d_data_analysis_methods/3_unsupervised_machine_learning.ipynb

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    "<img src='images/header.png' style='height: 50px; float: left'>"
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   "source": [
    "## Introduction to Computational Social Science methods with Python"
   ]
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    "# Session D3: Unsupervised machine learning\n",
    "\n",
    "There are many ways to think about **Machine Learning** (ML). For one, the term goes back to IBM researcher Arthur Samuel who used it to describe a computer program (a machine) that has the ability to learn without being explicitly programmed how to do so. Mitchell (1997; quoted from <a href='#Ghani_M_2016'>Ghani & Schierholz, 2017</a>, p.148) provided a compatible definition:\n",
    "\n",
    "> A computer program is said to learn from experience $E$ with respect to some class of tasks $T$ and performance measure $P$, if its performance at tasks in $T$, as measured by $P$, improves with experience $E$.\n",
    "\n",
    "In other words, ML is the ability of a computer to improve its performance on a task without being explicitly programmed (<a href='#Ghani_M_2016'>Ghani & Schierholz, 2017</a>). This definition refers to ML as a set of methods.\n",
    "\n",
    "For another, ML is field of practice devoted to building learning machines. It is a subfield of [Artificial Intelligence](https://en.wikipedia.org/wiki/Artificial_intelligence). **Artificial Intelligence** (AI) is the field that aims at giving machines intelligence (the ability to perceive, synthesize, and infer information), and ML is a fundamental concept of AI research. While artificially intelligent agents auch as [chatbots](https://en.wikipedia.org/wiki/Chatbot) had been around for many years, AI has been rapidly gaining attention since 2022 because the chatbot [ChatGPT](https://en.wikipedia.org/wiki/ChatGPT) has demonstrated to have historical knowledge and be able to provide detailed responses. If you know ChatGPT, you understand why Efron & Hastie (<a href='#Efron_C_2016'>2016</a>) refer to ML methods as \"enormosly ambitious algorithms\" (p.xvi).\n",
    "\n",
    "|<img src='images/machine_learning.png' style='float: none; width: 640px'>|\n",
    "|:--|\n",
    "|<em style='float: center'>**Figure 1**: Definition, types, and algorithms of Machine Learning</em>|\n",
    "\n",
    "ML is one of the methodological pillars of Computational Social Science (CSS). ***Figure 1*** shows the two types of ML in red and blue. We will build an understanding of ML methods session by session. Here, we start to deal with **unsupervised** ML which is about mining patterns in data. **Patterns** are any non-trivial regularity that may exist in data. Most ML algorithms require data to be structured the way we have encountered it repeatedly in this course: it must have the form of a dataframe or matrix with the units of observation in rows and variables in columns. In ML, variables are typically called **features**, but their meaning is the same: they are descriptions or properties of the units of observations. The matrix $X$ of units and features is called the **feature matrix**. Much work in a CSS research project consists of bringing data into this form so it can be analyzed (*e.g.*, using ML).\n",
    "\n",
    "There are two families of algorithms to mine patterns using unsupervised learning, shown in the bottom row of *figure 1*. The first is **dimensionality reduction**. The tasks performed in this area are not exclusive to the ML community. In fact, they have been part of the standard toolbox in the social sciences for a long time. The dimensionality of a dataframe is simply the number of variables (columns) it has. \"Dimensionality reduction is the process of reducing the number of features in a dataset while preserving as much variance as possible by combining highly covarying features into new composite variables.\" (<a href='#McLevey_D_2022'>McLevey, 2022</a>, ch. 19.4) These composite variables are **unobserved variables** because they have not been measured but are inferred. Depending on the dimensionality-reduction method that is used, the unobserved variables can have meaning in the sense that they can be theoretically understood to have generated the observed variables in the feature matrix. The unobserved variables are then called **latent variables**. Since latent variables have meaning but are typically not observable or measurable directly, inferring them from measureable variables is a viable way to measure meaning (<a href='#McLevey_D_2022'>McLevey, 2022</a>, ch. 8).\n",
    "\n",
    "Theory stays important in ML applications in CSS. **Theory** is an explanation of reality – call it \"social life\". To bring it into contact with empirical reality, a theory is reduced to a simplified representation of reality called a **model**. The theory is not the description of a model, [the theory is the model](https://en.wikipedia.org/wiki/Scientific_theory#Theories_as_models). There are theory-driven and data-driven models in ML. **Factor Analysis** is a model that reduces dimensionality in a theory-driven way, routinely employed in statistical modeling to infer latent variables. **Principal Component Analysis** is the data-driven sibling of Factor Analysis. It is employed when theory does not exist yet (*e.g.*, when a new data source for a new social phenomenon is explored) or does not play a role. (Data-driven) dimensionality reduction may be technically necessary to mitigate the **curse of dimensionality**. Some datasets are simply too high-dimensional (they have too many features) to be modeled in their entirety using statistics or ML (Pöge & Reinecke, 2022; <a href='#McLevey_D_2022'>McLevey, 2022</a>, ch. 8).\n",
    "\n",
    "The second family of unsupervised learning algorithms is **clustering** which refers to grouping not the columns but rows of the feature matrix $X$. Clustering may be advised to identify subpopulations and treat them differently in subsequent modeling steps. **K-Means** and **Agglomerative Clustering** are just two of many algorithms that potentially lead to largely varying clustering solutions. Clustering and dimensionality reduction require the researcher to use [heuristics](https://en.wikipedia.org/wiki/Heuristic), informed judgement, and interpretation. Clusters and latent variables must make sense and what makes sense is often a question of what one already knows about the subject matter (Bacher *et al.*, 2022; <a href='#McLevey_D_2022'>McLevey, 2022</a>, ch. 19.4).\n",
    "\n",
    "The reason to teach unsupervised before supervised learning is that the former typically precedes the latter in a CSS research project. Hofman, Watts, *et al.* (<a href='#Hofman_I_2021'>2021</a>) propose that data-driven research should **integrate different modeling perspectives**. Applied to the ML context, research should move from a focus on specific features or effects (unsupervised) to a focus on predicting outcomes (supervised learning) and, to invoke causal explanations, from past or present to future situations (data). McLevey (<a href='#McLevey_D_2022'>2022</a>, ch. 19.4) also points at this order of operations when he writes that patterns are \"interpret[ed] or [made] use of in downstream analyses.\"\n",
    "\n",
    "|<img src='images/inference.png' style='float: none; width: 480px'>|\n",
    "|:--|\n",
    "|<em style='float: center'>**Figure 2**: Three inference strategies</em>|\n",
    "\n",
    "In the end of a reserch project, we are often interested in **causal explanations**. Most ML algorithms are incapable of making such explanations; they can only make statements of association. But this is why theory is so important also in ML research. In CSS, ML is not an end but a means to an end, and the end can also involve causal explanations. To understand how we can think about causality even if the methods are silent about it, have a look at ***Figure 2***. It shows the three **inference strategies** that exist. Each one involves a causal explanation in the logical sense that a cause leads to an effect via a rule. Consider \"It rains.\" as a cause, \"When it rains, people get wet.\" as a rule, and \"People are wet.\" as an effect.\n",
    "\n",
    "The social sciences strongly rely on **deduction**. They collect data if it rains and if people are wet, they have a theory in form of a causal rule, and they test if the rule explains the data. If it does not, then theory gets revised and tested anew. This is how social scientists typically make causal explanations. Epistemologically, in deduction, the rule is hypothesized and the effect is inferred. Data-driven science involves the other two strategies. In **induction**, the rule does not originate in theory and is not tested, but is inferred from data on causes and effects. When the data says that it rains and that people are wet, then a possible rule is inferred that people get wet when it rains. We will see in [Session D5](5_supervised_machine_learning.ipynb) how induction and deduction go hand in hand in [Supervised machine learning](5_supervised_machine_learning.ipynb).\n",
    "\n",
    "Finally, **abduction** is a way to think about many algorithms in unsupervised learning. Most basically, abduction is a strategy to formulate hypotheses or rules from data. This is what is has in common with induction, but other than in induction, it is not the rule that is inferred but the cause. These causes are the patterns, latent variables, and groups inferred in unsupervised ML. Going back to the example, \"People are wet.\" is the data. A researcher may have two hypotheses: that people get wet when it rains or when children shoot with water pistols at them. If their algorithm infers a causal pattern that is compatible with the meaning of \"It rains.\", then the researcher can conclude that the first rule is the better hypothesis/explanation.\n",
    "\n",
    "Note how abduction logically complements the much more well-known induction and deduction strategies: it is always something else that is inferred, the rule is either hypothesized or inferred (it cannot be observed), and causes and effects are either observed (and used as data) or inferred. Hence, abduction, like data visualization, is an important tool in **Exploratory Data Analysis** (<a href='#McLevey_D_2022'>McLevey, 2022</a>, chs.7, 19.4; [Session A3: Scientific computing and data visualization](../a_introduction/3_scientific_computing_and_data_visualization.ipynb)). Though theory stays important, the growing importance of abduction in CSS is a sign of a **paradigm shift** for the social sciences from almost exclusively theory-driven to more data-driven research (<a href='#Kitchin_B_2014'>Kitchin, 2014</a>).\n",
    "\n",
    "The dataset from the [Varieties of Democracies](https://v-dem.net/) (V-Dem) project is well-suited to teach unsupervised learning tasks (<a href='#McLevey_D_2022'>McLevey, 2022</a>, ch. 8). First, it is structured. It consists of countries (units of observations in rows) described by several hundreds of variables (in columns) obtained by surveys, from country websites, and from other sources. Second, it is strongly connected to political science theory. It contains a hierarchy of variables that can be used to evaluate latent variables from unsupervised learning.\n",
    "\n",
    "[scikit-learn](https://scikit-learn.org/) (shorter: sklearn) is Python's standard library for machine learning. It has a huge user community and you will find many tutorials, questions & answers in the web. It includes many methods also used in the statistics community. Still, it does not satisfy all wishes that quantitative social scientists (*e.g.*, those versed in SPSS) may have. Hence, we will also work with the [FactorAnalyzer](https://factor-analyzer.readthedocs.io/) package that offers a supervised model.\n",
    "\n",
    "<div class='alert alert-block alert-success'>\n",
    "<b>In this session</b>, \n",
    "\n",
    "you will learn how to perform unsupervised learning using the scikit-learn and FactorAnalyzer packages. In subsession **D3.1**, we will introduce the V-Dem dataset, its hierarchy of variables, and how they will be used for ML. This dataset will serve to demonstrate all algorithms in this session. In subsession **D3.2** on dimensionality reduction, you will learn how to infer unobserved variables using Factor Analysis and Principal Component Analysis, how these methods differ in the way theory is used, and how we can think of Factor Analysis as an abductive inference tool. Subsession **D3.3** is dedicated to clustering, and you will see how different algorithms, namely K-Means and Agglomerative Clustering, lead to different solutions and interpreations.\n",
    "</div>"
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    "## D3.1. The Varieties of Democracy dataset and its design\n",
    "\n",
    "The social sciences often deal with abstract concepts that cannot be observed directly. Consider the concept of democracy. Since democracy is not a material thing, one cannot look at a country and measure the amount of democracy. Democracy is a latent variable. To still make democracy measurable, political and social scientists have thought how democracy can be measured and come up with a theoretical system of constructs. This system is hierarchical like a tree where the trunk represents the latent variable and the leaves are measureable variables.\n",
    "\n",
    "Since we are about to demonstrate theory-driven as well as data-driven approaches to dimensionality reduction, we need a dataset that has such a theoretical design. The Varieties of Democracy (V-Dem) dataset meets this requirement. The [V-Dem](https://v-dem.net/) project \"distinguishes between five high-level principles of democracy: electoral, liberal, participatory, deliberative, and egalitarian, and collects data to measure these latent variables.\" The dataset consists of countries (observations in rows) described by more than 1800 variables (in columns) obtained by surveys, from country websites, and from other sources. Consult the [codebook](https://www.v-dem.net/documents/24/codebook_v13.pdf) to become familiar with the dataset.\n",
    "\n",
    "|<img src='images/vdem.jpg' style='width: 800px'>|\n",
    "|:--|\n",
    "|<em style='float: center'>**Figure 3**: Varieties of Democracy variable structure on electoral democracy (<a href='#McLevey_D_2022'>McLevey, 2022</a>, fig. 8.1)</em>|\n",
    "\n",
    "For this session, we have extracted data about the latent variable of \"electoral democracy\" for the year 2019. We have only kept variables that have no missing values, have interval scales, or can be interpreted as such. ***Figure 3*** shows the corresponding tree of variables. The latent variable is depicted on the bottom level, and it is called a high-level **index**. The index is theoretically broken down into five low-level **indices** that explain the index. Electoral democracies are supposed to be describable by\n",
    "\n",
    "- the amount of freedom of expression and alternative sources of information,\n",
    "- the amount of freedom of association,\n",
    "- the share of population with suffrage,\n",
    "- the extent to which elections are clean, and\n",
    "- the extent to which officials are elected.\n",
    "\n",
    "These indices are still latent, but they are more in the direction of something measurable. Each one of the indices is then operationalized via a set of **indicators** that are the measureable variables aka. the observed variables (<a href='#McLevey_D_2022'>McLevey, 2022</a>, ch. 8.4).\n",
    "\n",
    "Load the dataset as a Pandas table:"
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       "'1.4.4'"
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   "source": [
    "import pandas as pd\n",
    "pd.__version__"
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       "      <td>0.648</td>\n",
       "      <td>-0.983</td>\n",
       "      <td>0.212</td>\n",
       "      <td>0.588</td>\n",
       "      <td>0.752</td>\n",
       "      <td>1.352</td>\n",
       "      <td>0.406</td>\n",
       "      <td>...</td>\n",
       "      <td>0.201</td>\n",
       "      <td>0.402</td>\n",
       "      <td>-1.696</td>\n",
       "      <td>0.970</td>\n",
       "      <td>1.0</td>\n",
       "      <td>94.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.915</td>\n",
       "      <td>1.638</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zanzibar</th>\n",
       "      <td>NaN</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.266</td>\n",
       "      <td>0.448</td>\n",
       "      <td>-0.468</td>\n",
       "      <td>-0.614</td>\n",
       "      <td>-0.085</td>\n",
       "      <td>0.769</td>\n",
       "      <td>0.730</td>\n",
       "      <td>-0.172</td>\n",
       "      <td>...</td>\n",
       "      <td>0.099</td>\n",
       "      <td>-1.608</td>\n",
       "      <td>-1.099</td>\n",
       "      <td>0.925</td>\n",
       "      <td>1.0</td>\n",
       "      <td>85.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.851</td>\n",
       "      <td>1.881</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zimbabwe</th>\n",
       "      <td>42.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.293</td>\n",
       "      <td>0.441</td>\n",
       "      <td>-0.536</td>\n",
       "      <td>-0.798</td>\n",
       "      <td>-0.640</td>\n",
       "      <td>0.319</td>\n",
       "      <td>1.370</td>\n",
       "      <td>0.790</td>\n",
       "      <td>...</td>\n",
       "      <td>0.157</td>\n",
       "      <td>-1.250</td>\n",
       "      <td>-1.620</td>\n",
       "      <td>0.950</td>\n",
       "      <td>2.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.579</td>\n",
       "      <td>1.995</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>176 rows × 30 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              total_score  v2x_regime  v2x_polyarchy  v2x_freexp_altinf  \\\n",
       "country_name                                                              \n",
       "Afghanistan           NaN         1.0          0.353              0.696   \n",
       "Albania               NaN         1.0          0.486              0.639   \n",
       "Algeria               NaN         1.0          0.287              0.521   \n",
       "Angola               64.0         1.0          0.365              0.653   \n",
       "Argentina            72.0         2.0          0.771              0.843   \n",
       "...                   ...         ...            ...                ...   \n",
       "Vietnam              24.0         0.0          0.149              0.137   \n",
       "Yemen                 NaN         0.0          0.119              0.196   \n",
       "Zambia               58.0         1.0          0.338              0.648   \n",
       "Zanzibar              NaN         1.0          0.266              0.448   \n",
       "Zimbabwe             42.0         1.0          0.293              0.441   \n",
       "\n",
       "              v2mecenefm  v2meharjrn  v2meslfcen  v2mebias  v2merange  \\\n",
       "country_name                                                            \n",
       "Afghanistan        0.327      -0.392       0.420     1.337      1.497   \n",
       "Albania           -0.039       0.526       0.476     1.086      0.438   \n",
       "Algeria           -1.063       0.476      -0.122    -0.096      0.810   \n",
       "Angola             1.026       0.552       0.997     0.855     -0.317   \n",
       "Argentina          1.274       0.948       1.320     1.419      1.525   \n",
       "...                  ...         ...         ...       ...        ...   \n",
       "Vietnam           -1.463      -1.008      -1.360    -2.123     -2.036   \n",
       "Yemen             -2.238      -1.355      -0.593    -0.153     -0.613   \n",
       "Zambia            -0.983       0.212       0.588     0.752      1.352   \n",
       "Zanzibar          -0.468      -0.614      -0.085     0.769      0.730   \n",
       "Zimbabwe          -0.536      -0.798      -0.640     0.319      1.370   \n",
       "\n",
       "              v2mecrit  ...  v2xel_frefair  v2elembaut  v2elembcap  \\\n",
       "country_name            ...                                          \n",
       "Afghanistan      1.532  ...          0.164      -0.569      -0.560   \n",
       "Albania         -0.604  ...          0.491       0.701       0.353   \n",
       "Algeria          0.469  ...          0.234      -0.931      -1.228   \n",
       "Angola           1.255  ...          0.255      -0.939      -0.772   \n",
       "Argentina        0.646  ...          0.873       1.614       1.624   \n",
       "...                ...  ...            ...         ...         ...   \n",
       "Vietnam         -1.439  ...          0.506      -1.228       1.475   \n",
       "Yemen           -1.161  ...          0.000      -1.278      -0.697   \n",
       "Zambia           0.406  ...          0.201       0.402      -1.696   \n",
       "Zanzibar        -0.172  ...          0.099      -1.608      -1.099   \n",
       "Zimbabwe         0.790  ...          0.157      -1.250      -1.620   \n",
       "\n",
       "              v2x_elecoff  v2lgbicam  v2lgello  v2lginello  v2exdfcbhs  \\\n",
       "country_name                                                             \n",
       "Afghanistan         1.000        2.0     100.0         0.0      -0.588   \n",
       "Albania             1.000        1.0     100.0         0.0      -1.225   \n",
       "Algeria             1.000        2.0     100.0         0.0       1.495   \n",
       "Angola              1.000        1.0     100.0         0.0       1.629   \n",
       "Argentina           1.000        2.0     100.0         0.0       2.257   \n",
       "...                   ...        ...       ...         ...         ...   \n",
       "Vietnam             0.000        1.0     100.0         0.0      -0.821   \n",
       "Yemen               0.000        2.0     100.0         0.0       0.942   \n",
       "Zambia              0.970        1.0      94.0         0.0       1.915   \n",
       "Zanzibar            0.925        1.0      85.0         0.0       1.851   \n",
       "Zimbabwe            0.950        2.0      80.0        20.0       2.579   \n",
       "\n",
       "              v2exdfdmhs  v2exhoshog  \n",
       "country_name                          \n",
       "Afghanistan        1.005         1.0  \n",
       "Albania           -1.068         0.0  \n",
       "Algeria            1.421         0.0  \n",
       "Angola             1.005         1.0  \n",
       "Argentina          1.879         1.0  \n",
       "...                  ...         ...  \n",
       "Vietnam           -1.808         0.0  \n",
       "Yemen              1.507         0.0  \n",
       "Zambia             1.638         1.0  \n",
       "Zanzibar           1.881         1.0  \n",
       "Zimbabwe           1.995         1.0  \n",
       "\n",
       "[176 rows x 30 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vdem = pd.read_csv(filepath_or_buffer='../data/vdem.tsv', sep='\\t', encoding='utf-8', low_memory=False)\n",
    "vdem = vdem.set_index('country_name')\n",
    "vdem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f6dc767",
   "metadata": {},
   "source": [
    "The variables we have extracted are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d636789a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# high-level index\n",
    "index = ['v2x_polyarchy']\n",
    "\n",
    "# low-level indices\n",
    "indices = ['v2x_freexp_altinf', 'v2x_frassoc_thick', 'v2x_suffr', 'v2xel_frefair', 'v2x_elecoff']\n",
    "\n",
    "# low-level index labels\n",
    "indices_labels = ['Freedom of expression', 'Freedom of association', 'Share of pop w/ suffrage', 'Clean elections', 'Elected officials']\n",
    "\n",
    "# indicators\n",
    "indicators = ['v2mecenefm', 'v2meharjrn', 'v2meslfcen', 'v2mebias', 'v2merange', 'v2mecrit', 'v2cldiscm', 'v2cldiscw', 'v2clacfree', 'v2psparban', 'v2psbars', 'v2cseeorgs', 'v2csreprss', 'v2elsuffrage', 'v2elembaut', 'v2elembcap', 'v2lgbicam', 'v2lgello', 'v2lginello', 'v2exdfcbhs', 'v2exdfdmhs', 'v2exhoshog']\n",
    "indicators_level = ['v2x_freexp_altinf', 'v2x_freexp_altinf', 'v2x_freexp_altinf', 'v2x_freexp_altinf', 'v2x_freexp_altinf', 'v2x_freexp_altinf', 'v2x_freexp_altinf', 'v2x_freexp_altinf', 'v2x_freexp_altinf', 'v2x_frassoc_thick', 'v2x_frassoc_thick', 'v2x_frassoc_thick', 'v2x_frassoc_thick', 'v2x_suffr', 'v2xel_frefair', 'v2xel_frefair', 'v2x_elecoff', 'v2x_elecoff', 'v2x_elecoff', 'v2x_elecoff', 'v2x_elecoff', 'v2x_elecoff']\n",
    "\n",
    "# indicator labels\n",
    "indicators_labels = ['Government censorship effort—Media', 'Harassment of journalists', 'Media self-censorship', 'Media bias', 'Print/broadcast media perspectives', 'Print/broadcast media critical', 'Freedom of discussion for men', 'Freedom of discussion for women', 'Freedom of academic and cultural expression', 'Party ban', 'Barriers to parties', 'CSO entry and exit', 'CSO repression', 'Percent of population with suffrage', 'EMB autonomy', 'EMB capacity', 'Legislature bicameral', 'Lower chamber directly elected', 'Percentage of indirectly elected legislators lower chamber', 'HOS appoints cabinet in practice', 'HOS dismisses ministers in practice', 'HOS = HOG?']\n",
    "indicators_labels_level = ['Freedom of expression', 'Freedom of expression', 'Freedom of expression', 'Freedom of expression', 'Freedom of expression', 'Freedom of expression', 'Freedom of expression', 'Freedom of expression', 'Freedom of expression', 'Freedom of association', 'Freedom of association', 'Freedom of association', 'Freedom of association', 'Share of pop w/ suffrage', 'Clean elections', 'Clean elections', 'Elected officials', 'Elected officials', 'Elected officials', 'Elected officials', 'Elected officials', 'Elected officials']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e2b7c84",
   "metadata": {},
   "source": [
    "We will be working with the following 22 indicators. Abbreviations in their descriptions are civil society organization (CSO), election management body (EMB), head of state (HOS), and head of government (HOG):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b99893a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Government censorship effort—Media',\n",
       " 'Harassment of journalists',\n",
       " 'Media self-censorship',\n",
       " 'Media bias',\n",
       " 'Print/broadcast media perspectives',\n",
       " 'Print/broadcast media critical',\n",
       " 'Freedom of discussion for men',\n",
       " 'Freedom of discussion for women',\n",
       " 'Freedom of academic and cultural expression',\n",
       " 'Party ban',\n",
       " 'Barriers to parties',\n",
       " 'CSO entry and exit',\n",
       " 'CSO repression',\n",
       " 'Percent of population with suffrage',\n",
       " 'EMB autonomy',\n",
       " 'EMB capacity',\n",
       " 'Legislature bicameral',\n",
       " 'Lower chamber directly elected',\n",
       " 'Percentage of indirectly elected legislators lower chamber',\n",
       " 'HOS appoints cabinet in practice',\n",
       " 'HOS dismisses ministers in practice',\n",
       " 'HOS = HOG?']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indicators_labels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "439540b4",
   "metadata": {},
   "source": [
    "As shown in *figure 3*, we will use them to measure these low-level indices (latent variables):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "05abafeb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Freedom of expression',\n",
       " 'Freedom of association',\n",
       " 'Share of pop w/ suffrage',\n",
       " 'Clean elections',\n",
