbaT6JQXU9vsr8vK6OoN00K6Y0/TWLi6CPoP/QGtjwjm3n50Vsv8slHbxY9llLfoCmFbt26MWnSpMXJ1O9//3tuvvlm3nrrLTp37syee+7JkCFD+Pa3v81DDz1ERDB37lwOOuggi1vtlLnS0syV2Jnsfcaq+j5FKnAVM1fq168fo0dnsy9POeWUxYWupmbNmsXUqVP56U9/unhbVVWVxa0KU3YFLuAcYFKjX9gNXgO+AF5s4fmqgK7AwJTSvbltUyNiA6A6Ii5KKX0WEesBvwS2AeYC7wMnp5ReW9kvpEFEpGXtX+2Rh1fsRJ9/TofvH0Hkubu3steuBF/f41j2GXbz4s/zTBlpdl/jeeYvTb7+3Dhq+LmtFdcZZ+vXuCkAACAASURBVJzR7L5HH32UffbZJ+++/v37r3KDqf+6vflv6/szpzHr/dcYe9IGS2z/Yt5n9Pne2cs996q8Zk477TTWXXddJkyYwMknn0xK+U+14YYbMmXKFHr37s0rr7xCVVUV2267LYMGDeKmm75sH1Co129N3dglPi+Xn5OUUpseGl7OTBi+1I4ShVX9XXwicGprBNKcYtzhfvGxa9lsp++yzbe+v3jbRlv0KcloqVLeoCmF1VdfnV//+tf06dOHmTNn8oMf/IBp06YtccwDDzzAeeedx9SpU+nbty8Ao0aN4tFHK6I9kgqjzeVKsOz3YuZKy7bZTt/hoB8/tPjzlc2VXnv2vhPjqMNPbK24SpkrNXbOOefQoUMHLrnkkmaLW5A1lJ8yZQrrrbcejz32GH369GHfffdl5513XuKGQlt4zSxPJedKZVXgiogeZA14r8qzuyfwckppXgtP+3/A1sBvmmz/DfBD4OvAs2RTSUallB7LxXI6cDPZXfiSWvTYFBbddTex7wAW/uoBYv9929VKDlHVOi/Tqg7FG33w5z//udlf2oX2/t+f45uHnk/v3X64xPb6s3dgowImCA29QwB++tOfLre41dBzq1+/fuy3337cdtttnHLKKUsUuKQialMJQ7EThXJ549MSB581iV477gusXDLwj5ennBLR/5RVjWNZCcCgQYOYMGHCUm/0V+XNf9MbJF26dmfmHx9k+qSr6bXDANb/au8Wn7Ml3/9C3KBp7ddfsd7Yn3DCCXz729/mzTffZLfdduPdd99d6piI4LLLLqNv377Mnz+fTp06ceKJJ3LhhRcyd+7cgsYH3ngpN+ZK+bX3XKmqtXKljm0vV9p2223p378/s2fP5mc/+1mzxzUUtxp6bh1++OFceumlnHnmmQwfPpyhQ4c2+1yVl7IqcAE9co/vNd4YEV2APYGJK3HOl4BvLWP/IoCU0izgsUbbfwectRLXW8ry3hx0enRis29MFj07jYXXXEuHC84ntt6aBT8cQnriSWLPFWv90RbemFTXMxC4u9HnS1nOyiAAbLfX8Vc8esPxP26tuKZMmTK2uX1XXXXVsAMOOGBcvn1XXnnlKt8Zqa4n72tm1nuvMW/2P+m147507dZjye1zZrHRFn2Xe+6WvmYa3lgPHDiQ9ddfnz/84Q/88Y/5B7vkK259+OGH3H333Vx11f9n787jrKzrxv+/3oC4pLcriYqglpil3eWS3ZkbBK6Re9KYadq4VN7jkoPS4jdFodtliJSgQixG09TSTFJSykz7hYZWmqHikoaWKRqoIPD5/XGdweHMwmzXWWZez8djHjNzXde5Pu8ZmHPO+/3ZrmS33XZjjz324MEHH+xSLB01btL0NX5/veHvRF1nwrCmvpIorLPuu7r3+PU27KFI2tZeD3dP2e+zk/mvQdvz2L3XcG/jWWy02bbsdeSFfGC/k9a4rv8667HpVu/LNZZyddCUyxlnZPvfnH322W0Wt6666qrVa2596lOf4qKLLmKvvfbi05/+NDNnzixxxKoAvTJXKty/zRcac6X21TWyH/DrZt+30JFcaYfdxvwwpfS5noqrnLlSU37StDN7Y2Mjr732WqvXtlbcWr58Od/97nc5++yz+cxnPsPZZ5/N66+/DvSO/zNrU825UqUVuJqG4g8HmncxnwdsRbYmSmf9FPgC2fanNzY7fjCwFHi0jcfVQWm2AW/LqkcfY+UlE+n/lXPo98FdAbJpI7OuJ/b5eG9c7Lct9wEr6P7/13t6IJaK9tLCeQxYdwMGDf3vNY4veuJ+Ntx8WzbY+N25tf2BD3wAgNtuu63V820VtyBbk2v27Nkcf/zxfOADH1hd4JJKpNclDKVOFKrpjU+TukZmAwcVvm5hbcnA4Pd85O6U0ie6G8faEoDJkye3SAC68+a/uINk4PobsdcRX2OvI77GG6/9k9/fciF3f/8Uhu4yao2OkndtMpg9x7Q+s7Yz//55dND09P+/PN/YNyVdBxxwAO973/t44YUXuPXWW1u7rkVxa86cOWy99dbstddenHHGGasLXNX496cuM1dqxlxptYeA/5CNHO+OXpcrNeUnrT3PQtvFLYAnnniCv/zlL+yyyy5sv/32PPLIIyWLW11XaX/1C8mmgVwQESdExMiImMo7O+it8aQdEUdHxNFAU7feqMKxg5uuSSnNBuYA0yLiixExKiIagBpgQkrpzeIgIuIbwHvpwV6JzkpPP8PKr19I/1O/QL+939mNvN+Yw+C110j3/rZcoZVcQw2LgO4uRPg0LUdS5GbGjBmzStVWcy8tnMeW2+9Jv/5r1gIXPflA7r3f999/P1dffTW///3vWz1//fXXt1rcanLnnXcyZcoUFixYkGucUiuaJwzNdTdhgCxBaK5iE4biRGH1Wlyzrie1sllELzBv7Zfk+viKs8HG72bHjxxNSqtYsfyNkrZdzg6acth9990BuOWWW1i5cuUa59oqbgHceGNWf9htt9165chKrZW5UoG50jsaalgCXNvN27zCmgXOXJUqV7r11luZNm1aq/nFeuutxx133NFqcavJddddR0NDA4sXLy5FuOoBFTWCK6W0KiKOIdtlairZFI9rybZZv4SWa6D8pOj7pl2ungW2a3b8SOBi4KvA5sBTZGucfLc4hoj4KtlCwKNSSqV9d9c8ju23Y52bWz7HxHrrsc6N15U8ngpwNdkuiF313YYaVq79sp4xf/78LYYNG/Zcqdprsu/xrW/0NuKkqbm3feutt7bZOwLZAvTf/va3GTt2bIviFsCsWbOYNassdUGpecLwCvACcDRwSOF8i4Sh8GXzhOF9wNJCokBKaXZENCUMg4AFwKFkCcP4tSQMXd3Zr8vaSxRW3XRLNopr//1KHVbeppOtvda/C49NZO9Vqtq82y7l3dvvwVY7/g/rDNyAfz37MPf9+DyG7Xogm25VXO/NVzk7aMrhwQcf5PLLL+fXv/51i3Mnn3xyq8UtgDfffJPJkyezZMkSBgwYwNtvv13CqFVu5krN4tjeXKnIVLq38cmMhhpavDfJS6lypfYWlX/rrbeora3lpJNOoqamptXdEi+99NI8w1MOKqrABZBSWgAc0PxYRPwIeKw4IejokOyU0hKyXvG69q4rJBeHkD1hW6atLPeSvUgf04XHPgq0eIHO05QpUw46/PDDW51X3lc99thjfOIT3Z7NI/U4E4a+mSg01PB8XSO3AUd04eG/aKjhmR4OqYW8e7hXLHuD3zaexX9efg769WOjzYey896f5b9HfznPZltVzg6acvj1r3/danELYObMmey///5ce+21re6WWFfX7ttZ9XLmSmpNQw2P1TVyNXBGFx7+LHBZD4fUrkrJle644w7uuKODm++oKlRcgasNewCtz3vqIRHxAeBCsgTk103DvlNKH8qzXXVMQw2prpETgM2AkcXn21kw8WngkIYaXs8vOknVzoShz/oK8HFgUCce82/gnHzCWVPePdz/c8xF/M8xF+V1e3XRihUrOP7448sdhqqLuZIA/hd4N9ko9DW0kyu9SJYrvZRfWFLpVNoaXC1ExIZk66K0vi1bD0kpPZpSipTSe1NKH2r6yLNNdU5DDW+RJYHfo7BA81rcA/xPQw0lnyooqVfYg66tv9VhzRKGzckShocj4uE829Q7Gmp4imyh+X8Wn6trbDUheJksESjJYoFTpkw5qBTtSKpe5kpq0lDDCuA4stFYHZm/PI8sV3os18CkEqr4AldKaUlKqX9KaUq5Y1H5NdSwvKGGWrJpQBdBi96GN8jWVflwQw0jy9UbMXbs2L6zsqXUC5kw9B0NNfyRbMfLRqDlAhyZt4HryRKBP5QqNklaG3MlNddQw8qGGr4CbAuMhxYd/cuBHwH/A+xViun2rTFXUl6qZYqitIaGGv4OfL2ukW8CWwAbk+1M9nJhpFdZnXLKKX8tdwySuq4wvbAri4+rCjXU8DRwfF0jZwMnAR8C/ots2/VHyBbfdfqGJKkqFF6zLqlrZBLv5EpvkuVKJVtMvi3mSsqLBS5VtcJQ3BcLHxVj5MiRtXfffXfZF06UJHVcQw3/BCaVO44m9nBLkrqjsIv8S7Sc9VJW5krKS8VPUZQkSeqL7OGWJEnqOEdwVYDlow7u0I5cUpOGGirm/0xHdpQbN2l6AphYXxvNv847Nkkt+ZpTPfLo4S7360e52y+3zrxmNvH1Un2dr1vqLJ9r+y5HcEk5GD58uDs3SpIkSVIRcyXlxQKXlIOpU6f+stwxSJIkSVKlMVdSXixwSTk4/fTTDyp3DJKk6mYPtySpNzJXUl4scEk5WLBgwdByxyBJqm72cEuSeiNzJeXFApckSVIFGjdu3D7ljkGSJKlaWOCScjBs2LBF5Y5BklTd5s2bt3O5Y5AkqaeZKykvFrikHDz77LNblTsGSZIkSao05krKiwUuSZIkSZIkVTULXJIkSRVowoQJt5Q7BkmSpGphgUvKgUmJJEmSJLVkrqS8WOCSJEmqQOPHjz+y3DFIkiRVCwtcUg5MSiRJkiSpJXMl5cUClyRJkiRJkqqaBS5JkjooIoZExLcj4v6IeCMiUkTs0s71oyNibkS8HhFLIuKRiLDXUh0yevToh8odgyRJUrWwwCXlwKRE6rXeC3waWAz8pr0LI+Jk4A7gz8DRwBHATGD9fENUb1FfX+9riSSp1zFXUl6qssBlD7oqnUmJ1Gvdm1LaMqV0CHBDWxdFxFBgClCfUjozpXRXSmlOSunKlFJjyaJVVRszZszx5Y5BUvUxV1KlM1dSXqqywIU96KpwJiVS9YmIfhFxbkQ8ERFvFd7g7xcRf4uI6QAppVUdvN3JQAKuyi1g9XpLly7doNwxSKpK5kqqaOZKysuAcgfQRfemlLYEiIgTgYNau6ioB/3yZqfm5B6h+jSTEqkq/QA4ErgIeAj4GHA9MAi4opP32gd4HDg2Ir4GbA88D0wDJnWiUCZJUmeZK6mimSspLxU3gssedElSqUXEWOBEYExK6bKU0tyU0gTgAbLOoD928pZbAzsCVwKXA6OAm4EJwCU9Fbd6t8GDB79c7hgkVRZzJUlqWyWO4LIHXVXPpESqOhcAv0wpFU/leBJ4G/hTJ+/XD9gIOCaldFPh2NyI2AKoi4iLU0pLACLiZ8AOwMpCWxeklH7VxZ+Dwj1Tdx6v0jnrrLPaPDd27Fhuv/322uLjI0eObHFMPad+4rQ1vi/131O5228upRTlalttMldS1TNXUl4qqsDVrAd9/2ZJxtyI2I3sibwrPehbk/Wgjwf+BhxG1oO+MTCuB8KWWmhsbLyl3DFI6piIGALsQvZaUWwo8GhKaVknb/tvshFcdxYdvxM4AXg/8IfCsRNTSosLsXwY+HVEbJZSWtnJNtXLzJkzh1GjRpU7DEkVwlxJvYW5kvJSUQUuelkPehN70nun9nrd20tK+mLPe1NvdESk5l+XO54mlfI3ak952QwpfH6x+cGIWB/YD5jdhXv+GfhoO+dX94o3FbcKNiabLtKt/wv+X6oe99xzz7S2zl155ZW1kydPnl58/Iorrjg136j6tnGTpq/xmlDqv6dyt6+K1itzpcL9K+K9mHpOpedKlZoPVIJK/d105PWwYtbgataD/pNWTnenBx1a70Ffl6wHvcmJKaUPppQ+DJwK3BwR/TvZngTAX/7yl3KHIKnjmobJDy86fh6wFdkUkM76aeHzwUXHDwaWAo82PxgRV0XEQrJ1uo5KKa3oQpuSpF7KXEm9ibmS8lJJI7h6XQ96s3vb89YLra3X/bDDDmvR6w59s+e9qTc6pRTNvy53PE38G+3zFpL1el8QEa8AL5BtlX5I4fwaBa6IOLrw5R6Fz6Mi4n3A0pTSbICU0uyImANMi4hBwALgUKAGGJ9SerP5PVNKXyzcez/gyojYt6nXXJIkenGuVLi/78V6mUrPlcwH2lbNv5uKGcGFPeiSpDIoLKJ7DNlrwlTgGrLXpKvIpmIUT/n4SeHji4Xvryh8P7XouiOBa4GvAr8ADgTOSCld2k4svyFLKPbu+k+k3mLGjBmzyh2DpIphriRJa1FJI7jsQVevYVIiVZeU0gLggObHIuJHwGOtvFZ0qBer8PpRV/hoVURsCGyeUnq28P2HgfcAf+3UD6Beaf78+VsMGzbsuXLHIakimCup1zBXUl4qZgSXPejqTebPn79FuWOQ1G170LUe8c54F3BDRPwlIh4mew07PqVkUUNMmTLloHLHIKkymCupNzFXUl4qpsAFWQ96SumAlNK7UkpDU0pfA3aljR70Nj62K7puSUqpLqW0VUppYEpp55TSd5tfExEbRsSwZt/bg65uMSmRqlthZNVwOr/leqeklF5KKX00pbRLSulDha9/kWebkqTqZK6k3sJcSXmppCmKbdkD+H3ObTT1oG8IrADewh50SeqzClMu3B1KklTpzJUkqaCiC1zNetCvzrOdlNJLtL+DiCRJUkmNHTv2t+WOQVLlMleSpDVVdIHLHnRVK5MSSVJ3nXLKKU7/kdQmcyVVK3Ml5aWi1uCSeguTEklSd40cObK23DFIktTTzJWUFwtcUg5MSiRJkiSpJXMl5cUClyRJkiRJkqqaBS5JkqQKNHz4cHcokyRJ6iALXFIOTEokSd01derUX5Y7BkmSepq5kvJigUvKgUmJJKm7Tj/99IPKHYMkST3NXEl5scAl5cCkRJLUXcuWLVun3DFIktTTzJWUFwtcUg4WLFgwtNwxSJKq27PPPrtVuWOQJKmnmSspLxa4JEmSJEmSVNUscEk5GDZs2KJyxyBJkiRJlcZcSXmxwCXlwGklkqTumjBhwi3ljkGSpJ5mrqS8WOCSJEmSJElSVbPAJUmSVIHGjx9/ZLljkCRJqhYWuKQcOK1EkiRJkloyV1JeLHBJkiRJkiSpqlngknLgtBKpd4qIIRHx7Yi4PyLeiIgUEbu0c/3oiJgbEa9HxJKIeCQifH5Qh4wePfqhcscgSVJPM1dSXixwSZLUce8FPg0sBn7T3oURcTJwB/Bn4GjgCGAmsH6+Iaq3qK+vt8AlSZLUQRa4JEnquHtTSlumlA4BbmjroogYCkwB6lNKZ6aU7kopzUkpXZlSaixZtKpqY8aMOb7cMUiSJFULC1xSDpxWIlWfiOgXEedGxBMR8VZhOuF+EfG3iJgOkFJa1cHbnQwk4KrcAlavt3Tp0g3KHYMkST3NXEl5scAl5cBpJVJV+gHwNWAacDBwI3A9sAPQ2b/pfYDHgWMLBbMVEfFMRJwfEb72SpKkPstcSXmpyjfZLvKrSue0Eqm6RMRY4ERgTErpspTS3JTSBOABYADwx07ecmtgR+BK4HJgFHAzMAG4pKfiVu82ePDgl8sdg6TqY66kSmeupLwMKHcAXdS0yO9DZIv8HtTWhYVFfqcBVwOXkk0Z2QUX+VWOnFYiVZ0LgF+mlIoXjn8SeBv4Uyfv1w/YCDgmpXRT4djciNgCqIuIi1NKS5o/ICJqyV6vmj+mSyIidefxKp2zzjqrzXNjx47l9ttvry0+PnLkyBbH1HPqJ05b4/tS/z2Vu/3mUkpRrrbVLeZKqmjmSspLtRa47k0pbQkQESfSxpN20SK/lzc7NSf3CCVJVSEihpC9mb+yldNDgUdTSss6edt/k43gurPo+J3ACcD7gT80i2FH4CTg951sR73YnDlzGDVqVLnDkFR9zJUk9UkVV+AqrE1yNnAqsC3wN+BMYDrwm5RSrYv8qtI5rUSqKkMKn19sfjAi1gf2A2Z34Z5/Bj7azvnVr2MRMQCYAZwONHShrRYcdVE97rnnnmltnbvyyitrJ0+ePL34+BVXXHFqvlH1beMmTV9jxFSp/57K3b4qm7mSegNzJeWlEtfgcpFfVb3GxsZbyh2DpA5repM1vOj4ecBWdP61B+Cnhc8HFx0/GFgKPNrs2NeA2Smlh7vQjiSpbzFXUtUzV1JeKuqJy0V+1VuMGzdun3LHIKnDFpKtsXVBRJwQESMjYirw+cL5NRKGiDg6Io4G9igcGlU4trqYlVKaTTbFY1pEfDEiRkVEA1ADTEgpvVm4117ACGBSnj+gJKn6mSuptzBXUl4qbYpir1rkt9k9Xey3F2pvYeB58+Zx++2379zaub64OHDTgrkRkZp/Xe54mlTK36jTUMojpbQqIo4he+6fSrZ+1rVkUzYuoeVrz0+Kvr+i8PlZYLtmx48ELga+CmwOPAWckVL6brNrDgDeAzwVEQCDgfdHxLCi9VDUB82YMWNWuWOQVFF6Za5UuG9FvBdTz6n0XKlS84FKUKm/m47kShUzgqvZIr/FiQN0b5FfaH2R33XJFvltHoOL/EpSH5RSWpBSOiCl9K6U0tCU0teAXYHHmkZbNbs22vjYrui6JSmlupTSVimlgSmlnYuKW6SUJqaUtk4pbVd4/O/JimAWt8T8+fO3KHcMkiqDuZIkrV0ljeDqdYv8NnFURu+0toWBDzvssBYLA0PfXBy4acHclFI0/7rc8TTxb1Rt2APfxKuMpkyZctDhhx/e6muJpD6n1+ZK4Hux3qjScyXzgbZV8++mYkZw4SK/6kWcViJVt4jYkOz1qLPrmXRLSmn/npzyIUnqNcyV1GuYKykvlTSCq/kiv68ALwBHA4cUzrdY5LfwZfNFft8HLC0s7ktKaXZENC3yOwhYABxKtsjv+FYW+d0/p59Nfcz8+fO3GDZs2HPljkNS1xTWHOlf7jgkSSowV1KvYa6kvFTMCK6U0irgGLKegqnANWQ9FVcBK2l9kd+fAF8sfH9F4fupRdcdSbZY8FeBXwAHkq1vcmmza5ov8vsM2VDdqyPinJ742dT3TJky5aByxyBJqm5jx479bbljkFQZzJXUm5grKS+VNIKLlNICsifQ1SLiR7SxyG8H77kEqCt8tHXNRGBiszZ/DXzHaSKSJKlcTjnllL+WOwZJlcNcSZLaVzEjuNqxB12bUy5JklS1SrVVuqSqZq4kSQUVNYKrWLNFfq8uZbsppf1L2Z56H6eVSJIkKU/mSqpW5krKS0UXuFzkV9XKaSWSJEnKk7mSqpW5kvJSDVMUparjtBJJUncNHz7cHaYkSb2OuZLyYoFLkiSpAk2dOvWX5Y5BkiSpWlT0FEVJkqTebMSIEae2dS4idk8puXi0JElSBziCS8qB00okSd1lcUuS1BuZKykvFrikHDitRJIkSZJaMldSXixwSTk4/fTTDyp3DJLUmojYNiLujoi/RsSjEXFpuWOSqlVE7F/4O3oyIr4fESXd0S4iJkfE8xGxopTtSlJ3mCspLxa4pBwsWLBgaLljkKQ2rADqU0o7Ax8GPh4RnypzTFLViYh+wPeBY1JK7wX+Czi+xGH8BNijxG1KUreYKykvFrgkSepDUkqLUkoPFr5eDswHfKMpdd6ewD9SSo8Vvv8BcFQpA0gp3ZdSerGUbUqSVKncRVHqovZ2vgIWjRgx4sJSxSJJXRERmwGHA6PLHYtUhYYAf2/2/XPAtmWKRZIqirmSysERXFIOUkoXljsGSWpPRAwEbgImp5QeL3c8UhWKcgcgSdXIXEl5cQSXJEldEBHbAMcAhwDvAwYDrwC/A76VUvr/2nhcAEcAXy48bmOyUSC/BiallBaWIPb+wHXAwymly/NuT6p04yZN3xWY1Ma5O4AHJtbXXlR06u+sOWJrKPB8F9t/L/Dtdtp/eGJ97QVdubckSX2FI7gkSeqaLwNXAjsAdwGXA/cBnwLuj4hj23jcZcDNwE7Az4ApwNPAF4CHI2KXnOMGmA78BzinBG1J1eAvwIbAwa2cOwi4o5XjDwJDIuL9he9PBm7pSuMT62ufBFIb7R8M3NmV+0qS1JdY4JIkqWv+AOybUnpvSumUlNL5KaWjgQOAlcDUiFi3+QMiYjBQBzwL7JxSOj2lVJ9SOois2LQRcHaeQUfE3sDnyXZemx8RD0fEmXm2KVW6ifW1CTiLrMhU7NqJ9bUPFR9MKa0ETgFuioingCXAj7oRxjlkzx3Fbp5YX/ub1h4QEdMi4nmgf0Q8HxFXdaN9SZKqmgWuMouIbSPi7oj4a0Q8GhGXljsmqdwiYnLhjfqKcscCEBH7F/4+n4yI7xemd6kPiIhPRcTtEfHPiFgWEc9GxHURsWtK6ZaU0m+LH1M4NhfYDNi16PR2ZK+996WUXis6d3vh86Ae/jGK4/tdSilSSrumlD5UP3HaUfUTp708btJ0/1+rTysUsWYWHV4KjG/rMSmle1JK708pvSel9PmUUpdftybW1z4OFBeolgPntdP+qSmlIYW/6SEppS92tX2pEpkrqVJUWn5SSSopV7LAVX4rgPqU0s7Ah4GPR8SnyhyTVG4/IRtdUnYR0Q/4PnBMSum9wH8Bx5c3KuUtIgZERCPZFMJdyaYdTQbmA0cB26zlFiuKPjd5gixh3TsiNio6d0jh891djbuLvgr8gJwLa1KVGE82EqvJpRPra/9Rwvb/H9lafk2unFhfm/u6fFIFM1dSpaiY/KSSVFquZIGrzFJKi1JKDxa+Xk6WPA0tb1RSeaWU7kspvVjuOAr2BP6RUnqs8P0PyAoc6t2mAJ8BvgO8J6V0WkrpvJTS4cB7yBaSb1VEDAVGAouAPzc/l1L6N1kCvR3w14i4OiImRcQdwP8B3y20WRKFha0/C0ydWF9bKX9zUtlMrK9dBFxS+PZZ4IoSt/8K8I3Cty81i0Xqk8yVVCkqLD+pJBWVK7mLYgWJiM2Aw4HR5Y5F0mpDyHbKavIca+6apV4mIvYBTgN+CZyZUlpjTZ6UUpu7pEXEOmRr8KxL1uPcYj2dlNJlhTVzpgOnNzt1HzCrO1OcmoybNL21dYTac9a4SdPP6m67Ui8zDHhj3KTp5Wp/S+C1MrbPxPraKFvjUhFzJakiVVSuZIGrQkTEQOAmYHJK6fFyxyN1V2E9n02Kjm3eytevFBb3zTueTWlj1GqzWF6f0yBAIwAAIABJREFUWF/7dtFp39z3PXWFz+OKi1vtKQzRngHsC3wvpdTqYtMRMZ5shMbXgVnAYuBDZDsy/joijkop3daN+CVJ6lXMldQTxk2avi7ZjrmtnWvKB1ZOrK9dXLqoKsO4SdM3AVpdO6vZ72bJxPraZUWnKypX6hVTFCNim4ioi4i7IuK5iFgeES9GxM0RsVc7j4uIODIi5kbEooh4IyL+VtiRZocSxt8fuA54OKV0eanalXIWwG+Al5sdK/56eimKWwXfLLT5civnXiabSrZuK+f+zpq9EEOBNkfwqFcYDTyTUnqkow+IiAC+R7bmwCyyEWCtXTcCuBj4TkppYkrp+ZTSkpTSfcAngbeBy7r7A0iS1MRcSVptY2AhbecDLwNfLmlElePLtJ8rLST7/RWrqFypVxS4yP4xrgR2AO4CLieb6vEp4P6IOLaNx10G3AzsRLaQ8BTgaeALwMMRsUvOcTeZDvyHbHtoqVeYWF+7gmzL9bYsB75SonAALgRebef8+