       " 'Elected officials']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices_labels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "385c496f",
   "metadata": {},
   "source": [
    "The variables 'total_score' and 'v2x_regime' will only be used in the supervised machine learning part. Hence, we remove them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "db2281a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "del vdem['total_score']\n",
    "del vdem['v2x_regime']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7530c2d9",
   "metadata": {},
   "source": [
    "#### Data exploration and preprocessing\n",
    "\n",
    "You should always know how the variables in $X$ are distributed, also in machine learning:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1f50749d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>v2mecenefm</th>\n",
       "      <th>v2meharjrn</th>\n",
       "      <th>v2meslfcen</th>\n",
       "      <th>v2mebias</th>\n",
       "      <th>v2merange</th>\n",
       "      <th>v2mecrit</th>\n",
       "      <th>v2cldiscm</th>\n",
       "      <th>v2cldiscw</th>\n",
       "      <th>v2clacfree</th>\n",
       "      <th>v2psparban</th>\n",
       "      <th>...</th>\n",
       "      <th>v2csreprss</th>\n",
       "      <th>v2elsuffrage</th>\n",
       "      <th>v2elembaut</th>\n",
       "      <th>v2elembcap</th>\n",
       "      <th>v2lgbicam</th>\n",
       "      <th>v2lgello</th>\n",
       "      <th>v2lginello</th>\n",
       "      <th>v2exdfcbhs</th>\n",
       "      <th>v2exdfdmhs</th>\n",
       "      <th>v2exhoshog</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "      <td>176.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.612642</td>\n",
       "      <td>0.595608</td>\n",
       "      <td>0.587642</td>\n",
       "      <td>0.862131</td>\n",
       "      <td>0.910881</td>\n",
       "      <td>0.843881</td>\n",
       "      <td>0.987625</td>\n",
       "      <td>0.911108</td>\n",
       "      <td>0.880045</td>\n",
       "      <td>1.102142</td>\n",
       "      <td>...</td>\n",
       "      <td>0.886551</td>\n",
       "      <td>98.128523</td>\n",
       "      <td>0.713244</td>\n",
       "      <td>0.881375</td>\n",
       "      <td>1.420455</td>\n",
       "      <td>94.767716</td>\n",
       "      <td>1.877841</td>\n",
       "      <td>0.055841</td>\n",
       "      <td>-0.027176</td>\n",
       "      <td>0.357955</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>1.527468</td>\n",
       "      <td>1.313167</td>\n",
       "      <td>1.263715</td>\n",
       "      <td>1.254942</td>\n",
       "      <td>1.291326</td>\n",
       "      <td>1.351425</td>\n",
       "      <td>1.392640</td>\n",
       "      <td>1.305326</td>\n",
       "      <td>1.464004</td>\n",
       "      <td>1.330738</td>\n",
       "      <td>...</td>\n",
       "      <td>1.436784</td>\n",
       "      <td>12.573203</td>\n",
       "      <td>1.587106</td>\n",
       "      <td>1.284305</td>\n",
       "      <td>0.506452</td>\n",
       "      <td>17.836404</td>\n",
       "      <td>11.228694</td>\n",
       "      <td>1.550796</td>\n",
       "      <td>1.749876</td>\n",
       "      <td>0.480766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-2.879000</td>\n",
       "      <td>-2.960000</td>\n",
       "      <td>-2.936000</td>\n",
       "      <td>-3.176000</td>\n",
       "      <td>-2.694000</td>\n",
       "      <td>-3.028000</td>\n",
       "      <td>-3.250000</td>\n",
       "      <td>-2.784000</td>\n",
       "      <td>-3.223000</td>\n",
       "      <td>-3.619000</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.759000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-2.934000</td>\n",
       "      <td>-2.552000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-3.438000</td>\n",
       "      <td>-3.565000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.421500</td>\n",
       "      <td>-0.136750</td>\n",
       "      <td>-0.054000</td>\n",
       "      <td>0.587000</td>\n",
       "      <td>0.406000</td>\n",
       "      <td>0.311750</td>\n",
       "      <td>0.112750</td>\n",
       "      <td>-0.221750</td>\n",
       "      <td>0.002750</td>\n",
       "      <td>0.637500</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.243500</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>-0.622000</td>\n",
       "      <td>-0.069750</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-1.158500</td>\n",
       "      <td>-1.689750</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.804000</td>\n",
       "      <td>0.598500</td>\n",
       "      <td>0.686500</td>\n",
       "      <td>1.097500</td>\n",
       "      <td>1.222500</td>\n",
       "      <td>0.946000</td>\n",
       "      <td>1.282000</td>\n",
       "      <td>1.166500</td>\n",
       "      <td>1.081000</td>\n",
       "      <td>1.527500</td>\n",
       "      <td>...</td>\n",
       "      <td>1.171500</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>1.055000</td>\n",
       "      <td>0.979500</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.010000</td>\n",
       "      <td>0.701500</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.697500</td>\n",
       "      <td>1.450000</td>\n",
       "      <td>1.331750</td>\n",
       "      <td>1.619000</td>\n",
       "      <td>1.803500</td>\n",
       "      <td>1.679750</td>\n",
       "      <td>2.077750</td>\n",
       "      <td>1.861500</td>\n",
       "      <td>2.004750</td>\n",
       "      <td>2.018500</td>\n",
       "      <td>...</td>\n",
       "      <td>1.978000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>1.883000</td>\n",
       "      <td>1.765250</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.315250</td>\n",
       "      <td>1.642000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>3.499000</td>\n",
       "      <td>3.766000</td>\n",
       "      <td>3.310000</td>\n",
       "      <td>3.058000</td>\n",
       "      <td>2.693000</td>\n",
       "      <td>3.395000</td>\n",
       "      <td>3.250000</td>\n",
       "      <td>3.187000</td>\n",
       "      <td>3.613000</td>\n",
       "      <td>2.649000</td>\n",
       "      <td>...</td>\n",
       "      <td>3.324000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>3.703000</td>\n",
       "      <td>3.229000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>2.579000</td>\n",
       "      <td>2.164000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       v2mecenefm  v2meharjrn  v2meslfcen    v2mebias   v2merange    v2mecrit  \\\n",
       "count  176.000000  176.000000  176.000000  176.000000  176.000000  176.000000   \n",
       "mean     0.612642    0.595608    0.587642    0.862131    0.910881    0.843881   \n",
       "std      1.527468    1.313167    1.263715    1.254942    1.291326    1.351425   \n",
       "min     -2.879000   -2.960000   -2.936000   -3.176000   -2.694000   -3.028000   \n",
       "25%     -0.421500   -0.136750   -0.054000    0.587000    0.406000    0.311750   \n",
       "50%      0.804000    0.598500    0.686500    1.097500    1.222500    0.946000   \n",
       "75%      1.697500    1.450000    1.331750    1.619000    1.803500    1.679750   \n",
       "max      3.499000    3.766000    3.310000    3.058000    2.693000    3.395000   \n",
       "\n",
       "        v2cldiscm   v2cldiscw  v2clacfree  v2psparban  ...  v2csreprss  \\\n",
       "count  176.000000  176.000000  176.000000  176.000000  ...  176.000000   \n",
       "mean     0.987625    0.911108    0.880045    1.102142  ...    0.886551   \n",
       "std      1.392640    1.305326    1.464004    1.330738  ...    1.436784   \n",
       "min     -3.250000   -2.784000   -3.223000   -3.619000  ...   -3.759000   \n",
       "25%      0.112750   -0.221750    0.002750    0.637500  ...   -0.243500   \n",
       "50%      1.282000    1.166500    1.081000    1.527500  ...    1.171500   \n",
       "75%      2.077750    1.861500    2.004750    2.018500  ...    1.978000   \n",
       "max      3.250000    3.187000    3.613000    2.649000  ...    3.324000   \n",
       "\n",
       "       v2elsuffrage  v2elembaut  v2elembcap   v2lgbicam    v2lgello  \\\n",
       "count    176.000000  176.000000  176.000000  176.000000  176.000000   \n",
       "mean      98.128523    0.713244    0.881375    1.420455   94.767716   \n",
       "std       12.573203    1.587106    1.284305    0.506452   17.836404   \n",
       "min        0.000000   -2.934000   -2.552000    0.000000    0.000000   \n",
       "25%      100.000000   -0.622000   -0.069750    1.000000  100.000000   \n",
       "50%      100.000000    1.055000    0.979500    1.000000  100.000000   \n",
       "75%      100.000000    1.883000    1.765250    2.000000  100.000000   \n",
       "max      100.000000    3.703000    3.229000    2.000000  100.000000   \n",
       "\n",
       "       v2lginello  v2exdfcbhs  v2exdfdmhs  v2exhoshog  \n",
       "count  176.000000  176.000000  176.000000  176.000000  \n",
       "mean     1.877841    0.055841   -0.027176    0.357955  \n",
       "std     11.228694    1.550796    1.749876    0.480766  \n",
       "min      0.000000   -3.438000   -3.565000    0.000000  \n",
       "25%      0.000000   -1.158500   -1.689750    0.000000  \n",
       "50%      0.000000    0.010000    0.701500    0.000000  \n",
       "75%      0.000000    1.315250    1.642000    1.000000  \n",
       "max    100.000000    2.579000    2.164000    1.000000  \n",
       "\n",
       "[8 rows x 22 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vdem[indicators].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76430541",
   "metadata": {},
   "source": [
    "We see (also from consulting the codebook) that most variables are scaled to have values somewhere between -5 and 5, with 0 approximately representing the mean. 'v2elsuffrage', 'v2lgello', and 'v2lginello' are quite skewed, they range from 0 to 100, but differ in their mean. 'v2lgbicam' has an ordinal scale with values 0, 1, and 2, and 'v2exhoshog' is dichotomous.\n",
    "\n",
    "The corresponding boxplot looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7b3bac3d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_theme()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d5534fa2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[12, 2])\n",
    "sns.set_theme(font_scale=1)\n",
    "sns.boxplot(data=vdem[indicators])\n",
    "plt.ylabel('Value')\n",
    "plt.xticks(rotation=90)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "843c54a5",
   "metadata": {},
   "source": [
    "There are large differences in variance. These differences carry over to covariance. We can easily obtain the **covariance matrix** of the feature matrix $X$ from the Pandas dataframe using the [`cov()`](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.cov.html) method. Also obtain the **correlation matrix** using the [`corr()`](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.corr.html) method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "eb4ec809",
   "metadata": {},
   "outputs": [],
   "source": [
    "vdem_indicators_cov = vdem[indicators].cov(ddof=0)\n",
    "vdem_indicators_corr = vdem[indicators].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba6c4201",
   "metadata": {},
   "source": [
    "Plot both of them as a heatmap:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e55823d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=[8, 3])\n",
    "sns.set(font_scale=.75)\n",
    "sns.heatmap(data=vdem_indicators_cov, cmap='bwr', cbar_kws={'label': 'Covariance'}, xticklabels=True, yticklabels=True, ax=ax1)\n",
    "sns.heatmap(data=vdem_indicators_corr, vmin=-1, vmax=1, cmap='bwr', cbar_kws={'label': 'Correlation'}, xticklabels=True, yticklabels=False, ax=ax2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0145fb0e",
   "metadata": {},
   "source": [
    "[Recall](https://en.wikipedia.org/wiki/Covariance_and_correlation) that covariance is the extent to which two variables depend on each other while correlation tells how strongly they are related (*i.e.*, correlation is dimensionless). The dimensionality-reduction methods we are about to learn are sensitive to absolute differences in variance and covariance. When the variables in a dataset have largely different variance, those with the larger numerical values will dominate the results. This can result in suboptimal performance of certain dimensionality-reduction or clustering algorithms. In order to avoid that, we must standardize the data. **Standardization** means that the data is centered to have a mean of 0 and rescaled to have a variance of 1. The standardization transformation $z=\\frac{x-\\mu_x}{\\sigma_x}$ creates the so-called [$z$-scores](https://en.wikipedia.org/wiki/Standard_score) of a variable $x$ where $\\mu_x$ is the mean and $\\sigma_x$ is the standard deviation. This transformation ensures that all variables have the same relative importance and helps algorithms to identify patterns based on the relative differences between variables, rather than their absolute values.\n",
    "\n",
    "It is standard practice to store $X$ as a NumPy array. We can directly obtain this array from Pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "23f3a103",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = vdem[indicators].to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bda4761",
   "metadata": {},
   "source": [
    "We can then use the [StandardScaler](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html) from sklearn to get the standardized matrix $Z$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ed510126",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "Z = StandardScaler().fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "120987b5",
   "metadata": {},
   "source": [
    "Let's plot our standardized data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c932dd86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[12, 2])\n",
    "sns.set_theme(font_scale=1)\n",
    "sns.boxplot(data=pd.DataFrame(data=Z, columns=indicators))\n",
    "plt.ylabel('Value')\n",
    "plt.xticks(rotation=90)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ac8e5a9",
   "metadata": {},
   "source": [
    "Create a dataframe with the standardized variables..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "429a17f9",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "vdem_indicators_z = pd.DataFrame(data=Z, index=vdem.index, columns=indicators)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aca8451c",
   "metadata": {},
   "source": [
    "to plot the corresponding covariance and correlation structures:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "53d63f0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vdem_indicators_z_cov = vdem_indicators_z.cov(ddof=0)\n",
    "vdem_indicators_z_corr = vdem_indicators_z.corr()\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=[8, 3])\n",
    "sns.set(font_scale=.75)\n",
    "sns.heatmap(data=vdem_indicators_z_cov, vmin=-1, vmax=1, cmap='bwr', cbar_kws={'label': 'Covariance'}, xticklabels=True, yticklabels=True, ax=ax1)\n",
    "sns.heatmap(data=vdem_indicators_z_corr, vmin=-1, vmax=1, cmap='bwr', cbar_kws={'label': 'Correlation'}, xticklabels=True, yticklabels=False, ax=ax2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d4ab66a",
   "metadata": {},
   "source": [
    "The covariance and correlation matrices are now identical because correlation is standardized covariance."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0adb89bd",
   "metadata": {},
   "source": [
    "## D3.2. Dimensionality reduction\n",
    "\n",
    "Dimensionality-reduction algorithms work with the covariance (or correlation) matrix and try to bundle those indicators that covary (or are correlated) a lot. Like many dimensionality-reduction tools, the two models we will take a look at are based on **matrix factorization**. Mathematically, [matrix factorization](https://scikit-learn.org/stable/modules/decomposition.html) takes the form\n",
    "\n",
    "$X^\\mathrm{T}=M+LF$\n",
    "\n",
    "where\n",
    "\n",
    "- $X$ is the feature matrix with dimensionality $n\\times p$ where $n$ is the number of the units of observations (in V-Dem: countries) and $p$ is the number of observed variables,\n",
    "- $X^\\mathrm{T}$ is the transposed feature matrix (transposition means that the rows become columns and *vice versa*),\n",
    "- $M$ is the mean matrix with dimensionality $p\\times n$ where $m_{i,j}=\\mu_i$,\n",
    "- $L$ is a matrix with dimensionality $p\\times k$ where $k$ is the number of unobserved variables, and\n",
    "- $F$ is a matrix with dimensionality $k\\times n$.\n",
    "\n",
    "Matrix factorization means that a third dimension of length $k$ is introduced which connects matrices $L$ and $F$ in such a way that their multiplication $LF$ results in a matrix with the same dimensionality as that of $X^\\mathrm{T}$ and $M$. If the observed variables are centered, $M$ is not needed. Matrix factorization is a very general principle that underlies most dimensionality-reduction algorithms. In the following, we will see that $L$ and $F$ have different interpretations – and consequently: names – depending on the model that matrix factorization is used in.\n",
    "\n",
    "It does not matter of what kind the feature matrix $X$ is. In [Session D4. Topic modeling](4_topic_modeling.ipynb), we will introduce dimensionality reduction for matrices where the rows are documents, the columns are terms extracted from the documents, and the composite variables are topics. The different tools do differ regarding the statistical assumptions that are made and the ways that dimensionality is reduced."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b69693b6",
   "metadata": {},
   "source": [
    "### D3.2.1. Factor Analysis\n",
    "\n",
    "The goal of Factor Analysis (FA) is to explain the patterns of covariance (or correlation) among the observed variables by uncovering underlying latent variables called factors. FA is a **generative model** because it allows for modeling unobserved variables as factors that, in theory, can causally explain the observed variables. This is the **generative storyline** of FA. FA assumes that the latter are linear combinations of $k<p$ factors plus an error term. Using the epistemological conepts of *figure 2*, the FA model is the rule how the factors cause the indicators. Mathematically, $X=f(F)$:\n",
    "\n",
    "$X^\\mathrm{T}=M+LF+E$,\n",
    "\n",
    "where there is now an additional matrix $E$ with dimensionality $p\\times n$. FA assumes that the total variance in the feature matrix consists of a **common variance** that can be explained by the factors and a **unique variance** that cannot be explained by the factors. Common variance is explained by the $LF$ part of the equation. The values in $L$ are called factor loadings, and, hence, $L$ is called the **loading matrix** in FA. $F$ contains factor scores, and $F$ is called the **factor matrix**. The unique variance is the remaining error stored in the **error matrix** $E$, and the errors are assumed to be independent of each other (*i.e.*, purely random noise).\n",
    "\n",
    "Observed variables being linear combination means that each observation of a variable is a sum of factor loadings multiplied by the corresponding factor score plus the error. Breaking down the matrix notation above, the value of the $i$th observed variable and the $j$th observation is\n",
    "\n",
    "$x^\\mathrm{T}_{i,j}=m_{i,j}+l_{i,1}f_{1,j}+l_{i,2}f_{2,j}+...+l_{i,k}f_{k,j}+e_{i,j}$,\n",
    "\n",
    "where $l_{i,1}$ tells how strongly $x_{i,j}$ loads on the corresponding factor score $f_{1,j}$, $l_{i,2}$ tells how strongly it loads on factor score $f_{2,j}$, ..., and $e_{i,j}$ is the error made in this linear decomposition. Hence, we can fully recreate (*i.e.*, generate) the observed variables from the factor loadings, factor scores, and error terms.\n",
    "\n",
    "We have just described **Exploratory Factor Analysis** (EFA), which is an unsupervised FA method. We will later see that there is also another FA method that is actually supervised. We will work with the FactorAnalyzer package because it offers implementations of both methods. EFA can also be [done with sklearn](https://scikit-learn.org/stable/modules/decomposition.html#factor-analysis).\n",
    "\n",
    "Before we dive into the actual matrix factorization, two statistical operations are commonly performed. The first is **Bartlett's test**. It tells us if there is enough correlation in $X$ such that FA makes sense at all. The [`calculate_bartlett_sphericity()`](https://factor-analyzer.readthedocs.io/en/latest/factor_analyzer.html#factor_analyzer.factor_analyzer.calculate_bartlett_sphericity) function tests the null hypothesis that all values in the correlation matrix are identical. If there are factors to be uncovered, the matrix will exhibit a pattern, and the hypothesis will be rejected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "d21a7ae7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from factor_analyzer.factor_analyzer import calculate_bartlett_sphericity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8379ee60",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test statistic: 4745.36147313039\n",
      "Significance: 0.0\n"
     ]
    }
   ],
   "source": [
    "statistic, p_value = calculate_bartlett_sphericity(X)\n",
    "print ('Test statistic:', statistic)\n",
    "print ('Significance:', p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6986ab0a",
   "metadata": {},
   "source": [
    "The test is highly significant, so FA makes sense. We are not surprised because the pattern is clearly visible in the heatmap above.\n",
    "\n",
    "The second operation is to calculate the **Kaiser-Meyer-Olkin criterion** which tells us if the correlations in $X$ are strong enough to obtain reliable factors. The [`calculate_kmo()`](https://factor-analyzer.readthedocs.io/en/latest/factor_analyzer.html#factor_analyzer.factor_analyzer.calculate_kmo) function calculates the extent to which each observed variable is predicted, without error, by the other variables. If a variable cannot be predicted well by all the others, it cannot be generated from factors and can be removed before performing FA. The function also returns a total score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "674fe41a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from factor_analyzer.factor_analyzer import calculate_kmo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d0cfdc05",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "KMO score per variable: [0.97395244 0.95429289 0.97081135 0.95122183 0.96780603 0.96313908\n",
      " 0.92484247 0.92497398 0.97810491 0.95105286 0.93964297 0.9394314\n",
      " 0.9534823  0.69907083 0.96028727 0.9050055  0.21707965 0.72750967\n",
      " 0.62343351 0.8048973  0.78483604 0.7616548 ]\n",
      "Total KMO score 0.9286853063965668\n"
     ]
    }
   ],
   "source": [
    "kmo_per_variable , kmo_total  = calculate_kmo(X)\n",
    "print ('KMO score per variable:', kmo_per_variable)\n",
    "print ('Total KMO score', kmo_total)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abb404f7",
   "metadata": {},
   "source": [
    "Scores below 0.6 are considered inadequate. According to this criterion, the whole feature matrix promises a very robust decomposition into factors, and this observed variable should be removed from FA:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "790af6b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['v2lgbicam']"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[i for (i, v) in zip(indicators, kmo_per_variable < .6) if v]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4457439",
   "metadata": {},
   "source": [
    "We decide to not remove it but keep an eye on it to see how it behaves in the following analyses.\n",
    "\n",
    "We will now use FactorAnalyzer's [EFA model](https://factor-analyzer.readthedocs.io/en/latest/factor_analyzer.html#module-factor_analyzer.factor_analyzer). Under the hood, it uses a matrix-factorization algorithm called [Singular Value Decomposition](https://en.wikipedia.org/wiki/Singular_value_decomposition) which we will not discuss here.\n",
    "\n",
    "<div class='alert alert-block alert-info'>\n",
    "<big><b>Insight: ML models in Python</b></big>\n",
    "\n",
    "The order of operations for using statistical and ML models in Python is always the same, no matter if you use sklearn or FactorAnalyzer. First, you specify the model and parametrize it. Each model is its own class in a Python package. Second, you fit the model to the data by using a `fit()` method on the model object.\n",
    "</div>\n",
    "\n",
    "EFA is a theory-driven method, and the theory is that the 22 indicators are measureable instances of five unmeasurable low-level indices. The goal, now, is to extract $k=5$ factors from $Z$ and discuss them in light of the measurement theory. First, specify a `FactorAnalyzer` model and store it in a variable `efa` (lines 3-4). Second, fit `efa` to the data $Z$ (line 5):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "54559523",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FactorAnalyzer(n_factors=5, rotation_kwargs={})"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from factor_analyzer import FactorAnalyzer\n",
    "\n",
    "k_efa = 5\n",
    "efa = FactorAnalyzer(n_factors=k_efa)\n",
    "efa.fit(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d31ebcf",
   "metadata": {},
   "source": [
    "The loading matrix $L$ is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "73e0abe7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22, 5)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_efa = efa.loadings_\n",
    "L_efa.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3357f9b4",
   "metadata": {},
   "source": [
    "The loadings in $L$ tell how strongly the factors are correlated with the observed variables. To ease interpretation, we create a MultiIndex that shows which indicator is supposed to measure which low-level index (line 1), transform $L$ into a dataframe (line 2), merge the two (line 3), and highlight all correlations with absolute values larger that 0.5 (line 4):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f0713b00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
       "#T_6a8df_row0_col0, #T_6a8df_row1_col0, #T_6a8df_row2_col0, #T_6a8df_row3_col0, #T_6a8df_row4_col0, #T_6a8df_row5_col0, #T_6a8df_row6_col0, #T_6a8df_row7_col0, #T_6a8df_row8_col0, #T_6a8df_row9_col0, #T_6a8df_row10_col0, #T_6a8df_row11_col0, #T_6a8df_row12_col0, #T_6a8df_row13_col2, #T_6a8df_row14_col0, #T_6a8df_row15_col0, #T_6a8df_row17_col2, #T_6a8df_row18_col2, #T_6a8df_row19_col1, #T_6a8df_row20_col1, #T_6a8df_row21_col1 {\n",
       "  background-color: lightgray;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_6a8df\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank\" >&nbsp;</th>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_6a8df_level0_col0\" class=\"col_heading level0 col0\" >Factor 1</th>\n",
       "      <th id=\"T_6a8df_level0_col1\" class=\"col_heading level0 col1\" >Factor 2</th>\n",
       "      <th id=\"T_6a8df_level0_col2\" class=\"col_heading level0 col2\" >Factor 3</th>\n",
       "      <th id=\"T_6a8df_level0_col3\" class=\"col_heading level0 col3\" >Factor 4</th>\n",
       "      <th id=\"T_6a8df_level0_col4\" class=\"col_heading level0 col4\" >Factor 5</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th class=\"index_name level0\" >Index</th>\n",
       "      <th class=\"index_name level1\" >Indicator</th>\n",
       "      <th class=\"blank col0\" >&nbsp;</th>\n",
       "      <th class=\"blank col1\" >&nbsp;</th>\n",
       "      <th class=\"blank col2\" >&nbsp;</th>\n",
       "      <th class=\"blank col3\" >&nbsp;</th>\n",