RPra5e0cvxBYEhEvL/w/clkC46rF4qITch69p7pxGP6ka038HngeuDElNKqNi4/tPB5bvGJwroOjwM7RkSrvYuSJHWBuZIETKyv/SdwUTuX/J2+29F4GWtONSx2UeH3V6yicqXoxOyLihURRwL/Kt6uvbCOyt1kT4hbp5SWNTs3GHiB7B/xv5tv1x4RZ5EtKnpNSunzOce+N9kLzF+AprVaZqSUvp1nu1KpjJs0/efAYa2cmjSxvnZca4+JiGlkhYBtyP5Ob+2Jrc/HTZp+JtlOeMUeAj4ysb621aJEYdTNd8hGeP0GqO2JdZJUeSJiU7IdzB5LKX2gA9c37RxzEnADUNPaulvNrp8CfAk4OaU0o5Xzfwe2BjZo/prV08ZNmn4NcBywvYvLS1LvZq4kvaMwTfFRsk2Dio2dWF/749Yel1d+UknGTZp+HFlnbbGngA+0Mj0RqKxcqWpGcEXEpyLi9oj4Z0Qsi4hnI+K6iNg1pXRL8RM2QOHYXGAzsm3em9uO7Oe/r/kTdsHthc+5b5meUvpdSilSSrumlD6UUvpQ/cRpPxg3afqJ4yZNXyfv9qUSOJdsi+fm2t0ZKqV0akppSOFvY0gPvnhMJRshU6yureJWIZ57UkrvTym9J6X0eYtbvVdK6VWyIdg7R8Qnis9HxE7Nvm4auXUS2dbRx7dX3Cpo2n3x7IhYY5h3RJxGtlDnA3kWtwp+AVxgcUuSeoc+litdPW7S9JPHTZq+Xt7tq/cpFGnObeXU/WSdla3KMT+pJDeQ/R6KndtWcQsqK1eq+AJXRAyIiEayYbG7kg13m0y2RexRZBXU9qwo+tzkCbIpUntHxEZF5w4pfL67q3F302nANcDuZWpf6jET62v/RjakvbnxE+trXy9DLG8DZxcdvmFife19pY5FFe18sjXkZkfETRExKSKuiYi/ARObXfd14ERgCbAA+GpEXFj08aGie/8EuBf4ALAgIr4XEf8XEXeTFWDfpOX/0R43sb72pon1tVfm3Y4kKV99NFf6DNno6VFlal/V71ZaLhdRV8K1gStS4eevKzo8l+z3VRUqfopiREwlK/h8BzireTUwIoYAr6WU/tPGY4eSJR2vANsW96xHxLnA/5ENMbyNbHjursAnyHrlv1zq6uO4SdPfRTZ64OGJ9bUHlrJtKS+FHQyfADYHHgb2mFhfu7aRLnnGMxs4CFgG7DSxvvbZcsWiyhQRB5KtEbcnsB7wT+APQENTL3hEzAQ+t5ZbnZRSmll073XJ1qc7lmxdk4FkoxrnApeklP7aYz+IJKlX64O50gDgr2SdS7v19YKEum7cpOn/DfyRbNDPDyfW167tPV2fMW7S9GuBE4BVZH9nHd54qdwqusBVmBd+L/BL4JBObte+DvArsu3aT2hnu/bjyBYubN4zcR/Z9vC/a+0xnTVu0vTK/SVLqhgT62sraptdSZJUuXpLrgTmS5LWriO5UqVPUWwaHjeuk0/Y/YAZZE/Y32vnCXs88EOytYC2JXvi3oest/7XETGmG7FLkiRJUl7MlSSpmUovcI0GnkkpdXhIXEQE8D3geGAW2ZDd1q4bAVwMfCelNDGl9HxKaUlK6T7gk8Db9N0tQiVJkiRVNnMlSWqmYgtcEbEJsCHwTCce07Sj1efJtrc8MaXU1s5ohxY+Fy8uR0rpRbKd1naMiA07EbYkSZIk5cpcSZJaGlDuANrRNL/y3R26OHvC/j7Zdu03AJ9dy3btAwuf29redhDZompvd6T99nRkrui4SdPPIesF2XtifW1rW3NKkiRJEvSiXAnWni+NmzT9BOBa4PCJ9bVVs6ObpNKq2BFcKaVXyXYT3DkiPlF8PiJ2avZ1U2/ESWRbsB+/lidsgKZFEc+OiI2L7n0aMAR4IKW0rOs/RccUdgM5G7jL4pYkSZKk9vSxXCnIdjZ+mGw3R0lqVaXvongsWQ/DCuBW4CmyXoqPAY+llI4oXHch8A2y7WInF64v9rOU0sPN7t0fuIdsccV/kj1ZLgZ2A0YAbwL7p5T+kMfPVmzcpOk7AAMn1tc+Xor2JEmSJFWvPpYrbQMMmlhf+/BaL5bUZ1V0gQsgIg4kq9jvSbZjxz+BPwANKaXfFq6ZCXxuLbc6KaU0s+je6wJnAccCO5ENxX2JbK75JSmlv/bYDyJJkiRJPchcSZLeUfEFLkmSJEmSJKk9FbsGlyRJkiRJktQRFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVs8AlSZIkSZKkqmaBS5IkSZIkSVXNApckSZIkSZKqmgUuSZIkSZIkVTULXJIkSZIkSapqFrgkSZIkSZJU1SxwSZIkSZIkqapZ4JIkSZIkSVJVG1DuACRJkiRJktpzzz33TGvv/KRJk3avr69/qLVzI0aMODWfqFRJHMElSZIkSZKq2l133bV7uWNQeVngkiRJkiRJUlWzwCVJkiRJkqSqZoFLkiRJkiRVtQkTJtxS7hhUXha4JEmSJEmSVNXcRVGSJEmS1CsMnDM75Xn/5aMOjq48rq6RXOMCaKihS7H1FuPHjz/y7rvvnp5nGxGR+79jSqlP/zt2hyO4JEmSJEmSVNUcwSV10T333DOtrXOTJk3avb6+/qHWzo0YMeLU/KKSJEmSJKnvcQSXlIO77rpr93LHIEmSJEl9xejRo1sdYKC+wwKXJEmSJEmqam3NoFHfYYFLkiRJkiRVtTFjxhxf7hhUXha4pBxMmDDhlnLHIEmSJLUlIoZExLcj4v6IeCMiUkTs0s71oyNibkS8HhFLIuKRiDiylDFL7Vm6dOkG5Y6h2HrrrUf//v3bvWavvfYqUTS9nwUuSZIkSep73gt8GlgM/Ka9CyPiZOAO4M/A0cARwExg/XxDlKrLwIED+cxnPsN9993Hm2++yZtvvsmKFSt49dVXueaaa9hzzz3XuP6cc87h97//PRdccEGZIu5d3EWxAgycMzvlde/low6Ozlxf10husTTU0KlYqtn48eOPvPvuu6fndf+IyO3fKaXUZ/6dJEmS+rB7U0pbAkTEicBBrV0UEUOBKUB9SunyZqfm5B5hDtKbb7LihJPo/+Uv0W/fj2fHli1jZf0FsNlm9P/q+US/8o0D+f6XtuajR32TXQ44ZfWxlBLf/cLGjDr1Wt675xFliauuka2AGmAw8AzQ2FDDq2UJpg2DBw9+uVxtRwTnn38+dXV1DBo0aPXx5cuXM2DAADbZZBNOPPFETjzxRB588EHOO+88dtttNy677DIAXnzxxXKF3qs4gkuSJEmSepGI6BcR50bEExHxVmE64X4R8beImA6QUlrVwdudDCTgqtwCLqFYf336HX0UKxuvI6VEWrmSlRdfCuusQ/9x55W1uLXklRdYungRg4Z9aI3jr/1zIcvf+g9b7rBHWeKqa+Qs4O/A/wFnkRU8/1HXyKfLElAbGhsby7JMzMCBA7nxxhuZMGECgwYN4uGHH6a2tpZNNtmEddddlwEDBrDjjjvyrW99i3//+9/ssccezJkzZ3Vx6+STT2bGjBnlCL3XscAlSZIkSb3LD4CvAdOAg4EbgeuBHYDO7jS3D/A4cGyhYLYiIp6JiPMjoirzyX5jPgmvvEr67e9Y2TCF9PLL9L/w68TAdcoa10sL5xH9+rP5kDWXQnv5uUfYYOMt2WjzbUseU10jhwNXAE0LSTX9m68LXFfXyJ6tPrAMxo0bt0+p24wIZs6cydFHH83ixYs55JBD+PCHP8z3vvc9XnvtNSAbgffkk09SX1/PkCFDmDt37up1ub7zne9Y3OpBVfmEJFW60aNHu0WtJEmSSi4ixgInAmNSSpellOamlCYAD5AtUfPHTt5ya2BH4ErgcmAUcDMwAbikp+IupVh/PfodcxQrL7uC9Kc/MeCSi4h3lX998pcWzmPTwcMZMHC9NY7/67lHePf25Rm9BZwHtDbar2lZk7oSxtKuefPm7VzqNk855RTGjh3L66+/zgEHHMDs2bPbvf6LX/wiBxxwwOrvTz75ZLbccsu8w+wzXINLykF9fb0FLknSWt1zzz3T2jo3adKk3Vt7PRkxYsSp+UYlqcpdAPwypVS8cPyTwNvAnzp5v37ARsAxKaWbCsfmRsQWQF1EXJxSWgIQEdsB1wJbAcuAM1JKv+3ST9GGta1Fu85dd3T8Zm+9Rf9PH0tsummPtd+W/5219oe9tHAei196kmmnbbHG8beXLWGPT56fW2xt3q9ff8784Yr2Lum3dPGiz0Rs/ZmebLctZ5111lqvuf3222tbOz5y5MhWj3fXmWeeCcAZZ5zBww8/3O6155xzzhrTEo888kgOPfRQTj75ZC655J1acZ7rLVeLrq4LXZUjuNzSVpVuzJgxx5c7ho6KcE15SapEd9111+7ljkFSdYmIIcAuwE9aOT0UeDSltKyTt/134fOdRcfvJJum9v5mx6YBN6SUhgOnAj+OiIGdbC93q351D6tuuJE4cDQrf3orKVVGPeGlpx9kryMv5DMTHl7jY8A667NlGUZwpbSKVatWtnvNqhVvlyiayrPPPvuwyy67sGjRIm688cZ2ry0ubs2YMYPJkycDcOqpp66esqjuqdYRXE1b2j5EtqVtqzt+wOotbacBVwOXki2QuAtuaascLV26tKxjnD/84Q9z7LHH8u53v5sBAwawePFi5s6dy89//nNWrnznRaq2tpYxY8Zw1FFHsWxZZ9/rSJIkqcIMKXxeY0u2iFgf2A9of/5U6/4MfLSd86sKbWwBfBwYA5BSuj8i/gEcQMviWJetbWTH2naoX/WHeaz8zlX0/+aFxI47suKEk0j3/pbYb98eab8ta9utfvGLT7Js6asM++CBbLT5kDWPv7GYLXdY+1JXeeyGXtfIbcChtD44Jm20xdDvpJTO7Ol2W9PeqGeAXXfddYNhw4a90dq5K664okdGPzcfXVVbmw0K+973vsfbb7dd6GutuAXwq1/9iieeeIIdd9yRgw46iF/84heAu9p3R1WO4KKwpW1K6RDghrYuKtrS9syU0l0ppTkppStTSo0li7Yb0ptv8vYxx7Hq3vveObZsGSvqzmHFNyeQVnV085Oe8/0vbc1f5n5/jWMpJaae8l88Oe+nJY+nrpGt6xrZt66RnUreeAWJCGpqarj//vv54x//yLhx4/j85z/PCSecwJlnnslPf/pTnn76acaPH88mm2xCbW0t06ZN49BDD+Xggw8ud/iSJEnqvpcLn4cXHT+PbNpgV5bRaHqDX/yG8WBgKfBo4fuhwEtFI8SeBoZ1oc1crHr0MVZeMpH+XzmHfh/c9Z21uGZdX5a8qrmXFs5jwLobMGjof69xfNET97Ph5tuywcbvLlNkXEpWxCz+Ba0i+/efXPKI2jB//vwt1n5Vz9lppyz9vOOOtqfFtlXcgiyHblqza/jw4j9ZdUXFjeAq7MRxNtmQ1m2BvwFnAtOB36SUavvSlrbNt7GNffaGVavKuo1tJW1dW9fIpmSj846iUKyta+T3wMkNNTxWskBaMXjw4JfXflXPGThwIDNnzmTs2LEALF68mB/+8If86U9/YsWKFWyzzTaccMIJ7LTTTlx88cV86UtfYvDgwQDU1dXxs5/9rJThSpI6YMKECWXZ7lxSVVtItsbWBRHxCvACcDRwSOH8GgWuiDi68GXTm/hREfE+YGlKaTZASml2RMwBpkXEIGAB2YieGmB8SunNPH+gnpKefoaVX7+Q/qd+gX57f2z18X5jDmPVTbdko7j2369s8b20cB5bbr8n/fqvmaIvevKBskxPbNJQwwN1jXwK+B7ZhgNNngKOb6jhqfJE1tKUKVMOOvzww6eXqr077riDhQsX8sILL7R6/ogjjmizuNXkgQceYNNNN+Vvf/tbrrH2FRVX4CLb0vZI4CKyJ+CPkW1pO4hse9LOaL6l7deA7YHnyYoikzpRKCurfmM+mT3p/vZ3rJr3IOnllxlw2bfKso1tpWxdW9dIP+CXwJ68s4MHwEeA39Q18sGGGhaVJJhWNDY2liwp6devH9dddx1HHXUUr7/+Ol/5yleYNWsWb7yx5ujcSy65hJEjRzJz5kyGDMmGPX/9619fPfdbUt+wtqkbXbF81MEdHkq/tikaXdFQg0P5OyiPhWudSiFVjpTSqog4hizfmUq2fta1ZB3+l9Bygfnitbqa8q1nge2aHT8SuBj4KrA5WXHjjJTSd5td8xywZUSs22wU1/aFe5VdbL8d69zccp2kWG891rnxupLHU2zf41tPdUecNLXEkbTUUMMddY0MI9ukAGB/4N6Gmp5/Ta8mF154Ybvnf/GLX3Drrbdy2223tVrcAvjxj3/Mj3/84xyi65sqaoqiW9q2rpK2sa2grWsPJCtmFb+p7gdsQTYCsGzGjRu3T6naOuecczjqqKNYvHgx++67L9OnT29R3Grynve8Z3VxC+ATn/hEqcKUJHXS+PHj3RBHUqellBaklA5IKb0rpTQ0pfQ1YFfgseLRVimlaONju6LrlqSU6lJKW6WUBqaUdi4qbpFSehn4HdksGiLiY8A2wNwcf1yVSEMNK5p9/Zu+XtzqiOXLl3P44Ye3WdxSz6u0EVy9ckvbHtvKtgTb2K5t+9rubF3bk73G+9RczocPrGt1imZKiUVPPvCNiL2/0VPttaa9bWrnzZvH7bffvnNr53pyi9r+/fuv3pr2s5/9LI888kib1zatuQUwfvx4zjnnHPbdd1923313HnrondHqbktbPo6CkCRJOdkD+H0J2jkNmBkRdcByYGxKaXkJ2pUYO3Zsj+Tvql4VM4LLLW3bVknb2FbK1rWrVq5oOXarSUqklX1ju9oxY8YwZMgQHn/8cW6//fY2r2te3Kqrq+OSSy7hmmuuAeCMM84oSaySJEkqvYjYkGzR+c7Ohum0lNLClNK+KaXhKaVdWhm4IOXmlFNO+Wu5Y1B5VdIIrl67pW13trIt9Ta27a2N0t2ta3tydEpdI3sD97V2Lvr1Y5v37XdOSqmza7Z1Snvb1F555ZW1hx12WKsLHPbEFrVNo6xOOukkAK6++uo2ry0ubjWtuTV16lTOOeccxo4dyxe/+EXeeustwFFEUnsKnTHnkfWEfwhYH9g1pfSXNq4fDZwP7E7WqfQU8P9SSi4errUaPXp0V3Y7k6Q1FGas9C93HFLeRo4cWXv33XeXbJF5VZ6KGcGFW9q2UGnb2FbY1rX3A61t/beKbErrD0oZTLEZM2bMKkU7w4Zl/0XvvffeVs+3VdwCeOqpp3j++edZf/31GTRoUP7BSr3De4FPA4uBdnulI+Jk4A6yzpajgSOAmWRFMWmt6uvrS17g2muvvairq+Mb3/gG5557Locddhj9+6+ZF3/zm9/kuOOOK3VokiRJ7aqkEVxuadtMJW5jW0lb1zbUkOoaOQ64kGyu/yaFU43AVxpqeK2kARWZP3/+FsOGDXsu73bGjRvHNttswzPPPNPi3Gabbcall14KtCxuNTn33HOJCF599dW8Q5V6i3tTSlsCRMSJwEGtXRQRQ4EpQH1K6fJmp+bkHmE3pDffZMUJJ9H/y1+i374fz44tW8bK+gtgs83o/9XzW137sCd9/0tb89GjvskuB5zyTlwp8d0vbMyoU6/lvXsekWv7AHWNvJusk+u5hhpeyr3BNowZM+b42267LfcOkwEDBvC5z32OM844g912263F+b///e9Mnz6dq6++mrPPPpvx48fz1ltvce+99/KPf/wj7/AkSZI6pGIKXG5pu6bYvvK2sa20rWsbalgGnF/XyDfINgagoYYTyhJMkSlTphx0+OGH5z48dvbstmfuvvLKK4wePZqPfOQjTJ3a+r/RDTfckFdoUtWJiH7A2WTrMG4L/A04E5gO/CalVJtS6ujw2ZOBRPYaVjVi/fXpd/RRrGy8jthnb1i1ipUXXwrrrEP/ceflXtxa8soLLF28iEHDPrTG8df+uZDlb/2HLXfItzOlrpENyd6DjCWbzrOqrpEbgNMaang918ZbsXTp0ty3TN5oo4246aabGD16NAD/+te/uPnmm/nXv/7Fu971Lg499FB22mknLrroIs466yw222wzVqxYwfHHH29xS5JUUYYPH577AANVtoopcEG2pS3ZulerRcSPaGNL2w7ecwlQV/ho65qXI6JpS9ur3dK2ujTUsLyusdxRVKaHHnpojR0SJbXrB2SdIheRjRr+GHA9MIh3OlE6ah/gceDYiPgaWafJ82SdOJM6USgruX5jPpmNFP7t71g170HSyy8z4LJvEQPXyb3tlxbOI/r1Z/Mhu6xx/OXnHmGDjbdko823zTuE64DDeGcbk37AccCmtFzuoOqts846/OxnP2PEiBG89NJLnHvuufzkJz9h2bJ3Vmw499xzGTFiBLNmzWLw4MGklDjjjDO4+eabyxi5JLVt+aiDK3I92YaaNrfIUg+ZOnXqL/NuozPrFY+bNH2N9a0n1tf6fyBnlbQGV1v2oGvrb3XWacBxEbGArLfeLW0lqY+IiLHAicCYlNJlKaW5KaUJwANknUGd3Xlqa2BH4ErgcmAUcDMwgWxUcsVavd7jZVeQ/vQnBlxyEfGu3AcSAVmBa9PBwxkwcL01jv/ruUd4d85T4esaeT/wSVru0RvAQXWN/HfLR+Vr8ODBL6/9qq77yle+wogRI1i0aBEf+9jHmDVr1hrFLcimhx5wwAGri1sRweGHH55nWJIkdcnpp5/e6tIR6jsqagRXsWZb2ra9RVwPSSktBDq2NaG0FmPHjv1tuWOQ1CkXAL9sZTvzJ4G3aTlNfm36ARsBx6SUbiocm1vYtbcuIi4ujDAmIrYjm5K/Fdl06zNSSt16DmnaabU169x1R8du8tZb9P/0scSmm3arvWL/O6vtS19aOI/FLz3JtNO2WOP428uWsMcnz++R9tsy/H+O4+AvXt/m+bumfe7hOP6H3W2mhbPOOqvNc2PHjuX222+vLT4+cuTIFsc6q3///px++ulAtiPvwoULW73u4osvZvz48axYsYLa2lquuuoqDjnkEHbYYYfVj+mJ378qkzsrS6omCxYsGFruGFReFT2CK6W0JKXUP6U0pdyxSJ1xyimn/LXcMUjqmIgYAuxCy7UdIdtl99GiXXY74t+Fz3cWHb8TWBd4f7Nj04AbUkrDydb/+nFEDOxkez1m1a/uYdUNNxIHjmblT28lpdLVLl56+kH2OvJCPjPh4TU+Bqyzfu6bmbzxWvtrya/tfB7mzMlvT4JPfvKTDBkyhMcff5w77yz+b5ppXtw67rjjuOaaa/jxj38MwGmnnZZbbJIkSV1R0SO4pGo1cuTI2rvvvjv3ReYl9Yghhc8vNj8YEesD+wFt7+bQtj8DH23n/KpCG1sAHwfGAKSU7o+If5CtR9l61aED2ht1MXDO7DYrVqv+MI+V37mK/t+8kNhxR1accFK2a+9+7Q9w7swoj7pGWm1/8YtPsmzpqwz74IFstPmQNY+/sZg1u/QqAAAgAElEQVQtd9izR9pvJ67+wBNkRc3+zU6tAv5x+Hm/3L6hhhXdbafYPffcM62tc1deeWXt5MmTW7yWXHHFFad2tb2m0VYHHnggADNnzmz1uuLiVtOaWzNmzOCkk07ioIMO4rzzzgMc5SNJkipDRY/gkiSpBJrWORpedPw8smmDXVkH8qeFz8ULkx8MLAUeLXw/FHipaITY08CwLrTZLasefYyVl0yk/1fOod8Hd31nLa5Z15NW5b8m/ksL5zFg3Q0YNHTNpa4WPXE/G26+LRts/O5c22+oYSVwBO+MvmvyKnB4HsWtcnr++eeZN28ef/7zn1ucGzduXKvFLYCnnnqK+fPn8+ijj7Z4nCRJ5eQAAzmCqwJU0k4f7u5RHTrSW+6uHVKHLSRbY+uCiHgFeAE4GjikcH6NAldEHF34smnO3KiIeB+wNKU0GyClNDsi5gDTImIQsAA4FKgBxhfvDFxu6elnWPn1C+l/6hfot/fHVh/vN+awbEfFe39L7L9frjG8tHAeW26/J/36r/nWZNGTD+Q+PbFJQw2P1DWyA3AMcE3h8LCGGpaWJIASmjBhAhMmTGj13M9//nO+9KUv8b//+78tdktctGgRu+22WylClCSpU77//e/v7FIxfZsFLikHw4cPf67cMUjqmJTSqog4hmwtrKlkI3iuBa4i2/GweIH54rW6rih8fhbYrtnxI4GLga8CmwNPkS0g/91m1zwHbBkR6zYbxbV94V4lE9tvxzo339jy+Hrrsc6N15Ukhn2Pv6LV4yNOmlqS9psUilkz6xqzAlc5i1szZsyYVY52H330UXbccUfefLOi6rCSJLXr/vvvf68Frr7NApeUg6lTp/6y3DFI6riU0gKyda9Wi4gfAY8Vj7bq6HpDhV0S6wofbV3zckT8DjgZuDoiPgZsA8zt3E+g3mj+/PlbDBs2rCwdJha3JEnV5tlnn92q3DGovFyDS8rB6aefflC5Y5DUbXvQtfW3Ous04LiIWABMB8amlJaXoF1VuClTpvhaIkmS1EGO4JJysGDBgqHljkFS10XEhmSLzl+dd1sppYVA+9sUSpIkSWqXBS5JkooUphf2L3cc0v/f3p3HR1Vf/x9/HUAQK3VFsSJRq1RUWmvtr1qLWwoKUlQWK0VbUIxFqw12SWzEWhFMWoEg1ZSIuNRo61r98hUUAQXFfkttcFfcAMWlaqstuALn98ed4DDMhJlkZu7cmffz8chjknvvzD0J4d7M+ZzP+YiIiEh6Jk2adFfYMUi4NEVRREREpACNHDlySdgxiIiIiESFKrhEcmDAgAH56NsjIpKxT/sPTKtJfq7UjyLU80dJLlaCSmeRhOq6Ro//uraqQv9mIiJS8GpqaoYuWLCgMew4JDyq4BLJgQceeOAbYccgIiLRVl5eXhF2DCIiIiJRoQSXiIiIiIiIiIhEmhJcIiIiIiIiIhJpahMjSnCJ5IBW8BARkfbq3bv36rBjEBERiYqqqioluEqcElwiIiIiBaihoWFe2DGIiIhExZAhQ04POwYJlxJcIjlQU1MzNOwYREQk2qqrq/uFHYOIFDcz62lmV5nZUjP70MzczA5u5fgBZrbIzP5jZmvN7Akz09+9UhDWrVu3XdgxSLiU4BIREREpQMuWLesTdgwiUvT2A74PvA883NqBZnYWcB/wFDAcOAW4Aeia2xBFRNLTKewAREREREREJBSL3X13ADMbDZyQ7CAz6wXMAKrcfUrcrvk5j1AkTT169Hg37BgkXKrgEskBreAhIiIiImEysw5m9nMze9HMPo5NJzzazF4ws0YAd9+Y5sudBThwdc4CFmmnpqYmLfRV4iKZ4NJccSl0WsFDRETaSyvyikg7XQdMAGYCA4HbgFuBfYFM/1btBzwPnBpLmK03s5VmdpGZRfI9pRQf9a6UqF6MNFdcCppW8BARERGRsJjZSGA0MMTdr3T3Re4+CXiMoE3NPzJ8yS8B+wPTgClAf+BOYBIwOVtxi7SHeldKVHtwaa64FDSt4CEiIu1VU1MzdMGCBY1hxyEikfQrYJ67JxYDvAR8BjyZ4et1ALoBI9z9jti2RWa2K1BpZpe7+1oAM7sMOI2gKOHUuOOzwsw8m68n6fvpzcGPPqx/g/Hjx2/1mDlz5lQk215eXp50ey5V1c7c7Gv97qbP3a0tzyu4Ci7NFRcREREREWkbM+sJHAzcnmR3L+AZd/8kw5d9L/Z4f8L2+4EuwIFx2+YRFCAszvAcIiLtUogVXNcBQ4GJBHPDv00wV7w7MDXD14qfKz4B2Ad4nWAeel0GiTKRjGgFDxEREREJSc/Y41vxG82sK3A0MLcNr/kUcHgr+ze9r3L3pbHzteE0W9fWyg5pv8omHML7N