       "      <th class=\"blank col4\" >&nbsp;</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level0_row0\" class=\"row_heading level0 row0\" rowspan=\"9\">Freedom of expression</th>\n",
       "      <th id=\"T_6a8df_level1_row0\" class=\"row_heading level1 row0\" >v2mecenefm</th>\n",
       "      <td id=\"T_6a8df_row0_col0\" class=\"data row0 col0\" >0.975955</td>\n",
       "      <td id=\"T_6a8df_row0_col1\" class=\"data row0 col1\" >-0.019727</td>\n",
       "      <td id=\"T_6a8df_row0_col2\" class=\"data row0 col2\" >-0.032819</td>\n",
       "      <td id=\"T_6a8df_row0_col3\" class=\"data row0 col3\" >-0.114580</td>\n",
       "      <td id=\"T_6a8df_row0_col4\" class=\"data row0 col4\" >0.044685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row1\" class=\"row_heading level1 row1\" >v2meharjrn</th>\n",
       "      <td id=\"T_6a8df_row1_col0\" class=\"data row1 col0\" >0.972817</td>\n",
       "      <td id=\"T_6a8df_row1_col1\" class=\"data row1 col1\" >0.039799</td>\n",
       "      <td id=\"T_6a8df_row1_col2\" class=\"data row1 col2\" >0.061405</td>\n",
       "      <td id=\"T_6a8df_row1_col3\" class=\"data row1 col3\" >-0.163580</td>\n",
       "      <td id=\"T_6a8df_row1_col4\" class=\"data row1 col4\" >0.027137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row2\" class=\"row_heading level1 row2\" >v2meslfcen</th>\n",
       "      <td id=\"T_6a8df_row2_col0\" class=\"data row2 col0\" >0.975938</td>\n",
       "      <td id=\"T_6a8df_row2_col1\" class=\"data row2 col1\" >0.123044</td>\n",
       "      <td id=\"T_6a8df_row2_col2\" class=\"data row2 col2\" >0.063921</td>\n",
       "      <td id=\"T_6a8df_row2_col3\" class=\"data row2 col3\" >-0.078494</td>\n",
       "      <td id=\"T_6a8df_row2_col4\" class=\"data row2 col4\" >0.163031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row3\" class=\"row_heading level1 row3\" >v2mebias</th>\n",
       "      <td id=\"T_6a8df_row3_col0\" class=\"data row3 col0\" >0.937833</td>\n",
       "      <td id=\"T_6a8df_row3_col1\" class=\"data row3 col1\" >0.025259</td>\n",
       "      <td id=\"T_6a8df_row3_col2\" class=\"data row3 col2\" >-0.008005</td>\n",
       "      <td id=\"T_6a8df_row3_col3\" class=\"data row3 col3\" >0.066396</td>\n",
       "      <td id=\"T_6a8df_row3_col4\" class=\"data row3 col4\" >0.300395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row4\" class=\"row_heading level1 row4\" >v2merange</th>\n",
       "      <td id=\"T_6a8df_row4_col0\" class=\"data row4 col0\" >0.874450</td>\n",
       "      <td id=\"T_6a8df_row4_col1\" class=\"data row4 col1\" >-0.016306</td>\n",
       "      <td id=\"T_6a8df_row4_col2\" class=\"data row4 col2\" >-0.005306</td>\n",
       "      <td id=\"T_6a8df_row4_col3\" class=\"data row4 col3\" >0.117262</td>\n",
       "      <td id=\"T_6a8df_row4_col4\" class=\"data row4 col4\" >0.292690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row5\" class=\"row_heading level1 row5\" >v2mecrit</th>\n",
       "      <td id=\"T_6a8df_row5_col0\" class=\"data row5 col0\" >0.957648</td>\n",
       "      <td id=\"T_6a8df_row5_col1\" class=\"data row5 col1\" >0.021267</td>\n",
       "      <td id=\"T_6a8df_row5_col2\" class=\"data row5 col2\" >0.018920</td>\n",
       "      <td id=\"T_6a8df_row5_col3\" class=\"data row5 col3\" >-0.089111</td>\n",
       "      <td id=\"T_6a8df_row5_col4\" class=\"data row5 col4\" >0.304181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row6\" class=\"row_heading level1 row6\" >v2cldiscm</th>\n",
       "      <td id=\"T_6a8df_row6_col0\" class=\"data row6 col0\" >0.907765</td>\n",
       "      <td id=\"T_6a8df_row6_col1\" class=\"data row6 col1\" >0.030620</td>\n",
       "      <td id=\"T_6a8df_row6_col2\" class=\"data row6 col2\" >-0.062001</td>\n",
       "      <td id=\"T_6a8df_row6_col3\" class=\"data row6 col3\" >0.071440</td>\n",
       "      <td id=\"T_6a8df_row6_col4\" class=\"data row6 col4\" >-0.244298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row7\" class=\"row_heading level1 row7\" >v2cldiscw</th>\n",
       "      <td id=\"T_6a8df_row7_col0\" class=\"data row7 col0\" >0.886855</td>\n",
       "      <td id=\"T_6a8df_row7_col1\" class=\"data row7 col1\" >0.020506</td>\n",
       "      <td id=\"T_6a8df_row7_col2\" class=\"data row7 col2\" >-0.028965</td>\n",
       "      <td id=\"T_6a8df_row7_col3\" class=\"data row7 col3\" >0.080619</td>\n",
       "      <td id=\"T_6a8df_row7_col4\" class=\"data row7 col4\" >-0.211277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row8\" class=\"row_heading level1 row8\" >v2clacfree</th>\n",
       "      <td id=\"T_6a8df_row8_col0\" class=\"data row8 col0\" >0.947907</td>\n",
       "      <td id=\"T_6a8df_row8_col1\" class=\"data row8 col1\" >0.084180</td>\n",
       "      <td id=\"T_6a8df_row8_col2\" class=\"data row8 col2\" >-0.044420</td>\n",
       "      <td id=\"T_6a8df_row8_col3\" class=\"data row8 col3\" >0.034973</td>\n",
       "      <td id=\"T_6a8df_row8_col4\" class=\"data row8 col4\" >-0.088427</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level0_row9\" class=\"row_heading level0 row9\" rowspan=\"4\">Freedom of association</th>\n",
       "      <th id=\"T_6a8df_level1_row9\" class=\"row_heading level1 row9\" >v2psparban</th>\n",
       "      <td id=\"T_6a8df_row9_col0\" class=\"data row9 col0\" >0.609649</td>\n",
       "      <td id=\"T_6a8df_row9_col1\" class=\"data row9 col1\" >-0.034939</td>\n",
       "      <td id=\"T_6a8df_row9_col2\" class=\"data row9 col2\" >-0.020068</td>\n",
       "      <td id=\"T_6a8df_row9_col3\" class=\"data row9 col3\" >0.461766</td>\n",
       "      <td id=\"T_6a8df_row9_col4\" class=\"data row9 col4\" >0.051356</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row10\" class=\"row_heading level1 row10\" >v2psbars</th>\n",
       "      <td id=\"T_6a8df_row10_col0\" class=\"data row10 col0\" >0.666444</td>\n",
       "      <td id=\"T_6a8df_row10_col1\" class=\"data row10 col1\" >-0.147655</td>\n",
       "      <td id=\"T_6a8df_row10_col2\" class=\"data row10 col2\" >0.053483</td>\n",
       "      <td id=\"T_6a8df_row10_col3\" class=\"data row10 col3\" >0.371746</td>\n",
       "      <td id=\"T_6a8df_row10_col4\" class=\"data row10 col4\" >0.083490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row11\" class=\"row_heading level1 row11\" >v2cseeorgs</th>\n",
       "      <td id=\"T_6a8df_row11_col0\" class=\"data row11 col0\" >0.806488</td>\n",
       "      <td id=\"T_6a8df_row11_col1\" class=\"data row11 col1\" >-0.045663</td>\n",
       "      <td id=\"T_6a8df_row11_col2\" class=\"data row11 col2\" >-0.077602</td>\n",
       "      <td id=\"T_6a8df_row11_col3\" class=\"data row11 col3\" >0.298741</td>\n",
       "      <td id=\"T_6a8df_row11_col4\" class=\"data row11 col4\" >-0.088906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row12\" class=\"row_heading level1 row12\" >v2csreprss</th>\n",
       "      <td id=\"T_6a8df_row12_col0\" class=\"data row12 col0\" >0.854617</td>\n",
       "      <td id=\"T_6a8df_row12_col1\" class=\"data row12 col1\" >-0.102407</td>\n",
       "      <td id=\"T_6a8df_row12_col2\" class=\"data row12 col2\" >-0.094694</td>\n",
       "      <td id=\"T_6a8df_row12_col3\" class=\"data row12 col3\" >0.089126</td>\n",
       "      <td id=\"T_6a8df_row12_col4\" class=\"data row12 col4\" >-0.163915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level0_row13\" class=\"row_heading level0 row13\" >Share of pop w/ suffrage</th>\n",
       "      <th id=\"T_6a8df_level1_row13\" class=\"row_heading level1 row13\" >v2elsuffrage</th>\n",
       "      <td id=\"T_6a8df_row13_col0\" class=\"data row13 col0\" >-0.064956</td>\n",
       "      <td id=\"T_6a8df_row13_col1\" class=\"data row13 col1\" >-0.060135</td>\n",
       "      <td id=\"T_6a8df_row13_col2\" class=\"data row13 col2\" >0.776147</td>\n",
       "      <td id=\"T_6a8df_row13_col3\" class=\"data row13 col3\" >0.068485</td>\n",
       "      <td id=\"T_6a8df_row13_col4\" class=\"data row13 col4\" >0.062112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level0_row14\" class=\"row_heading level0 row14\" rowspan=\"2\">Clean elections</th>\n",
       "      <th id=\"T_6a8df_level1_row14\" class=\"row_heading level1 row14\" >v2elembaut</th>\n",
       "      <td id=\"T_6a8df_row14_col0\" class=\"data row14 col0\" >0.943952</td>\n",
       "      <td id=\"T_6a8df_row14_col1\" class=\"data row14 col1\" >0.005217</td>\n",
       "      <td id=\"T_6a8df_row14_col2\" class=\"data row14 col2\" >-0.004682</td>\n",
       "      <td id=\"T_6a8df_row14_col3\" class=\"data row14 col3\" >-0.092015</td>\n",
       "      <td id=\"T_6a8df_row14_col4\" class=\"data row14 col4\" >-0.034461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row15\" class=\"row_heading level1 row15\" >v2elembcap</th>\n",
       "      <td id=\"T_6a8df_row15_col0\" class=\"data row15 col0\" >0.540059</td>\n",
       "      <td id=\"T_6a8df_row15_col1\" class=\"data row15 col1\" >-0.079057</td>\n",
       "      <td id=\"T_6a8df_row15_col2\" class=\"data row15 col2\" >0.166704</td>\n",
       "      <td id=\"T_6a8df_row15_col3\" class=\"data row15 col3\" >-0.265731</td>\n",
       "      <td id=\"T_6a8df_row15_col4\" class=\"data row15 col4\" >-0.222216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level0_row16\" class=\"row_heading level0 row16\" rowspan=\"6\">Elected officials</th>\n",
       "      <th id=\"T_6a8df_level1_row16\" class=\"row_heading level1 row16\" >v2lgbicam</th>\n",
       "      <td id=\"T_6a8df_row16_col0\" class=\"data row16 col0\" >0.004213</td>\n",
       "      <td id=\"T_6a8df_row16_col1\" class=\"data row16 col1\" >0.027253</td>\n",
       "      <td id=\"T_6a8df_row16_col2\" class=\"data row16 col2\" >0.024562</td>\n",
       "      <td id=\"T_6a8df_row16_col3\" class=\"data row16 col3\" >0.060938</td>\n",
       "      <td id=\"T_6a8df_row16_col4\" class=\"data row16 col4\" >0.001212</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row17\" class=\"row_heading level1 row17\" >v2lgello</th>\n",
       "      <td id=\"T_6a8df_row17_col0\" class=\"data row17 col0\" >-0.072602</td>\n",
       "      <td id=\"T_6a8df_row17_col1\" class=\"data row17 col1\" >-0.125239</td>\n",
       "      <td id=\"T_6a8df_row17_col2\" class=\"data row17 col2\" >0.967411</td>\n",
       "      <td id=\"T_6a8df_row17_col3\" class=\"data row17 col3\" >0.171333</td>\n",
       "      <td id=\"T_6a8df_row17_col4\" class=\"data row17 col4\" >0.015059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row18\" class=\"row_heading level1 row18\" >v2lginello</th>\n",
       "      <td id=\"T_6a8df_row18_col0\" class=\"data row18 col0\" >-0.022946</td>\n",
       "      <td id=\"T_6a8df_row18_col1\" class=\"data row18 col1\" >-0.073283</td>\n",
       "      <td id=\"T_6a8df_row18_col2\" class=\"data row18 col2\" >-0.537694</td>\n",
       "      <td id=\"T_6a8df_row18_col3\" class=\"data row18 col3\" >-0.024097</td>\n",
       "      <td id=\"T_6a8df_row18_col4\" class=\"data row18 col4\" >0.117074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row19\" class=\"row_heading level1 row19\" >v2exdfcbhs</th>\n",
       "      <td id=\"T_6a8df_row19_col0\" class=\"data row19 col0\" >-0.107694</td>\n",
       "      <td id=\"T_6a8df_row19_col1\" class=\"data row19 col1\" >0.859933</td>\n",
       "      <td id=\"T_6a8df_row19_col2\" class=\"data row19 col2\" >-0.018897</td>\n",
       "      <td id=\"T_6a8df_row19_col3\" class=\"data row19 col3\" >-0.021535</td>\n",
       "      <td id=\"T_6a8df_row19_col4\" class=\"data row19 col4\" >-0.039723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row20\" class=\"row_heading level1 row20\" >v2exdfdmhs</th>\n",
       "      <td id=\"T_6a8df_row20_col0\" class=\"data row20 col0\" >-0.095349</td>\n",
       "      <td id=\"T_6a8df_row20_col1\" class=\"data row20 col1\" >0.941301</td>\n",
       "      <td id=\"T_6a8df_row20_col2\" class=\"data row20 col2\" >0.000156</td>\n",
       "      <td id=\"T_6a8df_row20_col3\" class=\"data row20 col3\" >0.020660</td>\n",
       "      <td id=\"T_6a8df_row20_col4\" class=\"data row20 col4\" >0.018770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6a8df_level1_row21\" class=\"row_heading level1 row21\" >v2exhoshog</th>\n",
       "      <td id=\"T_6a8df_row21_col0\" class=\"data row21 col0\" >0.140762</td>\n",
       "      <td id=\"T_6a8df_row21_col1\" class=\"data row21 col1\" >0.630359</td>\n",
       "      <td id=\"T_6a8df_row21_col2\" class=\"data row21 col2\" >-0.040867</td>\n",
       "      <td id=\"T_6a8df_row21_col3\" class=\"data row21 col3\" >0.191379</td>\n",
       "      <td id=\"T_6a8df_row21_col4\" class=\"data row21 col4\" >0.038323</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x1ae6441f670>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loadings_index = pd.DataFrame(index=pd.MultiIndex.from_tuples(list(zip(*[indicators_labels_level, indicators])), names=['Index', 'Indicator']))\n",
    "loadings_efa = pd.DataFrame(data=L_efa, index=indicators, columns=[f'Factor {i+1}' for i in range(k_efa)])\n",
    "loadings_efa = pd.merge(left=loadings_index, right=loadings_efa, left_on='Indicator', right_index=True)\n",
    "loadings_efa.style.applymap(lambda x: 'background-color: lightgray' if abs(x) > .5 else '')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08dcbda4",
   "metadata": {},
   "source": [
    "The result shows that the variables supposed to measure the \"Freedom of expression\" in a country are all compounded in Factor 1. But so are the ones meant to measure \"Freedom of association\" and \"Clean elections\"! It turns out that 15 variables supposed to measure three distinct things actually measure just one aspect of \"Electoral democracy\". The one variable supposed to measure the \"Share of population with suffrage\" loads on Factor 3, but so do the 'v2lgello' (\"Lower chamber directly elected\") and 'v2lginello' (\"Percentage of indirectly elected legislators lower chamber\") indicators meant to measure \"Elected officials\". Factor 2 merely explains \"Elected officials\" but, as we just saw, not all variables meant to measure this index load on the factor. The 'v2lgbicam' that has a KMO score below 0.6 does not load on any factor. Finally, two factors are essentially meaningless. The lesson from this EFA is that measuring latent variables is hard!\n",
    "\n",
    "The factor matrix $F$ is obtained by transforming the (standardized) feature matrix given the fit. To obtain dimensionality $k\\times n$, we must transpose the output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "bc3458cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 176)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F_efa = efa.fit_transform(Z).T\n",
    "F_efa.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27eb1eaa",
   "metadata": {},
   "source": [
    "The factor scores in $F$ are like the indicator scores in $Z$. To display $F$, we transpose it because we are used to having the observations in rows and (latent) variables in columns. The following dataframe is the standardized feature matrix with reduced dimensionality and can be used in subsequent analysis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "bd3cbdc7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Factor 1</th>\n",
       "      <th>Factor 2</th>\n",
       "      <th>Factor 3</th>\n",
       "      <th>Factor 4</th>\n",
       "      <th>Factor 5</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country_name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Afghanistan</th>\n",
       "      <td>-0.168640</td>\n",
       "      <td>0.329326</td>\n",
       "      <td>-0.063358</td>\n",
       "      <td>0.993648</td>\n",
       "      <td>1.321712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Albania</th>\n",
       "      <td>0.082120</td>\n",
       "      <td>-0.656981</td>\n",
       "      <td>0.096253</td>\n",
       "      <td>0.758226</td>\n",
       "      <td>-1.096448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Algeria</th>\n",
       "      <td>-0.661127</td>\n",
       "      <td>0.862747</td>\n",
       "      <td>0.183040</td>\n",
       "      <td>-0.320958</td>\n",
       "      <td>0.107181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Angola</th>\n",
       "      <td>-0.356806</td>\n",
       "      <td>0.626662</td>\n",
       "      <td>0.407383</td>\n",
       "      <td>-0.171724</td>\n",
       "      <td>0.881374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Argentina</th>\n",
       "      <td>0.593528</td>\n",
       "      <td>1.193758</td>\n",
       "      <td>0.367373</td>\n",
       "      <td>1.467820</td>\n",
       "      <td>-0.593472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vietnam</th>\n",
       "      <td>-1.523285</td>\n",
       "      <td>-1.145586</td>\n",
       "      <td>0.669593</td>\n",
       "      <td>-2.447524</td>\n",
       "      <td>-2.001552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yemen</th>\n",
       "      <td>-1.443968</td>\n",
       "      <td>0.720517</td>\n",
       "      <td>0.209535</td>\n",
       "      <td>0.179586</td>\n",
       "      <td>0.532015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zambia</th>\n",
       "      <td>-0.220643</td>\n",
       "      <td>1.085593</td>\n",
       "      <td>-0.147955</td>\n",
       "      <td>0.495708</td>\n",
       "      <td>-0.041489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zanzibar</th>\n",
       "      <td>-0.893173</td>\n",
       "      <td>0.987913</td>\n",
       "      <td>-0.815085</td>\n",
       "      <td>0.780756</td>\n",
       "      <td>1.568232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zimbabwe</th>\n",
       "      <td>-0.986227</td>\n",
       "      <td>1.102118</td>\n",
       "      <td>-0.975084</td>\n",
       "      <td>1.198772</td>\n",
       "      <td>2.135164</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>176 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              Factor 1  Factor 2  Factor 3  Factor 4  Factor 5\n",
       "country_name                                                  \n",
       "Afghanistan  -0.168640  0.329326 -0.063358  0.993648  1.321712\n",
       "Albania       0.082120 -0.656981  0.096253  0.758226 -1.096448\n",
       "Algeria      -0.661127  0.862747  0.183040 -0.320958  0.107181\n",
       "Angola       -0.356806  0.626662  0.407383 -0.171724  0.881374\n",
       "Argentina     0.593528  1.193758  0.367373  1.467820 -0.593472\n",
       "...                ...       ...       ...       ...       ...\n",
       "Vietnam      -1.523285 -1.145586  0.669593 -2.447524 -2.001552\n",
       "Yemen        -1.443968  0.720517  0.209535  0.179586  0.532015\n",
       "Zambia       -0.220643  1.085593 -0.147955  0.495708 -0.041489\n",
       "Zanzibar     -0.893173  0.987913 -0.815085  0.780756  1.568232\n",
       "Zimbabwe     -0.986227  1.102118 -0.975084  1.198772  2.135164\n",
       "\n",
       "[176 rows x 5 columns]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vdem_efa = pd.DataFrame(data=F_efa.T, index=vdem.index, columns=[f'Factor {i+1}' for i in range(k_efa)])\n",
    "vdem_efa"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e3dcd6f",
   "metadata": {},
   "source": [
    "The following two heatmaps display the covariance and correlation matrices for the factors (instead of the observed variables, as above):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "df0d8d33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vdem_efa_cov = pd.DataFrame(F_efa.T, columns=[i+1 for i in range(k_efa)]).cov(ddof=0)\n",
    "vdem_efa_corr = pd.DataFrame(F_efa.T, columns=[i+1 for i in range(k_efa)]).corr()\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=[8, 3])\n",
    "sns.set(font_scale=.75)\n",
    "h1 = sns.heatmap(data=vdem_efa_cov, vmin=-1, vmax=1, cmap='bwr', annot=True, cbar_kws={'label': 'Covariance'}, xticklabels=True, yticklabels=True, ax=ax1)\n",
    "h2 = sns.heatmap(data=vdem_efa_corr, vmin=-1, vmax=1, cmap='bwr', annot=True, cbar_kws={'label': 'Correlation'}, xticklabels=True, yticklabels=False, ax=ax2)\n",
    "h1.set(xlabel='Factor', ylabel='Factor')\n",
    "h2.set(xlabel='Factor')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c6440bb",
   "metadata": {},
   "source": [
    "The small numbers off the diagonal show that EFA manages to reduce much of the covariance (and correlation) in the data by compounding variables into factors.\n",
    "\n",
    "How much variance in an observed variable is explained by all the factors? In other words, what is the fraction of common variance in an indicator? This is what **communality** quantifies, a [measure](https://en.wikipedia.org/wiki/Factor_analysis#Terminology) of \"the reliability of the indicator in the context of the factors being posited.\" Mathematically, communality is the row sum of the squared loading matrix. The communalities can be obtained via the `get_communalities()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "e6463c20",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Communality</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>v2mecenefm</th>\n",
       "      <td>0.969079</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2meharjrn</th>\n",
       "      <td>0.979222</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2meslfcen</th>\n",
       "      <td>1.004422</td>\n",
       "    </tr>\n",
       "    <tr>\n",
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       "      <td>0.974879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2merange</th>\n",
       "      <td>0.864374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2mecrit</th>\n",
       "      <td>1.018366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2cldiscm</th>\n",
       "      <td>0.893604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2cldiscw</th>\n",
       "      <td>0.838909</td>\n",
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       "    <tr>\n",
       "      <th>v2clacfree</th>\n",
       "      <td>0.916629</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2psparban</th>\n",
       "      <td>0.589160</td>\n",
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       "    <tr>\n",
       "      <th>v2psbars</th>\n",
       "      <td>0.613976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2cseeorgs</th>\n",
       "      <td>0.755681</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2csreprss</th>\n",
       "      <td>0.784637</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2elsuffrage</th>\n",
       "      <td>0.618788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2elembaut</th>\n",
       "      <td>0.900748</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2elembcap</th>\n",
       "      <td>0.445698</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2lgbicam</th>\n",
       "      <td>0.005079</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2lgello</th>\n",
       "      <td>0.986421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2lginello</th>\n",
       "      <td>0.309299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2exdfcbhs</th>\n",
       "      <td>0.753482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2exdfdmhs</th>\n",
       "      <td>0.895919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>v2exhoshog</th>\n",
       "      <td>0.456931</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Communality\n",
       "v2mecenefm       0.969079\n",
       "v2meharjrn       0.979222\n",
       "v2meslfcen       1.004422\n",
       "v2mebias         0.974879\n",
       "v2merange        0.864374\n",
       "v2mecrit         1.018366\n",
       "v2cldiscm        0.893604\n",
       "v2cldiscw        0.838909\n",
       "v2clacfree       0.916629\n",
       "v2psparban       0.589160\n",
       "v2psbars         0.613976\n",
       "v2cseeorgs       0.755681\n",
       "v2csreprss       0.784637\n",
       "v2elsuffrage     0.618788\n",
       "v2elembaut       0.900748\n",
       "v2elembcap       0.445698\n",
       "v2lgbicam        0.005079\n",
       "v2lgello         0.986421\n",
       "v2lginello       0.309299\n",
       "v2exdfcbhs       0.753482\n",
       "v2exdfdmhs       0.895919\n",
       "v2exhoshog       0.456931"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "communalities = efa.get_communalities()\n",
    "pd.DataFrame(data=communalities, index=vdem_indicators_z.columns, columns=['Communality'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "d78556d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[3, 2])\n",
    "sns.set(font_scale=1.)\n",
    "sns.histplot(data=communalities)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43f1ac03",
   "metadata": {},
   "source": [
    "Communality scores range from 0 to 1, though the values may be overestimated, leading to scores larger than 1. The plot shows that half of the variables have communalities close to 1, while the other half has values of 0.85 and lower. As expected, the 'v2lgbicam' variable has the smallest value, that means, it cannot be explained at all by the factors.\n",
    "\n",
    "Next, we can ask how much of the variance in the data can be explained by the factors overall? Again, the answer is in the loading matrix. The sum of the squared loadings is the **variance** of a factor. Dividing the variance by the number of observed variables is the **proportional variance** which can be cumulatively summed to obtain the **cumulative variance**. The `get_factor_variance()` method reports all those scores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ed918343",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Factor 1</th>\n",
       "      <th>Factor 2</th>\n",
       "      <th>Factor 3</th>\n",
       "      <th>Factor 4</th>\n",
       "      <th>Factor 5</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Variance</th>\n",
       "      <td>11.351536</td>\n",
       "      <td>2.117086</td>\n",
       "      <td>1.892137</td>\n",
       "      <td>0.688522</td>\n",
       "      <td>0.526021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Proportional variance</th>\n",
       "      <td>0.515979</td>\n",
       "      <td>0.096231</td>\n",
       "      <td>0.086006</td>\n",
       "      <td>0.031296</td>\n",
       "      <td>0.023910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cumulative Variance</th>\n",
       "      <td>0.515979</td>\n",
       "      <td>0.612210</td>\n",
       "      <td>0.698216</td>\n",
       "      <td>0.729513</td>\n",
       "      <td>0.753423</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        Factor 1  Factor 2  Factor 3  Factor 4  Factor 5\n",
       "Variance               11.351536  2.117086  1.892137  0.688522  0.526021\n",
       "Proportional variance   0.515979  0.096231  0.086006  0.031296  0.023910\n",
       "Cumulative Variance     0.515979  0.612210  0.698216  0.729513  0.753423"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variances = efa.get_factor_variance()\n",
    "pd.DataFrame(data=variances, index=['Variance', 'Proportional variance', 'Cumulative Variance'], columns=[f'Factor {i+1}' for i in range(k_efa)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "894e677d",
   "metadata": {},
   "source": [
    "We see that the first factor explains more than half of the variance in the data, almost 52% to be exact. Adding more factors increases the variance that can be explained, but the increases quickly become neglectable. It is possible to say how much of the variance can possibly be explained with EFA. This is the cumulative variance of an EFA model with $k=p-1=21$ factors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2ae73424",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7757245110620781"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "FactorAnalyzer(n_factors=21).fit(Z).get_factor_variance()[2][-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d737d67",