1i4cOHM1vb37dt3u7Kysg+T7Zs6deo5uYkqteq6xs0qtvS7m3sFVcGlueJSLLSCh0hx0iInkk9akVdE2qhloLV3wvZfAnuQeYN5gLtjjwMTtg8E1gHPtOE1RbKqubl517BjkHAVWgVXUc4V11zb3AtjPnhrc8Dnz59P//79k+7L1/xvzfmOHo3qRELLIiePEyxykrQHJGxa5GQmcA1wBcGU+YPRIieSJq3IKyJt9ArB+6Zfmdm/gDUEi20Niu3f7NpiZsNjnx4We+xvZgcA69x9LoC7zzWz+cBMM+sOrABOBEYBNe7+US6/IZF0zJgx44STTz5ZvStLWMFUcGmuuBSTp59+OuwQRCQ3Frv77u4+CPhzqoMSFjm5wN0fcPf57j7N3ZvyFq1EmlbkFZG2iLVhGUFQVdUAXE9Q1XU1sIEtiwZuj32cF/t6auzrhoTjhgI3AhcD/wscD5zr7ldk/7sQEclcIVVwFe1ccVVl5F4Y88FbmwM+bdq0isGDBycdPcjX/G/N+RbJjJl1AC4EzgH2Al4ALgAagYfdvUKLnEg+aUVeEWkrd18BHBu/zcz+CDybWG2V7t+IsZkvlbEPEZGCUzAVXGiuuIiIhOs6YALBtMKBwG0Ei5zsS+b3oPhFTl40s/VmttLMLool0kRERPLtMNr2niojZjbRzF4HjiCY0vi6mX051+cVGTly5JKwY5BwFVIFl+aKS9GYPXv2zWHHICLpi1vk5Ji4PpCLzOxQgikZbVnk5EsEi5zUEFSDDSZY5GQHoDoLYUuR04q8IpItZrY9QSHBNbk+l7tPIBgwEsmrsWPHPhd2DBKugklwuftGMxtBMHLeQNA/60aC6R2TST5XPN7U2OMqYO+47UOBywnmiu8CvEwwV/wP2YxfJF5zc/OuZWVlq8OOQ0TSVlSLnGhRifbL1+IlrS1YMnLkSObMmbPFwiS5XqxEi5RIC7U3KB6xe07HsOMQyaXy8vKKBQsWqMl8CSuoaRLuvsLdj3X3L7h7r1j2vy8p5oqn+Ng74bi17l7p7nu4e2d376PkluTajBkzUq6sJiKFRYucSKGaP39+2CGIiIiIREbBVHC14jDgr7k+iZlNBMYA3YG+ZlYPHO3uL+f63CIiEqqiW+REVRftl6/FS7a2YMn06dO3GInO9WIlWqREREREoqigKrgSxc0Vz7T3ScbcfYK793T3Lu6+S+xzJbdERIqfFjkRERERibjevXurRUyJK+gKLs0Vl6jSCh4ikaJFTkREREQirqGhYV7YMUi4CrqCSySqtIKHSHS4+0ZgBEFVVQNwPUFV19XABpIvcnI7cF7s66mxrxsSjhtKsFjKxcD/AscTLHJyRfa/CylGWpFXREQkfePGjVMf5BKnBJdIDuR6hSsRyS4tciKFqLm5edewYxAREYmKFStW9Ao7BgmXElwiIiLJHUbb+m9lxMwmmtnrwBEEUxpfN7Mv5/q8Uvi0Iq+IiIhI+pTgEhERSaBFTkREREREoqWgm8yLRJVW8BCJNi1yIiIiIhItCxYsaAw7BgmXKrhEckAreIiISHtpRV4REZH0zZo1q0/YMUi4lOASyQGt4CEiIu2lFXlFRETSt3Tp0v3CjkHCpQSXSA5oBQ8REWkvrcgrIiKSvlWrVu0RdgwSLiW4REREREREREQk0pTgEsmBsrKyN8OOQURERERERKRUKMElkgMqjxURkfbSirwiIiLpmzRp0l1hxyDhUoJLREREpABpRV4RERGR9CnBJSIiIlKAqqur+4Udg4iISFTU1NQMDTsGCVensAMQKUYqjxURkfZatmxZH2BJ2HGIiERJ5/lzPZev/2n/gZbL1xdpKzPL6e++uxf8774quEREREREREREJNJUwVUAcjnKoBGGcNTU1AxdsGBBY9hx5ENlEzn7/a0fRUa/v7kctYjCiIWIiIiISLZVNtEB+Fbc18OAV4Dl9aNy914gUwMGDHg87BgkXEpwiYiIiBQgTXcXEZEwVTaxE/AjYBzQO27XHbHHf1Q2cQ1wa/0oPsx3fImqqqqU4CpxSnBJZFU20Qk4Eegbt200cEf9KNaGFZeISCHLRdWwqoUlXbmo+s2k2jfs8+ei0lgVxiKSC5VNnA40Al1bOexQYBbw28omTqsfxfy8BJfCkCFDTr/33ntvDjMGCZd6cEnkVDaxW2UTFwOvAn8BJsbtvh54o7KJGZVNHBBKgKg8VkRE2k+rQYlIrplZTzO7ysyWmtmHZuZmdnArxw8ws0Vm9h8zW2tmT5iZrlVFprKJSuCPtJ7circzcF9lEyNyF9XWrVu3brswz19szKI3fhLZBJcuxqWpsolvAE8SJLV6pjisG/AT4InKJkbmK7Z4Ko8VEYmeyiY6VjYxsLKJi+K2nVjZRMcw4xIRyaH9gO8D7wMPt3agmZ0F3Ac8BQwHTgFuIP0kiERAZROnAdOS7asfFXyk0Am4ubKJo3IUmrRThw4dGDx4MPX19dx0003cdNNNTJ8+nZNPPpmOHTf/U2ennXZi6dKlnHTSSSFF2zaRTXChi3HJqWzi68BDwO5pPqUzcEusvDavhgwZkvdzSvq222479thjD3bccceUIxNHH300Xbp0yXNkIhKGyia6VTbxS+BFgr8XJsftngO8XNlEdWUTXwwlQOE/76zkgZmjww5DpBgtdvfd3X0Q8OdUB5lZL2AGUOXuF7j7A+4+392nuXtT3qLNAv/oIz4bcRobFz/y+bZPPmF95c9Yf9kkfOPGEKMLV2UTXQj+nduqMzCjsimzhaKypUePHu+Gcd5Ct8suu1BdXc0rr7zC//zP//DTn/6UM844gzPOOIMLLriAu+++m5UrVzJhwgR22203dtppJ+bPn8/hhx/O5MmTt0h+FbIoJ7hK4mKsC3CgsoluwP8C2yfbv5XRhNmVTRySo9CSUnns5mb95Es8vWjWZtvcnYaxX+SlZXfnJYYddtiB888/n+eee45169bxxhtv8O9//5sPPviAq6++moMOOmjTsSNGjODBBx/krrvuitQFXXJP1cPFp7KJPYDFQB2wT4rDyoArgEcqm1JWD2edpruLSHuYWQcz+7mZvWhmH8fuQUeb2Qtm1gjg7um+mTgLcODqnAWcJ9a1Kx2GD2ND0y24O75hAxsuvwK22YaO1b/EOkT5LXK7DQd2bedrfBX4dhZiyVhTU5MWZ0nQt29fli9fzhVXXEFZWRkvvfQSl1xyCaNHj+ZHP/oRNTU1vPDCC/Ts2ZPLLruMJ598kkcffZRvfOMbvPjiiwwYMIANGzaE/W2krSD/9+pi/DldgDcZBezRxuduA/w0i7FIBtb+aw3r3n+T7mWb5xg/+OcrfPrxf9l938NyHsMll1zCmjVruOqqqzjggAP45JNPeOutt/jggw/o1q0b5557Lk8//TQPPvggZ599NrfccgudOnXi8ccfj9QFXfJC1cNFpLKJHYH5kPYgSF9gfmUTO+cuqs9punvgoRvPZ+7vT2PVk/O44/JjePvV4v2xdO/enWHDhjF27FjOOOMMjjrqqC0qjQcNGsRZZ50VUoQSMdcBE4CZwEDgNuBWYF8g0/9I/YDngVNj79HWm9lKM7vIzCL3hqTDkO/Bv/6NL3mUDfUz8HffpeOll2Cdtwk7tLCdW2Cvk5Hq6up+YZy3UPXt25clS5bQs2dP/vrXv3L88cfTu3dvJk6cyI033shNN93E5MmTOeCAAygvL+exxx5j9913p0+fPqxevZpjjz2WNWvWhP1tZKRQL0a6GMcp9QtwrMS1vRfJ0yqb2CUb8aRD5bGfe/uVZViHjuzSc/Mil3dXP8F2O+xOt132ytm5zYwbbriB3/zmN3zhC19gwYIFDBs2jO23337TFMWDDz6Yq6++mv/+97+Ul5czc+ZMOnXqxMSJE7nkkktyFptEVlFXD5dg1XAdcFCyHa1UBh8ATMlhTJuUynT3N1Y8yl9+N4hrz9uDa87anuvH78vS2y/etP+YH81g4E/+RNlXT2D4xQ+x+z7fyFksYVUcH3744fzxj3/ktdde44477uDaa6/lpptu4uGHH2bFihVceOGF7LjjjgwaNIi77rqLWbNmccQRR+QsHok+MxsJjAaGuPuV7r7I3ScBjxH0SvpHhi/5JWB/gt5MU4D+wJ3AJDaf1h0J1nVbOowYxoYrp+JPPkmnyROxL5T2BIzKJvYie5VXI2Ir3ufVsmXL+uT7nIVql1124b777mOHHXbg7rvv5phjjuGBBx7APflivs3NzZu1Z+natSsbI/h3X95/6bYm7mJ8jLu3jI4vMrNDgaG07WL8JYKLcQ3wAjCY4GK8A1CdhbBzKv4CzE470ql+SqldgP8fwah5e2xLUAV2VfvD2TqVx37u7VeWsVOP3nTqvO1m299Z/QS77ZPb6q26ujp+9KMfsXbtWkaMGMG8efO2OOaZZ57hJz/5Cc3NzVx77bWYGe+++y719fU5jU0KT2zQ40LgHGAvgvvFBQRLZD/s7hXFXj0cXzVs/Y6EjRuLtmo4Vr3V1gTSaZVN/Lx+FO9lM6ZEpTDdfeUT85g741TKx17Ll8f/BYB3Vz/Jf95dlfdYwqo4/s1vfrNpQGXjxo08+OCDrF69mi5dutCvXz/2228/pkyZQlVVFTvuuCOdO3dm+vTpPPbYYzmJR4rGr4B5ce+nWrwEfEawaFMmOhAs5DTC3e+IbVtkZrsClWZ2ubuvNbOdCFbf6w18BLwNnOvuL7X1G0lkZsnfocds88B96b/Yxx/T8funYjvtlLXzR9Vu+3yDkRP/vunrVtq/JN1Xufnw3TYzf7zLZ9NP/1e2wgNg/PjxWz1mzpw5Fcm2l5eXJ92eS1W1Mzf7Op+/OxUVFZsqt0aOHMknn3yS8tiWnluHHnooL774Iu+++y5HHHEE5557LhMmTNh0XD7jd/c29XEruAQXRXgxztpFuEQvwF/59g844dzPr5iZXGzjL7TL779qup3+0+nZiqu1C+z8+fPp379/0n35urjm64L605tbf9m3X1nG+2+/xMwfbz6d/7NP1nLY9y5K8axAe2Lef//9+cUvfsGnn37KkCFDWLRoUcpjR4wYwR/+8AfMjLfeeosePXowfvz4vF/Q23ohl6y5jmAgZSJBtfC3CaqHuwNTM3yt+OrhCQS9nV4nqEyuyyBRlncdhnyPjXfchS95lI3L/o6/+y6drvxtMVYN/xBoawJpW4LBuLxUchWzJx+8mr0POZHeh39/07bd9z0sL9PXE4VRcXz55ZdTU1PDhg0bmDJlCtdccw2rVn2e3OvQoQMnnngiU6ZMYf/99wfghhtuoLKyMuuxSPEws57AwSRfCa8X8Iy7p363m9x7BBVc9ydsv5/genog8DeCwZ16d38wFssFwPUE98WCsfHBhWz8823Y8QPYcPc92MDjUy48VCo6dc5uB4Vsv56kr0OHDpxzzjkA/PrXv04rudXSc+vYY49ln332YcmSJYwdO5bLLruMzz77LF+ht1tBJbh0MU6u1C/A22ybtK98xjp37ZaV10nH008/nTLBVWrefvXvfGvopfT5zg832950UV92z2EF149//GMAbrzxxq0mt1p6bk2cOJH777+fRx55hLPPPjtyF3RpO1UPf66Eqobbe5EeQI4TXKUw3b1rt+688o97aZ43nbK+A9h5z/Bml+S74njAgAHU1NSwfv16hg8fzj333LPFMRs3bmTDhg306tVr07ZDDsnrujkSTS2LYbwVv9HMugJHA3Pb8JpPAYe3sn8jgLu/DzwYt30p8Ms2nC+lrQ0Idp4/t9VByY1/W8aG319Nx8suxfbfn/U/HIMvXoIdfVRWzh9VlU30Ja6YpDJJQ4WWYoJk+xKdddXrX6wfxX+zFB4ACxcunNna/r59+25XVlb2YbJ9U6dOPSebsaSjuq5xs9/FXP/utAzIDxo0aFND+fnz56c8Pllya82aNaxZs4annnqKvn37csopp3DbbbflJf5sKKgEF0V6MW7PRVgXYKhs4gdAU9zXW0jnYnvgUWOuemDmmKw1m2/tAjtt2rSKwYMHNybbl6+La74uqJVNpPz9ff+tl/hk3b8p++rxdNul5+bbP3yf3ff9ZquvnWnMLRf1rl27MmbMGAAaGhpSHp+Y3GqZIvLkk0/y1a9+lWHDhvGnP/2pTbFI5BRV9XBrFYe5qBqOYrXw8AmL2fMrwRhWWyqD33rp/waYHd7u77u1auCRI0cmnWqR60rgXFYAJ1b9Hn3GdL7YfR+eXXw9i5vG023nvfjW0Es56Ogxmx3XcZtt2WmPA5K+ZibxtVZ13NaK47b+fC644AIgmKKYLLkFbOq51aVLF6655hpOOeUUDjnkEPr168eSJUvadf506N4XWS3J8d4Ei520+CXBok1tWanhbuBsPu+P3GIgsA54JsXzKoG/tOF8ObHxmWfZMLmWjr/4GR2+GnRA6TBiGBtuvhXr952imorfBisJ/hbJRunVa8DaLLxORpqbm3ctKytbne/zFpqWQosbb7wxZc+tVMmtFtdffz1Tp06lf//+mxJcUVBo/4PjL8bx2nsxhuDiG6/gL8aJF+BNo+o331qMjX5b83yWXueFLL2OpOntV5bRqct2dO/1tc22v/niUrbfZS+222G3nJz3sMMOY6edduKJJ56gubk56TGpklsAs2fPBoLRdSl+cdXDtyfZ3Z7qYUhePdyFoHoYPq8e7u3uXwPmEFQPhyaxajjVH0ZRt+GzTP9JN7f+s4+zFElqrY26FovOXbvxrVMmMGrycs7+/VvsfciJLJg1lv++9/pmx31hxx58c0huCx9bKo5/MGn5Zh+dtuma9YrjffbZh4EDB/Lxxx+nHIiJT25Nnz6d8847j1mzggb4554bygJlEh2vEAzM/MrMfmhm5WbWAJwZ27/ZeyozG25mw4GWX/T+sW2b3j+5+1yCVWdnmtl5ZtbfzOoJetxOcvePEoMws18TrD6c1QqutvJXV7LhkkvpeM7ZdDjy817qHYYMhg8+wBcvCTG68MWqrbK1EM7M+lGpB8FzZcaMGSfk+5yFqFu3YObS6tXJc31bS27FP/eLX/xiboPNskKr4Iq/GP8LWEOwtPqg2P4tLsaxT+MvxgcA62IXYdx9rpm1XIy7AyuAEwkuxjVbuRgfl81vLhOtXYA33nFXUMV1zNFhhZdvzQT/9u1ZNulDsnfB3qrZs2ffnK9zFbK3X1nG7vt8kw4dN7/UvPnSYzmdnrjNNtvwxhtv8MILyXOaw4YNS5ncAnj11Vd57733Wp2vLkWl6KqHW6u6yEXVcBSrPCqbuI7Ym722VAb37HP0ze5+Rnvj2Fo18PTp07eoBs51JXAuK4Bbq/rdbofd2P//DeepBQ2s/zTpDJOkMokv1fnbU3Gcyflbqq0GDx5Mhw4duPvuu3nvvS3XKkhMbrX03Lr22muZMGECJ510UpvOL6XB3Tea2QiCvo8NBIMuNxIsfDKZLauSEwd4WvpOrgL2jts+FLgcuBjYBXiZoOr4D4kxmNnFBFPz+7t7+v+hc8j22Ztt7tyyEsW23ZZtbrsl7/EUqAZgbDtf4zOCvqYSkjPPPJNzzz035SqInTp1Ytttt02Z3AK499572W677fjooy3SJQWtoBJcuhjHxbGPLsAt6kfhlU1cQ/sulDfXj+KDbMW0NSqPDRx1evK+3MeNST1tMBsWLlzInnvumXL/ypUrWbt2LTNmzNgiuQXBBX3XXXdN8kwpUprKQUlO25jN59UMbaE/3ttp2b1XsNs+h7HH/kewTefteGfVch750y8p63s8O+2RWMyfW/muOF6/fj2rV6/mqaee2mLfgAEDkia3AF577TXWrFnDunXr6Ny5M59++mlW45Li4e4rgGPjt5nZH4FnEwf4002SuvtagvtUq6scxIoFBhG8n3o/k7glXPWj+EdlE4uB9PrhJPen+lGbDxpK/n38cepK83feeYdjjz2Wzp07J01uAXz22WeR7EVcUAku0MVYUvoTMIHNE5fp+gjI2uqJ6ZgxY8YJJ598ctIeXBK+xx9/nIMOOog33ngj7FCkMJR89XCJVg0vJfh3/2obnvsckNivTTK0/pMPWdI0nv++uxo6dKDbLr3oc+QZfG3A+XmPJd8Vxw0NDSmnJr788su888473HnnnUlXS+zZs2eSZ4mk5TDgr7k8gZkdBFxKUFDwUMvCWO6u1RGi4wcEvydbXGzSaC7/BPCT7IeUnpEjR5b2PNMMvPPOO2GHkBMFl+BKQRfjElc/ig8rmxgIPArsnLi/lYvtRuAH9aN4NnfRSRQpuSUtVD1cmlXDsergX/N5r85M/DofvUWKfbr7ESMmcsSIiWGHAYRXcZzMyy+/zKGHHlq0bz4kHGa2PUGl8jW5PI+7PwNo2myE1Y9iTWUT5cA8YJ8MnvoP4MT6UfwnN5Ft3dixY58L69xSGAp+vkHcxTjTJdoz4u7PuLu5+37ufkjLRy7PKZmpH8XzwHcI3kSm40PgpPpRhbNyi4gUJndf4e7HuvsX3L2Xu08A+pKiejjFx94Jx61190p338PdO7t7nxTJrV8D30PVw3kXuz/8LNm+yqaUgyfV9aOSLkiQdRSzTeYAACAASURBVM3NzZorXaKU3JJsi92TOrr7jLBjkcJXP4oVwBHADcDWVlX5D3AVcHTYUxNzvcqwFL6CT3DpYizx6kfxHPA14HyCKSLJvE1QNXFA/Sjm5Cu2eCqPFSkKh9G2/ltpi6se3oWgeni5mS3P5Tllc/WjmAqMBraWXPwPcHb9KOpyHlSMVoMSEZGw1I/i7fpRjCGYqvhzggV0/k3QRP49YBlwDrBn/Sh+Wj+KtaEFKxITlSmKIpvEmsX/vrKJqwlWODsY2IGgcfNK4L76UYTadVXlsSLRpqkcpaV+FDdWNnE7cBpwLnAI0BHYQDBFtQG4pX4U68KLUkREJP/qR/EeMCX2IVLQlOCSyIr1P3ko9lFQysvLKxYsWKAm8yIRFVucpGPYcUj+1I/iQ4KVFWdXNmHAtsDH+ei1JSIiIu3Xu3fvkl/FvtQpwSUiIiISJ5bU2mKly3zTdHcREZH0NTQ0zAs7BgmXElwF4NP+AzU9RSKrflThTK9y97Riqa5r3Kwio7aqomC+B5Fc0z0nOopxunvY94ywz5/OfUr3KJH20X2udI0bN+6EUk5y6b1QBJrMi0SRymNFRKS9tBqUiIhI+lasWNEr7BgkXEpwieRAKY8ciIiIiIiIiOSbElwiOTBu3Dgt7S4iIiIiIiKSJ0pwieSAymNFRKS9NN1dREQkfVrFXpTgEhERESlAmu4uIiKSvlmzZvUJOwYJlxJcIjlQVlb2ZtgxiIhItFVXV/cLOwYREZGoWLp06X5hxyDhUoJLJAdWrVq1R9gxiIhItC1btkwj0SIiImnSezBRgktERERERERERCJNCS4REREREREREYk0JbhEcmDSpEl3hR2DiIhEm+4lIiIi6dN9U5TgEhERERERERGRSFOCSyQHampqhoYdg4iIRJvuJSIiIunTfVOU4BIRERERERERkUhTgktERERERERERCJNCS6RHBgwYMDjYccgItlnZj3N7CozW2pmH5qZm9nBrRw/wMwWmdl/zGytmT1hZiqfl7ToXiIiIpI+3TdFCS6RHKiqqtLFVaQ47Qd8H3gfeLi1A83sLOA+4ClgOHAKcAPQNbchSrHQvURERCR9um9KJBNcGkGXQjdkyJDTw45BRHJisbvv7u6DgD+nOsjMegEzgCp3v8DdH3D3+e4+zd2b8hatRJruJSIiIunTfVMimeBCI+hS4NatW7dd2DGISGbMrIOZ/dzMXjSzj2ODIUeb2Qtm1gjg7hvTfLmzAAeuzlnAUvR0LxGRXFLRgBQb3TclqgkujaCLiEi2XQdMAGYCA4HbgFuBfYFMS977Ac8Dp8YSZuvNbKWZXWRmUb33iohIcVHRgIgUlU5hB5Ao9of/hcA5wF7AC8AFQCPwsLtXaARdCl2PHj3eDTsGEUmfmY0ERgPHuHvLH/mLzOxQYCjwjwxf8kuxj2lADcG9bDAwCdgBqM5C2FLkdC8RkRxb7O67A5jZaOCEZAclFA1Mids1P+cRimRA900puAQXwQj6UGAiwYj5twlG0LsDUzN8rfgR9AnAPsDrBKPzdRkkykQy0tTUdFfYMYhIRn4FzItLbrV4CfgMeDLD1+sAdANGuPsdsW2LzGxXoNLMLnf3tQBm9heCKrENsXP9yt0fbOP3Qew1vT3Pl/wZP358yn0jR45kzpw5FYnby8vLt9iWTVW1Mzf7Wr9P+VVIP393t7DOLe2jogEpRXoPJgU1TSJuBH2Iu1/p7ovcfRLwGEEyri0j6PsTjKBPAfoDdxKMoE/OVtwiiaqrq/uFHYOIpMfMegIHA7cn2d0LeMbdP8nwZd+LPd6fsP1+oAtwYNy20e7+VXf/OsEbkTvNrGOG55MiNH++iiNEpM007V5Kjt6DSaFVcBXVCHoLjXwWp9ZG3ZctW8acOXP6JNuX65H3FoU0AlxoCvVno5Hy0PSMPb4Vv9HMugJHA3Pb8JpPAYe3sn/TqLm7vx+3fQeCUfJ2/S7odyk6Fi5cODPVvmnTplVMnz69MXH71KlTz8llTNV1jZtdE/X7lF/6+Ut7adq9lKply5b1AZaEHYeEp2ASXHEj6NOS7G7PCPr+JB9B/yHBCPrfYttGt7zJMLOvAw+Z2c7uviHDc4qISLS09GvoTdBAt8UvgT3IfKQb4G7gbD4fNW8xEFgHPBN/sJldHdu3AzDM3de34ZwiIiJQpEUDLQplYFLyr7UCgxbJpvZD/ooM4hXqoHqhxhWvrYM7BZPgoghH0ONeWyNvRWhro+6DBw/eYtQdcj/y3kIjwKnpZyMJXiH4Y/9XZvYvYA3BClGDYvs3S3CZ2fDYp4fFHvub2QHAOnefC+Duc81sPjDTzLoDK4ATgVFAjbt/FP+a7n5e7LWPBqaZ2VEtbxZERETSpaIBESllhZTg0gi6FI3Zs2ffHHYMIpIed99oZiMI+pQ0EPwhfyNBM93JbDnSndirq2UBlFXA3nHbhwKXAxcDuwAvA+e6+x9aieVhM9sIHMmWbySkxOheIiJtULRFA3Hn0MBkiWqtwACgb9++25WVlX2YbF++igziFeqgeqHGlQ2FlODSCLoUjebm5l3LyspWhx2HiKTH3VcAx8ZvM7M/As8muVek9UdA7P5RGftIysy2B3Zx91Wxr78OfBl4LqNvQIqS7iUi0gYqGpCSpfumFMyqF7FlakcQXCAbgOsJLtBXE8zhTjaCfjtwXuzrqbGvGxKOG0owEn8x8L/A8QQj6Fe0EsvDBCMRR7b9O5JSNmPGjBPCjkFE2u0w2vZGIBNfAP5sZk+b2XKCe9jp7q4/zkT3EhFpi/iigR+aWbmZNQBnxvZvUTQQKxyILxoYbmYDW46JFQ+0FA2cZ2b9zayeoGhgUrKiAXffl+B92O9igzkiOaf7phRSBZdG0EVEpCDE7gu9gWtyeR53f5vWp32IiIikTdPuRaSUFVSCK4XDgL/m+BwtI+jbA+uBj9EIuohIyYoNjnQMOw4REZFMqWhAREpVQSe4NIIuUTVy5MglYccgIiLRpnuJiGSRigak6Om+KQWd4NIIukTV2LFjNVIlIiLtonuJiGSDigakVOi+KQXTZF6kmJSXl1eEHYOIiESb7iUikg3uvtbdO7r7jLBjEckl3TdFCS4REREREREREYk0JbhERERERERERCTSlOASyYHevXurmaaIiLSL7iUiIiLp031TlOASyYGGhoZ5YccgIiLRpnuJiIhI+nTfFCW4RHJg3LhxJ4Qdg4iIRFt1dXW/sGMQERGJCr0HEyW4RHJgxYoVvcKOQUREom3ZsmV9wo5BREQkKvQeTJTgEhERERERERGRSFOCSyQHysrK3gw7BhEREREREZFSoQSXSA6sWrVqj7BjEBGRaJs0adJdYccgIiISFQsWLGgMOwYJlxJcIiIiIiIiIhJps2bNUu/KEqcEl4iIiEgBqqmpGRp2DCIiIlFx6623avXhEqcEl0gOaFqJiIiIiIhI/qgPsijBJSIiIiIiIiKRpj7IogSXSA5oWolIcTKznmZ2lZktNbMPzczN7OBWjh9gZovM7D9mttbMnjAzXR8kLQMGDHg87BhEREREokIJLhERkfTtB3wfeB94uLUDzews4D7gKWA4cApwA9A1tyFKsaiqqlKCS0RERCRNSnCJiIikb7G77+7ug4A/pzrIzHoBM4Aqd7/A3R9w9/nuPs3dm/IWrUTakCFDTg87BhERkahQH2RRgkskBzStRCR6zKyDmf3czF40s49j0wmPNrMXzKwRwN03pvlyZwEOXJ2zgKXorVu3bruwYxARERGJCiW4RHJA00pEIuk6YAIwExgI3AbcCuwLZPp/uh/wPHBqLGG23sxWmtlFZqZ7r4iIiEiWqQ+yRPKPbDX5lUKnaSUi0WJmI4HRwBB3v9LdF7n7JOAxoBPwjwxf8kvA/sA0YArQH7gTmARMzlbcUtx69OjxbtgxiIiIiERFp7ADaKOWJr+PEzT5PSHVgbEmvzOBa4ArCKaMHIya/EoOaVqJSOT8Cpjn7omN418CPgOezPD1OgDdgBHufkds2yIz2xWoNLPL3X1t/BPMrILgfhX/nDYxM2/P8yV/xo8fn3LfyJEjmTNnTkXi9vLy8i22ZVNV7czNvtbvU34V0s/f3S2sc4uIiGQqkhVcqMmviIhkiZn1JBj4uD3J7l7AM+7+SYYv+17s8f6E7fcDXYADE2LYHxgD/DXD80gRmz9/ftghiIiIRIb6IEvBVXDFepNcCJwD7AW8AFwANAIPu3uFmvxKodO0EpFI6Rl7fCt+o5l1BY4G5rbhNZ8CDm9l/6b7mJl1AmYD44D6NpxrC6q6iI6FCxfOTLVv2rRpFdOnT29M3D516tRzchlTdV3jZhVD+n3KL/38RUTaRn2QpRAruNTkVyKvqalJS9SKREdLQrp3wvZfAnuQ+b0H4O7Y48CE7QOBdcAzcdsmAHPdfXkbziMiIiIiqA+yFFiCS01+pVhUV1f3CzsGEUnbKwQ9tn5lZj80s3IzawDOjO3fLMFlZsPNbDhwWGxT/9i2Tcksd58LzAdmmtl5ZtbfzOqBUcAkd/8o9lrfAo4D6nL5DYqIiCTSwl1SbNQHWQptimJRNfmNe001Zy1CrTUGXrZsGXPmzOmTbF+umwO3KKQmtYWmUH82moYSDnffaGYjCK79DQT9s24kmN4+mS3vPYm9uqbGHlcBe8dtHwpcDlwM7AK8DJzr7n+IO+ZY4MvAy2YG0AM40MzK3H1K+74zibrZs2ffHHYMIlLUtHCXiBSVgklwxTX5nZZkd3ua/O5P8ia/PyRo8vu3uBjU5FdEpAS5+wqCZNMmZvZH4NmWaqu4Y9NKRMYGUCpjH6mOqQVq4875EPD7bA2wSLQ1NzfvWlZWtjrsOESkaC12990BzGw0KRJcCQt3xQ++aCUMKSjqgywFk+CiCJv8tlBVRnHaWmPgwYMHb9EYGHLfHLiFmtSmpp+NpOkwNOAhIZoxY8YJJ598ctJ7iYhIa7Rwl5Qi9UGWQurBpSa/UjQ0rUQk2sxse4L7Uaa9H9vF3Y9R9ZaIiGSBFu6SkqM+yFJIFVzxTX7/BawBhgODYvu3aPIb+zS+ye8BwLpYc1/cfa6ZtTT57Q6sAE4kaPJbk6TJ7zE5+t6kxGhaiUi0xaYXdgw7DhERkUzFLdx1TFxv40VmdihBf8i2LNz1JYJWMjUE1WCDCRbu2gGozkLYIu22bNmyPsCSsOOQ8BRMgktNfqWYaFqJiIi018iRI/VHuoi0RVEu3BX32gWxOJDkX2uLfLWYM2dO0gW98rXQV7xCXdiqUOOK19YWMgWT4AI1+RURERFpMXbs2OfCjkFEokULd4lIKSuoBFcKavIrIiIiJae8vLxiwYIFqgYWkUwU7cJdLbQ4UOlqbZEvgL59+25XVlb2YbJ9+VroK16hLmxVqHFlQ0E3BVSTX4kqTSsRERERkRBo4S4pWc3NzbuGHYOEq6AruNTkV6JK00pEREREJARauEtKlvogS0EnuESiStNKRESkvXr37q3VeEUkI1q4S0RKmRJcIiIiIgWooaFhXtgxiEj0aOEuESlVSnCJiIiIhOS4445L2fTWzL7h7m3plyMikkgLd0nRUx9kUYJLJAc0rURERNpLyS0RyYa4hbuuyed53f2YfJ5PRH2QpaBXURSJKk0rEREREZFC4O5r3b2ju88IOxaRXCovL68IOwYJlxJcIjkwbty4E8KOQUQkGTPby8wWmNlzZvaMmV0RdkwSXWZ2TOz36CUzm2VmWv06j8xsupm9bmbrw45FREQkbEpwieTAihUreoUdg4hICuuBKnfvA3wd+I6ZnRRyTBJBZtYBmAWMcPf9gC8Cp4cbVcm5naC3koiISMlTgktERKSEuPub7v732OefAs2AkvLSFt8E3nD3Z2NfXwcMCzGekuPuj7j7W2HHISJSCNQHWZTgEhERKVFmtjNwMjA/7FgkknoCr8V9vRrYK6RYRESkxKkPsmgVRZE2am1pd3dPuU9EpBCYWWfgDmC6uz8fdjwSSRZ2ACIiIi3GjRt3gpJcpU0JLhERkTYwsz2BEcAg4ACgB/Av4FHgt+7+fymeZ8ApwPmx5+1AUAXzEFDn7q/kIfaOwC3AcnefkuvzSeGrrms8mGDKYbJ9Y4BVtVUVCxN2vcbmFVu9gNdzE2Fxq65r3Av4bop9Y4D3a6sq7s5vVCIi0aI+yKIpiiIiIm1zPjAN2Bd4AJgCPAKcBCw1s1NTPO9K4E7gK8BfgBnAq8DZwHIzOzjHcQM0Av8FfpaHc0k0/Ivgd3F2kn2zgW2SbP870NPMDox9fRZwV27CK3rvAJeQ+uevN20iIiJboQSXiIhI2/wNOMrd93P3se5+kbsPB44FNgANZtYl/glm1gOoBFYBfdx9nLtXufsJBMmmbsCFuQzazI4EziRYea3ZzJab2QW5PKcUvtqqijeAK1Lsvq+2quL+xI3uvgEYC9xhZi8Da4E/5i7K4lVbVfEx8IsUu18Arkm2w8xmmtnrQEcze93Mrs5VjCIiIoVOUxRDZmZ7ATcAXwI2Ave6+0WhBiUly8yOAa4GuhBMlzon9gampJnZdIKVwXq4u66bJcTMTiKorPp/BFMJ3yKYgniFuyetVHH3JWa2CBgA9CWocmmxN8Hg0iPu/kHCU+cAU4Hu2fweksT3KHG9k6rrGrcDuubynBIZU4EKNq8WWk8rlX7uvhA4MNV+ycidwGLgqITtF9ZWVXyW7Anq+Ski8rkFCxY0hh2DhEsVXOFbD1S5ex/g68B3Ym+oRPLKzDoAs4AR7r4f8EXg9HCjKhi3E1S7SIkws05m1kQwhbAvwbSr6UAzQbJzz628xPqExxYvAp8CR5pZt4R9g2KPC9oadxudC6ysrmv8Up7PKwWmtqriI+CXCZuvrq2q0CIEeVBbVeHAeMDjNt8PzA0nIhGRaJk1a1afsGOQcKkSIWTu/ibwZuzzT82sGfVZkHB8E3jD3Z+NfX0dcB5wY3ghFQZ3fwQg6A0uJWIG8APg98B4d9+UqDKznkBi9RVx+3sB5QTX9qfi97n7e2ZWA/wOeM7M7iXohdWXoMH0H2LnzIvqusYvECQ0Ho1NURO5jaC/3JEEfbkuCzec0lJbVfGP6rrG6wmmEW8AfhZLfImIlLzWVrEHKC8vv/SWW265NE/hSAFSgquAmNnOwMkE01pE8q0nwYpYLVaz+epYIiXBzPoBPwbmARe4+2ZvLt095SpxZrYNQQ+iLgTVuVtM8XX3K2M9cxqBcXG7HgFujk+mtVV1XWOmb4iPb8NzpPjtDLxXXacZHyHpCDwd5s+/tqpCIzsiEhnufmnYMUi4NEWxQJhZZ+AOYLq7ayqAhEF/xIoEKmOP1YnJrdbEpvnOJuifc627J222HavgugmYTJBE7gb0A7YFHjKzIe2IXURERESkJBVFBZeZ7QmMIOhfcgDQg6Cs/lHgt+7+fymeZ8ApBKX4BxA0EH6NoLl2nbu/kvPggzg6ArcAy919Sj7OKcWpuq7xIFJMb6qua1wU+7SptqpiVpJDXmPziq1eQMpKlaiprmucCHwnxb5FwGfA92urKv6d18CkEA0AVrr7E+k+IXY/uZagb93NBBVgyY47DrgcmObutXG7HjGz7wGvAFcC97YxdhERERGRklQsFVznA9OAfYEHgCkEUz1OApaa2akpnnclwYo1XyFoJDwDeJVgxazlZnZwjuNu0UjQgyXlKkUiaXqWIFFzTJJ9xwCHAvekeO7fgZ5m1rIa1lkEjbWLxV+Ao0n9s3lGyS0xsx2B7YGVGTynA0HPujOBW4HR7r4xxeEnxh4XJe5w97eA54H9zWz7DMIWERERESl5RVHBBfwNOMrdl8RvjPVRWQA0mNk97v5J3L4eBNNQVgFfi1+u3czGEyyVfSHBG5acMbMjY+d4GmiONbGe7e5X5fK8Upxqqyq8uq7xQuAJkiewL6utqngn2XPdfYOZjQXuMLMuwMMEvYSKQm1VxePVdY03AGOS7G61kbKZzSRITHSM9U66x93Py0mgEraWqbq7pXXw56uPjgH+DJyRrO9WnM6xx+4p9ncHNhIkqttsa31zqusaf07Q6P7btVUVj7XnXCIiIiIihSAyFVxmdpKZzTGzf5rZJ2a2ysxuMbO+7n5XYnILILZtEUGT1L4Ju/cm+P4fiU9uxcyJPaZ6A5I17v6ou5u793X3Q9z9kKramTOq6xpzfm4pTrVVFU8DM5PseomgSjEld1/o7ge6+5fd/cxsNLsuMDXAuiTbL2mtesvdz3H3nrH/qz2V3Cpe7v5vgmmCfczsu4n7zewrcZ+3VG6NAW4HTt9KcguCqfMAF5rZDgmv/WOCxR4eix+QyZEvA/OU3BIRkWJiZnuZ2QIze87MnjGzK8KOSSQTZnZM7Hf3JTObFWtnFDozm25mr5tZQb8/LPgEl5l1MrMmgulFfQmmTE0HmoFhwJ5beYn1CY8tXgQ+BY40s24J+wbFHhe0Ne52OgFYVV3X+K2Qzi/R92sgMXH789qqik/DCKZQ1FZVvEnQ2DvesyRPCErpuoigkmuumd1hZnVmdr2ZvQDE9826BBgNrAVWABeb2aUJH4ckvPbtwGLgIGCFmV1rZr8zswVAA/ARQfVwTtVWVYwD1MxeRESKzXqCVYz7AF8HvmNmJ4Uck0ha4mYGjHD3/YAvEvR3LQS3A4eFHcTWRGGK4gzgBwSNs8fHV5SYWU+2fBNP3P5eQDnwJvBU/D53fy+2ktXvgOfM7F6CPlh9ge8CfyBFs+5cqq5rNOBS4G2CJJ5IxmqrKt6prmv8DcFUWwiStWpaHZgKVABlsa/H11ZVFPRIhOSXu99mZh8AvwD6A98D/kkwHb4+7tC9Y4/bE1QHJrMSWB732hvMbAAwHjiV4P7WmeCafzMw2d2fy9b30praqop2TYMUEREpNO7+JsF7P9z9UzNrJlg4SSQKvgm84e7Pxr6+DjgPuDG8kALu/ghArKVSwbIMVkDPu1gPrcXAPGBQhsu1bwM8SLBc+w9bWa79NIIm7/FVXI8QLA//aLLnZKq6rrFwf8giUjC21jdJRERERNJjZjsTDDINcPfnw45HSk9iHmBrf+ub2TBgqLuPin3dB7jF3b8eZlwJMa5394ItlCrYwGIqY4/VGSa3OgCzCZJb17aS3KohmMp1CcHI+fvAIQQrMj5kZsPcXVUvIiIiIiIiEWFmnYE7gOlKbkm+VNc1bkMwa2b3FPv/Efv0ltqqiiuTHJKzwe7qusbfA9/eSlzNtVUVZ+Uqhnwo9B5cA4CV7v5Euk+woGbuWoK5qjcDP05x3HHA5cDv3b3W3V9397Wx0rvvEaxgleyXTkREREREpKiY2Z5mVmlmD5jZajP71MzeMrM7zSxlb2ALDDWzRWb2ppl9aGYvmNlMM9s3n99DLJ6OwC3Acnefku/zS+mKtX+4i6D/W7Kqq68D+wNNKV7iNWCvuK97Aa9nKbwbtxLX1ymAqZDtVbAJLjPbkaCvycoMntOyotWZwK3AaHffmOLwE2OPixJ3uPtbwPPA/ma2fQZhi4iIiIiIRNH5BDNZ9gUeAKYQtG45CVhqZqemeN6VwJ3AVwgWBpsBvAqcDSw3s4NzHHeiRoLeyj/L83lFIJhJ1lqBzuTYwlfJ/B3oaWYHxr4+iyBh1m61VRXLgJtaOeSO2qqKxdk4V5gKeYpiS3nebmkd/PmKA2OAPwNnbGW59s6xx+4p9ncHNhJUcrVLOnNaq+saBwL3AWfXVlXMau85RUREREREMvA34Ch3XxK/MdYXeQHQYGb3uPsncft6ELSVWQV8zd0/iNs3nmBxnwsJChByzsyOjJ3raaA51hB7trtflY/zi9RWVWyormscDyxMsnsVQRI5qdhiRGOBO8ysC/AwkLTdUhv9ChgObJew/VPgl6090cxmEhQJdTSz14F73P28LMaWFQVbweXu/wZeAfqY2XcT95vZV+I+b6ncGkOwfOXpW0luAbQ0kL/QzHZIeO0fAz2Bx+Iv4LkSt3LiSlrPqoqIiIiIiLSJmZ1kZnPM7J9m9omZrTKzW8ysr7vflZjcAohtWwTsTLDifLy9Cd5TPhKf3IqZE3tMVVCQde7+qLubu/d190NiH1dV1zVOq65rrMpXHFLaaqsqFgF3J9n1i9qqio9be667L3T3A939y+5+prtnbbX32qqKNcAVSXZNra2qeHUrcZ3j7j1j/796FmJyCwq7ggvgIoJqrLlmdg/wMkFF17eBZ4FTYsddAowG1gIrgIuTLF/5F3dfHvf17cA4gkb0K8zsXoIm84cCxwEfEYw25ENH4E/Am7VVFZ/m6ZwiIiIiIlICzKwTQX+dHwCrCaY9/QfoDQwjGGR/qpWXWJ/w2OJFguqPI82sm7v/N27foNjjgvZF3z7VdY1fJph+OSPMOKTk/IKg4qll5tgSgoUPwjYFqODzXl9vA5PDCye7LIPFCUNhZscT/HJ8E9gW+CdB+Wx9ywiDmd0A/GgrLzXG3W9IeO0uwHjgVII5450J/oEXAZPd/bmsfSMiIiIiIiIhMLMGgsW3fg+Mj68KMbOewAcJyan45/YiKCL4F7BX4kwZM/s58DtgDcEKcv8lqPT6LsEsm/OzWYWSqeq6xtnASGDfVnofiWRddV1jHcHUPwe+WVtV8XjIIQFQXdd4GkHPcoCzaqsqZocZTzYVfIJLRERERERE2ibWQ2sxMA8Y5Bm8ATSzbYAHCWa9/NDdk/YDMrPTCJq7d4vb/AhQ7e6PJntOW1XXNeoNrEiRS6ePeTIF24NLRERERERE2q0y9lidYXKrA8GKcEcB17aS3KohmOI4mWDaUzegH8Hsm4fMbEg7YhcRSZsSXCIiIiIiIsVrALDS3Z9I9wkWNDS+FjgduJlgemOy444DLgd+7+617v66u69190eA7xGsSH9le78BEZF0KMElIiIiIiJShMxsR2B7gtXa031Oywr1ZxL06Rnt7htTEeLTTQAAAm1JREFUHH5i7HFR4g53fwt4HtjfzLbPIGwRkTYp9FUURUREREREpG1a+tjsltbBQXJrFjCGYDX7MxKbyidoWSGue4r93YGNBJVcWZFOb57YyokvADNqqyrGZ+vcIlLYVMElIiIiIiJShNz938ArQB8z+27ifjP7StznLZVbY4DbgdO3ktwCaGkgf6GZ7ZDw2j8GegKPufsnbf8u2qSGIKn22zyfV0RCpAouERERERGR4nURQTXWXDO7B3iZoKLr28CzwCmx4y4BRgNrgRXAxUErrs38xd2Xx319OzCOoBH9CjO7F3gfOBQ4DvgIuDD739JWXQf8tbaq4s0Qzi0iIbEMFtIQERERERGRiDGz44FfAN8kWN3wn8DfgHp3XxI75gbgR1t5qTHufkPCa3cBxgOnAl8hmLb4NkFfrsnu/lzWvhERkVYowSUiIiIiIiIiIpGmHlwiIiIiIiIiIhJpSnCJiIiIiIiIiEikKcElIiIiIiIiIiKRpgSXiIiIiIiIiIhEmhJcIiIiIiIiIiISaUpwiYiIiIiIiIhIpCnBJSIiIiIiIiIikaYEl4iIiIiIiIiIRJoSXCIiIiIiIiIiEmlKcImIiIiIiIiISKQpwSUiIiIiIiIiIpGmBJeIiIiIiIiIiESaElwiIiIiIiIiIhJpSnCJiIiIiIiIiEikKcElIiIiIiIiIiKRpgSXiIiIiIiIiIhEmhJcIiIiIiIiIiISaUpwiYiIiIiIiIhIpCnBJSIiIiIiIiIikaYEl4iIiIiIiIiIRJoSXCIiIiIiIiIiEmlKcImIiIiIiIiISKQpwSUiIiIiIiIiIpH2/wHqbKJ9lrly3wAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# We construct all the tomographic circuits\n", "qst = state_tomography_circuits(bell, [q[0], q[2]])\n", "\n", "# We can plot them\n", "fig, axes = plt.subplots(3, 3)\n", "for i, circuit in enumerate(qst):\n", " row = i // 3\n", " col = i % 3\n", " circuit.draw(output='mpl', ax=axes[row, col], scale=2)" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "# We execute the tomography circuits on the real device\n", "job = execute(qst, backend=backend)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [], "source": [ "# We create a StateTomographyFitter from the job result and the tomography circuit\n", "tomo_fitter = StateTomographyFitter(job.result(), qst)\n", "\n", "# To obtain the \n", "rho_tomo = tomo_fitter.fit()" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_state_city(rho_tomo)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "plot_state_city(state_vec)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2.4.1 \n", "\n", "In order to measure quantitatively how \"close\" the experimental state tomography is to the expected state of the system, we can employ [quantum state fidelity](https://en.wikipedia.org/wiki/Fidelity_of_quantum_states):\n", "\n", "$$ {\\displaystyle F(\\rho ,\\sigma )=\\left[\\operatorname {Tr} {\\sqrt { {\\sqrt {\\rho } }\\sigma {\\sqrt {\\rho } }} }\\right]^{2} }$$\n", "\n", "The fidelity goes from one, in the case $\\rho = \\sigma$, to zero (when $\\rho$ and $\\sigma$ are orthogonal).\n", "Qiskit contains an implementation of state fidelity.\n", "\n", "> *TASKS:*\n", "> 1. Measure the fidelity of `rho_tomo` to `state_vec`\n", "> 2. Perform the state tomography after applying the measurement error mitigation. Is the fidelity higher?" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [], "source": [ "# Import the state_fidelity function\n", "from qiskit.quantum_info import state_fidelity" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Exercise code:\n", "# ...\n", "# ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References \n", "\n", "[1] [V. Paulsen, *Completely Bounded Maps and Operator Algebras*, Cambridge University Press, 2003](https://doi.org/10.1017/CBO9780511546631) \n", "\n", "[2] [R. V. Kadison and J. R. Ringrose, *Fundamentals of the theory of operator algebras*, vol I & II. Graduate Studies in Mathematics, American Mathematical Society, 1997](https://www.springer.com/gp/book/9781461277385) \n", "\n", "[3] [R. Bhatia, *Positive Definite Matrices*, Princeton University Press, 2006](https://press.princeton.edu/books/paperback/9780691168258/positive-definite-matrices) \n", "\n", "[4] [M.-D. Choi, Lin. Alg. Appl. **10**, 285 (1975)](https://doi.org/10.1016/0024-3795%2875%2990075-0) \n", "\n", "[5] [K. Kraus, *States, Effects and Operations: Fundamental Notions of Quantum Theory*, Springer Verlag, 1983](https://doi.org/10.1007/3-540-12732-1)\n", "\n", "[6] [E. C. G. Sudarshan, P. Mathews, and J. Rau, Phys. Rev. **121**, 920 (1961)](https://doi.org/10.1103/PhysRev.121.920)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.5 64-bit ('oqs-jupyterbook-_Llz9vLR-py3.8': venv)", "language": "python", "name": "python385jvsc74a57bd0a183628b7c25cbe14b32706b25a1d360b2cc05412b0aa00bca3856a97dc6cea8" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 2 }