   "metadata": {},
   "source": [
    "So, up to 78% of the variance in the data is common variance. The rest is unique variance and cannot be explained by EFA.\n",
    "\n",
    "Given $L$ and $F$, we can obtain the error matrix where the unique variance is stored. Since we have fitted the EFA model to the standardized feature matrix, $E=Z-LF$. We can multiply $L$ and $F$ (obtain their dot product) with NumPy's [`dot()`](https://numpy.org/doc/stable/reference/generated/numpy.dot.html) function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "fa1dad43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22, 176)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "E_efa = Z.T - np.dot(a=L_efa, b=F_efa)\n",
    "E_efa.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22193aef",
   "metadata": {},
   "source": [
    "The errors are normally distributed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "92cac573",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(data=E_efa.T, columns=indicators).hist()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f844729c",
   "metadata": {},
   "source": [
    "To sum up until here, EFA identifies the common variance in observed variables and regresses it to latent variables whose number must be specified. The latent variables are hypothesized to have generated the observed variables, and their number originates in the theory in the context of which EFA is applied. This makes EFA an abductive tool in which the effect (the data in form of the feature matrix) is observed, the rule is hypothesized, and the cause (the latent variables) is inferred.\n",
    "\n",
    "#### Turning Factor Analysis from head to toe\n",
    "\n",
    "There is also a version of the FA algorithm called **Confirmatory Factor Analysis** (CFA) that is even more theory-driven and lets you test a generative theory. CFA is EFA turned around. Have another look at *figure 2*: in EFA, the effect is observed, and the cause is inferred; in CFA, the effect is inferred, and the cause is observed. But in both cases, the hypothesized rule that the factors generate the indicators is the same. This is a turn from abduction to deduction. In fact, we are anticipating supervised learning here, and if you are wondering how the effect, that still is – and can only be – the data, is inferred, make sure to study [Session D5. Supervised machine learning](5_supervised_machine_learning.ipynb).\n",
    "\n",
    "Here, we will only quickly run through CFA. The idea is to test specific versions of the rule $X=f(F)$ by constraining certain cells in the loading matrix to 0. This forces the model to be consistent with the theory (*i.e.*, consistent with the hypothesized rule). In other words, not only do we specify the model, we also specify the fit to some extent! Since this can result in a suboptimal fit, we must also evaluate the goodness of the fit.\n",
    "\n",
    "Let's find out how good the model fits the data if we constrain the loading matrix according to the measurement theory that underlies the V-Dem dataset (*figure 3*). To do so, we create a dictionary that specifies which factor generates which indicator(s) (lines 3-9), parse this specification such that it can be read by the model (line 10), construct the model, and fit it to the data (line 11):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "37ffc8d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lietzho\\AppData\\Roaming\\Python\\Python39\\site-packages\\factor_analyzer\\confirmatory_factor_analyzer.py:753: UserWarning: The optimization routine failed to converge: ABNORMAL_TERMINATION_IN_LNSRCH\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "from factor_analyzer import ConfirmatoryFactorAnalyzer, ModelSpecificationParser\n",
    "\n",
    "model_dict = {\n",
    "    'Factor 1': ['v2mecenefm', 'v2meharjrn', 'v2meslfcen', 'v2mebias', 'v2merange', 'v2mecrit', 'v2cldiscm', 'v2cldiscw', 'v2clacfree'], \n",
    "    'Factor 2': ['v2psparban', 'v2psbars', 'v2cseeorgs', 'v2csreprss'], \n",
    "    'Factor 3': ['v2elsuffrage'], \n",
    "    'Factor 4': ['v2elembaut', 'v2elembcap'], \n",
    "    'Factor 5': ['v2lgbicam', 'v2lgello', 'v2lginello', 'v2exdfcbhs', 'v2exdfdmhs', 'v2exhoshog']\n",
    "}\n",
    "model_spec = ModelSpecificationParser.parse_model_specification_from_dict(X=Z, specification=model_dict)\n",
    "cfa = ConfirmatoryFactorAnalyzer(specification=model_spec).fit(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad9c8fbe",
   "metadata": {},
   "source": [
    "Display the loading matrix, just like we did for EFA:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "93ab7dae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22, 5)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cfa.loadings_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c8a8eb55",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table id=\"T_ae234\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank\" >&nbsp;</th>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_ae234_level0_col0\" class=\"col_heading level0 col0\" >Factor 1</th>\n",
       "      <th id=\"T_ae234_level0_col1\" class=\"col_heading level0 col1\" >Factor 2</th>\n",
       "      <th id=\"T_ae234_level0_col2\" class=\"col_heading level0 col2\" >Factor 3</th>\n",
       "      <th id=\"T_ae234_level0_col3\" class=\"col_heading level0 col3\" >Factor 4</th>\n",
       "      <th id=\"T_ae234_level0_col4\" class=\"col_heading level0 col4\" >Factor 5</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th class=\"index_name level0\" >Index</th>\n",
       "      <th class=\"index_name level1\" >Indicator</th>\n",
       "      <th class=\"blank col0\" >&nbsp;</th>\n",
       "      <th class=\"blank col1\" >&nbsp;</th>\n",
       "      <th class=\"blank col2\" >&nbsp;</th>\n",
       "      <th class=\"blank col3\" >&nbsp;</th>\n",
       "      <th class=\"blank col4\" >&nbsp;</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level0_row0\" class=\"row_heading level0 row0\" rowspan=\"9\">Freedom of expression</th>\n",
       "      <th id=\"T_ae234_level1_row0\" class=\"row_heading level1 row0\" >v2mecenefm</th>\n",
       "      <td id=\"T_ae234_row0_col0\" class=\"data row0 col0\" >0.975633</td>\n",
       "      <td id=\"T_ae234_row0_col1\" class=\"data row0 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row0_col2\" class=\"data row0 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row0_col3\" class=\"data row0 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row0_col4\" class=\"data row0 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row1\" class=\"row_heading level1 row1\" >v2meharjrn</th>\n",
       "      <td id=\"T_ae234_row1_col0\" class=\"data row1 col0\" >0.982427</td>\n",
       "      <td id=\"T_ae234_row1_col1\" class=\"data row1 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row1_col2\" class=\"data row1 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row1_col3\" class=\"data row1 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row1_col4\" class=\"data row1 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row2\" class=\"row_heading level1 row2\" >v2meslfcen</th>\n",
       "      <td id=\"T_ae234_row2_col0\" class=\"data row2 col0\" >0.971916</td>\n",
       "      <td id=\"T_ae234_row2_col1\" class=\"data row2 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row2_col2\" class=\"data row2 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row2_col3\" class=\"data row2 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row2_col4\" class=\"data row2 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row3\" class=\"row_heading level1 row3\" >v2mebias</th>\n",
       "      <td id=\"T_ae234_row3_col0\" class=\"data row3 col0\" >0.963327</td>\n",
       "      <td id=\"T_ae234_row3_col1\" class=\"data row3 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row3_col2\" class=\"data row3 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row3_col3\" class=\"data row3 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row3_col4\" class=\"data row3 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row4\" class=\"row_heading level1 row4\" >v2merange</th>\n",
       "      <td id=\"T_ae234_row4_col0\" class=\"data row4 col0\" >0.923796</td>\n",
       "      <td id=\"T_ae234_row4_col1\" class=\"data row4 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row4_col2\" class=\"data row4 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row4_col3\" class=\"data row4 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row4_col4\" class=\"data row4 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row5\" class=\"row_heading level1 row5\" >v2mecrit</th>\n",
       "      <td id=\"T_ae234_row5_col0\" class=\"data row5 col0\" >0.935245</td>\n",
       "      <td id=\"T_ae234_row5_col1\" class=\"data row5 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row5_col2\" class=\"data row5 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row5_col3\" class=\"data row5 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row5_col4\" class=\"data row5 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row6\" class=\"row_heading level1 row6\" >v2cldiscm</th>\n",
       "      <td id=\"T_ae234_row6_col0\" class=\"data row6 col0\" >0.972541</td>\n",
       "      <td id=\"T_ae234_row6_col1\" class=\"data row6 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row6_col2\" class=\"data row6 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row6_col3\" class=\"data row6 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row6_col4\" class=\"data row6 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row7\" class=\"row_heading level1 row7\" >v2cldiscw</th>\n",
       "      <td id=\"T_ae234_row7_col0\" class=\"data row7 col0\" >0.969064</td>\n",
       "      <td id=\"T_ae234_row7_col1\" class=\"data row7 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row7_col2\" class=\"data row7 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row7_col3\" class=\"data row7 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row7_col4\" class=\"data row7 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row8\" class=\"row_heading level1 row8\" >v2clacfree</th>\n",
       "      <td id=\"T_ae234_row8_col0\" class=\"data row8 col0\" >0.983629</td>\n",
       "      <td id=\"T_ae234_row8_col1\" class=\"data row8 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row8_col2\" class=\"data row8 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row8_col3\" class=\"data row8 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row8_col4\" class=\"data row8 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level0_row9\" class=\"row_heading level0 row9\" rowspan=\"4\">Freedom of association</th>\n",
       "      <th id=\"T_ae234_level1_row9\" class=\"row_heading level1 row9\" >v2psparban</th>\n",
       "      <td id=\"T_ae234_row9_col0\" class=\"data row9 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row9_col1\" class=\"data row9 col1\" >0.863293</td>\n",
       "      <td id=\"T_ae234_row9_col2\" class=\"data row9 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row9_col3\" class=\"data row9 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row9_col4\" class=\"data row9 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row10\" class=\"row_heading level1 row10\" >v2psbars</th>\n",
       "      <td id=\"T_ae234_row10_col0\" class=\"data row10 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row10_col1\" class=\"data row10 col1\" >0.921960</td>\n",
       "      <td id=\"T_ae234_row10_col2\" class=\"data row10 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row10_col3\" class=\"data row10 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row10_col4\" class=\"data row10 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row11\" class=\"row_heading level1 row11\" >v2cseeorgs</th>\n",
       "      <td id=\"T_ae234_row11_col0\" class=\"data row11 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row11_col1\" class=\"data row11 col1\" >0.976766</td>\n",
       "      <td id=\"T_ae234_row11_col2\" class=\"data row11 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row11_col3\" class=\"data row11 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row11_col4\" class=\"data row11 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row12\" class=\"row_heading level1 row12\" >v2csreprss</th>\n",
       "      <td id=\"T_ae234_row12_col0\" class=\"data row12 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row12_col1\" class=\"data row12 col1\" >0.900812</td>\n",
       "      <td id=\"T_ae234_row12_col2\" class=\"data row12 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row12_col3\" class=\"data row12 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row12_col4\" class=\"data row12 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level0_row13\" class=\"row_heading level0 row13\" >Share of pop w/ suffrage</th>\n",
       "      <th id=\"T_ae234_level1_row13\" class=\"row_heading level1 row13\" >v2elsuffrage</th>\n",
       "      <td id=\"T_ae234_row13_col0\" class=\"data row13 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row13_col1\" class=\"data row13 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row13_col2\" class=\"data row13 col2\" >0.765888</td>\n",
       "      <td id=\"T_ae234_row13_col3\" class=\"data row13 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row13_col4\" class=\"data row13 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level0_row14\" class=\"row_heading level0 row14\" rowspan=\"2\">Clean elections</th>\n",
       "      <th id=\"T_ae234_level1_row14\" class=\"row_heading level1 row14\" >v2elembaut</th>\n",
       "      <td id=\"T_ae234_row14_col0\" class=\"data row14 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row14_col1\" class=\"data row14 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row14_col2\" class=\"data row14 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row14_col3\" class=\"data row14 col3\" >0.839672</td>\n",
       "      <td id=\"T_ae234_row14_col4\" class=\"data row14 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row15\" class=\"row_heading level1 row15\" >v2elembcap</th>\n",
       "      <td id=\"T_ae234_row15_col0\" class=\"data row15 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row15_col1\" class=\"data row15 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row15_col2\" class=\"data row15 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row15_col3\" class=\"data row15 col3\" >0.813584</td>\n",
       "      <td id=\"T_ae234_row15_col4\" class=\"data row15 col4\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level0_row16\" class=\"row_heading level0 row16\" rowspan=\"6\">Elected officials</th>\n",
       "      <th id=\"T_ae234_level1_row16\" class=\"row_heading level1 row16\" >v2lgbicam</th>\n",
       "      <td id=\"T_ae234_row16_col0\" class=\"data row16 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row16_col1\" class=\"data row16 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row16_col2\" class=\"data row16 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row16_col3\" class=\"data row16 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row16_col4\" class=\"data row16 col4\" >0.740476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row17\" class=\"row_heading level1 row17\" >v2lgello</th>\n",
       "      <td id=\"T_ae234_row17_col0\" class=\"data row17 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row17_col1\" class=\"data row17 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row17_col2\" class=\"data row17 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row17_col3\" class=\"data row17 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row17_col4\" class=\"data row17 col4\" >0.490266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row18\" class=\"row_heading level1 row18\" >v2lginello</th>\n",
       "      <td id=\"T_ae234_row18_col0\" class=\"data row18 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row18_col1\" class=\"data row18 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row18_col2\" class=\"data row18 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row18_col3\" class=\"data row18 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row18_col4\" class=\"data row18 col4\" >0.569358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row19\" class=\"row_heading level1 row19\" >v2exdfcbhs</th>\n",
       "      <td id=\"T_ae234_row19_col0\" class=\"data row19 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row19_col1\" class=\"data row19 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row19_col2\" class=\"data row19 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row19_col3\" class=\"data row19 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row19_col4\" class=\"data row19 col4\" >1.132299</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row20\" class=\"row_heading level1 row20\" >v2exdfdmhs</th>\n",
       "      <td id=\"T_ae234_row20_col0\" class=\"data row20 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row20_col1\" class=\"data row20 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row20_col2\" class=\"data row20 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row20_col3\" class=\"data row20 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row20_col4\" class=\"data row20 col4\" >1.184111</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_ae234_level1_row21\" class=\"row_heading level1 row21\" >v2exhoshog</th>\n",
       "      <td id=\"T_ae234_row21_col0\" class=\"data row21 col0\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row21_col1\" class=\"data row21 col1\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row21_col2\" class=\"data row21 col2\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row21_col3\" class=\"data row21 col3\" >0.000000</td>\n",
       "      <td id=\"T_ae234_row21_col4\" class=\"data row21 col4\" >1.059263</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x1ae66853b20>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loadings_cfa = pd.DataFrame(data=cfa.loadings_, index=indicators, columns=[f'Factor {i+1}' for i in range(k_efa)])\n",
    "loadings_cfa = pd.merge(left=loadings_index, right=loadings_cfa, left_on='Indicator', right_index=True)\n",
    "loadings_cfa.style.applymap(lambda x: 'background-color: lightgray' if abs(x) > .5 else '')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b04191bb",
   "metadata": {},
   "source": [
    "As a result of constraining the loading matrix, loadings have only been inferred for the specified cells. Loadings are larger than 0.74 except for two indicators. The fact that the indicators are mostly strongly correlated with the five enforced factors means that the indicators are generally suited to measure the low-level index.\n",
    "\n",
    "However, CFA has also led to three correlations being larger than one, which points at a problem during the numerical fitting procedure. In fact, we have been shown a warning that \"The optimization routine failed to converge\". As a result, the procedure has not produced a goodness-of-fit statistic, which means, we cannot evaluate the specified model.\n",
    "\n",
    "Let's try something else. Let's create five different models with 1 to 5 factors (line 1), create model specifications where each indicator is only allowed to load on the factor where its absolute correlation, identified using EFA, is largest (line 2), fit a CFA for each specification (lines 3-5), and print the [Akaike Information Criterion](https://en.wikipedia.org/wiki/Akaike_information_criterion) (AIC):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "270150c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lietzho\\AppData\\Roaming\\Python\\Python39\\site-packages\\factor_analyzer\\factor_analyzer.py:662: UserWarning: No rotation will be performed when the number of factors equals 1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 factor(s): 7562.374741982145\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lietzho\\AppData\\Roaming\\Python\\Python39\\site-packages\\factor_analyzer\\confirmatory_factor_analyzer.py:753: UserWarning: The optimization routine failed to converge: ABNORMAL_TERMINATION_IN_LNSRCH\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2 factor(s): nan\n",
      "3 factor(s): 232.0\n",
      "4 factor(s): 284.0\n",
      "5 factor(s): nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lietzho\\AppData\\Roaming\\Python\\Python39\\site-packages\\factor_analyzer\\confirmatory_factor_analyzer.py:753: UserWarning: The optimization routine failed to converge: ABNORMAL_TERMINATION_IN_LNSRCH\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "number_of_factors = [1, 2, 3, 4, 5]\n",
    "models_dict = [{f'F{f+1}': [indicators[i] for i, k in enumerate(np.argmax(abs(FactorAnalyzer(n_factors=n_factors).fit(Z).loadings_), axis=1)) if k == f] for f in range(n_factors)} for n_factors in number_of_factors]\n",
    "for f in range(len(number_of_factors)):\n",
    "    model_spec = ModelSpecificationParser.parse_model_specification_from_dict(X=Z, specification=models_dict[f])\n",
    "    cfa_n = ConfirmatoryFactorAnalyzer(specification=model_spec).fit(Z)\n",
    "    print(f'{number_of_factors[f]} factor(s):', cfa_n.aic_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4e3a929",
   "metadata": {},
   "source": [
    "The AIC is a goodness-of-fit measure. The smaller it is, the better the model fit. Constraining the model to just 1 factor does not make any sense (the AIC is very large) because the differences in variance cannot be explained with 1 factor. For 2 and 5 factors, the model does not converge. The model fit is best for 3 factors, which is in line with the interpretation of the EFA model with five factors.\n",
    "\n",
    "In sum, when we use deduction (CFA), we find that the observed variables are well represented by, and can be thought to have generated, the five low-level indices. But when we let the data speak and use abduction (EFA), we find that three indices are sufficient. This is because the indicators are also strongly correlated across indices."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5db828a7",
   "metadata": {},
   "source": [
    "### D3.2.2. Principal Component Analysis\n",
    "\n",
    "Principal Component Analysis (PCA) strips dimensionality reduction of theory and is purely about identifying patterns in data. Recall that EFA introduces an error matrix $E$ that contains the unique variance in the feature matrix that cannot be explained by the factors. PCA assumes that all variance is common variance. Given a feature matrix $X$ with $p$ observed variables, this means that the linear combination of $k=p$ unobserved variables accounts for all the variance in $X$. This is achieved by doing a simple transformation of $X$ such that all unobserved variables are orthogonal to each other.\n",
    "\n",
    "Let's use a simple example to demonstrate the principle. The following left scatter plot depicts the first two indicators of the V-Dem feature matrix $X$. The point cloud is elongated, and most variance is in the direction of the red vector. Since the data is two-dimensional, the rest of the variance is in the direction of the green vector which is orthogonal to the red one and is second in importance because it explains less variance. The red vector is the first composite variable now called **principal component** (PC), the green vector is the second principal component, and their linear combination explains all of the total variance in $X$. The right scatter plot is the transformation of $X$ and the two principal components are now the unobserved variables and, hence, the principal axes in feature space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "0241b09a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x380 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca_ = PCA(whiten=True).fit(X[:, :2])\n",
    "L_pca_ = pca_.transform(X[:, :2])\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=[8, 3.8])\n",
    "sns.set(font_scale=.75)\n",
    "ax1.scatter(X[:, 0], X[:, 1])\n",
    "ax2.scatter(L_pca_[:, 0], L_pca_[:, 1])\n",
    "ax1.set(xlabel=indicators[0], ylabel=indicators[1])\n",
    "ax2.set(xlabel='PC 1', ylabel='PC 2')\n",
    "ax1.arrow(X[:, 0].mean(), X[:, 1].mean(), pca_.components_[0, 0], pca_.components_[0, 1], width=.1, color='red')\n",
    "ax1.arrow(X[:, 0].mean(), X[:, 1].mean(), pca_.components_[1, 0], pca_.components_[1, 1], width=.1, color='green')\n",
    "ax2.arrow(0, 0, 1, 0, width=.1, color='red')\n",
    "ax2.arrow(0, 0, 0, 1, width=.1, color='green')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c62d462",
   "metadata": {},
   "source": [
    "Mathematically, PCA is a matrix factorization of the form $X^\\mathrm{T}=M+LF+E$ where there is only an error matrix $E$ if $k<p$ (as in EFA). This \"simplification\" has epistemological consequences. PCA is not a generative model (*i.e.*, the is no storyline that the principal components have generated the observed variables) because $M+LF$ is just a data transformation. This means that PCA is not an abductive method (*figure 2*). It is not deduction either. It is not an inference method at all, just a clever massaging of data. Another way to put it: EFA is theory-driven, PCA is data-driven.\n",
    "\n",
    "Now we work with the full standardized feature matrix $Z$. Reducing its dimensionality with PCA is straightforward and follows the usual steps of ML algorithms in sklearn and beyond. First, instantiate the [PCA](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) model. Not setting the `n_components` parameter will result in all $k=p$ components being computed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "46d0c148",
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2f59ffb",
   "metadata": {},
   "source": [
    "Then fit the model to the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "3c9564b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA()"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.fit(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26aa2cb3",
   "metadata": {},
   "source": [
    "The matrix $L$ is the `components_` attribute of the PCA object and has the expected $p\\times k$ shape:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "9746b184",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22, 22)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_pca = pca.components_.T\n",
    "L_pca.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "091f2122",
   "metadata": {},
   "source": [
    "Other than in EFA, the cells in $L$ are not loadings, which means, they do not tell how strongly the principal components are correlated with the observed variables. In PCA, the columns of $L$ are **eigenvectors** and represent the directions of maximum variance in the data. This meaning of $L$ goes hand in hand with the argument that PCA is a data-driven method without a generative storyline.\n",
    "\n",
    "$F$ does not offer an interpretation in that regard either, but it does have practical use. $F$ can be obtained by transforming $Z$ using the model and has the expected $k\\times n$ shape after transposing the matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "84afa8d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(22, 176)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F_pca = pca.fit_transform(Z).T\n",
    "F_pca.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb53b53d",
   "metadata": {},
   "source": [
    "Transform $F$ into a dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "008dcfa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC 1</th>\n",
       "      <th>PC 2</th>\n",
       "      <th>PC 3</th>\n",
       "      <th>PC 4</th>\n",
       "      <th>PC 5</th>\n",
       "      <th>PC 6</th>\n",
       "      <th>PC 7</th>\n",
       "      <th>PC 8</th>\n",
       "      <th>PC 9</th>\n",
       "      <th>PC 10</th>\n",
       "      <th>...</th>\n",
       "      <th>PC 13</th>\n",
       "      <th>PC 14</th>\n",
       "      <th>PC 15</th>\n",
       "      <th>PC 16</th>\n",
       "      <th>PC 17</th>\n",
       "      <th>PC 18</th>\n",
       "      <th>PC 19</th>\n",
       "      <th>PC 20</th>\n",
       "      <th>PC 21</th>\n",
       "      <th>PC 22</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country_name</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Afghanistan</th>\n",
       "      <td>0.410273</td>\n",
       "      <td>-1.220150</td>\n",
       "      <td>0.216012</td>\n",
       "      <td>-1.005674</td>\n",
       "      <td>-1.087451</td>\n",
       "      <td>-0.501470</td>\n",
       "      <td>-0.326244</td>\n",
       "      <td>1.048082</td>\n",
       "      <td>-0.878298</td>\n",
       "      <td>-0.247468</td>\n",
       "      <td>...</td>\n",
       "      <td>0.399939</td>\n",
       "      <td>0.603575</td>\n",
       "      <td>-0.393594</td>\n",
       "      <td>0.125152</td>\n",
       "      <td>0.100734</td>\n",
       "      <td>0.442044</td>\n",
       "      <td>-0.349731</td>\n",
       "      <td>0.350081</td>\n",
       "      <td>-0.295480</td>\n",
       "      <td>-0.035876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Albania</th>\n",
       "      <td>-0.496792</td>\n",
       "      <td>0.807267</td>\n",
       "      <td>-0.773937</td>\n",
       "      <td>0.749736</td>\n",
       "      <td>-0.523094</td>\n",
       "      <td>-0.345472</td>\n",
       "      <td>-0.821771</td>\n",
       "      <td>-1.167237</td>\n",
       "      <td>-0.551321</td>\n",
       "      <td>0.098909</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.117763</td>\n",
       "      <td>0.143141</td>\n",
       "      <td>0.274460</td>\n",
       "      <td>0.164673</td>\n",
       "      <td>-0.685502</td>\n",
       "      <td>-0.012525</td>\n",
       "      <td>-0.245116</td>\n",
       "      <td>0.019039</td>\n",
       "      <td>-0.040034</td>\n",
       "      <td>0.034807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Algeria</th>\n",
       "      <td>2.620266</td>\n",
       "      <td>-0.758739</td>\n",
       "      <td>-0.431759</td>\n",
       "      <td>-1.072191</td>\n",
       "      <td>-0.388081</td>\n",
       "      <td>-0.868858</td>\n",
       "      <td>1.389032</td>\n",
       "      <td>-0.687168</td>\n",
       "      <td>-0.601821</td>\n",
       "      <td>0.574200</td>\n",
       "      <td>...</td>\n",
       "      <td>0.053072</td>\n",
       "      <td>-0.524305</td>\n",
       "      <td>-0.249107</td>\n",
       "      <td>-0.248984</td>\n",
       "      <td>0.235310</td>\n",
       "      <td>-0.139933</td>\n",
       "      <td>-0.017297</td>\n",
       "      <td>0.289441</td>\n",
       "      <td>0.206907</td>\n",
       "      <td>0.142557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Angola</th>\n",
       "      <td>1.611645</td>\n",
       "      <td>-1.665694</td>\n",
       "      <td>0.322675</td>\n",
       "      <td>0.912411</td>\n",
       "      <td>-0.703093</td>\n",
       "      <td>0.027464</td>\n",
       "      <td>0.355936</td>\n",
       "      <td>0.698674</td>\n",
       "      <td>-0.220570</td>\n",
       "      <td>0.725198</td>\n",
       "      <td>...</td>\n",
       "      <td>0.024145</td>\n",
       "      <td>0.008329</td>\n",
       "      <td>0.329757</td>\n",
       "      <td>-0.261629</td>\n",
       "      <td>0.708805</td>\n",
       "      <td>0.566185</td>\n",
       "      <td>-0.317347</td>\n",
       "      <td>-0.187826</td>\n",
       "      <td>-0.367353</td>\n",
       "      <td>0.160977</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Argentina</th>\n",
       "      <td>-1.928967</td>\n",
       "      <td>-2.323520</td>\n",
       "      <td>1.147798</td>\n",
       "      <td>-0.980982</td>\n",
       "      <td>0.868507</td>\n",
       "      <td>0.154465</td>\n",
       "      <td>-0.588733</td>\n",
       "      <td>-0.697299</td>\n",
       "      <td>-0.003527</td>\n",
       "      <td>0.087587</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.313687</td>\n",
       "      <td>0.219699</td>\n",
       "      <td>-0.098831</td>\n",
       "      <td>0.343059</td>\n",
       "      <td>0.003848</td>\n",
       "      <td>0.173963</td>\n",
       "      <td>0.222100</td>\n",
       "      <td>-0.289640</td>\n",
       "      <td>0.101841</td>\n",
       "      <td>0.110686</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vietnam</th>\n",
       "      <td>5.515877</td>\n",
       "      <td>2.221620</td>\n",
       "      <td>-2.471495</td>\n",
       "      <td>0.977933</td>\n",
       "      <td>1.803508</td>\n",
       "      <td>0.301858</td>\n",
       "      <td>-0.120729</td>\n",
       "      <td>0.777468</td>\n",
       "      <td>-1.504868</td>\n",
       "      <td>0.007896</td>\n",
       "      <td>...</td>\n",
       "      <td>0.245660</td>\n",
       "      <td>-0.075810</td>\n",
       "      <td>-0.120469</td>\n",
       "      <td>0.013092</td>\n",
       "      <td>0.059805</td>\n",
       "      <td>-0.128632</td>\n",
       "      <td>-0.061341</td>\n",
       "      <td>-0.657820</td>\n",
       "      <td>0.250562</td>\n",
       "      <td>0.086175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Yemen</th>\n",
       "      <td>4.817424</td>\n",
       "      <td>-0.530845</td>\n",
       "      <td>-1.177146</td>\n",
       "      <td>-1.262562</td>\n",
       "      <td>-0.651954</td>\n",
       "      <td>-0.535780</td>\n",
       "      <td>0.272160</td>\n",
       "      <td>-0.660296</td>\n",
       "      <td>0.618176</td>\n",
       "      <td>0.032477</td>\n",
       "      <td>...</td>\n",
       "      <td>0.130269</td>\n",
       "      <td>0.039734</td>\n",
       "      <td>0.165445</td>\n",
       "      <td>-0.259410</td>\n",
       "      <td>-0.693887</td>\n",
       "      <td>-0.317738</td>\n",
       "      <td>-0.205675</td>\n",
       "      <td>0.260798</td>\n",
       "      <td>-0.352293</td>\n",
       "      <td>0.194880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zambia</th>\n",
       "      <td>1.212845</td>\n",
       "      <td>-2.016916</td>\n",
       "      <td>0.919638</td>\n",
       "      <td>0.975531</td>\n",
       "      <td>-0.870230</td>\n",
       "      <td>-0.475068</td>\n",
       "      <td>0.213276</td>\n",
       "      <td>-0.291786</td>\n",
       "      <td>-1.034632</td>\n",
       "      <td>0.878102</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.428207</td>\n",
       "      <td>-0.328223</td>\n",
       "      <td>0.104596</td>\n",
       "      <td>0.097756</td>\n",
       "      <td>-0.055697</td>\n",
       "      <td>-0.565287</td>\n",
       "      <td>-0.061545</td>\n",
       "      <td>0.087243</td>\n",
       "      <td>-0.086175</td>\n",
       "      <td>-0.015573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zanzibar</th>\n",
       "      <td>3.155606</td>\n",
       "      <td>-1.787655</td>\n",
       "      <td>0.639861</td>\n",
       "      <td>0.908916</td>\n",
       "      <td>-1.227099</td>\n",
       "      <td>-0.064367</td>\n",
       "      <td>-0.034685</td>\n",
       "      <td>0.191947</td>\n",
       "      <td>0.105538</td>\n",
       "      <td>-0.152069</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.413274</td>\n",
       "      <td>0.272077</td>\n",
       "      <td>-0.298838</td>\n",
       "      <td>0.016924</td>\n",
       "      <td>-0.015816</td>\n",
       "      <td>0.354012</td>\n",
       "      <td>-0.270161</td>\n",
       "      <td>-0.029281</td>\n",
       "      <td>-0.169449</td>\n",
       "      <td>0.238811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Zimbabwe</th>\n",
       "      <td>3.373286</td>\n",
       "      <td>-1.862449</td>\n",
       "      <td>1.727464</td>\n",
       "      <td>-1.487104</td>\n",
       "      <td>-2.114484</td>\n",
       "      <td>0.604727</td>\n",
       "      <td>0.093872</td>\n",
       "      <td>-0.011420</td>\n",
       "      <td>0.463223</td>\n",
       "      <td>-0.560872</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.315967</td>\n",
       "      <td>-0.390650</td>\n",
       "      <td>-0.319859</td>\n",
       "      <td>-0.343059</td>\n",
       "      <td>0.562810</td>\n",
       "      <td>-0.187032</td>\n",
       "      <td>0.264111</td>\n",
       "      <td>-0.297430</td>\n",
       "      <td>0.138515</td>\n",
       "      <td>-0.055930</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>176 rows × 22 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  PC 1      PC 2      PC 3      PC 4      PC 5      PC 6  \\\n",
       "country_name                                                               \n",
       "Afghanistan   0.410273 -1.220150  0.216012 -1.005674 -1.087451 -0.501470   \n",
       "Albania      -0.496792  0.807267 -0.773937  0.749736 -0.523094 -0.345472   \n",
       "Algeria       2.620266 -0.758739 -0.431759 -1.072191 -0.388081 -0.868858   \n",
       "Angola        1.611645 -1.665694  0.322675  0.912411 -0.703093  0.027464   \n",
       "Argentina    -1.928967 -2.323520  1.147798 -0.980982  0.868507  0.154465   \n",
       "...                ...       ...       ...       ...       ...       ...   \n",
       "Vietnam       5.515877  2.221620 -2.471495  0.977933  1.803508  0.301858   \n",
       "Yemen         4.817424 -0.530845 -1.177146 -1.262562 -0.651954 -0.535780   \n",
       "Zambia        1.212845 -2.016916  0.919638  0.975531 -0.870230 -0.475068   \n",
       "Zanzibar      3.155606 -1.787655  0.639861  0.908916 -1.227099 -0.064367   \n",
       "Zimbabwe      3.373286 -1.862449  1.727464 -1.487104 -2.114484  0.604727   \n",
       "\n",
       "                  PC 7      PC 8      PC 9     PC 10  ...     PC 13     PC 14  \\\n",
       "country_name                                          ...                       \n",
       "Afghanistan  -0.326244  1.048082 -0.878298 -0.247468  ...  0.399939  0.603575   \n",
       "Albania      -0.821771 -1.167237 -0.551321  0.098909  ... -0.117763  0.143141   \n",
       "Algeria       1.389032 -0.687168 -0.601821  0.574200  ...  0.053072 -0.524305   \n",
       "Angola        0.355936  0.698674 -0.220570  0.725198  ...  0.024145  0.008329   \n",
       "Argentina    -0.588733 -0.697299 -0.003527  0.087587  ... -0.313687  0.219699   \n",
       "...                ...       ...       ...       ...  ...       ...       ...   \n",
       "Vietnam      -0.120729  0.777468 -1.504868  0.007896  ...  0.245660 -0.075810   \n",
       "Yemen         0.272160 -0.660296  0.618176  0.032477  ...  0.130269  0.039734   \n",
       "Zambia        0.213276 -0.291786 -1.034632  0.878102  ... -0.428207 -0.328223   \n",
       "Zanzibar     -0.034685  0.191947  0.105538 -0.152069  ... -0.413274  0.272077   \n",
       "Zimbabwe      0.093872 -0.011420  0.463223 -0.560872  ... -0.315967 -0.390650   \n",
       "\n",
       "                 PC 15     PC 16     PC 17     PC 18     PC 19     PC 20  \\\n",
       "country_name                                                               \n",
       "Afghanistan  -0.393594  0.125152  0.100734  0.442044 -0.349731  0.350081   \n",
       "Albania       0.274460  0.164673 -0.685502 -0.012525 -0.245116  0.019039   \n",
       "Algeria      -0.249107 -0.248984  0.235310 -0.139933 -0.017297  0.289441   \n",
       "Angola        0.329757 -0.261629  0.708805  0.566185 -0.317347 -0.187826   \n",
       "Argentina    -0.098831  0.343059  0.003848  0.173963  0.222100 -0.289640   \n",
       "...                ...       ...       ...       ...       ...       ...   \n",
       "Vietnam      -0.120469  0.013092  0.059805 -0.128632 -0.061341 -0.657820   \n",
       "Yemen         0.165445 -0.259410 -0.693887 -0.317738 -0.205675  0.260798   \n",
       "Zambia        0.104596  0.097756 -0.055697 -0.565287 -0.061545  0.087243   \n",
       "Zanzibar     -0.298838  0.016924 -0.015816  0.354012 -0.270161 -0.029281   \n",
       "Zimbabwe     -0.319859 -0.343059  0.562810 -0.187032  0.264111 -0.297430   \n",
       "\n",
       "                 PC 21     PC 22  \n",
       "country_name                      \n",
       "Afghanistan  -0.295480 -0.035876  \n",
       "Albania      -0.040034  0.034807  \n",
       "Algeria       0.206907  0.142557  \n",
       "Angola       -0.367353  0.160977  \n",
       "Argentina     0.101841  0.110686  \n",
       "...                ...       ...  \n",
       "Vietnam       0.250562  0.086175  \n",
       "Yemen        -0.352293  0.194880  \n",
       "Zambia       -0.086175 -0.015573  \n",
       "Zanzibar     -0.169449  0.238811  \n",
       "Zimbabwe      0.138515 -0.055930  \n",
       "\n",
       "[176 rows x 22 columns]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vdem_pca = pd.DataFrame(data=F_pca.T, index=vdem.index, columns=[f'PC {i+1}' for i in range(Z.shape[1])])\n",
    "vdem_pca"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a84cbe94",
   "metadata": {},
   "source": [
    "In the dataframe above the principal components describe a pattern in the data. This pattern is described the better, the more principal components are used to describe it. The PCs are features engineered from the data and can be used in subsequent analysis.\n",
    "\n",
    "The first PC best captures the pattern, the first two PCs capture it better, ..., but where to stop? How many PCs should be used in downstream analysis? The answer is also in the matrix $F$. Display its covariance matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "2c74c099",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vdem_pca_cov = pd.DataFrame(data=F_pca.T, columns=[i+1 for i in range(Z.shape[1])]).cov(ddof=0)\n",
    "\n",
    "plt.figure(figsize=[4, 3])\n",
    "sns.set(font_scale=.75)\n",
    "h1 = sns.heatmap(data=vdem_pca_cov, cmap='binary', cbar_kws={'label': 'Covariance'}, xticklabels=True, yticklabels=True)\n",
    "h1.set(xlabel='Principal Component', ylabel='Principal Component')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "511fa9e5",
   "metadata": {},
   "source": [
    "The covariance matrix of $F$ is zero off the diagonal because all PCs are orthogonal to each other. All variance is in the diagonal. This is different for EFA where factors still covary to some extent. The take-home message is that EFA maximizes correlation (inside the factors which leaves some amount of covariance and correlation between the factors) while PCA maximizes variance (inside the principle components which removes all covariance and correlation between the principal components).\n",
    "\n",
    "The entries in the diagonal are the amounts of variance explained by the PCs. These are the PCs' **eigenvalues**. These eigenvalues can be used to decide how many PCs are sufficient to describe the pattern in the data. As a rule of thumb, all PCs with an eigenvalue equal to, or larger than, one should be selected. The eigenvalues are also stored as the `explained_variance_` attribute of the PCA object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a6c9d63b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12.55209187,  2.23528175,  1.89412745,  1.03537501,  0.88297198,\n",
       "        0.68835798,  0.50304005,  0.43488701,  0.32731071,  0.24688569,\n",
       "        0.1987746 ,  0.16728466,  0.14334966,  0.13676558,  0.12213386,\n",
       "        0.11376743,  0.11099203,  0.09223689,  0.08800514,  0.0704661 ,\n",
       "        0.05443767,  0.02717117])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvalues = pca.explained_variance_\n",
    "eigenvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eadf3dc",
   "metadata": {},
   "source": [
    "The first four PCs are sufficient to explain the pattern. The percentage of the variance explained by each PC is stored in the `explained_variance_ratio_` attribute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "a946dc17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Variance</th>\n",
       "      <th>Cumulative</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>PC 1</th>\n",
       "      <td>0.567308</td>\n",
       "      <td>0.567308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 2</th>\n",
       "      <td>0.101026</td>\n",
       "      <td>0.668334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 3</th>\n",
       "      <td>0.085608</td>\n",
       "      <td>0.753942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 4</th>\n",
       "      <td>0.046795</td>\n",
       "      <td>0.800737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PC 5</th>\n",
       "      <td>0.039907</td>\n",
       "      <td>0.840644</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Variance  Cumulative\n",
       "PC 1  0.567308    0.567308\n",
       "PC 2  0.101026    0.668334\n",
       "PC 3  0.085608    0.753942\n",
       "PC 4  0.046795    0.800737\n",
       "PC 5  0.039907    0.840644"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(\n",
    "    data={\n",
    "        'Variance': pca.explained_variance_ratio_, \n",
    "        'Cumulative': np.cumsum(pca.explained_variance_ratio_)\n",
    "    }, \n",
    "    index=[f'PC {i+1}' for i in range(Z.shape[1])]\n",
    ").head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82d88cba",
   "metadata": {},
   "source": [
    "As a result, the recommended first four principal components account for 80 percent of the variance in the data. This means, to adequately describe the pattern, we can reduce the dimensionality of the data from 22 to four!\n",
    "\n",
    "Now that we have captured the pattern in PCs, we want to look at it. Three-dimensional plots are possible but are often hard to read. By using the first two PCs, we can already visualize 67 percent of the variance in all 22 variables. We use Seaborn's [`kdeplot()`](https://seaborn.pydata.org/generated/seaborn.kdeplot.html) method which adds a Kernel Density Estimate to the data cloud that depicts nested regions with a high densiry of data points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "bd0047c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FV6hQum/fPiZMmEDnzp3x9fVl3LhxLFmyhKioKIYNG0ZaWtrTKqcQQgghhHiBFSqUxsfH4+XlleexunXrsmDBAoKCghg9ejQajaZYCyiEEEIIIV58hQqlnp6enDhx4oHH69evz/Tp0zl16hQffvihBFMhhBBCCFEohRroNGjQIL788kvS09Pp1q0bderUyd3WrVs3IiMjmTlzJufPny/ucgohhBBCiBdYoUJp//79SUlJ4ddffwXIE0oBhg0bhqWlJdOnTy++EgohhBBCiBdeoUIpwPDhwx85qGnAgAG0b9+egwcPPnHhhBBCCCFE2VDoUAqgUCiwsrJ66HZHR0f69u1b5EIVhl6vJyMjI99tmZmZef4vXnxyz8seuedlj9zzskfu+fPt7tz2j6PQ6/X64j65Wq0mNjYWd3f34j50HgEBAahUqqd6DiGEEEII8WSMjY3x9/d/5D5Fqil9nCtXrjBgwAACAwOfxuHzMDIyolKlSvluy8zMJDg4mPLly2NmZvbUyyJKn9zzskfuedkj97zskXv+fLt582aB9nsqodTV1ZXRo0c/jUM/QKFQYG5u/sh9zMzMHruPeLHIPS975J6XPXLPyx6558+ngjTdQyHnKS0oFxcXxowZ8zQOLYQQQgghXkBFCqWXL19m+/btBAUF5bs9ISGBDRs2PEm5hBBCCCFEGVKo5vu0tDTGjRvH8ePHc0dSdejQgalTp2JtbZ27X2hoKFOmTKFXr17FXV4hhBBCCPECKlRN6Zw5cwgMDGT27Nls2LCBkSNHcuDAAQYNGkR8fPzTKqMQQgghhHjBFaqmdN++fUyYMIHOnTsD4OvrS/PmzRkxYgTDhg1j+fLlWFpaPpWCCiGEEKLoDp6JKvRzWtVzfQolESJ/hQql8fHxeHl55Xmsbt26LFiwgDfffJPRo0fz+++/F2sBhRBCCFE4RQmgBT2OBFXxtBSq+d7T05MTJ0488Hj9+vWZPn06p06d4sMPP0Sj0RRbAYUQQgjxaAfPROX5r6TOJURxKlRN6aBBg/jyyy9JT0+nW7du1KlTJ3dbt27diIyMZObMmZw/f764yymEEEKI+5R2MLz3/FKDKp5UoUJp//79SUlJ4ddffwXIE0oBhg0bhqWlJdOnTy++EgohhBAiV2kH0Ye5Wy4Jp6KoCr2i0/Dhwxk2bBhpaWn5bh8wYADt27fn4MGDT1w4IYQQQuR4VsPo/SSciqIq0uT5CoUCKyurh253dHSkb9++RS6UEEIIIf7zvATSez2PZRalq9A1pUIIIYQoGc97sJNaU1EYRaopFUIIIcTT86KNbn+RrkU8PRJKhRBCiKdsyZIlLFmyJPfn//3vfxw4cCDffV9+dTgA+3ZtfOxxF/88k3Onj+V5LCIshM7NK5KSnFigso1/u88jt9373+Z1yx95rBVL5hIfF5PvtrtBOyEhgT179hSobKJskeZ7IYQQ4hlx8EwUY9/7CoCNa5bStmPPQh/jwJ7NdOjSl4N7t/BSn9eeuEw//rKuwPsOGjr2sfss+/sASZEXad++/ZMUS7yAJJQKIYQQpWTo0KFYWlqyd/9R2nfpw8sDhzP+7T6079ybm9cvs2vr3xibmPL3n79gaGjEex99i6u7J59/OJzsrEzUahW16zXNc8zTJw/yydT5TPtsDC/1eY1zp4/x2/zpGBoaMm7S1yz88Uuys7OoVKUG4yZNJSsrg08nvUl8XAzj3p+Kb/Xajyzz9s2rOXFkD4kJsdSs05jI8DvcuhnIt3P/5Lf5Mxj69vvM/e4TdDotzVp1IioylKuXL5CRnsqkT79ny/o/uHTxH/r27cuyZcs4deoUjo6OLF++nOPHj/PJJ5+g1+uZPXs2TZo0eYqvvnjWFDmURkRE4OTkhJGR0QPb1Go1sbGxuLu7P1HhhBBCiBeVQqEAwKtqU+YO/oDRb3Tn5YE5Tfcv9XmNPTvW075LX8YN78WcXzeQmBDLvO8/p3X7l6hVtwkDXhvJF1NG5DlmVGQodvZO2Ds4YWBgSGxMJABuHl588tU8jh3ezbuTv8HNw4uRQ7oCkJ2Vxfsfz0StVvH9tA+ZNntpnmPe27z/9piPAHAvV57/zfiFvp1rs2LDcbZt/JOLZ/9b8TE9PZVJn87C1a0cWzf8yfDRH3HkwA6OHNhO996DKedVkZMXo0hJSeHgwYOsXr2aRYsWERQUxPTp0/H19eXy5cvF/IqLZ12RQ2m7du1YvXo1NWvWfGDblStXGDBgAIGBgU9UOCGEEOJFYGpqSkpKSu7PGRkZmJiYEBWfSWfvShgZGWNmbvnA85IS4wkPvc3Ekf0AMDIyIjL8Dj5VqgFQuap/nv0P7t1K8O3rTBo7kNjoSPbt2kgV35q4e3gD4Ojkwm/zZ2BqakZSUjwArm7lsLG1ByAzM/2BMtzffH8nJAgvbx8UCgWe3j6YmZljbmGFSq3Ks5+7hzcKhYLoqDCmfz6OzIx0KlTyy90eeucW23fspXXr1qjValq3bs0HH3zAxx9/zJ07d/jggw8K9uKKF0aRQ+no0aNxcXHJd5urqyujR48ucqGEEEKIF4mfnx/Tp0/n7bffRqfTcfr0aVp0fiNn4781pvmxsbXHp3I1vvtpFUmJ8ezfvQknFzeuXw2gQePW3AoKxK9G3dz9jx3ayY+/rMPS0prkpAQmjx9MFd+aKBQ545qX/vI9Y97/Cls7B17r2xy9Xk90VDipqclkpKdiaWVdsAt6RJnvUiqV3LgaQHxcDFO+mMOalb+SmpL071P1uHt407x1Z0aM+wSDzJukp6ezZs0apk2bhpmZGf369aNjx44FK494IRQ5lI4ZM+ah21xcXB65XQghhChLatWqRfny5alfvz5KpZJmbftgbWP32Odt37SSzi/1Z9zwXmRmZPD22I+o36gV+3ZuYMKIviiV/02iExsTibGxCZaWOcHSxtYeM3MLQkNu5u7TpGUHpkwYjLWNHfYOTiTEx2JlbcOMz8eTlBTPxCnfPFCGe5vva9drgqu7V4Gv28OzAneCbzL6zZewd3DC1s4Rdw9vfvz2Y5o074BGo2b8273RaDRs3bQGY2NjOnfujLW1NePHjy/wecSLQaHX6/VPcoCgoCCOHj1KTEwMr732GqGhofj6+mJp+WAzRHELCAgAwN/fP9/tGRkZBAYG4ufnh7m5+VMvjyh9cs/LHrnnZc/zfs9lzs78PWqC/ef9npd1j8trdxW5plSr1fL555+zdu1a9Ho9CoWCLl26MG/ePEJDQ/njjz9wdZUVHIQQQoi7JJA+3MEzUbLyUxlX5MnzFyxYwObNm5k6dSpHjx7lboXrhx9+iE6nY/bs2cVWSCGEEEII8WIrcihdu3Yt48aNo2/fvtja2uY+7uvry7hx4zh69GhxlE8IIYR4IUgt6ePJa1S2FTmUxsXF4efnl+82FxeXPFNfCCGEEGWZhC0hHq/IodTb25uDBw/mu+3UqVN4e3sXuVBCCCHEi0ICaeHI61V2FXmg05AhQ/jss89Qq9W0adMGhUJBSEgIJ0+eZNGiRUyePLk4yymEEEKIfOzbtZE1K3/FwMCA8hWrMvb9rzA2NsmzT1RkKAnxsVS7Z05TIZ41RQ6l/fr1IyEhgYULF7Jy5Ur0ej0TJ07EyMiIYcOGMXDgwOIspxBCCPHcedq1freDrrFjy2pmL1yDiYkpO7b8xdJfZzF89Ed59jt3+hjAcxNKZSR+2VTkUAowYsQIBg0axLlz50hKSsLa2ppatWrlGfgkhBBClEUl0Qx9YM8m+g8eiYmJKQCdu7/C24M7khgfR3RUONnZmXzxza9sWf8HKcmJ1KnflAU/fElqajIA079fyvczJpORnopP5eoMffu9p15mIR6myKE0IiIi998+Pj65/87IyCAjIwMAd3f3JyiaEEII8XwqqX6R8XHRODm75XksKyuTeg1b0K5zb9as/JUzpw7TvfdgAFTZ2XTr9SoNm7Thp1mfce3qRQB6vjyU+o1alkiZhXiYIofStm3bonjM2reBgYFFPbwQQgghHsPB0YWYqHC8ylfKfczSyoaAC6f45+RB4mOjaNupd+42WzsH/lz6E/t2bSQs5BbNWnUGwN1DBieL0lfkUDpt2rQHQmlGRgZnzpzhxIkTTJs27YkLJ4QQQjxvSnL0eOv2PZj/w//wr9OI1cvnkxAfS8MmbdDr9UwY8T4/zfoM9HoUSiV6nY6dW/6iVt0mdHmpP5+8/waQs/CNQlnkyXiEKDZFDqV9+vTJ9/FBgwbxzTffsHnzZlq3bl3UwwshhBDPnZKezqiCT1W69hjIhBF9Qa/HzMKSrKxMrl4+x5lTh7C0ssHOwYl6DVrw7VcTGTdpKrNnTGbrhhWYmJiREB9bouUV4lGeaKDTw7Ru3ZpRo0Y9jUMLIYQQ4h5tOvSgTYceuT/fuHaJylVrPLDfolX7AFj696E8j7fr1Ouplk+Ignoq9fXnz5/H0PCp5F0hhBDimfSsTPqeXyAV4nlQ5OQ4ZcqUBx7T6XRERkZy+vRpXn755ScqmBDPimfli+ZpkbkAhXhyL/rnhBAlocih9OTJkw88plAosLS0ZPjw4bzzzjtPVDAhnhb58sirKK+HBFkh/iOfKUIUjyKH0n379hVnOYQoFicvJ5GVZUvK5SSUypTSLs4Lq6BfwhJexYtOAqkQxUc6fornknwRPB8ed58ktIrnlXwGPV3y2VA2FSqU5teP9GEUCoXMVSqKhXz4v7gktIrnkXwmCfF0FCqU5teP9GEet9qTEPmRD3txr4K8Hxr4WZdASYR4vj+fNBoNc2d+QnjobfR6ePOdSVSvWb/Qxxn/dh9+/GUdc2d9ytj3vsqz7Zsv3sXa1o6R4z977HG2b14NQJeX+uc+lt8xRdlSqFAq/UhFcXueP+TFs6Ew/YhfpJrX0vzdeZFex8d5UT6jzp8+ioOjC+9OnkF6WirvjxnAgiVbi3y8+8OjWq0iNTWJ6KgwdDodyiKsEHX3mGXp/SXyeuI+pXFxcajVavT6nKXKdDodmZmZnD59moEDBz5xAcWL50X5kBfPH3nvFY+SfB1LKqC86O8NSysbTh7bR536zahesz5zfl0PwLpVv3Pk0E7SUpN5Z9ynKBRKzp85xhsj3mfxzzOpXa8pxiYm/PjtR7i6eZKdlQn8V2N61+mTh/CrXofUlGQunD1BnfpN+ejdIeh0Wpq16kRUZChXL18gIz2VSZ9+D8DubWvYtfVvPDzL8/7HM/+rhZ07l40bN5KUlMS3335L27ZtS/4FE6WiyKH06tWrTJw4kdu3b+e7XaFQSCgVuV70D3whxNOR32eHTqeTWTYKybd6bfq9+ja//PQ1EWEhvDHifbr3HowePd/P/4ub1y+zbvUiOnTp+8BzVy2bx/TZyzA0NGL8273zPf6hvVsZOGQ0qSlJ7Ni8mjr1m5KensqkT2fh6laOrRv+ZPjojzhyYAdHDmzHycWdqtVqM2Lsx8yeMZkrl84COX+EXDiqZ8+ePVy4cIG5c+dKKC1DihxKv/32W1JSUvjwww/Zv38/xsbGtGnThkOHDnHo0CGWLVtWnOUUzyEJokII8WwIvnWN+o1b0br9S8TFRjFpzEA6dOmLVqPh60/HoDQwyOdZOS2g6elpODi6AODs6vHAXhqNhjOnDhEXFwV6PbdvXUejUQPg7uGNQqEgOiqM6Z+PIzMjnQqV/ACo6lcTAJ/K1YiKCMXWyjj3eK+99hoG+ZZJvMiKvMzohQsXGD9+PEOHDqVbt25kZGTw6quvsnDhQtq3b8/y5cuLs5ziOXHwTFTuf0IIIZ4N/5w4yMY1SwGws3fCxtaelJQkjh7axcdf/USL1l1Ar8fY2JjkpHgAgm9dB8DS0pqY6AhSU5OJjY584Nhn/zlMu069+W7uSr77aRWt2nXj1LH9ACiVSm5eu0R8XAxTvphDzbqNuRt2g25cAeBa4AV6dmoAQGJiIps2bWL58uX07t07t2ugKBuKXFOqUqmoUKECABUrVuTatWu52/r06cPnn3/+5KUTzw0JoUII8ezq1W8os2dMYcTrnTE1NadXv6E4OLpgYmrKyKHdcHJ2Q61WUcWvJr8v/JaJI/thbmEJwBsjJvHJ+2/g5OyGtY3tA8c+tG8rnbq9kvtzq7bd2PD30tyfPTwrcCf4JqPffAl7Byds7RxxdffixtUAxr/dm0pVqlO3bl0AbGxsMDMzo3HjxpQrV47s7Oyn+8KIZ4pCX8Q/Qzp16sQ777xD7969iY2NpUWLFuzZs4dy5cpx7NgxRo0axfnz54u5uHkFBAQA4O/vn+/2jIwMAgMD8fPzw9zc/KmWpax61sJoTl+zTExNzYo0+lM8f+Selz1yz18sBRnMJt/nz7fH5bW7ilxT2rFjR2bOnImZmRmdO3emYsWKzJ49m7fffptFixbh6elZ1EOL58CzFkafZWFxqhI7VzlH4xI7lxBCPCmZ/kncq8ihdMyYMYSEhLB27Vo6d+7MlClTGDNmDNu2bcPAwIDvv/++OMspnhFlNYw+SbC0MjcqxpI82pOUUwKtEKIkSSAV9ytyKDUwMGDOnDmo1Tkj7Fq0aMGWLVu4dOkS1atXx8vLq9gKKUrfix5GCxLmSjJcFtWTlLEgr4EEVyHEk5IwKh6myKG0WbNmdO3alZ49e1K7dm0APD09pdn+BfOihdFHBa/nIXQ+TQW5/scFVwmtQohHkUAqHqXIofTll19m+/btrFq1Ck9PT3r06EGPHj2khvQF8byH0Yh4DSgefLysB88n9ajXLzVD/cjQKoFViLJNAql4nCKH0kmTJjFp0iROnz7Nli1bWLFiBfPmzaNWrVr06tWLLl26YGNjU5xlFSXkeQykuWFIDzq9AUqFBNCSVtTAKmFViBebhFFRUEUOpXfVr1+f+vXr8+mnn3L06FG2bNnC1KlTmTZtGhcvXiyOMooS8jyF0fwCjpW50b9TxagwNTUrhVKJh3lYYJWwKsSLTQKpKIwnDqWQsyTYoUOH2L59OwcPHkShUNCyZcviOLQoIc9DIL0/vEhN6PNPwqoQLyYJo6IoihxKdTodx48fZ+vWrezZs4eUlBRq167NhAkT6NatmzTdP0ee5UD6rAfRkOiSm4O0uHi7PPuhrlBh9d8uG+VMS6BgJWT75tX8uWQu9g7OZGakMXzMRzRo3LpIxxr/dh9+/GXdE+8DEBkRypJfZjLlfz8WqSzFYeSQrnwz908MDXPeIysWz0Gr1fL6sHcf2Pfm9csYG5vgVb5SSRezzJIwKp7EE42+T0pKwsPDg8GDB9OrVy8Z5PSceVbD6LMURAsSOm2tnq2g/ChJqeoCXdOzGlzzey/odDpSM3QPHdz2vNasvjp0LF1e6k9GehqfvP9GkUPpi6Z5686cOrafpi07Ajlrus/4cXm++x7ev53a9ZpKKC0BEkZFcShyKO3QoQM9e/akXr16xVkeUUKexUB6bxgtySD6qJD2PAXOgijI9TwuuD6LgdVIqXnokpPP+4wAWVmZWFhasW7V7xw5tJO01GTeGfcpCoWSNSt/ISszE4AZPy7ndtBVZk37ABtbe2KiIljy1wEA9Ho93331HtFR4WRnZ/LFN7+SmZnB15+MxtrGjoS4GAAO7NnM33/+gqGhEe999C0WllZ8+dE7aDQa2nfuQ+Pm7bkddJX3R/dHpcpm6szFWNvYlejr0ar9Syxe+B1NW3YkNjoCewdnZs+Ywgeffs+3X75LdFQ4bu5evDtlBju2rOb44V307v8Wp47tJykxDls7Rz6fvpCDe7ew4e8lZGSk8fLA4dSo1ZDvvpqIgYEB5hZWuJcrz4kje3hn/Kc0atq2RK/xeSJhVBSnIofSL7/8sjjLIUrQsxRISzqIPixsvWjh80k87rV43gLr89pv9c8lc9mxeTWhIUGMevdzkpMS+H7+X9y8fpl1qxfRoUtfjI1N+XrWEmZ9PYlrVy7w95+/8NV3i7CwsGJAj4a5x0pOiqdewxa069ybNSt/5cypwwReOsf4D6fhU7kag3o1QafTsWblr8z5dQOJCbHM+/5z2nXqTZ36zXl92Lvs27UBAKVCyXc/reKvFT9z+uQh2nbsWaKvSznPCsTFRqHVaDhycCdVq9Xi1s1Ajh3aiVf5Skz5Yg5/LvmJ0ycP0bl7f2rXa0pUZCiu7p58Pn0hk8YMIC42ioT4WGbOW01GRhr/+/BtatRqSGZmBguWbGXKu6/TsElr2nfuzYa/FksozYeEUfE0PPFAp+TkZDIzM9HpdA9sc3d3f9LDi2L2rATSkgqj+QUoCaBP5mGv38NqWJ/FoAqPft89C7Wrd5vvs7OzmDCiL01bdODrT8egNDDI3cervA8A9o4uqNVqUlOTcXbJ+dz19PbJ3c/cwoqAC6f45+RB4mOjaNupN5HhIfhUroaRkTHlfaqSlBhPeOhtJo7sB4CRkRGNm7fjWuAFJo7sR9MWHQDwrlAZhUKBtY0d2dlZJfJa3K9ug+YEXPiHM6cOMWLsx9y6GUhoyC327drIqeMHUGVnYWFplec5Xt55XytLK2umfTYWSytrdDptnn2sbexwdc/pjqZSP3/9xp8mCaPiaSpyKA0ODmby5MlcuHDhofsEBgYW9fDiKXgWAmlJhNHoZAOUqZrcn0s6hN6MKp0v6vtVci3ZkT8Pe50fVrP6rIZVeLYCq4mJKWZm5hw5uIOfl+3gyIEdHN6/7d+teTvRmpmZEx8XjbmFFeGht3MfP3l0Lza2DkwY8T4/zfoM9Ho8vCpw/WoAVf1qEhoShI2tPT6Vq/HdT6tISoxn/+5NXDx3klp1m/DWyA8Z/eZLNGvdGRT5dNwtYa3ad2fl0nmYW1hibJIz/Zt7OW969H2dni8P4ejBnTg4uXDiyF5An/Ok+8q9atl8fl+5l5vXLzN35if57iP+I2FUlIQih9KvvvqK4OBgxowZg6ura759ucSzo7QD6dMMo/eHHlNDLaamRigNiv89WdDA6WBduoErPkVV4LI+7fCaX1h93mpV71VSgfXPJXPZueUvdDotTZp34NyZo4wc2g0nZzfUD6m9GzJ8Ip9OegtrGztMzcxzH6/iV5Mlv8zizKlDWFrZYOfgxKtDxvLZB29hbm6BuYUVBgYGdH6pP+OG9yIzI4O3x36Ed4UqfPbBWyz//Qdq1W2MUmmQ73lLmpd3JW5eu8Rr94y4b966C998MYE9O9ZhbGzK/775BZ/Kfsyf/T9e6vMaRsYmeY5RxbcmI17vjK2tQ0kX/7kiYVSUJIVer9cX5Ym1atXi66+/pnv37sVdpgILCAgAwN/fP9/tGRkZBAYG4ufnh7m5eb77lAWlGUjv/ZI2N1bw65xPiQy7jR49r745Cd8a9Qt9zJWLZuJUvgGVqzfJfexu8NFpdWRlZWFqavpEofRRga60A2dxik95dNNkSda2JqWq8338cUE1Z8GEzIcOdHoWpGbkf21QvLWrO7b8Rcu23VAqFYx5sye//bm72I79LHke7vnz7lkLo/J9/nx7XF67q8g1pZaWljIX6XPgWQikd2uWzv9zEHsHF96ZOJ2M9FQ+f28g3y3cUqhjhkSrSErX4kTxNcvnF0BfpOD5KI+7zoeF86cRVgtao/o81Kber7CDrYoaVC0trZnwdm+0Oh1D336vSMcQ4lkLpKLsKHIo7dmzJytWrKB58+YopB/OM6m0AunDmuotLG04fWIv/nWbUrV6fYaN+5Llv87gteGTGflqc774fhVR4cHcDrpCZNhtDu5eT8XK1ek5dCpBgac4vGMZNnb2aNRq6tRvTljwNZbN+xiNRkWXvu/QoHlXvnqvJ5ZW9iTGRzL6owW4lfN5oHz3B62yEkCL4mGvTUmF1fyCan7N/k5WDzz0XMgvrD5JUG3eujPNW3culrKJskfCqChtRQ6lZmZmnDlzhg4dOuDv74+pad4vI4VCwbRp0564gI+j1+vJyMjId1vmv/P33f1/WXLyclKpnDciPmeAkYVZTt+ze2dl8Klak5f6DWfpwmlERYTQf8i7hAQFkhAfg0KpJDDgH+7cvkazNt3Zvn4pehTUbNKHbau/x87eEQ8vH0ZNXsD8GSPR6fSsXfotb7//IzZ2Tsz8dDB1G3ciIS6SiV+u4MI/uzl1aAsv9R/LrZi8X/B2Vnnf9vnNHFHcrkc+vcFPVdxKfikjO8sHPzoSUzXcvO86KzoXf+C3Ns/br1Gn1xGdbIAiRZ3nD2RPp2JZRbnEWZg+2G8zPVNLWGze97G7w/N5fcXh7u9sSfzulhWNqts+9Lv0WVCWv89fBHq9vkAVmEXuU9q27aPnbVMoFOzdu7cohy6wgIAAVCqZruN+MRm2JX7OuLT/vkiNlJp89wkLuYG9oyvmFlYkxEcz4+M38fCqRP0m7cnISCUi9BYJcVG89NqXTJ3QDgtLW9JTE6hQuTbmljYYGZuQGBdJXHQoNeq1IujqOWIjg1EaGKLX6xj/2VL+/OUzzC2sadh1LLtWTWXA+F/ZvfJrVFnJAAx5bwGLvx3GW1OWoFAoWTpzBG988GuRrzs4vmC/Ptam2iKf43FSsgo++KS8Q8m2aqRnP1i2crZP/7xZmvxfExebp3cfSppalzeUOlq+ONcmSpazeVJpF0GUAcbGxk+vT+m+ffuK+tRiZWRkRKVK+S8hl5mZSXBwMOXLl8fMzKyES1Y6Tl5OwrSEK84i4jUoFf/VjkL+/ecCL55Cpcqi76AxuLh6YmPrQLWaDdm1aTkfT1/KN1+Mw9rWGSsbRxyc3Onc+21iIkMID7mKnYMLB3asYPL01ezbupyw24E4OnuQnpbEzEXH+WXWeK5cu0FaehpavQGgB60aCyM1Lbu8im/tVqxf/CWx4TepUrMFYUEXMDQ0plL1RpiaPvq98ahaThe70p/ztKBv7dhkDXcSH779adS45vdejEh58I+WJ6lR1el1qLJVGJsYo1TkDHrJ70pSMrTEpuYdFPO0a1O1Gg2/zf2MyPBg0OsZ8Ob7HN23ibfGfvHEx77/GhPS817bi1yTqtPpUKmyMTY2kYFOxcDPz620i/BYZfH7/EVy8+bNAu33xJ9aQUFBHD16lNjYWAYPHkxoaCi+vr5YWlo+6aELRKFQPHYknpmZWZkYrXfwTFSJf0CHxalAUbBpnrr2GcrC76cw6Z1umJqa06XXELwq+rJl7TKS1daYWdhQs15T7G1NqVq9AVvXzMPY2IzsrHR8/Oqh02lZs+xbDAwMcHYvT836bbh+5RSfjOtO5ZqtCbt1Dq06ixoN+hAbfAYLa3usbB3Zu2EB545uJjbiNjUbdaJus+4c2bEMA0MjmnYY9MBrdjX8wSYsF7vnv9/p467hYeHb16N4f3ccbPKWIz5Fxa37mqYL1Tf13wpCpUL5yBkXbK0e3BYam3dUfHEPorp44TgOjq6MfG9GkQf3FZSVRd7ri0jIe23PwipVxU2pVEooLQbP0/djWfk+f9EUdOxRkUOpVqvl888/Z+3atbl9BTp37sy8efO4c+cOK1aswNVVOk2/yO4fXf84RkbGjP1wVp7HQqJVfDJnH7ZWRoz/ZH7u45X86lHJrx4tOvbnzPGd/Pb9RIyMjOk3dDJVqjfgf+8PwNy9Hs7lqjFx+hoAFs8ciV+d1pSvUpetK2bQ+83POXVgDZWqN6ZR21f4bcYw0Otx9axCfEwYhkbGuJSr9EAIfRECaFE87LrzC+nFGVTvH0yV3xyrT2tqqvsHUhX33Kn3D+6bNncdH4/ry9dz1vLByJewtXMkJjqMSf9biI2tI998NhytRoOBgSGvDJlAanIi29YvITMzjZdeHo6ffwPmzpiIQqFAq9UweepvZGdl8sO08WjUKpq07EqvAe8w5vXWWFrZMGzcV2xZ8ztRkaE4uXoy/N3vUCgUL2RAFUI8/4ocShcsWMDmzZuZOnUqrVu3plmzZgB8+OGHjBo1itmzZ/PNN98UW0HFo5X0SPvCBtL73fvl/7ipneo16cTeyjWpXK0By3+djlqVRY1G3alQ3hsjw//++rJ3LoeZuTXlfGqSEBtGRd/6mJlbsfzHCRzfswojY1NSk2O5Gp6BmVNVICdwPa0QGhwW+1SO+zDlyzlx+8oJggNPYOtUDoA6LV8mLiKItfMnMGjSIixtnB57nMTYMA6s+4HeI2YC+YfVpxlUn6WQ+qRTUlX2q03PV95m2c/TiAwP4dU338/dFhcTwfS56zl6YDPHDmzFxMSMDt1fpWW7Xnw2sT8AiQkxfPH9KjIz0vj287fx829AVlYG3y7YzNH9m9m/42+iIkIYPOwD/Pwb8uWkwbTq0IfMjDTmLNnHySM7KeddiQkf/8jaFT9x7cJBfGu3zjO6v7gC6vZNq9i+eRUajYY69ZsyfPRHBX7uudPHOH/mGG+MeP/xOwM7tqxGrVZjZGRE5ar+VK5ao6jFFkI8Q4ocSteuXcu4cePo27cvWu1/Hex9fX0ZN24cM2fOLJYCiscryUD6pGEU/gukjwqjLTr2z/Nzn3GLAfBvPypPaBn71d+5/+75+se5k2pPX3YJpVKJp09NPpqz74EQZWakx79pjycKpAUJne4OxR94Lx7dyOVTOxj47oLcnxPTtEB3omKTSEpJR2OQCsDVazfYs3gCTfp8zNkTB2nZ6WUWTx3AG5+synPMc4fWcGTzApJiwzA1t8bFyxeASye2sHvVDN794Uhu4G3Td8IDr1t0ouqB1/huSA08ux+APevn57lfj7Lu9//R563/AQUIqXpwty7QYQvtcSH1cQH1TvB1ajdoRbM2LxEfF8UX772K8b99mF3dvTEwNMTOwYXwO0HEx0ZSr0nOANJKVWsBOTWtP3w9FgtLG3Ra3b/baqJUKqlQuTpXLp4kKiIkd//ylaoRHXkHZ1dPlEolEaFBHN67kXOnDpCdnYW5hVWe3937p58qakC9fvUi/5w4yA8/r0OpVPLNF+9y/MgemjRvX6TjFVTn7v2l+b4YHDwTJdNBiWdCkUNpXFwcfn5++W5zcXEhJSWlyIUSz6aSrB29697wUZT5RO8NSneD1L6/Z5GaGI2Lp2+Bj/OwAPo0QmdBRIVc4fr5A1Sp3RoAO0sD3B2MUccZEq1OJPDwbnRaDVcOLaZ177EcXvMpSbERXNj3OwmRN5j3UQ8USgP0Og2qrHR06kwMDY0wMDBEo84i9PoZkuMj2fvXTCysHAi9cZazB1ajUCj49fPeKBQK2r0yiQrVclbVelRIVbg0+vfR+RTU3UCanwdCarKKsCRQKlW5S8GXVnP//SH1/KmDqFRZvDx4LLZ2TljZ2pOVmQ482MfK2c2T4KBAPDx9CL55hToNW7N+5Xx+XLyH2zcv8+uPn+ac89ZVAG5dD8DdsyJ6vZ6b1y7g59+QoOsBdO09NDeoubp707nna3TpNYSTR3Zi75g3eDwsoBY2nB7at41uvV7NPe+4D77mxrUAJo7sR1ZWJi1ad2HgkNGMHNIVGzsHVNlZ1GvYgoN7t9Dz5aG4lyvPmVOHuHjuBFbWtnz69XxCbt/ghxlT0Oq0vDxwOO069WL6/8YTHRmGUqmkVfuXWPLLLOrUb4aBoQFLfp6Z51xCiOdPkUOpt7c3Bw8epGnTpg9sO3XqFN7e3k9UMFEwJd1s/6SBtDCrMN0NpIUNo8HxepTKnOfmVxPatt/jV7rJL4QWJICGXDvNoU0LQK/H0MiEDgM+wNGtQgFK/XAXj27ExbNqbu0lQKOOr3N480J8ajTLfSwlIYo9q2eSEB2CjaMHqqx0MtKS2L9uDplpSej1Wuo0f4lj234nOz2O9OR42r78LuePbcexciPSk6JJSYrFqVw1Yu9c4s9Zw1CrMjGztGXT71OwsXcjOPA4Du6VUCoNWPn92xgaGWNuZYeNgztarYbY8BuYmdtg41SOtMQYFEoFGamJGJpaoc5KZ+ZHA0lNCCc7MwW3chXp9/bXhAYFEHjuAGnJ8VjaODD0vfnM/bQfY7/6m0NbFxPwzy4y05Pp8frHVPFv9sDrY2dl+O+Sk8YolcoHalKf5lKp976f86tF7dJ7CAu/n8J7b3fJHdy3fcPSfI/VsfurzPxiFNvXLyUrMx0DAwN8qvrz3ttdsLH5b3329LQUPh7/MoaGRkz630Iy0lP5cfoEsrMyadGuJ47O7rn7Nm7RhTkz3uXQnvUYGZvwwRe/PPRa7v3dLmztaVJiHI5OLrk/m5mZExEWwpff/Y6pqTnjhvdi4JDRxMdFM+e3Dcyf/QX2Ds7MXriW/00ezqtDx+Hk7M7n0xeycuk8Du/fzt6d6/l02nwcHF0ZN7wX5bwqYGZmwQ8/r2Xhj1/lOX9+5xKFI7Wl4llQ5FA6ZMgQPvvsM9RqNW3atEGhUBASEsLJkydZtGgRkydPLs5yinyUdLN9SQXSotaO3lsr6mRjWKhmvftDaFFqQDPSkji4YR5N+nyEiZkVqQkRbF85k1avfFroY93L1rsR2cCdsJz7HZ+YDBjhVrkJu9YswNTSFoDra+bhWaMtPv4qzh9ej9LAACNjUxRKA5w8KpOdmUqVWq05sG4OCqUSM0tbzh9eS3xUMFkp0aSlxKLX64kPu4KpmQWpKQk4elQnKeYWqqx0HL3rYmHjjHv5GmRnpaNRZaLVqOk2dCondy2mWcchXDi8jtTEKKrUbsPx7YuoUrs1ppa22Ni7sfev7+g17CvWLXgXIxMLmg74ltWLvqJCzQ5g5sqY9+az4MtBJCf8977Wo2f0/1YSfvsKh7YtzjeU3u/+90xp9Ee9N6D2GDo9Tw1q87Y9APh6zloA/Os0xb9OUy6dP84boz7Du6IvX0wahL2jK+Mmz85zjujIUHyq+DP+ox9yH7O0suHrH9fk2e/usQ0MDXn3k7mFvpa7v+sFrT11cHQhJjoC7wpVAIiKDCUtNZlZX3+ApaUValU2AG4eXhgZGWNtY4eruxcWlla5c01X9asJgE+Vaty8dpn0tFRcXHP6Rru6eRJy6zo+lXNa5yr71iAtLTX3/I6OLg+cSxSeBFNR2oocSvv160dCQgILFy5k5cqV6PV6Jk6ciJGREcOGDWPgwIHFWU5RikojkD5JGC3oih9PGkTvhsS7bl3Yg1vlJlT0/LfGyLESVStP4/SBv7l2/iDGJmZ0G/wRhsambFr8OaqsTFy9fWnXZwx//jgWhUJJgzavcPPyMeKjQjCzsMHZI2eZVK/KdVAqDTiybRHJ8VG4eFWh+2uf8Mf3I/Gt0wYLawei0mKo2KA1B7YsxszaCbeKdbh6ciOevi0IOr8LnU7Lqb1/YGnrjHfV+lw/fwD3Cv5YWNmTlhyHe4XqhN44R5+R37Fi5tuYmFnR+qWhrP5xNJY2TmSlJZKeHMf1i4dxr9yI9LRUKvg2AKBagy7s//t7YsKvAwoy05IxNjElMSYUXy8/lAaGOLiWZ/ef00lPiQf0VPIpz2F1GtYWhuBSgavhGeiNHbgW9l/XH51Ww/Ifxz9Rv8F730slVYv6uBrU/Dg4ufH9V2PQajXUbdgGV/fSb20qaDht3qozK5bMpV7DligUChb/PJNbN64wb/EW0lJTGD+89797PnxamKAbVwC4duUC3hUqc+nCP0RHheHg6Ep42G08vSuxbdNKAG7dvIqzq0fuc3+bP4M5v22471yiKCSYitL0RPOUjhgxgkGDBnHu3DmSkpKwtramVq1a2NraFlPxxMOUVC1pfmtwF1RhAmlRakfz6y9akGUH7w2jBQ2i9wdQAA/HvKPN72iS8aiQM6r//NFNXDm9h5TEaBxdyzP43XlEBF/h5N6VWFjbU61+B6o36MiOld8RGRJIekoCQz/8nYSYUBQoGDThJ47tWIpO998gwsS4cHoPm8q1cwc4vusPDI2MadZlKNtWfEPb3qOxdXAjIeYO7p4VuXRqJ9qsFMwsrGjSqhvXTm3Axt6V6xeOkBIXhoGRGUpDYwJP78bc2hFNdhoRty6hVmWx56+cabsUCnDzroZWo8bUwhqFJoWqddtyM+Awdy7txbdJf25f3E25mkkc/PNLWg+ajkPgbhJjQ2nQYQhn9v+JvWt5kuLCsXUqR1RIIO9M387an8aSkhhDYmwYRsY5g36sLYxwsTPG1CQnfGZk67hwI5JTR3by4bdrCTi1kwsndhToXj3KsxRQ7w+nbh7lHzuHqYubZ55a0pKSX9P+veG0sq8/teo2YcxbPdDrdNRr1BJXN09GDumKtY0dZubmaDT5r/R2V3xcNBNG9MXO3olXh47Fzd2Lrz4ahVqjov/gkfjVqMOeHWsZN7wXZuYWeUJpo2btHjiXoeGLu3jA0ybBVJSWIi8zGhER8dBtSqUSc3NzrK2f0pDYfwUEBAA8dNmqjIwMAgMD8fPze+Em2y2JUPokA5uKEkiLUjt6f59RnU5HZmYmZmZmeWrXChtECxJCAZbNHEH/0bMwMbPk4oltBF06jl+9dvjWaQ3AzHfboTQwRKk0BPR4lK9OxJ1rtO3/Cdb27ty8sBcjYzNuXthDuwGfcefqCVTZ6VSq1Y4Lh1ahNMj5YnX2rIZepyXq1knSUxJIjo9k5Jd/k5YSz4ofxtC04+t4VanDtj9ypszyq9uOBm1f4c8fx/Hq+DmoVVn8MXs0Lbq9xam9q3h1/Bzu3DjHnRvnqNBwAEHnd3H5yF9kpiVi51IBcwsLFAoFWekppCbH4lWlPtGhV1FlZeDiWYXo0OvYOZUjJuwG1vauaLVqMDAlKz0JVWYqVvYeuHhUoOuQL1n0VT8MjUzIzkjFxMwSrVZDamIUDq4V6TvqB8KCzgM501et//l9WveZwIaf32fIR3/y58w3SUlJwtLWFa1GRdcRCx+YeurujAumpmZFrlGNT3mCyfuLKCn1v8nti3vS/pKQmpFT/tKY87Q47rl4vGcpmL7I3+dlwePy2l1FDqW+vr6PnaHfxsaG119/nVGjRhXlFI9VVkNpWQ6kDwujd90fSgsaRnVaDet++x+pCRHo0VOr9WvUrlP/seX5a957VK7VgjrNe5GRmsTCLwbQZeg3mFs5kJmWyM5lH2Fibk2Xod8QFxnEia0/odfradVlMNXqtmbnmp+oUb8dh3csZ8A704gMvcHlM3tp3+sdfp0xnGp12wDg6ePPno2/027A56izM9i76ku6vTXroeXy9i732LI/Snhc3umdvMr99+UUcu00Zpa2OHtUYtWPo+n06hTsnB48X0R83qBXvtzj50h9nOjEvMf09TAv9oBS0gFVwmnhSSgtOc9KMH1Rv8/LioKG0iK3b8yYMYPPPvuMhg0b0r17dxwdHYmPj2fnzp0cOHCAUaNGkZ6ezoIFC7C1teXVV18t6qlEKXneAum97kTEcbf/2uNqRu+ERREZdBYzK3t6D/mA7Mx0Vs9/77GhNCQkjGrNBnLp2BrsPeuTkRqPpY0zO5dNQa/TYmZuRYNWvTi2awXr5r6FTqulc/8JHNmxnFMH1nFkx3Iy0pKJjw4lIz2Zn/43CGtbJ0zNLfnho5fR6jRcPLmTrIw0EuMi8Papxto5b2JmYU12VjppEedw86rCsd0rad97JNtXzyYrM51slYYWvSdhaPTgdRc0rD7QNeGemuO0bCX7136BTqelYvWm+QZSyPu6R8Sr8vyBUNCAeu5QzgCeOi1fBuDKvvmU92tMhWqN80w7pdPp8fV46GEK5WFN/E+7ef9RTfvPsrufE0WdTko826QpX5SkIofSrVu30q1bN6ZPn57n8Z49e/L5559z6dIlFi5ciLW1NStXrpRQWkxKspa0sJ5WIC1MGAWIjk9DqVQ8MozeG7I8HM1RpjsQePQMYbca4VG+OoPGz2XV3HcxMbMgOSGKDv3eJUtrysntC1Bl5cwz2aL3JILPb0GVFsc/234kMz0ZjSqNNi8No1qdVqxcMJlGbfryz8F12DuVIz76DlfPH0ShVOLfsD23r53F08efin4NOHt0M/Vb9ECVnc2lf3bh36gjgWcP4FOtIQmx4ZiYWVCxaj2uXTjCKyO+xsTUnO2rf8DNK2e0c2pSLP4NO1Khal32b/oNQ1UU5Tyq5bnmsJg0QkLC8jxWlJAajjttX/+uQM+7qzgC6v3u7UccnajiemTOe6o4VpY6ue8v9qyfj7VtTtmq1WtHlE9jbgYconbzvlw68CuD3/nyic9zrxchnD7JXKfi2SXBVJSUIofSU6dOMX9+/pNhd+zYkdGjc+aJq1evHj///HNRTyNKWFGb7Z+FQJoTdPTYm+swNcu/Vuv+MHqXm7cfDdq8wsGNP5MUF06zrm+SlhJH3fbD0WrVHNi8iJot+tOwRdc8wQ/AvbwfITcvYGZuTbOOgzi0bQkRIYFoNWriou9g7+TBq6O/4drFo+xZvxAjE1My01Nwdq9AWkoCjm7lyc5MJ+TGBWIjg0lLSSDk+jnUqmyiw4NIjItAnZ2Ji3tFAOydPHLXPr/LzNKGkwfWcvXCYRJjw/Gp3oj7lXO2fOCx+0MqPD6oPqoWFfI29efnSQPqhl/eZ+jHq7BzKsfiqQMY8tGfbPphANZ2TiTHR9Dm9e8xs3Rg5+/jMDXUoTQwpFO/8aSnJnJk+1KyMtNo3X0YFfzqs+ibtzE0NsHNswrNOg3G06cmS2aNoqJfQ9r3HkWjtq/kOXd1/9rEp6ho3OsjbkZlPZXa0+c5nN4/Wl+C6YtDgqkoCUXujGNra8vVq1fz3Xb16lUsLXO+ADMyMjAzMyvqacQ9SmrEfVGnfyr9QAqudg8vw93w5OFo/kCwiosMpoJvAwa9+xPtXv2SE3tWYWBkgYm5NVV8vDFARQUvN65eOMya3/5HwD+72bN+AcE3zuPo6k1mWjKW1vacP74NOyd3mnV8FbUqm5Dr50hPTeT2zaskJSTkhEm1mqSEeIJvBBB55yZXzh0lOTGGmk17Y2RijlJpQOteYzExt6JSjZZYWjviXrE2cbHRaLUagoOucfvmf797iXGR/DFnImG3LmNpZYe5pS0UsKt4OWdLdCm3sDfXknTnJIkxwYSEhOX+VxB3X8+7r+mdsKjc/x7H3cE49z/IuY/3T9V1ZPMCFk8dwOKpAzh/eE1+hyEtKYp+Y+fRrNsIoq/uITxgE35N+9Fx5DIyVXruxGWRmhTDqM//pHP/CWxdmbMMspGJGe9O30D9Vr25eHIHalUWGrUKE9O874/tq77nxqXjrJj7LmRF8+d3g4Cc9/P986AWF1sro9zfqftXjnrWWZkbYWVuRFic6olm8BDPlpJerEWUPUWuKX3ppZeYM2cOhoaGdO7cGXt7exISEti1axc//fQTAwYMIDk5maVLl1KrVq3iLLN4Sp602f5xnnYgdXcwzndKqHvD6MPcvnqKuNg4qjXqgYm5DdbWtqQmx+FoBalJcZiYWXL59D5cPHy4FncEjwrVadCyF+eObeXahcOosjOpXKMxNy6f5vrFQ/w87S3MLGywdixPVmYG+9bPwUAJ7uUqkpaWRFLMLbIz0snMSCX4yhEqVKrO4c3z0GpUGBoZ4ulqh42tHdfO7kKdncGVf7bjVcEXvU5DORcbwqKTycrM4NK5oyQlRNGo3SBOH/iL88d3YGphTUZa0mNft7sun9lH0w4DqVG/XZ7H72/uL0hTf55m/riM3Nf+cbWnkLcG9e49jUtIpflLI3P7lO5f+wPnD6/hyqltnD2wmrSkWJZOexWNKpvAf3ZgaevMntXfUrl2Gxp3bo2jnTHuXpW58c8W3Cs3YN6MMZgqs0Gf8z5xdPECoKJfI3b+PYezRzfnlmHP+vmc2v83AHZO5ahEkzzlvfs+ftr9Tu8Pps9LrSnkbdKXWtMXg9SYiqepyKF0woQJxMfHM2PGDGbMmJH7uFKppG/fvrz77rvs3LmTK1eusHRp/svqiYJ7VmtJCzs5fnEG0nvD6MMUJJCGhITh4N2Q4BuL2L/qM4yMTfGsWIOLJ3eybeX3ZKSn0KHPSPR6PeuXTMXQ0BhbIyMy0pJIiI3ErXw1dLcucXTXKmo17cGtK8dy1pFXKvD2cKLf6xPZv2MlOq2GqjUaUMmvLptWzSM7KwMHJze69BlOclIcx/ZvwMDAkHbdBgPwytAPHlrmci42DBr2Icf2b6BTzyF4VfCjpr8/alU2m9cu5uyxHQRdu4CltQM3Lx1FaWBA94ETMbe0Yeean1BnZ2FqYUWb7m9x+9pZVNmZOLp64+njj1JpwLHdf6JWZVO5RmMatu6b+zrdVdiAem+taWEC6g1ygmlwWGxu076hoTHZmek07PA6/+xZzpCP/mTx1P6c3vcnrftMAHJCZHToVRzdKpIQE0KzbiPY8ccX9Jm0kSvH/uZ6wAkWffs2yfFRhAcHsmnZVKJCr7Nj9WzenbGRjUunolGrcPaohEadhb2T50PLWpLh9Hlu0pe+pi+Ou99HEk5FcStyKDU0NGT69OmMHDmSkydPkpiYiIuLC3Xr1sXTM+cDvGXLlhw+fBhjY/kQetY9SRNbQZvtSzKQHtz6B8GXD/D6hB8ACDixHQD/xl1y9wkJCePO1RN4+TbmyqEltOs2CBv7nNWY7gQFcPn0Xvq8+Vme49Zp2hW9woSwoPPcuhFAdlY6ty4dwczckkHDPyTo2gUcnN1p3q4PO9Yv4mbgWXZvXoqdgytV/Oqxbd2veHhVJir8NuW8q5AQG0nQtQtcv/wPBoZGaNQq9mxZzusjv2D9ih8xNbMgPjaCNl1eRa/TEhZyHf96Ldm7ZTlqVTYpSfH41viv/6iRsQmW5qb4+rfCs0JV/lr8LYPfnsLN26HsWreQqrXb4F21MfbOnlw8tg6FQkGFqnVp2mEgl07vBSApPpKer03ByNiUlQsm54bSe/ukFjWgFrb21M7SAMi5z8FhsSSlpOPl35Hzh/7GytYZG4ecdd4z05JITYrm0vFNAEQGX+HQxp84uO5HFEoDjmxZiJt3DZZMbohGq0GrysbQwgVdQhzrF39BalIczToOZu+GBWxa9jW3r57B3NKW4OtnSUuOe6BvaX5KIpze39/0eQmmILWmLyKpNRXF7YmXvPDy8sLLyyvfbTY2Nk96eFGCilpL+jiF7XP3pIE0Ji4JgMTIm9wIOEJl/+YP7HM3VN25so+mLdsT8JBz7V47n5jIWygNTGjY7lWCbwSQGBsGeg2Nm3fEw82Vf47uwMjYhA1/ziUpPprU1ESO7l1PemoSR/auQ63KRqfVEnjpJHqdDp1Wi1ajoWqNRhgbmxAfG0Fs1B3sHF0xNjEjPTaJzIw0UpPj6dp3OAlxkVw5f4yqNRoCkJIUR8OW3XF1L8+y+Z8RE3UHeye3f7fFo8rOxMbOkYz0NKxtHVEqDajiU56LR9SU93Tn+IGN3LpynMS4MEJuXyctNZnrF49y5ewBPH38sbS25+/fPsfQyBitRp3v63I3oObXxL91+TSad30DGwe3B55X2NrTms165v7b3cEY9wFjiIhXYW7jQsDBpRgam7J02qtUrtOeiKBzvPTWNBZPHYBPzRY0aD+Yw5vmoVZlYWRsSuU6bbB39cazcn02/joJM1MjbJy8KN+gH0Fnt3Nwy+///mGQjYmpOZVqNKZj37H8+HFfkhNjHvIOedD94fRp15o+b8EUpNb0RSLBVBSnQoXSKVOmMGrUKDw9PZkyZcoj91UoFEybNu2JCidyPO2m+6ddSwoFb7Z/0kAaFp4THmwtjWjYbgBHty2mol9OTWJachyr571HWmoKXlUb41fNn9iI2+zf/DsAh7YvIyUxBr86rXB09cbIxIyrF49i6+CGc7kKhF87TGz4DRQKBU5uXlw6exidTktKYiwKpQFN2/TEwdmDcyd2Ex8bgVarwdTUnEwjY9JSEzExzRnE1HvwBOZNH8OZYznLZppZWGFoZIKRkQl6nQ5DI2NSkxMwt7DGxNQcC0sbtNr/lhs1t7Dh+IGNGBgYotPpuHbpFFVrNAAUnDi4mbCQ6ygUCszMLUlOjEWn05KWkoShkTHnT+2lRp3muHtVZvWi6bg6WBGIgvi4GNKS47l85hDx0bfwb9gRjTqb88e2P/J+3Ft7ejegpqVnPOIZ/ylq7am7gzFxlgb4txpC5frdAT1Odhb8Nfut3H28qtRn3YJ3iQ2/Qa0WfVFlpZMYfQf3CjkTNxubWpCVnoK5uTl3zm+hnG9LQgOPYmhsknMvjE1JT0lk2eyxpKck0LD1y1Su0YTje1ZiYGDI2K/+fmw5777nn3at6fPWnA9Sa/qikWAqikuhQunJkycZMmRI7r8f5XGrPYlnS2nXkt67jv3jPCyQ3g02DlZKEgFLawd867Thn/1/kRgTxuXTu2nzykfUrl2XDUunYduiA07uFWjz0ltsXfU9do5udBswkZULJtOgdR+S4qOo2aQ7afEhGOgywcAIvV6HtY0T4cHXiTUxQ6GA6nVaEBEaxJljuzA2MQMU2Du6ER0ZQmZmGiiU6PWQlZkzv6mhoREKpRKNVo1Oq8PFoyKGRsakpyah0+koV74q1rYOOYvP5+P+YOniXoG/Fn+LXq/Hq6IfFavkDCxUKpXUqt+av5d8h16vp2OPoSQnxbFv25+YmltgaGhMRnoK5Sv4cOnsYdw8fQi5foZyFWtyZMcfKJQGaFSZrJz/IVVrtaBus+789cunmJiak5IYQ7teI3Byq5A7aT9A7zc+ASAsPIqkNO1Tb9p3dzAmIj6b6Pg0srL/q9V1cC3P8C/Ws3jqAJp2Hc6BdT9g61SOiNsBeFaujyorHXuX8mSlJ+NVozkXDy3FwECJmaUDCUkZGNt4civwFB7lq2FobAJ6PWcObyAxNgxrO5fHlu1eDtbGUmuaDwmmT9/2zasB6PJS/6d+LgmmojgUKpTu27cv33+Lsqk4a0mh4M32+bkbZtwcTMnK+i8I12/zCn98PxIjczt0Oi1Xj//N1RNryM5MIyXpv+NpVNnER4eiNDBArVZzJygQ0HP93F5s7Z1JSYrHq4Ifdg6uDHhrCptXz6ecd1US4iOJjbqDOjsTaztHsjPTMTQ05OUh77NswefYO7oRfCMAn2q1sHVw4fypnH6bRkYmmJpaYGhkjImpGY1adGXPluVkZ2VgamaOqZnFQ6/Vq2K1PMHS26cajVt1z3dfv1pN8Kv136hxeyc3KlTOu8ybW7mKGJvkhKX0tBQUgGe7XuzfvprmXd/CwcWbC0fX4Ve7JWkpCXQfNAmtWsW+Tb/SovNreSbtjw4LwsLUEDcHc1I1/3WTeBrh9NiOxVw8tgk9oNPqMDGzZsOS6XnCaZ7Xon4n1i2cyM0LB/GsXI/e78xi6bRBRIdexdjEgpfHfIqDmw8H1v1A5cavsnf5ZRJiI9BpNaQmx1KvRS/qtej12OvIjwTT/Elz/otFgql4Uk/cpzQoKIijR48SGxvL4MGDCQ0NxdfXN3eeUlF2FWctaUFG2ns4mj8wJZShkTHNugxl45IvUSoUdOgzCgcXTzYsm5YTosJvEXLjPIlxEaSlJLB19VzSUxLwcHPhprklNraOxETewd7ZnZjoUFKS45n/zTgUCgXV6zTn7MndNGndg+SkOM4e2429sxuGRjk1kAA+VWthampORloK9Zp25PSxHaxZ+h2mZuY0a9ub+NgIjI1NsbKxp/eg8XnK/vLr7wFgbetIx55DAShXvirAA8GyuNRp1I6/Fn9D5Wr10eu13Di3i0tqLersTK4G/IONnTPmFtYAqLIzHjlpf379TosrnNZs1jO3v6lOpyMrMwtTM1OUSmXuhPzlyznxxierAOg9Imde0n5j5j5wvvsfu7uvk9c2UuLDOL3tJ+o27/nA8wqrJJrzn8dgClJrWlLWrfqdI4d2kpaazDvjPqVW3SZ8/ekY4uOicHJxZ8r/5rB6+QKOH9mNkZExn01fiK2tQ6HOIcFUPIkiT56v1Wr55JNP6N69O9OmTeO3334jLi6OefPm0bNnT6KiZJLd4lAS/UmL0nRfErWk5w6tYe6kdiyeOoDNc18nK+r0g2W59g+b/8h/ycvLp3cDYGxTAVt7Fyr41mf/5t/4Y+77ZKalMGDkdCr7N2HP+p+xc3THwcUbv7rt0WmzqeRXFzNzy5xVkxTQqlN/zMwsad6uD516vYmNrROOzu54VfDjwj8HiI4IwcXdm25936ZC5ZpYWNrQoFlnAJq27UV2dgabV8/H1t6Zl4dMomLV2hzZu47bNwLwrlT9oa/Lzg2LWbNsFgu+ncCy+Z8x9+tR6HT/9S9dNv9zrlw4luc5Vy4c48/fvgbg+uV/8jweGxX60HNBTteCRi27c/b4LhQKBW27DmLQsA+pWa855lZ2xMeEc+3yuTxzt3pWrEGXV8Y/dNL+cs6WuQG1KJPyw4OrRj3K3cn485uIvzBc7IypXKkibV+bUajuJY9zfzgtTs/rZPvwYK2pKH569Hw//y8++PR79uxYz+H926ngU5Uff1lP+QpVOLx/G2dOHearmYsYPvoj0lJTinQemWRfFFWRa0oXLFjA5s2bmTp1Kq1bt6ZZs2YAfPjhh4waNYrZs2fzzTffFFtBxYvpcV/2zV8aiV3FVqiz0zmy8kMqVm/KxaMbObZjMZbWDqQkJ2JqYYNhVjhQOfd5NRp1oWaTbiz6ZgTtBnxKg1a9cx7/d4L404c2sG3V9ygUSty9q+JZpSGBZ3bj6WpLxSq12LRqHlbW9rzUfxRrls3C1b08t6xsCQu+hkqVTcWqtbC2daRDjyEPlPlurWa1Wk1zH3vljQ/z7NOq4+OnGALo1OsNANYsm0W1Wk04dXgrEaFBlPOuQnJiLGp19gPPqVarKVcuHAfg4plDVKne4IHyPIpP1dpcPH0Ad8/KHNz1F9lZGbi4e1O3cXtOmhrzz/6VZGemU7dFH9zKebNt1WwCTu3KqSF+xKT999ecFqTWFHggmBakvynwb39TVZ45Tu93tyb1UVzsjIlOVHE1PANfj4fPd1sYT7M5/0WpMQVpzi9uWo2Grz8dg9IgZ6q1iLBgqlbL6YNexa8mN64G8ObID5g59X30Oj1j3vuyyOeSGlNRFEUOpWvXrmXcuHH07ds3z8hgX19fxo0bx8yZM4ulgOL5VJhaoIKs2uRgqcPEzJLA07s4svVXlEoDurz2KUE3r5EZE4iNvSur5r7773rwCpp1GcK+Db8AcGTdNGrUb0dmWjLbV/9AZf+mnNj7F84ePigNDIiLvEPwjYs4u+RMYVS+Ug0O7V6TW9MJEBsVSnpaMh17vsG5k3tzB/bcFRZ8jbCQ6zRu9VKBr/vKhWMc3PkXI96fhVKZ8yWxbP7n1G/W6aEBUqPREHwjgHLeVVi/4kc8vKpw+thODu9eg1aroUq1+lha25GdlcHWv38mPOQ6v3z/PpV86xB88zIGBoZUqV6PiNAgNGoVPr51qN/0wfP1HjQh3/MbGZvy8uvv5lxzdDKZWRrefH9enn18a7d85HXfW2sKBWvSh5xwerdJvyDB9O4fL8bmDmg1KspVbUrPIZPz7HPuUM6ypXdXjIoMuUJUyJXcn+9ysNRz+theoP1TD6Y/fzeO+JgI7ty6jFfF6jg4u9Oy4wD8HvFHRUjQJe4EXc79uUXH/oUKpisXzaRGnab41ynYHy5P090aU2nOL16pKUkcPbSLH39Zx5EDOzi8fxtuHl5cu3KBhk3acO3KBdw8vDh+aBdTZy7m2OHd7Nq2hiHDJxb5nBJMRWEVOZTGxcXh5+eX7zYXFxdSUopW7S+eL4d3rWbLX/OwsXNGpcqiXbfXaNExZ6RnQZvuH+XI5gUYmq4kLeEO7ftN5PiOxVhYO+BXrwOHNs7Ho3o77tw4R3TYTSLvXMXI2JSM1EQuHt8CgImxAXq9noB/dhMVegO9TkforctoNGpiI2+TlZGGqbk1rTv1Y+/W5Syd9ymOLuXIzkzHp2rt3HLY2juTGB/FX4u/wdzCGrN/+1U+KTNzi8fWfN7L2NiEuJicMKdSZeHo4kFE6E0GvDWFa5dPc/ncEfxqNgYgMyMVCysb+g6eyOXzR/Gr2RgX9/Ic3buOV974ECNjY/5e8h31m3YqUtnLueTMQ3z75lUAKlTyLdzznS2feq1p085vULNZT/R6PYumv8mNoBAq+3g/dH8372q4eVd74PHUpFgir+6jcauuT6XG9F4jJs0BYNqkl/nouzWsWz7rscfx9qmBt08NDu9anfvYs1Rjunf7atau+Ak7e2e0Wg0mpuZ8Mn0JRsYmD31OQfuZLv55JrXrNaVO/dIP1M+ipb/OYv1fi9DrdFhYWjNyaDecnN1Qq1W0aNOFrz8dy9hhPXFxK8erQ8eyJu5Xhg/qgKWVDe9OnvH4EzyGBFNRGEUOpd7e3hw8eJCmTR/8IDh16hTe3g//4BfPr/z6qnV/ZTQtOvZHp9Xy41fD8KvdHChc5/iHsfOogUv52jRr242fP+1NWnIcep2O8KCLKBQKrl84hFKpxMDAEFNzKzq+8i7Hd63g+oVD2LtWAkCn01K3aTfc+k9gyx/f4V25NlfOHaByjSbcCbpEVloCSQkx6HQ6Xh/1BUHXLhAecoPkxFjOHN+VO+Co/5uTH1VU0tNS2LTqJ9SqbOJiIhjx/iw2rfoJU3NL4qPDadiyGxWr1GLPluWkJieQkhyHh3dVju3bgJ2DC2Eh1zA1syA1OZG1y2ah1Wqp5FuHuk06EBN5B1V2JilJ8Ti6lCP8zk2yszK4eOYQWZlp7NmynIz0VFKTE7h07ggGhobUadSe/dv/ZOvaX7C1cyYuJoyLZw6iUatY9fs0ypWv+m/NcsHdfS3uVc7FhrDoZG7fvPpEwRSKVmtazt35sfvrtBqMDRWc2/0z+5YHodRn02PYf92Lrpzazs2LB/Fv2ovgwBNUa9iZzYs+Rq/T0rz7SMJvXeTmxYMEBRzm0tmjbL4TgIEugwGjviM06CKB5w6QlhyPpY0DQ9+bX6jXwMHa+LHN+DvW/8raZd9RpXpDXnlzCrs2LuLs8Z1kpKcw4K2PUSiUBF48jpNLzusXEXqTPxZ8hlqVhYunHy+/+T8WfTsEK2tb7ty+zjsTp1HZtzbffDac7KwsNBoVNZ5yLWnfQWNo1yXnD9aVi2Zy6fxx6jRs/cjnSHP+k+nyUv/HTgf1+fSFeX7uP/gd+g9+p1jLIcFUFFSRQ+mQIUP47LPPUKvVtGnTBoVCQUhICCdPnmTRokVMnvzoL3BR+ooyyAkePhWU0sCAxq16EnjhKHt3rgNtFnWa9aBl16Es+HIQ5pa2RIZep9/bX6PTatm8ej4adTZunj7odVruXD9Nn1E/YGhkwo7lX5AUG4ZGB7416rHyh1FkZaRiZGKGoaExrt7ViAkPomO/sexb9xNmlrYolQbYOXsRF3kbPQoyUhNIzkoFBdy+dpbje/8iKT6SrKx0MtNTiLpznaS4cCwsrbl26SRajQa9Xs/x/RvRajUc2v03zdv1JSz4GudO7kWtzvli7DlwDOv/+IE+r72LQqFg48qfqN+0EylJcTRp0xNnV0/mzxjH30tnEh8TTutOA2jTeSCbVs/DrZwPXhV8qVqjIdvX/YZSoSAjPQXfmo3Q6bSEBl/jzLGduHv5oAeO7FvHjatnUauzqVm/NScPbkav07NzwyLMza2oVb8VR/aspUad5hw/sAkjYxN8/Rtx4Z/9hIdcx9TMgirV6vHPkR1UrFoLR2cP/jm6HWMTMxq36sGapY/uZpOSFMeJg1ty+8lCTv9WAAWg1Wpo1ak/5dzL5wbTmNBL1KjfDgsru3yPeen0XvZv+o3Rn//Bga2LaNtjOItmjqJS3W5AqzzB9M8fx/Hq+Dn5HuduMA0Lj8HRPm/NdVpyHDcCDhMbfpOLxzejUCip3aIPquwMGnZ/lzuXD3L1zC6s7d2IuHWB1MQY+o2bx51rOYPpbl8+Tr02A6nRuDs3LxykXtuBpCZFU96vMQnRITTuMZHbF/cQcGontg5u2Dt7MvS9+Sz4chDJCVHY2Bf+C/hRwdS/biva9xjK52O7AlNAr2fyjNXcuXWZ3RsX07Rtnzz7R0fcZujY6Ti5evHF+JzpwiLCQ5n9v4WEhdxg7/bVJCXEUb1WE3oPHMm3n48odHmfRHxcFF9++Brr94fy9/I5aDVqBrzxHlMnD2HoyE/4dc5nqLKzqFC5Om+Pn8rn7w3E1NyG8JDrTPpkBlV8a/K/ycNRq1RoNGpq12vKxfMnWfLzTLKyMmnRugsDh4wu0WsSj3Z38JOEU/EoRQ6l/fr1IyEhgYULF7Jy5Ur0ej0TJ07EyMiIYcOGMXDgwOIsp3hOWFrb8cMXbzL4g+XUrtuY32YMo16LniTEhjPkvflEh93k5L6/qNeiF0Ym5rwxZTHzJ3dm4MRfiQ69ys0LB3D2rEq3N6YSHHiSzb9P4diOxaTER9Ks23BCb5zlduAJbl48hGvFOuxbP4/0tCQUSgPio4JZ9PXraLU581RmpsblLBupUnHl7H7sncuBXk9qUixajZqE+AjMLe1IS4mjbuMO/HNsB7//OAVVdib2jq607/46G/6cQ5c+w3LWqi9flZCgy1w+dxR3r8qsWTYLVXYWWo2a4KDLWFrbsWHFjygNDNDpdXTqOZR1K35k37YVXLl4DK1Wy/lTe7kZeJaDO1eDQoGhgRGZGWno9Tn9NY2MTcjKTKf7K6MwNDTi9x8n07LDy2z4cy5KpRJnN2/CQ2+QmZFGOe8qAFhY2XJ073oyMlIxt7DKHZ2fmZFGWkoi507uxcbeiTu3rnD98mmUSiVx0WHsWP8bxsYm6HRa1v3xQ55a0Lsj+u+e4353902Mj+b4/o10ffnt3BpTZ88aDw2kd5maWxEeHEjbHsNJio9CnZ2FvXVOICtsc354bAYxcUl4ef73ZWdp40hl/xZU9m+RO3WUXq/nwPq5RGz8kpSUdGxdfbC2dyP0xjnMLG3/XSFLy43z+zA2syQhKpiTO5fQpMt/K0UpDQxJjo/g2OoppKSmkZWeSLUa9XH28AHA2s6ZrX9+x6tjHt/kfq/HDXxy984ZxGdimtNtQKvVsPDbsbl9ke9nZ+/KmiXfYGxiRkpyPLZWRljZOGJpZYOdgwsatZqoyBAq+OR0VfCp8nSmGLvX2hU/sXPTH8RGh9Ol1xC69HydqIgQosKDycrKIDLsNh6eFYkMD2bkezNwcfNi0ohuAMRGh/HtgoVcvxbI+rWradUqBv9ajRj0xli++ngkABFhIXz53e+YmpozbngvCaXPKKk1FY/yRPOUjhgxgkGDBnHu3DmSkpKwtramVq1a2NraFlPxxPMmKSEagL1/f8fh9Uoy0pJJjA3HysYRcwsbrO2c0WpyahxtnCsAYGZpi52zJ6f3/cmVU9voN3Ye+/6aSUpiFAaGxjTt/AYXjm7EytaJ8NsB6P+dizQxKggnN2+S4iLJTE/G1NyaFt3e4uDmX1FlpaHTadGptBgYGKHV6kiKi8TELGfCeVV2BpZWjrhXqM6V0ztxcHZHgYKsjDT0ej0xkaH8tfgblAaGHNz1F2pVNinJcSiUSs6e2E3thm3R63Ro1Nk5qzeFBxMWco2ufd/GyNiUjSvnEnIrkJTEOAaN+Iz01CQ2rpxLbGQICoWSjr3eYMf639EoVOjRc3TvOjr2GEJo8FUUQExkCO6elVCrsrG0tsfB2YPrV86QlpKIja0j9Rp34GrASaLDg1GrsvGt0ZDAgJNUqd6Ahs27cu3SP8RGh6JUKvGr2QRHFw+uBpwkLiYcWzsnYiLvoNVo6DFgDKcObyMxLoq/lnyLW7mKtGj/MqG3rxIRepNg9/IYGj68yVStysbQ2JgrF44RePEEJiZmaPQGpKd24ObFA5hbWBMVdoNGbV+has1mHN+zikun96LVarlx+ThHd/9J5RqN0WjU/HNwHanJv2Jp64qdcwWUqIgJu8HBTT8DCiLvXEWVlU6XVz/k/NFN+DfqgqtXVU5v/gbfFm+w6OsPMTJSUL1RVyr5t+D84fX4N+nOuoXvk5WRSnZWOvbOXvQcNo1Te1YQG5dIXEIqjToNJSE6mItHN5CaFIOxqSX1276Ktb0bO1dM5dTuZXj7NgC9nqiQK6QmxdD7nVmc2LGYC8e3E5+mweWe1bc6vTKhSL87+fUvvUvBf8dPT03i3IndfPTdGs4c38npo9se2H/9iu8Z/M6XWNs68MGwFuj1+pzWrGgVdyOve7kKBF0PoE7D1oTcukqVanWLVO6Cutt8/8uPn2BmZoFXveZcOn8cFAr0ej0Xzx6lVoNW2NjY88evMzAxMSM5KR4AWzsnLK1s8PDwQKHXcvXGbTwr5IxpqFw1J1A7Orow6+sPsLS0Qq16dN9sUbokmIqHeeLJ8y0tLWnRokVxlEU853RaLcf3b6Bxqx7UaPMWvr7V2L/5V+ydy+W77Gx+j6UmxrB18Se8PPYngi4eJPxWABqNOndfl3JVyExPQa/TkpIcR7+R3/LXvPdJS4knJSGaI9sWYWhkjFplCHodhkYmKBQKLK3t0em02Dq6k5mRgpmlDebWTuh0Omztc/okGpmYYGZqSXJSLLYOLphbWBEZeguNOic4vjL0Aw7t+purASe5ff0ier0ec0sb4qLD0em1WFjacvzAppyVloyMOHN8J3q9jl0bF6PX61EqDahSvT4hQVfYt20Fer0eKzt7TEwtiAq/hVqTU8Nbr2knju/fiFqtwtTMAitrO9JTk6hZrweWVrYc2r0GJ1cvThzagrGJGcYmpqg1Krr2fZtta3/m1vWLuLh5Y+/kxs3AswQHXcLRxQNTM0u0Gg2J8dEoDQxITUng8O6/sXVwwdjElFeGfsDC7yYQHR5MbHQYLTv2Q6FQcnTvOv5a/C2VfOvgWq4CyYmxrFk2i8z0VAwMDKlYtRZnju0kKyuDzr3eIvDiCQCSEmJo0eV1TEzN2b76B7wq1STyznWatB9ATMRtIkOuYmBkTHTYTfQ6Lf4NOmJt50RoUADXAo7Trs8YsjJSycxIxdzChgFjvufGxcPcuHiYqrVbc/3iIRzdyqPRqFEnBeFaoRb+rV4lLeJ87vspMz2Z2s37ULFGU3asmMada6dZOuN1LKwdsbCyB9yBnKnHlnw9EP+mPUiIDkarUbNt6ecYm5ph71Kev+eOJSbsOuUq1SE86DzThtXAwNAYGwc3Qq8cIvzyHhJiwwFYOms0E7/ZxOY/ZnDn5kWyM1MZMOo73L0f39+2IP1LzSysMTYx5YsJ3bF3dMvtVnKvOo068P1nr2NpbYeNnTPJibEYGuRMSx3+b//Mhs06cWjPBj4e/zJKReGmrA44d4xL544x8M33C/U8gCHvfMzEYZ35avZffPPZcJq07EpmRhq7t67k6x//ZuYXoxg27itsbB0YNfi/QH2v8uV9CLp5mYh6rbl0+TJ+Nery2/wZzPltA2mpKYwf3rvQ5RIlS4KpyE+hQukHH3zApEmTcHLKf86//ERFRfHdd98xa1bhmrPE82PLX/M4vPtvNBoVbboOplrtZsz95j22Zafi6VMzZ1L1AvKsXJf46GBWfPcGOp0WA0NjTuxYQlZGCke2/kZ2ZirmVvaoMtPQa7XM/6Qv2dkZmFvYoDQwQKtRo1alYmBkgladjVqVhdLAEFfPyoTcvEDYrUsYGBqhUCiIi7yNiZkVWRkpHN27AVVWJqYmOc2jSfHRJCfGAXpSkhMwMTXjj5+/IjkxFp1WQ1JiLKkpCYACA6USPaBUKFGrs1Crs1AolDRq0Z1dGxcTFxOOg5MbSgMlgQEnMDAwwsLSGlVWJsmJcXj7uODk4snJg5sxt7TGv27L3Kml7vbf9PaphoubN3aOrvjXbcH5U/vQ63QolEoy01NRKpSUr1QdZzdvatZryfEDm3NrrbUaDdVqNSX09lWat+vDgR0r8apYDZ1OR1xsBCkpiSiUBkRHhmBoaEzXl0ewZulMFAoFYSHXcXL1pNer49iwci5VazRErcri5dffY8f632nZsR/XL5+mXtNOpCTFc+3SKQDOHVoNKLB38kChUJCSFMuZw5twcisPQHJCFGaWNqSnJmJkYoaljQOg5+r5w0TeuYY6O5OjO1eQnhSFKisDW0c3ti7/GlV2Jk7uFfH0qcmxHUu5ffUfKvg2wNu3AQlRt9izbDI1GnQAwM7ZkzqtXmbvX7O48s8OEqJD6DRoCqZmVkSHXstt1o+IV2FiasGIrzYBYGPvxsmdS0hLjqV12/FcOLqetz5fQ1pyHDv/+IpuQ6dy9sAq+o76gf1rf0BvbEf15gM5tHQ0/d+ZwbLZY9Bq1Ng5uvPS4MkEnNpJwKmdBQqld92MyuKj73Kmq+rz2n/dKu4+9v7UPx54zv1TRrXu8mqen+8+FzwZ/9EPAHzwxc8FLlNxMTEx4+XBY1m9dDZajQbfGvXJykzn8oWTmJia06BZB7768DWsrO2wtXciKeHBBRAaNOvIgd3rmDFlADoUxCaradSsHSOHdMXaxg4zc3M0Gg2Ghk9c7yKeIgmm4n6F+o319fWle/fudOvWjR49elC7du2H7hsQEMDq1avZuXMnI0aUbCd6UXCpGeoiDXa6q0XH/rlTQN1r8PtL8kwJNfarvwFwcPZk0NjZAFSu0YSr4Rm5E5g7uvvg6O5DWlIsCoUCCxtHgq4FEHR2GxbW9mg0arKz0jE1tyY1KQZzaycyU+MAMDQyITMjFRt7R7RaDXaO7kTeuYZGnZUzWj/4Ci4elQgPvgLoUauyUSiVaLUaLK3tAAUKhZK01CSUSiU6nQ69Tou1rQOpyQmoVdlkZaTRpusgzp3cQ3pqMkZGJqiyM9Erlej1OjwqVCU85Abpqcno9XDx9AEMDAzR6/WkpSRhoDTE1MqCilVrc+ncYaztHNGosomNvIO1nSN1GrUnMyOV0NuB+P47rVNGWjLL5n+GVqsl9PZVrG0dsbSyxdLaFp1OS0xkCDq9jmuXTpGRngqAtZ0TPlVrYe/kRmJ8NLHRYcTFhGNkbEp8bDh6PXTr9w5H961HqVBibmXNrWsXSEmMw8jYBDNzS1KT49HrdcTHhGPvmPOl4eRcjpTkOAyNjImNDkOtysbcwhqdTkvA2cOosrJwcHbH0DDn/WRibEhw0LXcEfmm5paE3gzAzsmD9JREbBxcSYqPokm7V7h+8ShHd6/MWRnKypYrZ/dTo2kfAk9toZJ/Y2LDg+j22secPvA3mempKJRK7J09uXhsCx37v0/E7UuUq1QLnyaD2PH7u1Sp3RqAgGOb8KpSj5rNerJm3rvo9eDi5YuLV96AeHeC/ZjwG/j4t6B6o26kJEazbPogMtOSWDptEAAG/16bnbNX7nOrVqsNgJtXVRLjIoCcvqeJcRH8MeddsrPScfcqeCB9VDN+cSmOaaIunT/OByNfwtDQiLcnTGXx/K8eGJx072j/ajX/W4K2TaeXadMp71ywtRu0AqBj90F07D4oz7av56wFwMUtJ1DrdDrGf/QjpqZmKJVKUjPUVKvVhA59xz0zI/S3b1rF9s2r0Gg01KnflOGjP3pgn/Fv9+HHX9aVQumeHRJMxb0KFUrffPNNWrVqxcyZMxk4cCDOzs74+/tTrlw5zMzMSE1NJTIyknPnzpGYmEjr1q1ZsWIFVarkP1hClK5yjsaFXtLP28W4UMuMFkWTLm/y2//6Ur1RN2yszNFqVKQm5dRQmpnbYGZhS5ZlCm5evmRkZpAaF4KzZ5WckKlRozQwoHWvUaz4YQzO7j6kpyZgY++CQqlAr9eh1WhQKg1wdCtPZnoa2ZmpGBgYYGFli6GRManJ8XTq8Qa7Ni3JnSS/buOOXDx9gIy0ZPxqNubYvo0YGBhiYWmDpbUd8bERxEaFoVAoMTYxQ63OJjY6DANDI8wtrKnbuB0nD28jOzuTxLgoFChwdC7HresXMDAwID01iZBbl8lIS6FqjQZ5Xo/6zTrjU7U2O9b//m+4NKGid03Cgq/x+qgvWfLTJxibmNJjwGiWzf+cA9tXkpaSiNLAEL1eh1JpwN9LvsW/XqucEK3X8cvM9zAwNMLE1IzkpDjMLKxISY4nJSmeVb9PR6FQcurwNpRKAzIz0rgReJaAs4e4fTMApcKAgztWkZGewtrl3xMdEULTNj05d3IvIUGXMTI2Qak0xNrWPs91mJpZojBQcnDbEtBDgzZ9uXbhMJv/+A6dTouFtR3bVn2PXp/TtePiwT9ITogmLTGCzPRkls18h4y0RDLSkomLvEXNJt04un0JG37/FL1eT1zUbRxdK2Bibs3aBe+RlhyHT41mbP/ja07vW4WphTX7/v6eFj3eITLkCrYO7gRdPkZGSgIKE1uGfvALx7b8QvC1U5hb2NKo4xAsbZywtnfltQ+Xk54Sz+WTWwFQ3NPcHR16FQ97P65fDaB192EAhN++TEpiNIPHzebAlt8fudJVSSvO+Utd3b2Z+OlP/HNsd76DkybdM9r/3lBa3O6fcB9Kd/qo61cv8s+Jg/zw8zqUSiXffPEux4/soUnz9qVWpmeZBFNxV+E6EgE+Pj4sWLCAjRs30qNHD2JiYti4cSO//vorO3fuJD4+noEDB7JhwwYWLFgggVQUmqGRCa37jOPYtpwVmQwMjfGqUo/Ogz7C2MycFj3foXn3EYQFnUOrzkajzkarUWNp40j1hh2pWqcdR7b+hoGhCeZ2HtRq1InMtGTMzK3R63Q0bN0XpYEhKYkxZKQmYGHj8G+/U1vsHVxQADevnsXIyBg7BzdAQcDZg6iyM9HpdFwLOIVSaYBCkTPCPT0tGVt7ZywsbXAtVwEbOyeUSgOsbOxwdPag96DxnDi0BQ+vyniWr0rbbq+iR0/XvsNxcHLH0sqOqjUa0qnnG9g7uaG/Z/34+v+uKmViak7PgWPx9qmOT9XanD66k5TkBBb/9DGpyQmosrNY+N27pKclkZWZjlqdTVpKIughIz0FVXYWwTcCiAq7jUKhRKfTkpWVjio7C41aRXJiHAYGhtjaO5OUEINanU3thm1p1fEVsjLT2btlGQYGhhgZGWNgaERCfBRZmek5Ncp6HWeP7yY1OR6lUkm/oZPISEtCr9Nx89JRABq1eZlT+9cQHx2KqZnlvzWyVtg7eWBmaY2Lhw/2Th6Mn/o35pbWjP9qNcM+/Jn+7/1BlXpd6dj/PTr1n0h53/pMnLkD3zptCLp0HEMjE9r0HkXvEd9iZetEj6GfoVOl0v6N2bzx8Qoun9pB77e/wa9+R/qOnIWNowfGpv9NfG/r4M6g939FlZnClStXcPX2o4JfzvRc25d/Qf12g6jdsh+Lv3qFP74dgoNr+QferzcuHGDLnFdxr9wQK1tHABzdyhMdFsTsKb0IunyC1KS4Qv0O3O1b+rQU1x+VLu45Ncb2Di788esMfvrmvQcGJ90d7V8SrMyNcgNqWJyq0H90F5dD+7bRrderKJU5X7HjPviavTvXExkRCuTUkALEx0UzaexAxg3vRURYCPFxMUx593UmjOjLZx8MK5Wyl5a7U0aJsq3IHW6qVKnCe+89OJG2EACVXE25GZVVoFWdohNVDyw16luvI6d2LwfAwtaVqLAg4iKCyMpM5di239FkZ6JRZ2PnWpHYsECS48Ip79uAGxePYGRsRkJMCAqFguDLR0iL9yIuOhRDYxP0eh2nDqzBytYpZyJ+vZ6kuAgMDI2Ijwkn3cwCnV5HZGgQquxM0lITUCgU+Po34tyJPZw6vBWFUvlvf86cmsisjDR0Ol1O87lej7mlFQaGhtjYOhIReosd63/Hw7MykWG3cHHL+RI3NjZl/jfj0Gq12Du6cuGfA9y5HYiJqTnm96wWdencEdJTkwk4c4jUlERq1mtFVPhtKvnWwdbBmetXzmBmbkVs1B2cXDzJzspApcpm0IjPWPrTpxgaGWNjbkFqUk7TfHpqMgb/9rMzNjAkKzMNd8/KWFjZoFQqMTY1w1yvQ6NRY2ZmSVRE8L/9UFeh0+txcvXiRuAZer86ng1/zqHnwDGcPLQFK2s7Th/bRd/XJnL+5F6cXD3pN3QSfy+fQ2Z6zupumRmp+NVujbNHBY7u+pP0lESSE2MAyM5Mx8DAkHPHckaSr1v8FdZ2TlhY2XP19DaiHd2Ii7hF8NXT/Phhd9DrUauzMTI24fCW3+k+9Ats7F3Z8PunpCTGEHbtOOU7vExWZirl/Rryz74/sbZ3pXKtvEug2rvmLPLh4OiMVqPG3MoetSqbcpXqYGphTY3GOXN81mzaM8/zKlTL6V7Rpu+EPO/jq+EZuV1VJn6z6bHv/dL2pLWldwdIrVry/WMHJ5Wk0q45TUqMw9HJJfdnMzNzDAwe/LpVq7L5etYSgq5fYdXy+XTq1o8hwybiW702n056k5joCJxd3Eus3KVNakyF9AIXpcrXw5yr4RkAD6w3/vrk5dy+coKwm+fwqNKYbgPGsGPFNOq3HYCjW0VO7V6Of9OeJEbfpmv/8Zw+sIahH/7OiT2r8FbVw87Rnbj4BCrWaMXxjd+QnpqEiakFtZt259SBNRgZm2Fj75wzUMjAiA79JkJmVO4a9muWzaJH/9GsX/EDd24FYm3jgEKppGGLrpw+uoNX3viQHRsWocrOpELlmty4cgatRo2JmTkKQK1WM+rDH/O97uETv2PNsllY2zjQuFV3rP+tYctPzfqtqNekIwd2rMLI2ITkxFgq+dYBcvp5hty6nFODaWCIWpWNmbkl6AEF6NGhRIGhoTHRkXcw/ndZRycXTzIz00hOiCUuJgxDIxMO78npt6fTatDpdGSrsrhy4Ti3r18kKSEGQyNjrgacQKNWk56WhKWVLYt+mIxOp6Na7SYYm5gSHxNBQlwUsVGhrFk2i/TUVFKSYkmKj8TB2ZPI0Gs4e1TIvTYDAyOc3Lxx9axCbMQtajfpzD8H11G5RhMq+tVn1YLJdHtzJp6e7vw1/30q+NZHo1bj6lmFaxdyRt+nJccTFXqV8FuXeHnkt+xb9xPXTm2mRp0mGBmbojQwxNLGiUsnt9LjrWnEhF3LPf+9Uy0BHN36MyOnbScq5Arbl39RsDfxv1zsjIlOzL9m7uS+vwBo1PYVosODWDZ7LCM+WYq17aMHjT5sJP4fCz9j8DtfcvLQJhq17FGoct51txm/OBRkcFJpuLe//L21pk87oDo4uhATHYF3hZyWwqjIUNLT7l16O6c1pIKPL8bGJvhUqUZUZCj2Ds78vvAbjAyNCQ8NRqvVPtVyPoskmJZtEkqfca3quT71Zo2iDHZKSlUXqAkwPkVVoNrSgoiIV9G0y5tsXfoF2ZmpuHpXy12DPlNpT3zMHVbMHo2phQ1WNg7YObrj6JDTr1FhbEPvoWNITohm68pZWFo7kJWZitLAkD5vfY4qK4O9G39Bq1Hh518fAK1Gzc4Ni9BqNLi4e+NTtTa7Ny3l8vmjJCXGYmpmgXu5ipw6vI2khBhUWZkoDQwwNjEjJjoUrUbNknmfogA0GjX1mnQk6Np5oiNCMDQ0wsomZ4L5M8d2ce3yP9jaO1POuwqBASfITE/F0Mg4z9rgzdv1YcUvX6HRqImOyJmf1NDIGFV2FoZGRsRGhWLn6EpCbAQrf/sa9HoyUlPINshAp9eiVCiws3dGpcomIS4SM3MrlAYGmJiak56WhIGBUU4NqYU16alJHNm9BkcXT5q17cXGVfNQq7IwNMopz+0bl4iLCcPVoyJJCTFcDTiJo7MnOzcuQqfTYmZhzcuvv8f+3ZuxsXMhKvTmvwO+ElBlZ+Zek9JAScSd60SEXMPNqwqJcZFkpCVx9uhmzh7djEatYsP8d3ImiVcoMLOwIfz2ZYIuH6dyzebER98hPCiAkOtn0WrVHNgwH1VWBimJt1n54zj6jfoOgKp12/LPnj9z3y8P41ben18+7Ym5tf0j9yuqtJQE/vhxPK9PmPPYQPqoAU+D3/kSgL2blxU5lN5VlNpS/zpN8b9nWdKCDE4qbfnVnsLTCajNW3VmxZK51GvYEoVCweKfZ3Lz+mWSE+MxN7cgMSGnO8ed4Juo1SquXblAOc+KrFn5C916DqJmnUaMHNoV7unKU5ZIMC27JJSWcU8y2Olx7jbhP87d2tL7m/Ahp5m0QrWc0fnBYbFY27sy8N0FefYZ9sly7oRF0W7I97jZm5KVlYWpqWlufy4AuryDjb0lNvYu+Pg1oF6Lnji4eOZuvnR6LwNGfEVYaDAHNy2gftNOpKUm0W/oJG5cOcPRfeupXrs5lavVx8OrEpFht0hNSeTm1XOYW1jj7VOd8DvXMTE1x87JNXfAlbWNA3eCr1KrfmtMTMzQajQMGfUlJw5t4U7QZfR6HRZWNji6lKNOo3b8c2Q7Ti7l8CzvR2x0KDcDz+aW0dDImCrVGxATdYfkhBg0GjW1GrTh/Kl92Dq4oFQoyUhPwdLaDq+K1bgZeBYjYxM0ahVaVc4SqokJMbkTi/d97T1WL5qOWpWFpZUt7p6VCLp2Ht2/tTNarZboyGAunD6At081EuOj0Gq06HU60lITMTYxQ6fTotfrMLe0IS01EbdyFWjdaSB/LfmWZQunYudUDlNzS9SqTLwq1SI2MpgzhzdhaGSMm1dltBoNRsYmNGzVl0un9xB26zI1G3WicvXGHNq+FDMLaxSGJrz02kfsWfMjJqYWuJf3w8LKDr1eT8VqjXByr0j47SskRP2fvbMOb+ps4/CdpEmT1F1pgba4u7vLcBm2MRgyhgwZQ8ewseEMxnA23Bnu7g6FIi11d00b//4ILRRtodi+3NfFRZO85+Q9J/Y7z/s8vyeY9v2mYW5px4Uj6/Co1BF7FzcAVFmKnPeNZ/GqeBbPXUzW9ptpAFjYjqGwe94t7/KDRq1i9e8DaN93Mk7u3vwxqQtDp23D/+5FAu5eJDzQl69G/cmdy4d4ePssPYfOY8vCgXw3+jfWLBqLMjMDc0sbhk5cwcwxnenWfwKhgffYuPwXegz4+a3mVJDR0s+FZy/A39fyvk+JspSvVJPv+32BXqejcvV6jP9lEbOnj8KjsA9Ozob3pUxuxrgRvVGr1UyYtphA//vMnzUWSysbTE2lJCbG4eLm8YZn+29iFKb/nxhFqZG3QqvVsHzeRJLjQ9Hr9XTsPRqfUlVeOnbnqil07DeFG+f2UKnOq6M6L8stDfK7RPD9Szm5e5EJKlztXvzx8HB3JjT8aUT57uWDCARCytZoCYCnpzshIeG4O5pjZmlLWkp8jihNSYpFmZXBkZ1/YiqVo9NqCI9JwcraHqFQhFKZRVamgvMndpIUH02Qv8E4X6/TkqUwFBXVaWKIYqZEhyJAQFpqIiKRCWkpichkZggEAkylclKS4zl/chfJCbHIzCwAAelpySTGR+eYzoeH+KNWqbC0tqdkuRr4lKzElXMHuHfzPFKZGXIzS2RyC9QqFZ5epbl15QRCgRCfkpUI9L9DemoSEaH+SGVyxKZSFGla6jbtgr/fNWQyc1JTEklOjCE+JhwLKzvkZubERochlZlhZm6Ns1sRnN0K43//BqlJ8djau3L76nF0Oh2OLp5oNWoyFenIza2QSKSITMQo0lNxcHJHIBBx+ex+tFoN5Wq2oWKNJmz68yeiwwOIjwnFwsqe9NQEQxR53lBAgKdXOVw8ihETEcCDW2dISYoh8ME19DodHl5leXD7PJeOrkdkIs5pIQsgMZUR/OAaYY9vo9fqKF+rDfv+mY4yM53iFRvmasF549RWSlVt/uo39Afg0Nb5WNu5kJ6S8NLHvUrXIPjRDUIe3cyJKItN5cTHhNO+xw8ULV6BhVP7kxhnsJ3yKl4Rj6Kl31qQPktBVOJ/jrzP5f0OXfvSoWvfXPet2nT8tbcdnVypUafxOz+3ESOfK/muvjfy3yRNkb9oSWrEVaxsnfhx5iaGTVzBxuVTXjrO21lK/S4Gf77zh9e9cn8l3OSvfCyb7AhWZMLLo7Qe7s5EJbw6Muvp6U54bDqWLuW4c+UIep0OvV7PhSMbuXftBC27jaB2sx4IBAKKeJdAqdYSHpNCRMgjihYrh6OzB606DTAUIun16PWg0RoikH63LyCTW2Bt40hychwIBJhKZYbMsScFH8GP72FuYU3NBu0wlcrIVKShzFKQmZGGrb0zTi6eKDJSKVaqCinJcQTcv05Y8EP0ej1Bj+7w1ZCp2Dm6ocxSUKpCTQRCIb7XT2NlbU+3b8YSGvwArVaDSpWFs1sRzCysiY+JQI+ec0e3YyqVExURaMh7lcpJS0siPTWJxIQYSpWvRWjgfUylMoID7uJ3+yJOrp7o9DpuXz2Omblh3rYOLgBIpXLsHV3JzExHrcxCLDFFp9ORmhxHnSYdkZnbkBT9mMD7VxGKRLTrM57CPhVp1G4Aer0esUSGtZ0r5la21GjUhSunduBWuCRqdRbuRUqj1WjISE3Eu3QNTCRSVMpMTGXmJMVFoFJmInvSkCFLkUadln0RmYiJCL5HUnwEnQf9RtD9yxxa9QPXTm7m5pntxIQ9xPfiPq4e38TGeQNZPb0HwfevEPLwKtuXjGDjvIFsnDcQrSb35yDI7xIndyx47ftyzfTuABxcNxUnG0lOjvTzVG/UlYET/ubglnlkZaY/feDJEm2xcnV47HcFZVYGVrZO3L16FM/iVUnWWnFk9ypWzBtJbGTB5xm+T3u3z4nsyn0LuTincv9jVe8bMWCsyP//460ipffu3SM0NJRixYrh5eX1wuOJiYmcOXOG9u3bv+v8jPD+80rfZgnfzNyKezdOcqN0TSpUrk6vQVPZtnYWXb7+iTH96jB25mZio4IJDfTj/OlD1GjxDRFBfhzf/RcPb59Bq1GTFB9JlXodqFi7LdtXTCRNoaRCo2+o2bANS8Y2Q2pmRckqzQBIS45j76qfUGUp0IvkNOw1iwubxyK3sCEq+B61WvenZOWm3Dq6hNjIEKSmJpR5SWTM09MdgHgHHzb+ORa9Xk9hnwpY2jiy4Y9RSOUWSEyl6LRapDKDUI4IC8TdqzweRUtx4sBGNE/aOu7dsgS53JzE+GjCgh6SnBBjqAgXm6JSZaFWGrpJadUq7t44i5WdI/ExEaxe+BMmJmIkUjmKjDRUykySE2NJiI1Ao1YTHxtOZoZBtKQkxREUcA8TsYQrZw/gUaQ4D+5cJDY6FKFASJC/L1Y2hiIpB0d3Ht67glhsilgsITkhFgcnd8pWrmcQmS6elKlYB0+v0uxcv4D46HBkZuYU8SlHXEwY6ekp9Bv2KycPbkKn03L3xjnUaiU9v53E9n/mcOn0XrRaDZZWthT2LsODu1dISYpHo1ai0aiRSExJTUli18Yl+JStS0JUAMkJ0cRGBCIQCnF0M3xXWNs6kxgXTkpSDFKZOQe3LiQxLhyNWolOpyMk4DYZaUkIBAJOH9qEUCikftsB7Fk7lcyMFFwKlyQxNoyE6GBSE2NIiA7G2sEdS2sHhAIhm//4AVOZOc2/mcuRVcNxcPVCp9Vibe9GdOh9eoxcRkzYQ66d2EyZGq0QiU3pMWQBB9ZNIyHiPl6F367auWXvya993MGlCOZWdtRu1ov9G34nS2F4jaPDHwHgVrgU+zb8hqNLUdyKlOLojsX0G7uCw7tW0LjFlxQvU50pI9qQXSQDhuudgqp0/3+Nlr6Mj1UgZeRFjMv4/1/kS5Smp6czbNgwLl68mPNF2LRpU6ZPn46l5dMCgrCwMMaNG2cUpZ8Z+Sl48ilZga49B7J9w2+snR9K+54/EB70gNTkeIRCEQH3rxMe/IAaDdpx4+IRildsgluRUjRuP4jG7QeRkZbE2rnf0aj9IDYs+oHewxdhYePA3AlfUqR8U5RZGQz+9RDHt84mPvIxyXFh1G8/DDev8mxeMIiMlBhSUlJo0HEYUpk5e9dMwtreDYmpjB4//MWRrfNJSle+dO4GYdoMn4rNOL55GnVa9AKgdrPcbRm7D5oJQOsvR3L78jHiEtNo1Gkk7k5WOWP8bl8gMjQAVw9vvug+hO3/zKVU+ZqcPLARJ7cixEaGUKdpF6xtHTi0ezV9vpvC5TP7EQgESExlODi7E/LYj2p1W1G8TDVWLxqHlY0DCbGROLkWJi4mDL+bZ9FoNOj1OkzEEszMrSlethqhgX6IxabYOhhEVGx0KHaObmQp0qnfvBumUjnunsVwL1wcv9sXsbS2JyYyBE+v0rh7FkOjUeF//xqVajTFysae7f/M5d/Ni+ncx2D1tnfLn8REBnHn+ml6DpyMIj2VLatn4VrIm7TUJExEJlSv1xq/2xfIUqRTs+VADqyfhqlUTpDfRdSqLCrUbIWTuxcikQnx0cG4eBTDRGKKhbUjrbqPYPfaGZhb2lKp9hd4eJXhyI4ltO4xmr3rf6NoiSokJ6VQyKsUSfERNO40lNhwfwLvX0EmsyAzI5UO385AmZnBg5unUGWlU6VhF0pUasSqWd9ycMUwstIT6P3jKhKig/C9uBc75yLsWTUhl/m9nZPBFsrcyv6FSClA8P1LbJo/ALXSEAHtMXo1UcH3OPD3z1jbu6FWGQq31kzvztcTNnFyw3iOK2JRq7LoO3opVrZOufZXu3lv5o1ti9TMgvnj2uPk7o2NneuTFA8zPItVoJBXeQ5vW4i9sydeZeqydvE4zC1skEikpCQ9rWwv7FOe1Qt/pN+I2W/4xL6e/8fc0rxiFKgfn9PXo6la8vVFikb+G+RLlC5atIj79+8zf/58ChcuzJEjR1i5ciU9e/Zk7dq12NnZva95GnnP5DdaGhr8iApV6+NeqjkpiTEs+/UrXD18uHfzHM3b9yPgwXWS4qNwL2xor+jtLEWtMUR4dDodGxePot1XE5HKzImPDmHdwmEAaDMTyUpPwszaNVehkrmVAye2z0VkIiExJhhXR2sAlGJX7K1N0WrUJMeF4+jmA4BPqUrExsUREa/Azf7F1IDsiClAeGw67o7mrz1eE5GA1IQwXAuXJjwm5Y3nx8LKls59RrFt7Wwe3ruCayEv5HLznIhWgxbdeXjvKkkJsQQH3OXRvavcuHQMgUBASMC9nBailWs1x/f6GSSmply7cBhTUzkSqYxgf1+yshQ0aduBQztXEBcdioWVHWkpCei0Wnaun098TAThwY/oXLg4CbER+N2+QKYiHd8bZ9Bo1Di7FgEEnD6yBaFASFx0GBLT3PZDzm5FycxIY/fGRaiUWbh5FiMzM4Ow4AdkpKUQEeqPicQQWT62fS56vR5Xj+LcvX4CVVYGKlUmsZFB7FozDaFQRFx0CImx4eh1OnatmYZWpyU67BExEY+5fu5fhEITju78E5Uyk0d3LyGVWxAf9RBTqRl3Lh0AvR4TsQTQo1IquHR0A57FqxAb4U+RElVw9ihBeMBtHD3LUKJsDQ6un45EaobIRIwqS4H/7VP0GrOKR7dO8vDGk3y+PEQZTcSmfPnDcvauGk9koC8XDqygx8iViEzErJn+tM2uIi0R9+K1aNuuK6f2reKR73mq1u9I9UZdc8YIhUJGz97/0ufpO/ppEd/kpYbGAz7lG9Kyectc47L72H/57aQ3zj0/GKOlr8coUD8el+8lY2lMOPzPk6+X+MSJE4wYMYIWLVpQokQJhg0bxtq1a4mOjqZ///6kp6e/eSdG3ooPtXyR19zSW1dOc3D333g6SbCwskdqZo1PqSoc+XclVeu0IToiCJn8xSvbhFQVh7bMo2SlhrgXKQ0YljW/+XE5Q37ZQqXabSnv44JAIMzl+Xjp0GoqNehOYkwIIhMJKQmRpCeGEvX4KluWTkCn03F+/0oig+5y9t/FnNyxkKBbB9GosziwfRn7181g3dzBXDq6gR3Lx/H37AGoVVlIpaZcOvAnq+f9wJWLZwE48e8KNv35E7vWTEeZpeDKye2IxaYEPbzB6T1/Eu5/hT1rJ7F79UT8Hz0gMOAeF08fYPnc0YYuSkBaahI6nQ6dXodUKic8+CEpyQns2fInifHRxEQGc+nUHu7dOo9QKDJ0SYqLJCtT8UQkCZCbW3HryglUqiyKFq+AWGxKVmY66SmJVKjWCPR6Du5YgUqpRCAQUqx0FRJiI0hJjketVmHr4IKNvTP7ti5Fr9eTqUij2Rdf4+BUiIGj5lLEpywWVjakJSdi6+DC4B8XoNfpiI+J4Oyx7SQmRJOWmkhmZjoyuTmuhbwQS0wJ9veleftvcHTzwcLGCYmpHPQ60OsoX705QQ+v0/6r8ZSu3JjHfldAr6dZp+8pUaEe6qxMbB0LodfrkZlZolWrnhSN6UEPjq5FSE9JQKvRAAJKVGyAXq/n6smtqLMUWNu7IRKJycxIRSq35IuvJnP91DY0aiXBD6+zc8V4bBwLEXz3NJcOr0Uqt8gpeEpOiMREImXtzN74XtyfY+qfF+xdigJgbm0w2VdmpmNh44jcwgYru6fL/aYyc6ICr7Phj5Hcv3ECnVaT5+d4n5w9soWzR7YAEBUWwOTvW+SKuELecksXzhxBTFRYzu1Nq+fge/PCa7e5c+N8Tpen/xIv6x5lzEF9v8QqrD/2FIy8Z/IlShMSEvDwyG1PUalSJZYuXcrjx48ZMmQIGs2n8SVsJP/k52q/ZYeviIoIZtSAlqyc1Ys6zXpRpmI9MtJSsLCyxczcihLlauTaxsXZmdO7F3H832XcvniAPyZ1Yf/G32nedQSrZw9k7pjWCEUmCEUi5KaGt2ZGlqGow6tcPfavnUhMqGHJWpFmEH+1GrRGp1UTG/GY+u2/R63O4v61wzi4eeNSuAyJQZewsjRH7lCM2l1+5tb5PXTsPwN3r3LERgQgEAho0mEgX49Zyv2re7lz5w7Jqel8+d0sSlSoy+1LhwzzSE+mSPFKSGVmWFjbI5Vb0KbHKLIUSaiVmei0GlQqJSlJcUTHxKPTalm7eCKxkSF4l6yMxFSGpbUdzdv1JVORyokDG9EDJcoaWlrqtNqclBiRSAQCEApFqFWGFqp3rp1Go1E/6Wev5/yJXSgy0rBzcMXS2o6YyCDOHNma0+8+NiqE6Igggh7dISPD8JqUKFudfzcvxs7RlVOHNnP35lkUGWnY2Dtz8/Jxtv09B5Uyi7Dg+6iUWVSt3QIn18Jo1GpkcgtD96vkZHR6HUkZOsytHbBzdKNslcY4uhalSPHK2LsURiKVc3LPSoIeXicq9BEqVRYXjm0mLPAuGenJqDIzAP0T4QmVardBr9cCeuKigpBILTCzdkSrURIVfB8HlyJ4l6mFQCggLtKQnyqVW2JmYYOlrROWNk6Uqd6KPqOXY23nyp41UyhathH9Jm/B2t5gvdN+wG/YOXnSffgSvh6/jk6D59B16CI8i1el3heDAaj3xWBcvCq/4h2fO5oqlVuQkhBFZkYqqYlP8739b51CZm5Lz6HzcHL3ydUy9lMgLSWRZbOHM2jsYqxsXm59lRe7t/xw8tA2w8XWf5RnC6Tg47Y3NWLkcydfy/eFChXi0qVL1KxZM9f9VapU4ddff2X06NGMHTuWHj16vGIPRt6FD2Gkn72M/6bcUrFYwtCxc3NuZ/+Q/b7KEG0cPHZxzmPZS43fjfsTgPrtDUv1z5rqD526Ndf+s1s1PnAqio1TUYpVaEixCg1ZM707fSduJik2DO9y9QGo07I32wNvIHOtiqN3KtHB91GpMokLf4TMzBKhyATvEuUQyi0xNbcnMjELU6kcrUaNidgUuyetJmUyGVITNbbORQmPTUcvcyE58O4Lx372oMFFwO/GKSQSGRVqtsTe2ZMsRTr3b55ErUynaOlalK/ZFpUyk5O7/8DRzQdVfBQ3Lh3D1t6VtJQE3Dx8iAz1x83DG2s7J3yvn6Fc5fpcv3QUR2cP1ColltZ2SCRSUlMS8ShakpDHd5Fb2mDn6EZY4H08ipTI6UOv1WgQiyVoNGrsHd3JzEzHxa0osdGhpKcmERxwD6FQSHxMOCplFqUq1ObK2f3Y2DkiEJTHtZAXmRmpCARCwoMfERHyCJVag7WdKzHREdg/6fsuQEBKbCDlqjbi1L7VeHqXR2hiQqYiFbm5FcrMDJp3HsrZw+sMRVBqJbWadOfi8c1Y2TpRuFglbpzfS6W6X3Du4D9UrteeG+f3IRJLAAGKtAQsbRzR6/WYW9kR9OAqalUWAoEAoVCIVqshKTYMN69yrJs7mIy0RKo37c3B9dOxsHYgKTGOooVKAtBrzCoArO3dcrxIX8WrXB1eRsNOP7B5wUAsbZ2RmT/NMXYpUoZj2+azYPxlZGaWWLzBID8v2FlKXtnZKT+o1SoWTf+WLwf8jGshb7at+ZXAR7fJVKTT/4c5+F4/zc1LR8lSKklPjubP9WdYMHME6WnJAEyc9XfOvlYsnIRX8XIA7Nm6nI2rfqdk2Wr0GTie5QsnEhzgh9zMggEjZnDjykkyFen0+nYsKxZNRqXMoohPaQYMn87Po77EwtKa0KBHDBo5k1Llqr/TMX5sjMv775/L95JpWPXNbi1GPk/yJUp79uzJ1KlTycjIoHXr1lSsWDHnsdatWxMVFcWcOXO4detWQc/TyAcmv12esg3189LpKdtUPy/dnlxsJEQlqXI8TA2V3iriIvwBQ+Xxhf3LqdakJzH39mNh64VryXq07TmSiMe3USszCQ+8jUBgsIySmhqeL1WhJi4lC41aSVJcOHILQwcfKzsXgh9ex9PTnXuxfujFVqg0sag0WQhEIpLiIw3CKysD96KliQjyIy05HntnT5ISIgEBSXHhlK/ZkiLeJUhJjEGv05IUF4ZXmXoE3D2PKisDp0LFMZFaY+tszeO75550eZIQHuqPUCAgPiYcc0trpHJzshQZqFRZBPnfQZzd5UkPAqGQ+NhIbB2cefzgFjb2zqhVSrxKVuLB7UtotWr0Oh1m5lYIrATYOriQmhyPu2cx7t06z9WzB1CrlJQqX5tThzZz9tgORCYSBFI7HAuVxMLakfSUOEqWr8WBLfNRpCVg7+SOTG7G7UuHCA3wxd7ZE6ncAoFAiJmFLSlJsVjaOHBy3yriIoOQW9iQlZnBoe2LkEikKLMUBoEJ3LqwH51Oyz8LRuDgWpS4yCDEpnLMbWwMzQeEQsIDDJ6wXqVrkpIYjUatpHm3UYQ8us6j22cRS6Q4uBQlPTmOMP+b2DgWQigy4eqBxVSt05yU+Ehiwh5Srna7V7zDcvO8cf6zzRsgd6/7gdNy97bvO9Ewruu4PXmyOPvQ7N4wH1t7F9JSEtBo1Ng6uNKl7ziuXzzM9QuHaNdjBC07DWTF/HGUrjyUuNhImrbpQaVqDVj5x888fngHgAM7V2NpbUujFl3YtHoOFarWp3XHvowaYMh7DfK/y+TfN/DQ7zoSUymVqjWke99RhAY9YPCoWTi5eDBmYGsA4mLCGTPlL8JD/Dl+cMtnL0qf5WUdpIzitGAwVuT/d8nX8n23bt0YMWIEe/bsYf/+FxP1+/fvz5QpU4iPjy+wCRrJzYf4IGZ/cebXuzS7QCIvVbzZUZ9XtVF8lttH/2T77x1ZMq4NLsXqsvqXLvjfOQXAzTPb8ChWhfodhuF39RA+xYqj02pYM6sfhzbPw86l8Av783B3xsrSUNik0ZtwZNcKtiz+gZrN++BauBQmYgnr5w/B79oxmrTvR8mKBnujoAc30Gi0aPUCMjPSCA24Q3iQH8mJ0Zw/spHA+1extHEgMS6C47uXsXbu92xeOg6VMhOJqZS7Vw6gUWdhbmWHhaU1ZubmKDNTQCBApVYhlshIT01BbCpDIjMjLSURgVCK1NwOiVSOQCgiMzODlKREEhPjsbCyJeTxPa5fOIK7ZzGK+BgiV3evn0EkFmNh7YRHsWokxMeQlaUkKjKc9LQU7AtXwblwOVr2nIipzIK7d+9QuVFvWnQZhqNrEarUboGFpRUxofdIS4rCwbUIw6ZuRq/XUblOW2o06oKTuze9h8+jbc8xlKnSmO6DZtK4/UASYkLR6XSIhCLkFtb0/H423QZOx8raEZGJGA+vsgwYtxIrO2cq1GpN6cqNGDxxLYqMdMws7ek/YS0WNo6o1UqcPUpQrnYbTGVmhD++g6mpHL1OB0DZ6q1wdPPG3qUIGWlJ6HSGNI/GX8+nZf+FyM2t8bt6BCePEnkWpP916jbrysip/7Br3VzUKiUJsZEsmzOc88e253ifXjixEysrS0pVbIiVtR1nj+9m4a8j8L9/M2fMg3vXUSmf+gEXKmzo7y6VGoR4p55DmT1lEMf2b8pVrGhr58T6FbNY/NuonBxTaxsHzC2ssLFzQqP+b1b/G5f2jRjJO/n2Kf32229fW9TUvXt3mjRpwunTp995ckY+Hm/jXQoFHzGt3qhrrsrlBxEKaPX9S1uS9pu8DZ1OR5s+E5HJZIRGJpABeNful9MFKns5NzuPsFqd5rk6QQE07TIi1+0qDTpTpUFnANbPH0KdDj9x/8oezCwdSIyPo3SdHthbmXJ63xoyFWmUrdaUui37EPzwBo6uRblwdBMtu41g2cxvGPDTSsKC7hH22JcixSshEIpIiAnl5vm9tO4xhg2LR2Pn5Em5ak3RabVcP/fvE1N+Jzp+M4n7N89w/9ZpXDyKEfb4HkVL10IkMqFUlWb4XTtChTqdsLG15eKxLZSv0QKRiZiqdVuzb+NszM2tELkWwbt4GcIeXuL8wRU4uHhStV5rzMytgRKUrGhIiWjYtt8L57fX0KfpGoWLVXzhcVOpnJZdhwNw7/oJVMpMLK3tsbS255sxf6LX69mybILhtS9dg4ggP+w8KnDh7FFMRCJUSgV71k7F3rkw5lb2RAX7cenIemRmVji5F6Nqo66c2LWEEzuXoEhPokWPHylcvAr/zBmY49wpEAjwcHdGp9MilVsQ8vAqIQ+vUaJSEw6un4Zep6Nmi29wK1qWXSt+QqdVU7p6Kyo36Mb57dM4k5WIWqWk69AlXDuxkcIla1CkVI2ctJGCRqvVsGPlZOKjg9HrodWXoyhS/FV5rbBz3VxKlqtJyfK1XjnmVTi7FsHS2o6GrXux9LchmFvYMHD0Qg7vXklGWjLhwQ84d2w7o6b9Q5pCz45tmyhToSaNW3Zj5oRvcvJjR05awuLfRxEVEQyQyyNVrVIS8OAWk39fx/4dq7l28bghHVevZ/PaefQfNg0razu+61W3wPxVPxeej5wao6bvhjFa+t/krczzBQIBFhYWr3zc3t6eTp06vfWkjLyeD5FbCnnPL32e97WUD4bOTw8iFDmV+S8Tp9lkL8UGh8fl5Au+qkUpQGh4NBHxTwsynreSig59SGpSDFcOLEStykKRFIbMzAzfc9vIykhGo1ZiYetCanoWO1dNpWy1Jrm2t7JxRPBM5EhuYc35wxsQiUzQarWIRCYM/WVTrm3KVW+W63aVeu2oUs8Q+bt7zWBpVKaKoS1hEe8SOeN8yuTO++4zYmGu2w2/6P/CeShI0lLicXLzBuD2pUPcv3UGRVoScgsbw+MZKsIC7xEbHYaJSIi1gxupidH0+mEJK6b1xMWzFOZW9ljZuaLVqoiPDkKRnkTxCvV5fPcCTu4+HNo0G0sbJ0zEpmSmJaHTw5G1Y5CYCElLiqFIqZrEhj8EIPjBFSrW7UTJqs0JvHuByOC7FC5elTptBuB39RCK9CRcvKvRqE0vLh1aQ+C98+/1/GTj73sBK1snug6cSZYijT9/6cnI3/a8ecN3oFHrPpw6tJHbV44THRGIlY0jltZ2bF45nfTURH4f1x29Hpp2Gs6WFRM5um8jElMpyc9U6/cZMJ41f06liFepXPsWS0xJT09l9IBWWFjZMHz8QhQZqSyd9xO1GrRm2tjeWFjaYG3rQHJi3PNT+7/g2agpGJf0jRh5FoH+UysPzQe+vr4AlC1b9qWPKxQK7t+/T8mSJZHLP70cr3flQwjT7C/O/ApTeFr8lNc2hgHRhiXBvIhTIKed47PCVKfTkZmZiUwmy7V0CAZxms3LxOmzPB89dbOXc3rPMty9yuNV2uAq8M/sASgyUhg0ZQs3zuxEkZ6MnZMnKr0MK3t3jm2cQq02Q/E9v50arQZzbudMug+aSehjX8Ie+6LMzMC7TA3ci5Riwx9jaNv7R6xt/xtX/r5XjwFQtupTYf73orEANO4+CZSxhAXcwsrW0LY0JTGKQt4V8CxWiY0Lh9Gu7xRWz+qbY2wvMjHhi6+ncGLXEgCSYsOo1/Zbbl/YS1pyHEUrd+D+pR30n2goQgsPuMWN09spX6cdIQ+vUb1ZH07vWkxshD8V6nSgZJVmnNu3nLCAm/iUq0/lht3Y88/vSMWQlhxDmZpfkBwX/kyktBt9J27J07HHJKnynFMa4n+Lnaun0K7PBAoXr4xOq2Hp1J4MnbaNhNgwDm2ZR7dBs1g9exAZGRlIhFo69RmDUGTCrvVzUGZlUqV2S1p3+Y5fRrTFysaB+Nhwhoxbiov7i9328kt2Ks6n5l2q0+nIyspEKn3xc/45kZ0iZRSmb+ZVr7kxWvp58Ca9ls3n+2k28kF42/xSyF+OKeQvzxTI+eGPeVII9SYKuzvkRE8jE1Svrbb2cHfO+QcQEa/goe8lxHZPo5FeZWuTpUhj3bzBRIcZWkXauxbl5onVXPh3NhVrt8anREkUqdFEPL6BUqUlPDaduKRMUjNUmDuV4NC2JWz5azwmYgmKJ1XO/wW8Slbl3rVjBIZGEx6bjn9gGIrUeIRo8PR0JyE6+IVtnl3KlZlb4ejmxZfDFtLum1/wLlObu5cP4eFdgda9xiG3sEGv19P2q8l0H7oQN59qmJo+/WE3t3JAp3tqT/fY9xwV6nag58jlXDuxmTD/m3gUq0yv0St5cOMoV86fwMnFjfYDZ+Pg5pNj0q9ISzAUw8WG8T7w9KlAg7b92bv+V37+tipXTm1/Yczda8fxLlWdPmPXY21n6A4VGxXMsEkrmTh3F9fOHwQgKT6KoROX07rzd1w993Jz/vyS1wtKI29Hdr6pMdfUiBEDb7V8b+TT4EMv4+e3Ih9yL+XDm3/knl3OhzdHTbOF6bNL+uZvCDo8W2Gdl+hptjAdPG1HriX+wlW6ULhKlxeW+b/+cWWu233HGvJYazX6Anja5hSgZsO2hISEA6DD0F3qZbyp49TH5sV5iyhRoyvXjyxDr9eh02lp2mUoEYF3WTdvMHZOnljaOL5yf0KhiLLVW7JxwVBUqkzqfzEQuZkV+9ZN5/bFfZiITcl44lUblfC06Gb97H4IBEJ0eh3NvxxLZoah+5aDqxd7V09CLJVTunor7F2LsmPpSM7vX4FHsSrYFyrF2Y1rCbx33uCBamlPySrN2b5kGLfP7cLSzqXAzxlAdNgjSpSvR8VabUhJjGbp1F5ITGWGB58sYiXEhOJW2GBxVdjbEGWwsXNmzaKxyOUWaNSG972DiycikQnWto5EhT8usDlaW4iNnZ7eMxZy8X8m1/Tg3i2cOLyL2Ys359wGaNm22yu3UamUXLlwkjoNWjB8QEcWLt/50nFjh/Vg4fJdACz4bRxOzu7Ur/x6qzcjnxdvLUoVCsULS+K3b9+mfPny7zwpI3nncxGmQL7yTIF855qCQZymZolIV2lem2+azcvyTuHNAjWb5/NQ4cVc1DfxbMvTV5EtXAsad0fzVwrh/PL8cXh6ulO5VqNc9xWv0OCN++kxfBEApao0pVSVprke6z9hXa7b2efe0d6anqNWvHQp17N4VQC+mZQ7X/ern/7J+TsyQcXgmQdf2HbQjIKJOL6KB7fOoFYradpxCBZWDphZ2qLMzECjVhEdZrA9c3ApTFjgXRyK1uT+/Xt4Fa/I9rW/MWHOThQZqcwY3REw+Me+L4zC9P3zXxKmD+/f4fzpw9Su3zxP4xPiYzl76iB1GrTI0/htG5YB8OVXQ4wFT/8x8i1K79+/z7hx42jWrBnfffddzv0pKSl8+eWXFClShEWLFuHl9e75TEbyxucgTCF/BVCQ/6gpQDEXKVlZmYQmkadiqGyej57mRaBC3kQq5F+oPk9ehOvb79v6ve37fZJ9nt3dHMnKzHrD6A+Hk42EBxGKPOWV1mnRh23LJzBnTGtMpXLqtOhDcmI0C8Z3yHE4KFO1GTfODuHBnF5oDK5MlKvaiCnDW2NuaYNUZob2A7QzzRam8OnlmP5X+K8I0269BrF2+Ryq1WqYc19sdAQzfx6GRq2mbqNWdOs1iK+71sfcwgq5mTn+D+9y7dJpEuJjGPdDH5IS4pg0cylu7oVz7fv8mSNcv3qOGXPX5uy3YcMvUalUdOzYkVGjRlG6dGlsbGxYuHAhixYtIjQ0lCJFirBq1SrOnz/Pzz//jEKhoEOHDvz4448f8MwYeRP5KnQKCwujc+fOyOXyHGGaTWZmJjt27GDVqlUoFAr+/fdfnJ3f79XL/3uh07N8CFH6LAVRAAX5L4KC14vT55Phs4uhssmLQH2WZ5f34c0FUi/j+aKpZ3lXsfo543vpIJeObsDM0haVUkH9tgMoUrJanrbNFqQG+ycdWZlZSGXSXJFStSqLs3v+IiM1gcz0ZLoO+wOA9JR4Fo1pyncz9+W0IY1MUL1gnP8u5KfYKT8kpKreubPTu/IpFD/9VwqdXsXnXACVvVyfmBCLAAE2dobP1UO/2zRu3p6yFaoxdlhPfpw8n8FftWTz3qvEREewdvkcxk1ZSOdWldi4+yIXzx4lIiyYHl9/Dxhe877dGmJpaY1Or2PRit2IRCIW/Dae0cP7Ubt2bVq1asXq1aupVq0awcHB/Pvvvzx48IBx48bx22+/Ubp0aRISEmjfvj1mZmbUrVuXixcvfrRz9f/Eeyl0Wr58OTY2NuzatSuXIAVDi8ZevXqxfft25HI5f/31Vz6nbORd+NDLF+9aAPU2RVDPFkLlpxgq+x/kvSgqm+ziqOx/2QVSbyqUepZni6ZeVkD1qn//D9Ro2pMewxfx5bBFXD62MU/bPCtIX0f449u4FTU0FEhOiESjVgIQcOcsFtavzmf9lMluOfoxyb6QfPbi8r/I8YNb+K5XXSYM68TI/s25eeXUC2N8b15g0+o5ed5noP9djh98s4vD87ZRnyNdegzg5NF/SUyIBSAyIpjipQzpfV7FShEdGYqza6EXLirc3D2RSEyxtLJFqcz9XheJRPzy+0oqVqnNzs0rc/ZbpUoVAMqXL09QUBCFCxdGKBTy6NEjNm/eTIMGDdi5cydhYWG4uroycOBAhgwZglKpfN+nwUg+ydfy/cWLFxk0aBDW1tavHGNnZ0ffvn3ZsGHDu87NSD75UMv42RTkcj7kLWr6fL4p5N1C6mVFUZC/6Onz0bTnI6mQ92jq60TVq9IAnuW/FGXVqLIwlZqxceEwegxfREpCFOcOrKFsjZac3rsckcgEtyJliY2NJjUhnLLVmnN5923Sk2PpMXoF/rdP4XthF+osBVWb9KRMjdaEPbpOlUZf8ujWSQqXqEbIg6t4la1DmP8NPHwqodNpWTe7H73HrEKpSGXbH79QrdlXnNqxALUqkxJVmlGnzSBWTumImZU9KfERdP7+D8L8b+B/6wTpKfF4lqhGUmwYsWEP6fXjWpLiwji1YwEKhYLqdVvRuMNgfh3eGJmZFZ36TaGQV7kCOV8B0VkfNWJqbSEmOU39n1/O79Tzexq37IZCkc6v47+hYrUG77S/oj5lKOpTJk9js5fyP1ckElO++nYUv08byeARP+Pi6sFDv9uUrVAN/we+tO/SF4HAIEgFTxosGHh1brSZuQXWNnb0/mY4A/u0pF7j1ri4enDt2jVq167NjRs3GDJkSI7QLVq0KIMGDWLw4MHs2bMHV1dXvvvuO86ePUtycjL16tV7z2fBSH7JlyiNi4vD09PzjeOKFStGdPSHXU42YuBzFKbARxGn8G4CFV4uUp+PoL7Nkv+booB5Ea3w6QvXS0c34Hv5IImxoTTqMIRb5/e+MMbazpW2X03iwPZl2LuX5IuvJ7J2Rk8Gz9jL8W3ziA17hCI1ke4jlqJRZbLzrzGUqdEaRfpTs37vcnXxv30GzxLVEApFgKHC38bBncTYUMIf3KB4pSYkxYTSbcRSxKZy1kzrSp02g0hNjKbvpK34XT6A35WDWNg4YePoSZehS5j7fXWGzT3FjdNbCHlwBa1GnbP98p+70LjDYLIy0xk7/2iBLTPbWUryvFLwPsn+nGaL009VmB4/uIUdGxZjY2uIjptbWDNuxqp87UOVlYnczIJ/tyzj+KGtmJiIcXRyp3Wnb7hz4zx+vlcQi00ZN2MVk4Z3wUQsoUyFGphbWnP53GEy0lP5etBEBEIhd29ewNGlEDcunyQlKQErGzvGTHn1yuLnnF9ap0ELdm9bAxiKkmZNGYEyK5NGzdrh6OSaM87axo7H/ve5cPZonvZrKpXRb/CPLPhtPMN/nMHEiT+iUCjo3r077u5P8+87dOhA37592bhxI1KplG3bttGqVSuqVauGnZ0d5ubmaDQaTEyMRkSfCvl6JWxtbYmNjX3juMTExNdGU428Xz6GMIV3yzPNb4V+Ni+IUz3I8vH0BSlQ4UWRCu8WTX0VbxKt8HlEW2s07UnZGi3RqJVsXDQ8p7f9s6nu1vauOcfhXaIccnNrLG2dEQiFSGRmaDRqTGXm7Fs9CamZBXqdDo1aiYn4aSTR1smTpNhQQh9ew7NEVYL8LgFQolJjHt08Sbj/PWoPmU3E49vsXT0Bqeyp1ZKNYyFEIhPMrR2JjwoEwN6lKAKBADuXokikckxlFmg0KixtnHK212qeXCw5ur+XvMePHS3N5vnl/E9RnGZHPPPLjg2LOXFwKxGhj+k7ZDIRYY/x8inLF12/Zd+O1QBY2zowdupyli+YQKD/XVzci1C/WUcqVKnH3u0rmTZ/K0EB99i3YzUNmj3tdOjoXIgxU/7i51FfkhAfjZ39i5/pzzFa+rz105wlT9MVFizbkeuxbOsnqVTOyo0GQVqrrsFxo2KVWlSskrud7m+Lnqb41G3YiroNWwFw8uTJXONOnToFgImJCevW5XbsmDJlClOmTMnPIRn5gORLlFatWpWdO3fSunXr147bvXs3JUuWfKeJGXk3PrQwhXePmkJucQp5L4TKEadRWWQoRWSqNdhZ5e/HsaAFajZ5Farw7mL1WfIqXN/EhxCuJmJTJBIZyqwMtBo1CdEhOY+lZRoqy60szXlVq/RrJzbQ/+etxEX4c2Tz74Q/voNb0dwJ9fYuRbl6fANt+83IEaVFStXk5pkd6PUSpHJLjm+bwzeTtpKlSGXNtOwf15c86Ssm8uz2K37pyoMIRc4SZUHyqURLn+VzEKdguOCZPWUQSQmxOLt60qJ9H66cP0Lvb39icI86/DJvM9ERwdy8cgrv4uVISozDxs6Rrf8sxMrajkf3b5IYH03w4/uUr1yXx4/uMGV0D0KDHlKuch0C/e9SoWp9AHRaLfOnD82Jzj+Lm4fBocbWzgmN+tXCM9tc/3ONlhoxkh/yJUp79+7Nl19+yaxZs/jhhx8wNTXN9bhKpWL+/PmcPXuW5cuXF+hEjeSfjyVM4d2ipvB2+aYARR0lZGVlIZVKCIx7+qOd16X9bJ6vnH7XKv7neZVQfVnxVEEK1ed51zSBdxWsl45u4O6VQ+h0WrzL1kYoELF+/hBcPUuiUGqIS8nKmWfwjVfvx9G9OGtn9sLsyXJ96KNrVGrQNdcY73L1iArxQ25unXOfyESMqcwCR7cKBIfH4VO+ISt+bo/M3AaJNP9WS89uL5ebo3uPVk3ZRU+fQrT0WV5WCPWxBWp2xBOgiE8ZFBlpTJ23mWsXj+NZpATb/llIclK8wbHj3jVCAx/iUaQ4YcH+OZHOX8b0QiQyoW6jdtSo24I/5xja5mpUKqbM2cikEV0JeHAHMHQnS09L5sr5I8xYtIPLZw9x8UxuH1zBq66wjBj5PyZfllAAGzZsYObMmVhaWlKzZk3c3d3RarVERkZy+fJlkpKSGD58OIMGDXpfc87BaAmVNz60MM3mXYVpNvmxkNJpdU9EqRShyBCher5aOb8C9XmeF6jw7iL1dXyIqOrb8KYo69sK1mdFcF6iva+yhMore1dPpHHX0SQr5QVqCwVPvXLfhz0UPG3J+6kJ02d51mGjoMRpfiyhsqvdn12+P3l4O6eO7MDR2Z1vh01j4a8jqF6nORkZaUSEBBAfF0XVWk1Yu3T6k0i3HnsHV6RyOWFBjyhdoSZ3b55nwIiZ7NiwmIVrjjFjXF/cPb25cfkknXp+T51GXzBtbG/S01Kwc3BBo1bSrtugnJzS7DktnDmC7n1H4fTkvpfxOVtEFRSves2NxvmfB3m1hMp3dm/Pnj0pUaIEq1at4vjx4zmWCmZmZtSpU4dvvvnG2NXpE+NjREyhYKOmkP9iqGye/cF+m8Ko53lZFPV5m6mCFKmfSlT1efISZX0f+y1I9q39GXNrR+Tm1iQrVQSHxxWoMHWykRCTpMqzmX5+yV7G/xQjptk8+1n9FKKnifExKNJT+WXuJtYs+QX/+7coWbYqe7evYtKsv1kwYzg2do5Ur9OcEwe35op09ug3ho2rZjNiwkImDOtE8dKVc6rpa9QzdCOSSEyxsXNEKBTy8+wXXWjKVsydJzl8/II3zvldc0s1Gg1/zJlIRFgQej18M2gMpctVeeX4P+ZOYugoY/tOIx+etyo5q1y5MpUrVwYgKSkJoVCIlZVVgU7MSMGSfTX5scRpdq4pvLs4hbcz4IcXBWo27xI9/dAiFfIuVD9mNPVDisu3pc3Xv+T87WonybP3bH7IFqbvi89BmGbzfMV+Nu9boK5b9it/zRuHiYkE0COVmXH62C5s7ZzwLlkeC2tb9u9cg6W1HWYWVpSuUBO5mSUSUyljBrXJiXQmJcTg/+AWVy/krUr8U+HWtfPY2Tvxw0+zyEhPY/T33Vm69tUtdI2C1MjHIt/L9wB37twhIiICT09PSpUq9T7mlSd8fX3R6/V4e3u/9PHMzEyCg4MpXLgwMpnsA8/u0+XyveSP9tyRCYYcOzPZi4n/b0NY3NOcPUu5CJ1eh0qpQmIqQZiPApPA2Kc/kDYWBWsP8ijqRbNzB6v3b0ESGhn/wn3ONu+WSvEpotM985q/Y5V7dJLhwsnD1b4gppZDXIrhfVrM5f2JxqQ0w3MUdfy8lnhTFdpctws5vPmzodPpUKmUSCSmeXrNs/NJG7Xs+oaRubfZuXEJ1rYOZGZm0Pvbn3hw9xplKtSkzHPRzrdh85q5lKlQk4d+N2jUois2dq9v6JCRqcXV7u2+Nx743WLx3MkMGjaJUmUrk5yUwPxfxzJtzmoCA+5zaO8WIsKD0em01K7XnOOHdzNv6TbmTB9NbEwESmUWP/+6DDt7p7d6/oLgZa959dLWH20+RvJHQEAAAoGgYJfvU1NTGThwILdu3UKv1yMQCKhQoQLz5s3DxcXlnSb8tqjVau7fv//aMcHBwR9mMp8JlkKIVVh/lOe2NTP8H59usP4RC9+tEMTBwvB/TIqI5Cf7lJqASpm/yJSr5dO/w5Ofbmtmqn3J6PzhYZP7dnCCPlfkzFL67s/xMhxszHLdjklIzxUJtJXr3svzfizy+5q/DGspJCqEBIfH4WRnXgCzMmAugdQsEQ8iFBS2ez8FLjIxZChFBERn4W799P4LJ3ZweNdyLG3s0Wm1mJrKGDzuL8Ri01fu62Uc2rmMmg07YmVTsHm3kmc0ZZZGlCuC6mT1+s+GSpW3jjzqJ/ZeWVmZOfft3LiEW1dO4eDsjomJGKncnPpNO1LUpwyLfh2BhaUNQpEJesDC0oat6xYRFx3OlfNHmLl4d56P71VoNBpUKhWtO/V7YW4vQySA8Hgd9ub5/74oXLQ47Tp/xbI/phMVEUqvb4ahVGaRlBjPqeP7qF6nCf+smMvwH2fi6l6Yowd3EBsTQdmK1WnQpC27t63l8oUTNGrW/m0OtUB59jW/fz/qI87ESH6RSN58wZwvUbpgwQL8/PwYOnQoZcqUITAwkL/++otJkyaxcuXKt57ouyAWi42R0regJB83YuouNURNtXrDm/RdI6eeTwJQobFqsjQiBAIBAoEAS3n+9+v9zKrz+4iglnDLffv5SOr7iqIWdn/6GQiNjCc56+m5+ZwjqAUZKQVwlRkipnFJGQUaMZXJDBHT0KT3FzGVSg0R08jUpxFTsVhMm65DqNvUECXctWEeIf63KFOpfr723b7H8AKf7/M8e1ZSFVri0p6+ns9GUPMbKRWLJezcuISzx3cD4Fm0BDFRofz+1z5OHdnBnevnqNvoC25ePol3sbLotBrMzC0xNZUyY+F2Nqz8ndvXzyAQwDdDfiY1KZ7Na+fRqEUX1q/8DZGJCSXLVKVClXqUqViLicM7M33hdn4Z0xNzC2vCgh8yYMRMfEqU5/efB6JUZqJRq6lQpS7L54+n+9cjc4qfXoc2U4tUmv9IeHDgI2rWbUrTlp2Ij4tm7LCetO3Ymzs3LxHwwJe+A0azftUCChctjlAoNDSWsHXgod8tbt+4SEJcDI2at0Mq/Xi/o8+/5oYo6ccJhhnJPwEBAXkal69fv5MnTzJy5Ei++uorAOrVq4eTkxOjR49GoVB8lAp3gUDwxueVyWT/19X3r6JhVcM5+VjV+e4OTwuhMrIMV//vWqnv4SjOqdAMi9PkLA3mJ+/0WbxdCiYHdf3CESTFRxAR5IdbkVLY2LvRa/gCwJCTunPVFDr2m8KDCEXOUi+8v6r+wu5PlwqDw+OITjI8Z/yDg1w4tAZzSzs0aiWV6nehXO1272UOr8Pv6mFKVW3O0c2/07T7j68clxwfwd+/9sHawQOhUIBamUm7b2dh5/zmznMv4875fwEoV7sdkQkqQiMTOLl2KH0nbubguqm07D05X/vzvbiXC/uX02HwPBzdfHCykXD+2G6o3Iqjf33F0Gnb8ryv4Ec32bfhN/Q6LTIzK3oNX4BU9mI0187KkGMaGKfC21mKUGiIzGa7USQnxrBv6xLEElNKlq/FzDGdGT97O+v+nERokB9yuQXfT1jG4d0ruXX5GCZiMUPG/cWmFVPp0GsUwQF3OLZ3LVmKDJp36E+tRh3zdU7yirVFbrEZFve00CdboBoE1JtFqUAooFOvpwb6j/xucvncIYRCIcVKVcT3xnnKVKjJtnULuX39LBWrNyQ2KozYmDAmjehCcIAflWo0JDkxHoFQaPgnECAQCnF29WTkpMVsWj0HwZP5CAQChEIhcTHhjJnyF+Eh/hw/uIXU5ATKVKhJhy8H8/vPA3PtJ08XVALtW114Xb9yBpVKSc+vh2Jn74SVtS11G7Zk3q9jcXb1QCQyXKA+29no6sWTWNvY03fgaBbPnYwAwXtpApFfsl9z42/650VeLdDy3Wa0dOnSue6rXr06Wq2WqKgovLy88rM7I58IH6s6P5tnq/TftRjqWV5WtQ/vIFDfoUgqW4D+ManLS4VIx35TgNf7o74/gWpYjg0OjyMpXUutFn0pV7sdOp2WHX+OwrNENazsPmxE4saprZSq2vy1gjSbIqVr0aTbOKQyKWH+1/G98C8NOg575zlkFz5lKQ3vnfwKUoDAu+fo/P0f2DkXzrnv0aXNeFduhUKZ9/QJlTKTf/+exrfj1yA3s+LKye0c3rqAdl9NfOn4Z4ufAPZtXcKJA+tJjIukcZs+2Ni9WIQW8vguo6evJ+D+dTIVady7eZbhk1cRGx2CIiMlZ1xKYhxjZ24mMzOdxTMGvjdR+jzPFkmFxWnQ6UQI0zRvVSTl4ORGaNBDAIID/ACD2HEr5MXRfRv5/sc5/Lt1OS5uRZixaAdb1s7j1NGdaLVqQ7exZ0oxnFw9Xth/dqmGtY0D5hZW2DwxyI+OCqGIl6EOw6vY63PrCpL2Xb5m/qxxDOzTAqlUTvsuX+Pg6EJGeir1GrV66TbFSpZj7fK5XL9y5skxFGzaxrtgtIH675IvUarRaF7ICciuus+2hjLyefKxhSm8f3EKb28r9TzvIlBTk2LZvHQsyqwMzMxt+ObHZfwxqQtte4/n7tUjtOk5lulD6vHdzxsRJoYQEexHfJqOPXeOo8pMpUa7MdhamnLp8GrUSoNo7TF69ZPK4rensLsDSYEWxCemEZmgwtVOQqmqzQl9dJ3CJauxb83PqFVZlKranCqNurNp/iBMZRakJkZTqmoz7l8/SpGSNajX7juObP6N6JAHyMws+aLfDDLTU9izeiIaVRZVGn8Jej2+F/dhKjOnerM+nNmzFI0qi2IVG2LnXISYsIdcOryWgDtn6TVmFQF3znB2j6E/eMs+k3H2KPHSY0hLikVoIkan07J/7c+kJEZjbe9G66+msG/NZEQmJsSEPqR8nQ5UatCF9bP70WvMKkIeXiXk4TWs7VzxvbQf34v7sHEsRKs+BiEaHB6XEzG9cWoL105sRCgyocv3f2BlZ+jhrcxMZ9vioagy03EtWp5ytdvx6NYJEqKD+GaSodDm2omNRIf6EX1vH2qVgoVT+6NKjaTLt9Px8C7PxiWjSYqPwM6xEF8OmZMTXQh6cA3v0jWRmxm+b6vU64BalUVWZjpr536HMjMdD+/ydOj7M0un9kRubk1U2CO6DJhBVFIWepEUsdgUoUhERMgjpHJz/vlzAlKZGZkZaQC07fY9S2YOQia3oPeQ6XTqM4bVC8eg0+noNeipS4Hc3JK/Zg9Dbm6JTvd+8qFfh7WF+IkfsRqVTpjnDlLPGugDlKtch3Hft8fM3AorG0OaRq36rdm0Zi7WtgYBlpwYx4RhnbC0tsPOwZm4mEhWL55C974jc/aTXVAplpiSmpyAWqUkOtLQkez56JCrexEeP/KlYrUGhAQ+oFipSu94NvKGWCzhx0lzX7jfwtKa8pVqAk9bfj7796pNxz/I/IwYyabAYvFvUcRv5BOjfmXnT+IK1N1ekiNQ0xTqAu397OkkyfnxSk5T54qgvi3eztKcfwmpqpx/ryIhNozmXYYzdOpW9HodyfGGZH0Pr3JEhTwgLTkeoVBE8KPr+Puep3i5ujhaiflx1lb6jpiH//V9JKWr0erF9PlpPTYOHkQG+r7zcWRjb2uoHotMUCEztyI9OY6Lh9ZQ94tB9Bm7huD7l1GkJ5OaGEPL3pMoWaUpWYo0+vy4luD7l4kKvodGlUWfsWsoVbU5N89s58rx9TTpOpKvx68jNdFw8ePmVZ7OQ+aTFBdGp8Fz6f3jah7dPEmxCg1wKlScGs2/JkupIjQ8mjP7VlO/x0zaD/yd2PBHueYbdO8C2/74jsVjmxN47yLVmvTC/9Zp7JyL0Gv0SuycChNw5ywAxSo05Kvx67h7ad8rv7NcC5em5+gVBgEX6Iup2CAssiOmt85sp/+UnbToOZGYsIc52107sZFytdrxzeRtqJQZ6HU6vMvVp8OgeTljqjTqgbNHKcrX6YhOraB+96nU6DSFK6e24Xv1CE5uXgyduhVHVy/uXX8qCNJS4rGyfVr5LBSJMJWZceHweqrU7cDwGTtRZikI8b9FYlwEXQbOpNugWVw9tYOUmEfYOHjQddR6Sparxf07F3l49zKN237N2FlbiIkKQZmlIPDRbUZNW4dP6arcvnKcm5ePMnzyKhq07MH54097lu/f9iff/bSERq16odN93GI5S7koVwepZ4uknqVxy278uf4sMxbtYMaiHUyevR47e2d+Xbyb+k07Yvukqlyj1VC7YZuc7RQZaSAQkJwYR+XqjWnV4WtEJibcvnb2heeoUa8l29Yv4rfJA7B3dH3pPKrVbk6g/10mDO9MUkLsux7+OzHm++5UqV4/Z+n+c8FYcf/fpsAqKowt0/47fApRU3h/kVMoGM/Tl5EdQX3WpB9yR1AtrR3Yv2kOJiZi4qKD0eoM+ZxCkQixqYxHvueo1+Ybgh/eJDkhClfPEjy8fYZ1C4cjFAqxlIKHvZQIxyLEJKkQSO3QagpOuIMhahocHkd4RDRWljaEPLrGyZ2LEABZijRSE6ORW9oiM7NEZmaFzMzKkBcnMiEpLhxnT0Oaj7NnKUIeXSctMRqnQiUQikyo02YAd87/i42DOwAW1g4cXD8dU5k5Go1BhGaLUTB0hjIVi/B0tSUiXoG1R7Wcx9KT43KW74Pvn8fv8gGkcgsSY0Lwu3qYwHsX0KiVSGQGJwKXwmUQCkVY2rqQmZ6cc7zP6lNnz5KAoXVpSkIk8NTv9f6Dh1jauSIUinD3rpjrnCXFhlK8YmPD+MJlSYwJee05Nreyx9PdEf+sdOKTMrCNDOLGuT08uHUatSoLqfxpvqiVjRNRoU8FsFar4cHN08THhFC6alMAChUtS3x0MBZW9sjNrLC0cUSrUZGZkYqzq6GIxsqtHBVMxFw9f4BTBzfge/UkMrk5mRlpKDJSmDKsNeaWNgwYvYC0lAQmDWmO3NySr7//lb1bFhveGz7l+HloKyys7V57fB+Slxn0vy5yamoq477vVQ79uw6JqZSfpq/k8tlD7Ni4JMfwvlL1hkgkpnz5zehc27brOiDX7WwzfHcPbxasyu1fOmORQcw7uRTKMcn/8ZdlL93+QzN78eaP8rzvgqM8GWNx03+bfIvSKVOmYG7+9MsyO9owadIkzMyeWtAIBAL+/vvvApiikY/BxzTbf573KU7h3TtGvYxXdZECOLVvFTWbfIlXyWrM+6ltLkVUtERVTu9bzYAJa1m/aASWNo4o0pO5e/UoQ6dtw/fKYW5fOgSAg6WEEm5yrgJJ6WqKvNOMX8TD1ZYjqw7T6dupRAX7UaVRd+xdinLl6Dqs7Fx51WWotb0rt87uBDoTFXwPK1sXBAIhseGPcPYsxZ5VEyhSsnrOheypXYvp/eMaHj9+zON7lwAwFYtyxCiAVqtGrVJiJVZw5fhmGnX8HoAUgYw7ikxi45MxdypLlmoPj26dwtrBjYr1O1O5QVce3TqFhbUDkYG+xEb442lehdSkGOQWNiizMgCIj3qcM//YcH9KVmlGdMg9KtV/6mtpKhZgKrMkNjIYnU5HVPBdQh5coVar/objdnAnMsgXe1cvIoPuUKFelzecYcPx21sZ3n9KiRO1m/eiTos++F45kisyWrh4JfZvmoMiIwW5mRVXT+0gKvQBdo4ehAXcwcnNi7DHd6jeqOsLAYIKtVqTFBuOnaWEmLAHuBYpj5tXDING/oqNnRNTR3yBuaUNPQf+kmu7lp0G0bLT03bRA0YvAODbkfPIL6P71qbnoClUrN40X9vtXDeXkuVqUrL8q4VbyOO7hD6+h5WtoXivXJWGucz5XyVOh/6U+ziq121B9botcm6XrVjrowlGI0b+X8mXKK1atSrw4lL9y+43Luf/N/hUoqbw4cQpvL/oqVqjx61YLbYtG4/cwgaxREpa8lOT+2LlanP24FrMLW2Rm1nhXaoGUrklYomUeWO/wNrOBY0m9xKl/ZP5xSSpCqQY6tzepdw6sx2tVk3RCm1I09lQq+U37P/7F5SZaTh7lkJmZvnK7V2LlMX34n7++e1rTGXmdBg4G0VqIvv+/hmtWkWlBl3RP5OLaO9ZgT9+aoVMJkcuN8PFRkJmegr71/+aM6ZG015s/mMEKYnRdBn8O/evH6dk5cacP7gWmakIOwshUqmUio37cnzbDFr0X8Cti/O5d/kgJmIJHQfNBuDa8U2c2rmIyg0MYtOzeFX+ntUHe+eiWDwRgdGh91k3ux9OhYrlRE2zcXeUU7VhR5ZObIdQJKHHiD9yHqvcsAc7/xzB1WPrcfeugEexylw/ueml5+j5+6WmQoqUa8rJDeO4fnY3JmIpfccszXlcLJHSpucYls/oi0BgiLL2GjofrU7DuvnDOHfoHzyLVaRIiRdbR5ar1px/5g9l8eRuaLVqSpStRv0Ow5k3dRBigZaWnQdiIn5/hvuPH9ygVIXaXD61J9+iNC94epXB06tMrvue7xz1sVqaGik4qpe2NvqS/h/wVh2dPhV8fQ15dK/qEKBQKLh//z4lS5Y02kcUAJ+KOM0mPP6pOMsWpzqdLscSqiDsSwpSnGZTUO1NX8aDCEWBCNObZ7ZzaP1Uflx6g7CoJFztJCyb1IGaLb5+wSIqu1joTfZNLyN7GT4x4DQAZWu0BODcgdV4+FTEw6fiS7fbuHAYPYYvArJf8yykUmmu1zwiXpFrm9tHllD3i0FY2z9nFPuWZDcieFnL17clu6nC8y4M70JE8H2yFKl4larO1mXjqFCrDcXK1s6J3r/v1qSbVkyjSu2WbF87i97fzeCfJRMACAu6z9CJy0hPTeLQrhWYmEjoO2wWyYmxbFs7C5GJmGKlqhAadJ/MjDRKV6xLh14jOfLvam5cOEx6ejLd+01EJBJx/85FHJwM6SBeJSuzfulk1KosPIqWpm3vyfw5vTcO9raEBj1i0MiZlCpX/b0e8/siTaHOuTj/f6J+ZWfj7/lnzpv0WjYf33TMyGfDp1AE9SzvUhB1/OAWvutVlwnDOjFhWCd2bvrzpePeZ2EU8NqCqLehhJu8wPqsy81tCHt0DYCkuHBUSsVrx+dFkIY8vMa62f1YOa0Xa2Z9g1QTh5t97h8Y30sHiQkPIPzxHTb/MYJ1cwdz+dhGwCBGb53fQ2xEAHevHGbjwldbP7nZy3P+AWQoMomMjgMMfqTZnqQAZ/YsJeTh1TfO/1my80yDw+Ny7rt5Zjs3z2wHID7yMcsmtiU9Je6l27+M7AuKZ63A3hVrO2cObJrDnDGt0ahV+JQxLElnXxAFRGflulAqaALuX8e7ZGXKVKpPWNB9xs/eTpe+Y6lQvTElytXi8O5VTJyzi8E/LWbHujkAODp7MmH2DkQmEipWb8LEubsI8r9NckIM6PX8OHMTfb6byaVTu194vpjIIL4e+ivjZ+/g8YMbWFuISUmIpHXvqXT8ZjonD29/b8dqpOD51H53jLxf3n8DbiP/KT6lXNNsnl3Wz8jUIspjzV2nnk/NtN/E83mnBRE19XaW5so3LcioaUEs5ftUaIj/7VP41PHC//ZpfMrXQ6NWsWn+YDRqJU6FitPsy7E547Mjpq9CkZ7M6d1LqNlxPKYyC+T6JE79u5QO/acDcOnoBnwvHyQjNZHMjBSKla9Lh/7TEUukbFgwlOpNegBQofYX+F07RplqzblzcX+ejsXNXk6X/pOJiFcQGh5NQlIKdjZW73B2DGR7mQaHx+WKmGakJbLzr5F0/G4B5lb5i6Q62UiISVLxIEJRIBFTMwubV5r0Z7/nsj1NCzpqGuR/h4S4COZM7IVKmYnczJLSFeuwfe1vjJiylrSUBGIig5j1k+FzaCI2fK4cXJ56fxb2LgeAu2cJEuIi0Go1LJszHL1e/9LKcRtbZ7av/Q2JqYzUlAQALG0ccHW2JzMjleTU9yfA3ycF6UJixMinilGUGnkrPqVc02zc7SXodDrC43VoM7VYmOV9IWDT6jn437+Fg7M75SvX5cCutWRmptO287eULFuVP2ePQSAUoshIY8Kva4mI1PL3wqEoFalUrt2CNl2GsGL+SBJjI7B39qD/D3Pz5EjxfLV+QQjTEm7yAom0uRQuw92Le/GpA9EhfniWqIpamUWLXhOwtndj7cxe+drf4ztncfGpianM4kn0Uk77ftM4vWc5/r7n0GrVNO0ygujQh5w/uIarJ7Zy4eDfeJaojCIjmX/mDiIhKpiQRzdQZqazc/l4YiMC2LpkFK2/mkLuJpUvJztq+hhISEohNDwaD/enkZiYsIcc3jCT9JQE0lPj6T95K4c3zkQgEBL66DoNOw2nWIUG7F7xEyYmpmjUStp9+yvW9m4Eh8cRn5iGjYUpWxcOpnnPiTi4GhqKnN+3jPvXDiM2ldN+wGxunNpCSkIkCdFBFPKuSLMe47lxeivXjm3Awd2H1MRoWgxaXWDC9E08a7ZfkML06tn99B32G+WrNgLg56GtWD5nBD0GTkEmN8fUVIZH0VKMmbGRtJQELp/ZC4BA8PSzGxZ0n6LFKxAa5EfzDv3ZsmomP83ayqUz+/C99qKP5q4N8+g1aCqW1nb82L8uer0ewZOiMkuzp/ZRn2Oe6f/b0r0xSvr/h3H53shb86n4mj6PvbmhiOZNS/o7NizOWb6PiQqjRv2WDB41i6TEWH6Zt5lf5m7mxKEtACgU6UyZs5FqtZtx6+pp/G/spkajbvww8180ajU3Lh3B1d2bcb9vx8Xdi1tXjuVrzu9jOb8glvGt7d1Iin6MRCpHgACtRs3pXYs58PcvKNKS8rWvsJDHWNi64mYv59b5PWxcOIzlU7/E0saR6o2/xLtMLfyf+ImaW9ljYiLGs3hlfMrWJT05jm5D5uHg5sW5A6sBEIklOLp5Y2XvSmy4f77mkhHzkDsn1nJ6w0+snN6bS4f/AWDj3AG0+3YWtVr1Q/+kwl6ZmUHznuMRmYiJj3zMlaPradJlNN1H/EmWIi1nn9nL+ce3z0etykKRmghAekocQX4X6T9lJw07/cC5vYZUETev8vSbvI2AO2cAuHV6G/1/2UmlBt3QaTXvZSn/dTy7nF9Q+F4/RanytXNuV6jehJDH99i4/BdmjunMtQsHqdO0KzNGd+T3CT1wcn3RQ+LOtRNMG9mOkuVqYmFlh8RUytSRX3D59G7S05JfGF+xelPmTe7DnIm9sLJxJCUpd/qERGz82fsc+BR/W4y8f4yRUiPvzKcYNXW1M0EoFOZU6r+sSv/Z5ftNq+fg7GLol25mbsWCGUMxM7dCpzWYg7sVMkS8bOwc0WjURIUH0bZLY9ycJDRqP4yju5dy68IefK+fRqXKQiZ/sSf5m8hezi8ICipaalWoMlf3L6BWs+5kZaRybt8y+k3egtzClmUT2+XJZSO7mMnFxRlIBwxL8BVqf8HGhUNJTYohLOA2Go0K7yf5juZW9ijSk3l87xIRgb4IhCLEYglCoQgwPKdaaThX5pa2aLX5X9r0Kl2Tlj0N6QcHti8jJi4RjUaDlZ0LQqEQK1tnAnzPYefsif/t0zh7lCQjLZHQR9eJDLpLicpNcCpUnE3zB2NmaUvT7j8SdH0nQqEIsdyeEzvmITO3Zv/aSSjSkwi4cxqnQiW4e2kfJiYSvMs3QNewO+kp8ayc0pG0ZIOZulvRcjlzfFaYfqiIKTwVpu8aNZ225HCu2x16jaRDr5EvjKvVsEOu29kWUB17j3ph7Ojp6590dHpS3CYSUrJ8LU4d3IjEVErdZt1o0LJHrm3GzzbkkTo4F8qxtvpco6X/DxgF6f8vxktGIwXCp/olkp9CKMGTyu1dm/5k1OQ/af5Fr5w2is8vxTs4uRH8+D4Ae9b8hJWNEzUa92D87O180X0YRYpVeOs5F3Tx07vg6l2NxAg/ipSsAUDjLiPZumgoWxYOwczKnoxUQ86eTqshMSaUTfMHsXHeQMIf3waeClIrSSbJ8ZH4XjqQE11cN3cwYQG3SU9JoNfIPylTrXmOZautkwc9hi+iaKnqtO4zASc3H9RqFZ0GziImzJ/GnYbi7FEspwL/XQnxPYaDlRSdTsvK6b05vWcZalUWIQ+ukpmeQnSIHynxkTz2PYeJ2BSdTsv5A6uIDvVDrcyk95jVJMdHYGHtSMMO32HnVhxr5xL8u2IsHQbNw9G9OLHh/pzduxRnz1JUavglOq2W+1cPITGV0fdJG1K/KweJDr3/wvycbCTvdJFx+cRWZgxtwB+TujB7dCse3Dr9whj/uxc5uNng3fk+oqbP8tdvQ7lx8UjO7YVT++Hvd+2t9xce/JBj+9ZStHiFfG33qg5QRowY+TgYI6VGCoxPsQgKXvQ3fZO3qVfxsowa0BIrq1d3rGn+RS/mTf2evdtWUKVmEzp07MzMn4czZcQeZDIp309Y9sptX0dBRkvfhYr1OgOGyvKRCw1L6tlWUBXqdsw1tteYVQT5XaRSg67UafMtysx0Ns0fTKM+Bm/Q7PzRem36Ex7oy+5Vk9HrdcRHB9Oq1zhunvuXdfMGY25hi9zCBms7F2LCHrFx4VAc3bxxLlScWi36sGXJSPQ6Hdb2L2/hWBBIZXJMBFrUqiwkUnNs7Z1JiAnBs3hVdHotep2Oul8M5u7Ffei0GpSZCqzsnBEIhSTHhmP1xG6qWImyPLoPwb7H0Ok0FC1dG7+rB0mOC6fL0CUE3j1HhXqdiXh8C4nUDJHIhFJVWnBk40wK+VRCKHrxqzlbmOYnYnr5xFaO7foT9IYGBNUadkGtUrJ/42zCAu9SvWEX/p435KWFUG/KM710+l9q1G/H+r8m02vQ1HycZej6zTjmT+lL+WqNeHj3MnIzS3xKveixmlfcCxdn+pIjbx74DNYWYqOP6SfIpxrgMPJhMIpSIwXOp7icDwZxmi1Mn6+6f7aV4LCf5r+wbXaLwGe3mzx7fa4xk2YsISRGVSCV+QVV9KTVajj4zy8kxgQDehp2Gkkhn0ocXDeVlr0nv3bb4PC4nDzJ17F+dj8adf6Bx3fP4lmiCu5Fy1O/50wATm8Yi0AgpFj5ekSHPqR17/F0H2o4vxsXDqNs9ZaUrW7wJlWrsti/bib3rhrERZfBcziyZS5Ht84nKuQ+pao2pUqDLmxcOAx7lyKcP7iWtOQ4ZGZWXD2xiQsHV9Gw3WA8i1d+45zdvcrlum1l64KHT0Wc3IvRZfDv3Dq/l8sntlG4fAsu7pmP3Nwaj2JVeHD9KDdObcPGwR2BQICJiRiRieEcWdm7otNpKFe7Hef3r6CQRyFii1QiVWlKjRZ9SYwJpkSlpqSnxNKw0wj+XTEWz+LVKFPT0Gs9PjqIJt3HYuvowZVj614677cRpk06fAcY/FzvXD5E864jeHj7DPbOnqz6fQDRYY+IiXja0So1KZbNS8eizMrAzNyGdoP+YPpPfZCJ9VSq2ZyLJ3czfvZ29m1ZTGRoAPWbf8nUH75Ap9PRpusQqtRu+cY52Tq4UrFGM84c3syVs/to9+VwZo7pjEajomWnQVSt04opw9tgYWWLWpVF6Qp1uXpuP43bfEXdpl1ZMW8kcdFhOLl60n/kPFbM/QGpzIzAh7eo2agDzdv3z9O5yRamRj4NjILUiHH53sh74VP9cnl2Of998a4/cgVZ/RzsdxELG0f6/LSOrsOWcmj9NIA3CtL84lqkDNWa9OLkjkUsGNWEwFvHcLOXk5GaSOdBv+Xkir6O1KRYytVqQ/eh83FwLUpMmKHXu1eZWpSv9QUndi5Bp9Wg1ajZ988MUhKjCX5wDb1eT4dvZ9Hiyx/xu/76AjODB6o/qUkxpD9JPXiWxNhQtBo1KYlRWNnYUblaHTSqTHyvHMLZsyQexSqRmZ7MY9+zaDQqfCo2zEntKF6xEbERAfzzW1/io4IoWbU5TTt/x6kNP7F8ShfK1GhD5UZfcvP0NlZN7YKtU2HK1vqCmLCHrJ7ahZT4CC4eWMWBv6fQoMPw1x7H2yzln/j3L+Kigpg3ti1O7j5sXz6R3sMW4Ozuw9KpPdm2bDyxkYEkxIYhMZWh02oIfHAVdUoIUcG3Kd+oH4UqdSYk8B43Lh4hJjIYf7+rLJzan4YtezL+95fbTr2K1l2+49DO5ZSv1pjDu1cx6MdFTJizk+P71qLX60lOjGH4pJW4ehTDytaRcb9t4/KZvdy4dAQXdy9GTl2Ps9vTosIKT/xMzx/Lvw+pcRnfiJFPgwKJlJYsWZJp06bRuXPngtidkf8In0PEtCDblILBz/Rj/MBlL9NaWjuQlZlBhRYjKFSyDlK5Jf63T1GkVE3cvSvRd5LBTWDN9O4ULlkDRVoi0aH3kZjKKV+3E5FBd4gO8UOHBCsrSy5kZeDkXozE2BAe372Atb0bjTqNIDXR0O7PqVBxYsIesmZ6D0QmElQaLTXbjeL8zl+JuH+KrMx0TMSmxEeHEOh3iX/mDqJKgy64FS5lsHP6czTKzAw6DfgVnU7LwQ2z0Gm1iE2l+JSrA4CtYyEyUhMRikwID7xLbIQ/to6FUKsMaQ46nZYjm3/HRCzOsf55FU87Rq0hKvgej57kVkY/EcBiiYzty8ai1Who02ciYomUroNnc2LPKpxLNKaQT0X2rJqIpa0TJmJT3IqWo9mTpgEiEzEdBvyW6/lcPEvRf+I/Od2fZGZW9BqzJteYLt//QX54Wx/TJh2+w8rWiRW/9uPS8c1kZabxz4KhxEYE4lTIh+ZdRrD1r5+oVKctYY/v4FWqOolx4Vw9vQMAT09DIaBOp6dSzWY4uhbGp1RV1ColwQF3OXdsG/Waf5nn+ZhKZXiVqETlmi04e2QLf/1uaISQlpJAWkoiDs4emIglmFvY4OBUCJmZBRq1iuiIQC6f2cPtayfRqlXIzS0AcHH3wkQsQSrLX5GhMVr6afCpBjKMfFgKJFL6GXcqNfKe+VRto953xPRj/Mg16fAdQ6dtY+i0rdw8tgInGwluXuWp2eIbjm3+jXnDanL77I6c8Sqlgqjgu/SbvI2GnUYQFeyLU6ESWDqVyMkHrdygK3W/GIRep0OtzESZlcGeVRNIig0DwMmjBACla7TCvnBFmn09G0tTLVK5BV0G/45YIuXxvYtcO7mVQt7lEYnEXD+1HZ1Oh16no+t3c/AuW5vgh1c5smUuZWu0pGip6qiVmRzZaljmz45EyswsCfS7iItnKYqWqoHIREymIpWLh9eRlhxLZnoKoM/p8pSSEMX+dTMJ9b/JunmD2bhwKKf3LCfo/hViIwIwt3ag06BZmFnZ4eFTkV2rJvHNuDWIJTJsHQuxY/k4Htw8RWpyHCKBFkdLIcd3/olYaomJ2JQu3y+kdLUWeXptXtb96V14W7uo1KRYLKzssbB2QG5uTZ+RSyjkXY7KddsjlpgiEAo5d3g9Zao2o/vg35HKLEiMDQcMhYB2lhJ0Oi0B0VmosjIBSE9Lon6LLxk7ayvH9q553dO/Eme3IgybvIKffttK9fpfYG5h/coLDEdnDxq27MWoqRto223oM0WFeeya8QqM0dKPx6f4G2Hk42DMKTXyQfgUo6bZEdOC5mNFS7NRKTORSA3Ro2WTvuCrcetxLVqeo5t+5eyepdw4tZX4yMdY27uTFBvGwpH10em0WNo4k5WRSmJsFDf2zuDx3XMIRSYUKVWDqGA/w5JqXBiFvCtx78oh9HrtkzxKHdfP7EaZkczdMxsws7QjPTWRBWNaotfrCLhzjoTYMDJSE9Dr9Ti6eaFIT0Kn0zJvVHP0eh0W1g7IzKy5emIrOp0GkUiMWP204Cs+IRGBUExIwD20GjVRESGolUouHl6PKiuD2PAAtFoNLoXLInrJpba1nSttv5rEuQOrEZmIKVu9BR4+FUlJiKJ2i69w8SzJrhUTSE2KJSUhCnMrO7oM+o1tS38EgQA7J09Sk2Kp3qA9pg5luHZoGdEh90mKDQWeFoG9jld1f3pb8hsxPbpzCempCZiYSChSrBJRYY9YO2cwMREBVK7bHpUyE/R6SpSvx+GtCwjxv4VWq0Emt0AgEJKekoBUZo5YLGH19M6kZxjsvUxN5aycNxJTmRk1G3Z8wyxeTrseP/DHtG9RZKRRrW4bhC/p1JRN5dotWT7nBy6c3IWpqYzvJ75dUeGzGKOlRox8GhhFqZH/e97HMv7H4NiuP7lychuRYY+p2cHgv5mVkcLVYxsoU7MtJhIpUpkF1vZumIhNkVvYIDWzxLNENWq26Melw2tISU1HZirCtXAZ9DodYf43yMxIJTMjBStbZ2QWNsRG+NOo4zBO7fqDwxtnoVYq0Gu1oNeh0aip2aw3x7Yv4uuxqzi8eQ53Lh9Er9NhIpYgkcpJjAll79/TkJlZMeiXLayc3puszHQEQiFfjVnO5WOb0AmlRAf7IpBYsHHRSNJTYjERi3FxL0r5mi05sGkuUpkcBxdPHvtdxbtMDSKD/ajXcQzHN0/jxL51+N84grWjYclZbm7Nsl+6Y23vhodPRQAig+9jZmFD8MNriEzEJMVHoH9iASYzs8Lcyh5TmTmte43j3IE1yM2tuXR0A3CchMgQomJikQrg4a2TXDm2AancsLxs4+BOu29/felrlBdhumZ6d/pO3JxzOykunFM7F1CjxTdEh/jlOCPAU2H6pveFpbUDZhY2NOv0PQkxYXiXqYn65FZadBvJtuUTeOR7nvioILoPmU3xcnVIiAklPOgeDs6Faff1JCrXa8/mP3/Eyd0bD+9yDJ68geW/DSZJocNUKs/xAc0v2Z6hAON+z72P7H0+61Wafd/A0Qtz+ZQ+u5+3nQt8ut6laQr1f7abkzFKauRZjKLUyAfj/yla+i68rSVUkw7fUb1RV+4GJ3FgSR+q122JhY0TiTHBbJr3LRmp8VRp2AM9etJT4pFIzdColTy4fpSo4Hs4Fq1Btrm9rXNhIgLvIJVbIJWZIxJLSE2KITUpGq1GTYDvOZRZGdTsMJbj6yeQlRaPqdwcAWDn7IlGreTv3/uj02kxEZviXaE2gfcuoUhLwq1oWdwKl+bu1cME+J7Hys4Fc40ac9tC7Fj5M4q0BLxLVkagUxFy7zTmlrbUbNSRh3fOExPxmNP7VlGoaBk8i1Xk2O6/EJlIqNaoGxsWDuPs9ukoUqJIDL2NQKAh6vF1TmYkkxQTjKnckvSUeI5tXwToadjhex7fPU/5Wm1w9yrHujmDclKR1MpMti0dQ0y4P+cPGbo9/TNnAEKRCQ3bDSbk0XyuH1qGqdwSCytrqjXtxb3LB9Hr9USHPiAhOoQjm2YhM7MiLvIxLXqOp9ATMZwtTPPKmundsXP2xMWzFIfWTc0lSuH1FfnVG3WlZMUGXD65jaYdhwCwf+PviEQm9HzigjBo4j8vbNf522m5bnuVqs7Y+bktlwaMXfrEU3dono/lU8YYLTVi5ONjrL438kExXhXnjbe1g3oQocBEbIpEagaAVqOmdd9pNOk6Bu9y9SlcqiYCgTAnEtd+wBy8y9alQvOhmNu4UKJMZZwKFUcggLbfTMNEbGooVjIR06TrKDoM/B03r3L43z6NVqvB98QqhAIBDq5Fadb1BwCun9lpED0/LEFsKsPC2oGk2HAkUrkhmqhRERpwm8z0ZPb+M4PQRzdJjI3g0Y3DZGUkIkRP6SpNSE2JR5mVQWJcBMd2/UVYoC9mFtbERoXw6O5FjmxfjK2dK2p1FpsXG6JpKlUWUrklwf63SI6LQqNR4eDgiCorndSEcDLSUshUpJOWksCe1ZNBD4c2zWbRT21JiA3l8rGN6PU6rp3eTkpiDAKBAFVWBsEPr5ORlkRKQjSHt8wFvZ46LXtj6+JDZmYWacmxtOg1gZ6jVpCeEodIZEJiTAipiVHo0XF2r2GJec30HmxeOIQjy77hzu2b3DyznZtnDJG9XctGkxRnyN/c+ddIVvzcngsHVlDIpyJJsWEE+V0iOS4cjUbFloWDWfFze/atmZTrtX8ZljaOOYL0ke95/G6cwrmQz1u9v57nfZvsfwyMuaUfDuPvgZHnMYpSIx8c4xfR++HYrj/5d1Fv9i/uhXe5ekikcsrUaMPqX7rgf+fUK7crXrcf1w8uxtrs5V8HUpk5Go2a07uX4HtxP3qhFLGpHJFITKOO3z/Jt4zh/MG1CEUmZCTHIxSZsOmPEaiVmQgEQlRKBTqdFo1ahampnOSEKEzlVkjNrNDrtfQaNgcBULd5L+ydPQl6cA2xRErhYpWwcyyEk7sXA8avwsWjOO6FS1K/1Vd4l65GSlIsYrEUWycPeg9fQO2m3RGJTHBw9sTJ3Qs7p0J4FquIjYMrZhY21G/VG6mZFdVbDMLevRROhYpRsU57mncfzZBpOzGztKVqo+7odTo69J9O2eotsbJ1xtreBStbZ36YfRCRiZhaLb6iVOXGeBcrBcCd83tYM70Hc4fXRSgUYe3ghkqpoP2A3+k8eD5xEQHo9XrSUxPo/N18mnYfy/3zm4lPTHvhfAsEAup+MYSvxm/i0sHVlK7eGrUqE80TtwH/mydJTYhCZCIh5OEVjm7+DRlJ7FvSj4UTOnLmwFoAFk3szB+Tu3Jm/xo2/PEDKmUm5w+tQ25uxZo5gw05pAVAQfjpfioUhMewESNG3h7j8r0RIwXMu0Ra3jbiVL1RV6yKt8mpys6mZst+1GzZL9d9RUoZWoY27DQCMFSE93/JEi4YujUBfD/rIIc2zCQs8C4mYiktvhyNXqfl3P7VKLMyaNx5KCYmpuz7ZzopidG4e5WlVouv2Pv3NNSqTEylZgyYvIm1vw9AhxiNWomJiRgrazsy0xLYsvQndDotxcrVxv/uRbRaDSKhCLUyk2Jla3HpxDa2LZ9E0ZJVSYgNJ+HENtQqJbYObiTFRyIUCjm6YzFyc2uSE6KxsHEgOS4SnV5HSICh5alQZEJ8dAiOTm5o0yOQyMyJT0hEnR6DV5ma7F83gxZf/kjA3Qs4unlzaNPv6HU6pHILJBIZWo0akYkYqdyCmLBHAMRFBSKViMgyNefr4Us4tnk2EYG30ev1aFRK9qwaj0atRKPOQpGehKObNyZiCU6FiqNOWw6UeHqyn6QOiCUyHFy9AFBmZeDiWRpLGyfC/K8bXq8Hl5Fb2NJzzGpO7/4DnVbL+b1/UaXV9zgXqci5dcOoXLcdaclxjJl7iLSUeMIC75AUH0mNJt0pWbEBO1dPISzQF6+S1d7q/fY8dpaSV3Z+MmLkZRiDE0ZehlGUGvkofIr5pQXJu0Rc3iby9LZ90fPatUlkIqZs44GUbZzdNtRAqSpN8b9zlvOH/kaZmYGzZwnsnTyRSM24cOgfGrYbzM3ze7C2cyYqOgETiQwLczkpcnPafzUBR5fCnDn4NwkxYajVSmRyC6o17EzYY18atu3Pqf2radDmG2IjA7G0cSTssS+unsWpUq89p/auxkQiAfTIza3RqpXEhAegR0/NRl1JjA/n/o3T+F0/ibWdC6ZSOYlxEUSHPUKv1+FTrBxJ6Sp0Ail+t65QsW57Vs7ojanMnCoNuhDod4nIYD88i1VCLJGSqTBENSWmckQmYjYs+B6JqRyhSISDe0k2LRiCmYUVKmUmyfGRmEhM6fTdPLIy0tj51yhkZlYkRAej1aiJDr2PrZMnIhMxEWGhVNDriY8ydFVSqzJJiA4mLTkGjVrJrmWjSU2MJvDehSdnXY+JxBSA2PBHmFs5kBAdRHToPNQaQJ1GUlwEFtb2SExlOa+VuaUtx3Yu4ca5PcRFBlG2WvO3es+8jv+KMP1UC56MGPmvYxSlRox8IrxtlDRbkD4fJX0T+fHMDA03XEA8K0iz8SlXF59ydbl5djfnD66lebdRqJVZ3L9+jBKVGhIeGsS9i7u4f/04ZhY2NO00jf0b53Bs51K0WjXFy9VGpVQgM7PMtV9nDx/0eh171v9GRloS3qVrULVeB07sW8mutdPR63SUrdoEvU5HalIsIpEImbkVcnNr7J09Ob1/DZY2DijSUzAztyI+JoxKddoik1vQstsI7l47jq2lFO8a9dnx9288vJFJtUbdKFyiKvvWTUcqt8SpUDGKVahPkN9l2vX9OWduTTo/7bh07sBqPHwqUrnZt3i4O3Nu33IeXDtCz1HL2bF0FMrMdEpWaYZQKAKBgC2LvkejVtGu/wxMJFI2zB/Gut9uIpUbjt9EIuXUzgUE+V2kQcfhlKn5Bad2LiA84CZqdRZlqrdh57JRrJ7WFZ1Oi72LFzaOhajW9Ct0cg9un1iLraM7AkHudIwrp7bjXboG1Rt1ZeWs/jmR2YLCzlJCQqrqsxemxoKn948xSmrkVRhFqREjBci7Fkm8bX7e2wrSvERJXydIn6Vi3fZUrNs+53azPr8REhKOT8VmNGye27+yw9cTc92OCntE14EzAPDwKouHV1kABo5f/cLzeJXOveSs0+nIzMpCJpUiFD4VYqWrNCbo4XWs7V1o1vl7rO1cAChXrRkAZao0zhnbc/A0wmMNzgPOHu70n5C793ypyk/H9hi+KNdjdVp9k/N3aHg0ddoMyLnda/TKXGMtbZzoMTK3r2abIYZjzLaIyu749NeENtRs2Q8TsSkdBs7h9K5FXD22nkLFKuNVpg5BfhdJTYgiPSkWuYUtqy91wcaxEDZuZZGbW79w3rxLVWfdwhFcPLYZsURKWkrui5INf/xAi24jsXMslHPfH5O68NXIJbmq919HtjAF2LDsZ0ID/Rj3m6H9aHpaEsH+vji5FmHX+rm5bJzexJkjWzh7ZAsajZpS5WvRqc/YPG9rxIiRzwejKDXy0fivLuG/zdJ9QHTWB1u2fx+C9HlCQgxV5O6Ob275uH3lz3iVqmaIJBYgdZr3pE7znnke7+5oTnhsOiEh4Xh6ur/Tc98+v5s75/eg02rwLF6FBh2HvXLsqyyiBs3Yl+t2/Q7DqN9hGCkJUXiXq4ebVwX8b53Eu3x9KtXvyskdCyhUrBIW7oac4aHTDGLQzrFQjv3T+EUn8n0sz1bv54Xs/NLggLtMmP20g1hY4H0e3buKk2uRfD1/sL8vd6+fZtzv2xEKhayYN5JbV45TolztfO3HyKeBMUpq5HUYRakRIwXE20ZJP+SyfUELUt9LBzm+8w+G/boHociEkJBwDqweTYlqbanXqPVLt0lJjOHC0U207DYCgM79f8nz/N832cL0dYT63+LcgVXo9XpMxKY06TQMO2fPnMdvXj3LvQt7qdmiL97l6rJv7c8E3DmDd7l6OYVj74KZlR03Tm0lNvwhpjILOgyaB0BaUjQikQQZScwZ3w+xQEnF2l9Qr9XXLJnyJVK5oWVol2+no1YrCbh7kZbdR3Jw8zy8y9QEYM/fM0hOjKZGo27UbGroY58QG8ahLfPoOXQ+W/4aR0TQPaztXPhq1BJEIsNPSESQH9uWT0Cn09KgbT8Sk9IIC/Rj88rpdO9viIqfPLiBAL9rVK3TivCQh/w+/kvUKiXDf16FWqVkxdyRqJSZVK//BU2/6JtzvNfOH6B+iy9zouB9vpuOUGhCkL8vm1dORa/X0rz9t3iVqMSaRT8iEAhRZKTyw5S1qJSZ/DnrO8QSU1TKLL776U/8/a5y5N/VmJiI+er7mRQqUvKFc2xtITbmlRox8hEwilIj/9cUtHH+2xY45TdK+ikI0mxkZpaEB95FL7EnPTkGvVaFreXnlVN4YPN8UpPjiIsMwtLeAzNLO7oNnvnCuMyMFM7uW0nHATORmVmSFBfBqX+X0qH/dMBwvm6dOE/tNgMoUrI6AM2+/Imk2FD+mfUVSXHhNOk2BreiZdn/9y8IhSJMZWbYOBRi980ztO4zCY9ildm2eCiqzHRci5anRa+JrJneDYFASM2W/Qi8e56sjBRMZRaolZn8Oa45KfGRWFg7ULvNwJxK/AZ1arNyVn8q121HSmIMX41cgkalZMfqn6nXqu8LxwZQo3E3ipevx8KJnajWqEuux8ID7yIQCBj52x6unNxGUlwE9k/E+MEtc+kzcjFWtk4smtCJ4TN2cufC7hxBCtCwZU+c3YoilZkjFAgZM2Mjh3Yu4+6NMwT4XadDr5H4lKrCwqn9qNGgHRaWtgCkpiRgbfc0umYqlaPT6ti7eRGDf1yMraML00d1YNCPf5CpSOPnBfvYu/kP7t48Q+DDm/QY8DOFfcoxYXAT9HodR/esZtK83SQlxLDuz4n8MGXNO7xzjOQHY5TUyJswilIj//cURIvRDx0lhU9DkAJ4la7JzYtHqVD/SzJi71G0VFU0ahXbV/6MRq3EwbUojdsN4NbFA9y9dhwrGydMxBLUKiUHt8wnKzMDgA59J5IYE86RnUuQmVmSlhxP31GLOXvwH6LD/VFmZdK8y1DQ6zm68090Oh3VG3bCq1R1Tu9dSWJsKBbW9rTtMYbzRzbk2iYmPIB7109gKjWj/VfjXziGVt0Nxv+b/xpP90EzXxktfXz3IiUrN8opyrJxcKN9v2lsXDiMHsMXEep/kwj/a9jZ25OWGE1yQiSpidE8unWSEpWb0mvMKpZP7ohYKicpNoy+EzZwdMtswgPvYCKRsmflWKo26U25Wu0oV7s9e1aNI+LxbdKT4xg4Yz9xEf6oVZl8M3kbe1ePJys9BZ1eh4dPZSxtnVFmppMQHURo4Fx8Dy9AkZ5CUlwEto7umD8ReVmK3Mem52nBUyGvcghFImwd3MhIS8o1Li4qCPcipQGo1jC3YM1UpGHr4AaAraM7aSnxr33PuHh4IxAIMLewQa3MIjoikK1rfkWAgIz0ZBJiI3NEqbWtI4lxkbh5GAz/42PCSU9NJlORhp2jG0KREAenQqQmx+Ps7pWzjVatIjoiiMLeZTExEeNZtDRpKQk4OHkgEplg7+iGIiP1tfM0YsTIh8UoSo0YKSDyGyXNFqRvEyX9GIL0+aV6gBO7l+JSpAJ6VQrujubcORFAIa9yXD6xjc79f8HK1okNi0cTGnCHyye207Tjd0RHPCYlIYq05DjKVmtGkeKVOLlnJTHhj7lxbg/t+4xHIpWz4tf+aLUaLKztqduyDwH3LhFw7xISUxnlqjenePk6BD+8QWxEIAKBgB5DfsfvxkmSE6Je2MbCyh43z5LUadHrjecgIy2JK/sXcyI9A2s7Bzr0m8bOFROQm1sTcPcC5Wq2IuThdQ5vmYsiLQmlUoFzoRKc3rOcoAdXSEuMIDTwAZbm4UQE+aJRZSEUioh4fJuN8waSqUilaNm6pCXF8vevfbB3KUqFeh0xdSjH6fWjiQi8TamqLQyvWeGyJMaEYGZlsHdKig3FtUg5AKzt3QmIDKTNNzM4uX0elw6vxbNEdWwcC1Gleg9qVi7Lyb0rsHV0Jzk+EkVGCqpMBXJzK0zEEtJTEwCICfPHp0wtACJC7uNdugaJcRGYW9rlOi82Du489jPkiJ49uBb3ImUoUqIKAFKpGYlxEVjZOhEXFYyZhQ2Q2yJKIBDAEwEsQJBr3w7OHjT5oi9uHj4c2rkcB6enOb2VarZg35Y/KF2xLgKBgJ3r5lC5ZgukMjMSYiOwdXQhJjIYc0ubF/frVIjQoPsU9ipDeMhDzC1tiY0ORavVkBQfjekzlllG3i/GKKmRvGAUpUb+bymopft3qbh/22X7/FJQEdLspXoPnwrcu30dnVaNmUyM0MyRuOgQxKYyBAIBer2ec4fWYSIxRZGegjJLgUQqp2jJKji5e3HmwN/IzK24fGoHD26fJSkuAq/S1cnKzMDC2h4wRCGFQhGpyXEc2DIftTILe2dPylZpwtnD67l37QRlqzUhKSEyZxm5TJXG6PV67l4/nmsbACs7pzydq5TEGGo26Y7W1IUbR5aSmhRLliKN+m0HYOvsyZ0L+6jX5lsGTN7Ig5snObFzCSZiCZY2jjRs/x2Xjm4gOvAmFuXqIJVZILZ2JMjvIhbWTmg1apSKNB7dPIFAIMDW2ZO0lDgC7pwhU3kKRXoSHpZViQzyxd7Vi8igO1So1yXH3snawZ0bdzcDPUiOC0duYYPf5f10GDSPiwdXcnDdL/T5aR3bl47l4tZ0CnmVQ25ujYlYwroFw8lITaDrwF9xLlSMA5vmsPjn7khlT4vRLp/Yyv4Nv1OvVd9cTgYAhYtV5MrJrSya2BlLawdqN+ud81jL7qP4Z973aDQqGrUbiIlYgtjkOYHo4sG1PydSoVqTF855m25DWDV/DIqMVIr4lMPMwvrp83qXoUTZmkwb2Q69Xk+ZinWpWKMZZpZ2LP39e7QaNS07D8TE5MX3eKvOg1k+ZzgmYgl6nQ6xWEKTtl8xfVR79Hr4dpShAOzquQMc2W1wSnD18KHXoKkYGx4aMfLhMYpSI//XFMTSPbxdlPRD5ZEW5JK9V+maBPpdRC+xJ+LxDZzciqLTaoiNCGHz0p9w8yyJS6FipCbF0nXANG5dPEh6aiK+V4+iylLge+UoiXHhhATc5vbFQxQqWga/GyeRyiw4f3g9CbHhHN+9jLqtviIuKph1C0eQkZbMVyP/4P7NU2Qp0gl8cJ1y1Zpi7+TJxj9/pEGb/oT43wHg5oX9OLoWISM1iVbdfuD6uT05y9XP+3a+CrmFNecPbyBLDYnRweh1WgBsnTyQmVlx/sAashRpZKQmcvPsbgQCAaqsDFKTYvC9fBBVlgJTmQX+d86g02jwLlcX73L1CHlwFQQC7FyK4lO+HncvHQC93pA7WqQMNkUbcHTVdxSr2Ijrxzdy9dh63L0r4FGscs7c3L0qcOfcLlZN7YJUZkGXoYt5eOMYK6d0wFRmTrtvf8PKzpU2QwwFVSXcDK+nqdSMgRPW5jrOIVM25brt86TY6VmyK/izq/e7Dvz1pefMvWgZRvy664Vts+2hAOwc3Jj513EABhRfAEDdZt1yHv9x5saX7hugyRdf0+SLr3Nu67Q6PIqWZuKcXQhFT1/XbJup7P1ev3iYwWMXY2PvwqTvm2NuZUudJl2o0+Rp+kFMZBBnDm/ix5mbEEtMOXt0K7s3zKNp59GvnM+HJE2hxt3eWHBl5P+Dtxalf//9N35+fsyaNSvnvjNnzrBq1SqWLl2KXJ4/CxkjRj5H3iZK+jZ5pJ+CIAUQyewJeXCRIhXaokwJw8rWCa1GQ6vuI9n45485eYjWds5sX/UzmRmpODgXxq1wSUQiEy4e34K5pQ0WVvYggIvHtqBRK5GYyihcrCKNvhjAjtW/EBcZhF6vo13vcexcO43tKyZjZeuI3Mya4uXqcHDLfMQSKSUrNsDFoxi3rxxhy7IJmFvYUKpiAxLjwtm45EfMLKyRm1ljZZu3KCnAjbN7KVutGe5FSrFm/kj0T0zmBQIBcgtrrO1d2bliArERAdg4utOo4xAe3T7L7Yv78S5Ti/SUeNQ6IZ4+FVBkJFOhbgfunN+Dg5sXJmJTSldvxfFt87FxcKNo6dpEmftx+/weRFdPYu9SBLUyk55jcvuz9p24OefvVl/ldisoW+sLytb6Itd9TjYSYpIKtojvc8TK2p4FU/uh02lp2LInEsmLBXiXT++heYdvET/pklW3aVe+61qGh/duIJeJkZtZ4OzqyfWLx/n6u0kU8S7NktmjycxUYGFpw0/TVjBzwjdYWdvh/+AWXXoPp3aDNgV6HDMnDyUmOoKAR/fwLlYaJ2c3xk/946VjD+7dAkDLtt1e+nh+8X94l4BH917Yn0ql5MqFk9Rp0OKN+zAu3RvJK28tSl1dXZk9ezY6nQ6BQMC5c+c4efIkDRo0QCr9vCpvjXwcPqZHaXi86qNESd82jxQ+viCNT0gEwNHJBVNdAmJTGS6FipGlSOPS8S0UK1uL0IA7lKnSmLvXjlO/dV8C7l6kbss+RIU+RKNW4VXKYHxftEQVTu5dSblqTXH1LMmD22eICvMn2P8WYlM5bt6VSEqMZf+WhUikFpSv+QVmTwpf7J096D18fs68dDod9dv0z2We3/P7OXk+V89TuFhFju1aikxugchE8kLBj6nUjKKlqpOaFINEIuP66Z3Ubd2PpPgIEmJCMLewxURsQSGfigB4Fq/KnfN7aD/gN/atmUyFOh14ePMEWRmpxEU+RiAQMHDqTiITVDkG+u9KTJIqJ0oKTyOe/294l6zM1D8OvnZMQlwkVevkti+TSKQolQpm/3mA6T/1oWK1BtRv2oEDO9ciN7Og21cj8SlZgV8n9CM+NpKMtBT6DBiH3MyShTMLXpRmC9DhAzqycPnOAt33m/ApXgaf4mVeuD8hPpazpw7mSZQaMZJX3lqUNm3alPnz5/PDD4aq1cOHD9O0aVPmzZv3Qi6SESP/RUJiVG9lAfWhCpveRGh4dJ4r7LPN8G0tpUidqnB632oq1GxJVmYGF45t5qsRC5GZW7F69uCcyKK1nTOxUcEAxEWF5Nqf3NwKjVpFZMhDHAqVRqsX4lW6DjqdlruX9vLo5jFcXD1o3WUgK+aNIejuCVp06MeNi0c5sesP6rTsh0Qqp4h3iZx9bl02ge6DX768/Coy0pK4e+041Rt2BqD7IIMNVNGSVXhw6yzmrhVx83TP1cUp++8aTXMb8/cZ9VfO3xHxCjzcn0aH2n4zDeB/7d11dBRXH8bx726yEndXgoQAgeDu7l68LVKkCqW0QEuFvljx4hQrXtydosXdggQSSIi7bbL6/rEkJSVA0CD3cw4Hdmd2dmY2yzy5c+/v5tYp7frVrGfaz/fNkT1/sW3NLGzsnAGwsLLlqx8XPOVVj3fi0Gaq1W2b7zIrGweSEqI5c2wXtRt/gK29MwaDARd3PwBMZQp2bFhC789+RKNRY2fvzIqFv3Ev9Ab3w28zflQ/EuKicXH3QSaTo9XmnaJ0we8/0u/L0c+97/l5OJx+1b8Dw3+ezo/D+iBXKKlRuzH2ji4c2r+NU8cP0KhZR/5aPge1Ohsvbz/0Oh2XL57i+19nYWfvyIRfBpOVpaJ+47Z06NKHYZ93xcrajrA7Nxg8fBw6rY4LZ49Rt2FLJo/9Fr1OR/ePP+f6tQucOn6AMycOcf7sP1y/epHMjDSGjZrCjeCLnDp2gOSkeEoU9aTu6tVPOSJBMHqh9JgTTE1MTGjSpAnTpk3DxOTlzsoiCC/byxjg9Lpv2xdUQUfa57SQFsTDgRTAp3gQUeE38XnQElivZR82LB7NhoU/Y2FpR2Z6MgBm5lZ4+ZVhxcxhhN48l2eboSHXsbBxQW+Q4OVqR606TYi6c5awa0dw9ShCjwE/4ubpx5+zfzT22cxWPXjdZXr2H0FWcii7/5rIn1MHs2r2d5w9tIHYqNC873HjLKE3zvLPnpXcu32ZkwfWPdLqaWFllxtIH3blzH5OHXq9LVLvqiMPpgjNsWHZZIIvHsuzTn7PtfrgM0ZOXMfIiev46scFBF88xoZlk3OXpyTFsW1N/uH+xKHNeR7/vW1ZvusBVK3Tmh3r59Gs/SfY2jtzcOdKSpSpAv8ZyZ9jy9o/sHNwpkLV+nj5lmDYT3ORyeScOJx/i+yLBNK0TM3TV3pAoTRj1qKt2Du6cOPaBfbuXM+Q4RMAMDOzYMrsNVw6f5LuH3/BJ5+N5NSxv1n150w+7v8NMxZs5tzpI6QkJxIdFcGQEeMZOvI39mz/t4X93OmjtGrfk2nzjBUYWrXvRZXq9QmqVANnFw8mz/6LHr2/5OhB43lwdfdi6tx1JCUlERkZ+dznQHi/vPBAp8aNG3Po0CFsbW1FC6nwNWDuZwAAcwhJREFU1njcrXudVssfv48iKiIUAwa69xlGyTKV8l33v62k1y7+g6dPSfZtXUJA2eoElKuRuywnkIac2UQIULXBB8Tcv83SqV8w4Ic/sbZ99Lbts/YjfdZAWpBW0oenC/V0/nf+9y9+MQ6SyZk/vmzVJnlel9PiWKVeB6rU+3fe+9CQ67n/rtugee6/FUozWnf5NM82KlRvTEZGCn4lyrFz/R+snP8/4mPvs2XVLFw9iyBBj7m5GYkJcdwOPo1Oq2HD4l/JTE+mVfdvcHb3Y/e6mcRH3eXe7ct0GzSOTX+OxdzCmuALh6nXui/J8VHERYXi4OJNTEQIer2OgPJ1kUpNSEmIJvTqEeLD5Ny6dJRsVTr12g5EIpVy5sBaEuOM56b3dwsxMX05XUGEJ7t24QhXzh3C2c0XO0d3XN19ObLnL2o36cL8SYNp33MoYSGXWPL7cHaum0fT9v3Izsrk3p2r/LNvHRKpNM9sTmG3LnF0/zqyVBkM7lUJeycPkhOiyc7KJEuVyWc9L5KVraK4f1DuPsRGR3DxzGHMLSxx8yzC+FH9cHTxoHbDtuzf+Reht68BMH3sYLr2Hsrv4wYz5vf1fNm7Id6+JbgXepOBX4/Fv3QlZoz/mrjY+7i4efHFd1MIvnyKVYsmk52tolrtZjRu1/+Jg5xy7koAuHv8O6vY1UtnsLKxw9TUeIn39jXWb7W2scPNw5voqAjUajXh9+4wf+YYQEJ6Wgqx0fexd3DCysoGe0cXNJp/Q3GLNt1YMHs8u7etoUXbbrnPm5iYEhMdwbifvkSVmUGRYsYZsrx9ilK3oiuL3dxQq0X/ZqFgXsroewcHh6evJAgPKaz+pE9rJb18/h/sHVwY+PU4MjPS+GloNybOzTsH+eNaSY/uXUv7nkMfu20HazkhD/6dnprI8ulf8eHg318okIYFn+DA+qlkZakxkSlo1Ws4yyf+77HTWT5vIH1RD4dRTxebAr8uKuIO3kUCsHdyp3RQDS6eOUh2diahty4TVKU+pcvXYtH0EciV5uj1OgwGPVmZ6Vw4vgtTUxnOHn64eBTlXshFtiybQHpqItmqdExlcg5tW0Tdln2IvHuda+cOIlcosbJxRCo1IT01ESs7J2LuXeW+KhmdVo13iQpcO7sPE1M5EXcuY2Ftj1xpzrVz+7lwdDMGvZ5qjXtg4ZH/LzFPEpnwfl205036CmdXH1JT4ilSvCxOrj7sWD+X9UsnUrp8bRydPVi7ZALL5/4IEik1GrSndFAdUpLi6f/NNBb/Phy5wpzDu1dRpXYrxgzrSOS9Wzi5+hAVfgsDULdZNzatnIq9ozt6vQ4bexeWz/kBFw8/MtKSGT/8Azp/PJziAZXo9PF3uaH24qn9VKjTlXljuiJXKPls2CRWL56Mi5sXX42cBsDILzowdoaxJb1n6zJ4ehdl8axf8PYrSd/Pf873mKMiQhn7+wYi7t5i/86/SElOxNOnGIO/n876FTM5c3wfaSlJDP/fApRKc0Z80Z7G7frnuy25XE5yUjxJiQm5z0keahTq0LUf98ND2btzPY5Objyu1dfdw4f2H/TGp0gJ1q6Yh6u712PXPfHPflq2606RoiX5rE9rypavCgYDITeukBAfy4hffmfdqj9IS01+sEP5b0cQnkSUhBLeO08a4GRhacOZE/sJrFAD/9KVci88B/dsYNv6hchkMtp8OJqESGNrSE4LTZ2mXbl89iBZqgw8fUuya+MfrF86kRKlq1ChxZA876HVqFn0W3/a9f4RF89iAOzfNJdLJ3YiV5rT4/MpnN6xlOTIK9g6elCmWiv2r50MBgONuw3Hq3hFtiwYTmLMXaLDrtJ80AJsXfww08Xw9/ppjz22wgikzxtGAWKi7pKWksiJQ1tJiItCq1EjkUrp+NHXLP59JMcObOLk4e3o9TqsbV1IiA5DnZWJpbU9184dAMDS2h51toq0lARksnBM5UrsHFyxtnPGYICju5dh7+SJVGqCX0AVrpzeS3zMPcwtbZCamBJ77ypKcwsyUhOJj75L0dLVuHvzKDKFGaYyBZlpSUTfDSaoRhtKVmhAaPBJgDz9SQvqZQ5yehMkpKop5qok6tKjywYO+x2/kuWZ9nMfOn88nIO7VlG+aiMatPyQKT99hJmZBQqlOdOWnSYlOY4V834mJSkGmVzOhmWT6DXoV04c3gpAbPQ9SpWriYOzB+YWVgRVbcTVC0e5F3oNg97A8PF/8ePnzTmy9y9s7F2QK5QM+XkjX3QvT3xMOE5uvnn2zdzSmmUzhhATeQ9nN29mThjKvbAbjB/1CcN//YPvv+yITCZnxOftGTdzIz5F/On92c/8+l1POnT/lN1bltOg2QdcuXCMiT/dJC7mPjevnUer0bDmz2mUKF2B0//s5dzJg+i0Gs6fOkjIjYu4uvuSpcrg6IEtODq5k5X1+O4+Ldv14JvPuuFfqixW1vl/r7p//AWDB3Tg4/6PL23V/aPPmfi/oaSnpeJfqhxW1raPXbdI0ZKM++kLzMwtaNysA7Z2Dty+FUxcbBT3wkL4rE9r7B2csLVzxNXdm5K+z/Z9FwQQoVR4jxSkL2nxgCDaftCfpfPGEnX/Lt37fEOjlt3YvmERE2Zt5tL1cDYv/YVKNfKOOHVw8iCwYj3a9xzKkb1rCKxQl0ZtPmb4oGZUaDEkz+CmXWumYuvgRnqKsZUjNTmOW5f/Ycj4zYReP8OaZdMws7QnoFJTKtbvypKx3en57RIkSPhr+iA6DJqCX+ma+JSswg0rOxIib1CqVEnAiw4DJzHvh7asmfElGakJtPtkPDKFGevnf49WrcLG1i7PDEVR965TvUkv/IPqsnPlBFKTYslIT6Vm668o7uf1Quc7J5A+axjNEXLtHA1b9sS3WBluXTvL3q1/otVquHbhGNnZKmrUbYdviTKsmP8r3j5+hN08Q9dB45nxY1ccXX1RZaRiaeNobLAxGHB08+XurQuYyhQYMP5ykDMDkFyhxM7BhWadv2T/lvkYDAays9TotBpMTEzp9/1S5o/uTlpyHBp1FjKFkowHMyL5lapGaPAprpzaRdnqLR9/QK/RwyPvC5tMrkSVmZb7WJ2twlQmZ/mcH2navh/2Tu4A+BYzzlTl6VOSjPQUUpPjGD/cWIbIVCbDxs6J2Kh7mJlbERl+CzC2Dto6uJCdlcm5Y7txdPLg8J7VeHiXoEGLnlw+c4i5v31BYnwUHj4lSE6MoXipSsTHRKBQmKPT6ZD+p0Vvy1+zGD5pF9N/aEN2ViYdun3KiSM7ycxIIz7W2DeyZv3WrFk6DQCNRs2M8UPwL1UBO3tntFoNGemppKel8NOkVYz/oS8+RUuiNLOgz+c/sXH1XALL16BKzSYs+2McY35fT8/WpRn0zW9M/fUzSpSqQLM2vfjus/aP3LrPGdxUr1Fr6jVqnWfZiJ+nA3lLQc1fthuAGrUb53l9+Uo1KF/J2L1o4sy8g5By1nFz98rdZs6685fvybPugpV7jduvk7f7DvxbBmrJkiWPLBOExxGhVHivPK0M1L2wmwRVrkvN+q1JiI/ml6HdCapcFxc3L0xMTbF3enS+7IfnDs/h7mOcp1smN39ktH3VBh9Qr1U/Zv7cFf9ytUmMjcDjwZzimcpipMbdw9HRCTtnbwDiIm6yclJfAFQZySjMLLl38zThIefRaHTY+1Th/OF1XD25k/TUBDTqLDoMnETIpcNcP7sPua0PgXW6U65ceZZM6Me8X7qiykjFxt6VIiUrc/HYFryLBeHrXwkLp5LcOLsTTXII8Hyh9EXDaI67d65StW4rEuIi8fYrRcXqTblw+m/On9yPlbUdF88e5NqVE+h1Oi6c2odBr+PurQuYWdoglUqxtnMiIvQKJlJTdDotMfdDMBgMaDVqkhOi88xkpFFnceXM3yQnRCNTKMhWpWMis8Cg1yJXWrFhwQ/G2ZiyM7G2cyGgYgPjrfsz+4gMu0bZ6q1wcivCot8GUrxiJodWHkSv0+LjX4l6Hb584nG+i7fuc1pJAdy9i7H1r5nUb9ETvV5P6K2L2Ng5YWFlS7nKDXJfEx4ajJ9/EPdCrxFYoS46nQ6DwfBgStAo5AozipeqRFx0OLs2zKdU+TrYOrhwdN9aFAozigVU5OKZA/gUK8OZoztY+cevpKclMvDbGYwY0IDoyFAqVm/KkT1/ceXcYQIr1s133738Avl9VFtiIu/h5uHL/p1/cS/0OnKFGTqdcSKFxq26s3b574z4vB03r53DwtKajweNwq9EGWZP+o6JPw3A0dmDWb99Q3pacp7pT23tHLl+9SwKM3My0tMY8Xk79Dodnt5FCQiswo6NS7h49h+UZuZotdrcfqFvE1GXVHheYmSS8NoVZn3Sp7lw6hA7N/0JgK2dE1a29ljb2BMdeY87kZloM2NQPLh1m5qSiMFgICr8NvDo3N6PG23v5FYESxsHajbpyfYVv2Hn6M790KsAxIZfxsnN88H2jF9PV5/S9Bq+lJ7fLiGwehtuXTiIuZUDRSt1QG5mg62llPJ1OtFz2EIsrR2wdfbCVCbHzNIGjSYLM0t7Lu2bz4qpn5OZnkRQzbbI5Eo++nYBF/7ZgkadjVxpTvDF45zcOZek+1fQ6/X57vvfW/544vl7WYEUoPsnP2BqKuPenWtcOnuIqnVa8smQiVhYWqPKzKB8tUaUKFURExNTgqo0wsLagVMH1yOXm+FVNBArWydKBNZEampK617f4e5dEgsrWwwY0Gk1gAEnd1+CqrdAp9ORmZ6CnZM7Hw2ZgUQipXT19pjKFbT+cCQfDp2LTK6kVa/vUZhbcvfmOU7tX02xMjUoWaEBO1aMY9WMr3DyKUNK1DV6frOAj0YsJT01gZBLh596rO/SrfuHZ3EC8PYrjaOLFz9+0ZzRg1tTuVZL1i/9jTs3zjN2WCcWTjXeXr505m9+/botAWWr07R9P/oMnojBoEetVtHrszHIZAqKl6rMbwuPYGIqIyszHZlMwYgJazGVydFq1ARWqEv/odPwLVaWKrVaUjygEr8MboW7V1GsrO0IrFiPus268/P0bVjZOFC2Uv3c2Z/6fzMNmYUrPT6dyOT5O/EtGoB/6Yq07tyPWcuPYCqTwUMTKTi7eDJu5iZKl6vGhNlb2LJ2Pja2DhQtEchXI6fTrE1Pxs3cSN1G7bkVfAG/EmUwGAxsX7+I2csP07Pfd1jb2jNu5iaKFCuNpZUNDVt0oXnbDxk5YTVLVu99KwOpILwI8RMvvBcKWiy/efuPmDtlBEP7N0epNKd5u49QmpnTov3HTBvVCROphE+GTsXK2p6pP3/E1fOHMbewBsCnWCBLZoygaMkKudv77/zfD6vZtBdTvmtNckIkRUtXY+zQNkhNTOk+eBZn9q/4d72W/Vk6rifZqnSqN+uLW5EyHNw4DZ3ehPTEcJLjywGQlhxLSkIUNg5uua9NSU1HdXErXsXKYe/sxT+7/gQM2Dl55k6fmZIQzcJxfchWpfFB/9Ec3LqQC8d3cPXs35hb2tK6xzBuXj7G+WPbUWeruHbuIB6+AexeNwOp1AS5wgxbBzeuX/yHwGotCSjpz5bVM9Gos1GaWdKy84Bn+qz+q2ylehzYsZJVC8YikysoW7EuURG3+Wf/BvQ6HcUCjOe7aKkaqNLjyEhN4u6tC6gy0yhTsQH64kFsXTYBiVSKQa/D0toBiURCo3YD2b56MpdO7UadnUnF2m0JuXqCzX+OwczamWIly3D/pk/u+XT2LI6LZ3HcfQKIibiFi2cJbOzdcHIrwsffLuB+fCYX/l5CYLX2uYNOmnQbTsy966yY3B+tOosS5etTvVlvloztibmlHRmZKtyKVWH3jcNUbtSToDqd2Dz/W1ISIrF18qLtJxPYNH8Y2ap0XL0DsHfx4eSeJZiYyGjZ+1dsHT1ZO/ML41SlfuUo3/JbDiz8hJOWtkSF36Rz/zEUDajyQuf/WeQE0pxW0hxd+ozM87hR64+fuq0a9dtTo377PM/lVLToNeh/XDl/hM4ffYvURMqPU7fkWW/kxHUANGjZ65Ht5myjQ6+8gxKT04wjzX1c/r2zUb5KPeZOHo6VjR0KhZLkpPxrAHv6FMfV3YfjD8pC2do7ce3yKQ7t24i9gwvFAspRzL8ssyYOo2K1BnwzoCVW1naYmVmg02rzbCtbk/8vhG8L0UoqvAiJ4eGaEm+Zy5cvAxAYGJjv8szMTIKDgwkICBDTnr5BXmVLqV6vJytLhVJplqdE2YvO4PSshfILOnPTyb/XsG/jbKztnEnLyKJUxfrUbffFU7efM2NTRMgFDm+Zg0GvR6/XUblhd878vYqewxZy6uhuYsIu4R9Qlp0rJyBTmCMBdFoNaSlxeBcLIi4qlCxVBraOXqgzk0AiQZ2ViUQioVz15sTev4NBbyA9LZHyNVpw7dwhTGVylOaWhN08j5OrD6YyOd7+VVEoLIgOPUOpctWRSE1wdfdl25o51G1mLMb9Kly7eIzT/+zCzMySxIRYGrXrz4XjO+gycCyZackc2LqQctWbc/HELlr3GMae9bOIDr+Fk5svNRp3Y+ea6VRr2IVLJ3eRrcqg8yfGmpIRsen4+Hg+077cj8/kyt/zqdK4J45ufrnPXzq2hRJB9ZErzFj2Wx8+GrGUmd81Y9CYrWxe+hv+ZSoTULkZa2d8RqUGPYiPuk3tNp9ydOtcnDyLc+3UTsrWbEeRUjVY+EtH+vy4lrSkGHYu/Rlv/8pY2TpTtmY7/pr9Hc3b9mL574MZMn4zMREhnPx7DV0HTXiZp/yxHhdIXwW9Tk9WVhZKpRKpyYvf8MsvkD7O9191Ysz0dS/8no/zNs91/yoDqbiev92eltdyiJZS4Z33MorlP4+CztzUqP2n2Pi3wtlWxpIxXanWrA8KpcVj1394xibPYkF0/3penuUlKzbiXkQ0rr7lqFipOgB1W+dtrbx8ciddv5jG7FGdsLRxIjMlhqysDBRKC8yt7HBw9iQhJhwTUxkZacmUqdSQiNBrpCTFYGvvgodPAKYyOXKFOTcu/kPJis2IuXOakOvniYsOJztLhZtnEZKT4ti+bh5d+wwv0LlYt3QynT78twUrLOQKAL7FjNMcZqSncO3icSrX/HegWaXqTbFyLYVep+XApt/RqLNYM38UYKyhCGDv5AEYi+XXa92Xq2f2577ep1hZfIuXY/VcY2teRGx6gfb1YffjjSW8LG0cSU2Mzg2lKQmRZGWmsXP5/1CYWaLVGn8WbRw9iEkxoDC3wdbJC6W5FVqNmoToUK6c2ErIpcNoNVkoHvR7tXP2JjMtATsnL0xMTLF19CArM5Wk2Hv4l29ITJIaJ6/SxEeHYWXjiLmFDdZ2zui0r+dn/3UG0pftWQLp5r/mYWVl+8r25W0OpILwMohQKrxWhdWf9EVbSZ/Fs87cFJWkxgbQ6TQYDAZO7VnKzQt/I1eY037gJG5dPMTFoxtQmlmhMLeiWPVe+Bf3ZfnEvo+tRwoFK/2kMLfF0s6Vdj2+YuZP3bC1d0GlSud+WDBm5lZY2TgCcO3sAT76+neWTh8CSIiOCCHq3g0kUhPAQHrsTfR6HUWKBaJQmqFRq/Es4k9CXCT5jAMrsJwwmsPC0iZPIH1YUf8ynLNzQWoipVO/0WRmpHDj4tGnvofkodHXOYH0WVtJwVgGSq5vwLEdCykSUA0kEg5vnkPs/Vt8NHwpWao0lv/Wx/ieD15ja533lw87Zy8qNehB5UY9uX52L1Z2LkTcvoBEIsXcyp6kuHvodFrSkqKRyc2wdfIkMvQyLqW80CRcx77cB3mO53V4XwIpQNsuA2jb5cW6ozzOs8ze9CYSt+2Fl0GEUkEogGed4/5Z5rc/v3c+oec2I5FIqVCvC1dP7qDvj2uJCDnPP9vn4+zpj1fxCjTs/A3Lpnz+1O09yxSimemJmJoYWD59CAaDAanUhOKlq5GcEE1achyxUaGYmJhSxL8Cf4zvT2pyLCYmMqztnPHwDSA5MY7UpBhOHtmOg5MHKclxyBVKdFotN6+eRmoiRa/Ts37pZFSZ6cjkClKS4vD0LUnkvVtYWtuRlBCNlbU9PQf+RFJCDHN/G4wBaNmpPwmxUVw6ewiZTIZWq0WuUKLOzqLbJ9+zZ/NiEuOiSEmKx9bJg1NKc4qVroqltT2r54xAo1ZRu/lHBT4XOZ7ntn1OXVJX75J4+1dk6YSPMRj0+AZUw8bRnSVje2JmYYNcYY5epyVbY8DX04nQk3m3VbJSUzbPH8blY5sxlSvo/MXs3GVSqQmVG/Vi0ejOgIF2/SdhaevMqulfYvL3CnxKlKdIyWcv3P8i3qdA+irlBNK3tZVUBFLhZRF9SoXX6lW3lP63T2nOrfvX3Z+0oKH05N9riEpSU7d5VwAiQs6zdsbn2Dp5AQZsHT3xLVUdg0FPhbofsGzK5zTt/Cm2jh4sm9iXXvm0lN6LiH6klfTyiZ38s3MxZhbGUfHR4Tfo+s1K9q8YibmlLTqdFp1WQ6e+P7NzzTSiI0Iwt7ChxxeTmPlzD778ZRWr544AiZR6LXuzbsGPWNo4IzOVkJwUh06rofcXY1k25yesbBxITY6neEBF/PzLcWDHSj7oM5wV80fTrd/3rF38G+aW1ljbOJCWmohP0dKc+WcXn42YwaxxXzDgmylE3L3Jod2r8S0WSFpKIqXL1yQ5MY6i/uVYvXAc1nZO1KjXBhNLTy4e20KZyo3w8w96oamOn6eVNOe2/bMUy88pAfUyRtznjLZ/3XVJHx5h/7RAemTPXxw/uJlvx67MfQzgXbQ0PkXLPOmlj/Vwn1IDepbNGUVsZBgGg4EOvb6heKknh/OcQJpy/zQ+fiXZsWExZcrXILB8jUfWfZaph3OsWjTpsdv7LxFIC0Zcz99uok+pIACH96xFqTChYXNj2ZcnXSwW/P4j/b4czZH9m6ndsC3w+EC6YdnkR+a337d1CUcObEdmakK56s2p1bQX90OvYSpX4OJR9JFt3Lp8jLtRiciV/9bLtHH0xKtEJTp9Np24+yFE3b2KTqvJLQ9lYionMy0JudKCzNREAK6e2sXJ3X/Suu//cHI3vo86W8WsH9rTc8hsnNz9CKzWnMBqzfO8/927EXw05Pfcx6vnjkRhZkG7j77nnz0r8fIrg4mJKQqFOZkZKSTFR2Lv7MWhHUtw9SpBpfrdQRXN/h0ryMpMZ9ua2RQpXpaAstXYs+VPQq6fJyE+Eq1WzaaV01Fnqdixbj5ZWRmYyuRE3LuJT9HSaDVq9Ho9d25eRqfT8sfUb1GaWaBRZ+Ho4klqcgInD23DYDAQff8OOq0WE6kJN66eJlN1DE12OvoHlQSelwikBfc8raOhty5y7vgeKlT/t8j68wbS/wq+eAw7exc+/nwcqow0fvu+Gz9N25bvujlhFIwtpNMXrqVr78dPDQwFm3r4eYlAKgh5iVAqvDZvcn1SgH5fGkde79q8NDeUFlR2looLJ/fR69tlOFjLmf1Ld8pUasSlk7soVqZ6vqH01MG1SK39sLb492toZeuEm29pFv36ARp1Fq37jCUm3Fj7Mywijip1W7Nj6Wgc3IpgbW+8IIRdO0G7AROwd/bObSUNPrufgIoNuXZmH3XbPDp/ds40ok/0oG+iraMbZhbWOLkVoVO/X/Ltq6lRZ5OSFI+FlS1ZqkyyszLx8SuFXq8jThNBQGA1/jmwiWbt+7Jszk8olGbo9To02VkkZWchkUg4smctAHWafMDpo9sxGPScOrIDnVaDk6sXaSmJJMQZQ25iQjTuRSuSlnYNMwsbMtKS2LVmOmUqN+LormVIpSY0bNefQ9uXoNVk4+TuR8O2/dm/eT5xkaEolBa07vUdpqayFwqk22d/QqMuwyhers5TX5NfIA29doKw4BPU7zi4wO8Nb1Yg/fmrVnw7dmVuabStq2fg4lGEKrVb5a7TouNANi6fTNlK9QDYuHwKji5eOLp4Mm/iV6izVTRu24fAivVYNH0Y2aoMLK3t+OKHP5j608fo9ToqVG9KfEw4d25eRJWRRo9BY0hNiuHPmSPIysrg7LFddO37A6YmxoB37O8NLJkxAm+/UlhZ23M//DY6rYbfZm9k2fxxNGrRlXOnDqDKTMfHryRb1sxn5cLfCAiswocD/i1h9biph7//siNjfl9PTFQ4qxdP5tNvJjDhx0/IzspCq1VTpnwNrl06yapFk8nOVlGtdjM6dP+Mbwe1xtbOkeiocD4fMYvKQSVf6Wf2qohAKrwKIpQK76XpYwejNDPnVvAF6jbuQOvO/fj+y47UadSe0JCrHNi9DrlcwZoV81AqFPT+cjyOLl7MGNMfdbYKrUZDQNnqudszMTUlLvoe18/upnKNRgz4/k/joKUDa7lyZh8Dvl/C6jnfkZ2VgYWlHe16/0jw+UM4+qRSo9Folk34EE22itLVWlGzZX9SEiKJuRfMwQ3T+ODLWZjKFIRFxOHi7Y+VrRNpSbG4+5Ym6u41Qi4fITH2Hr2+XZS7PzcvHqZ++0/ZvOhnAFISoti5cgISqQkKpQVSuRVx9y5Rt+XHePgEsOOvacRG3uHwzj+p0/wjrl84TNjNc5Sp1IjYyDtIpSYolOb8PsrY4lyhTmd0d89y7eJx0pITsLFzws8/iHPH9xAbdQ+dVkNoyGUkEglajYbL5w4jlyvY+tcs9HodGWnJZGeruHsnGDCg1+uoWq81f29bzv5tSwGwsXWkXJUGnDq83TiiP1uFja0jCqU5er2B0ODjpKck4OpVnKyHprG0sXehZbeh3L52mkbtB2Fj78KKmcYC7bH379Cx709E3btBdlYG0ZnG/wKfJ5CaqOPwKVmZa6d3PTWUvu0tpE9qHa1YvSmXTh+gWj3jL3JXzh2iSbt+edaxtXemSp3W7Nr4Bza2jrnP7964gG79f8S3WCBbV88gLvoe7boPwc8/iOmj+5EYF4kqM52+Qybi4OzJoV0r6dx7BGeO7uTiqb2kpyZRLKAi1eq2YdH0b5k5diCW1nbo9Xr2blmET9EytOn1A6vnDadhm/6E3zzGpXPGX6gcXTyoUKU+XXsP5e+dfxFUuS4tO/RmaP+8dxTym3q4Sesej5yH08f2Ubpcddp3G8RvPxkHQ0Xfv8vw/y1AqTRnxBft6dD9M+JjIxn52xpOHt7OjXO739pQKgivggilwnsnZ3Ry5RqN6fP5z3w3qDWtOxsvok3b9OTwvo3UbdyBkV+0Z/DotUh0yayY9zNV67SmZGB1WnQayMyxA/Ns09RURqtPpnJky0y2//kDFWq2pkPf0VSp35liZaqTEBtO085f4VM8iIUTPkEqkRJQvi7F6w7in61zqddhMF7FK7B66gACq7chOuwqPb5dQkTIebIy07C0UQBw/tA6SldtQZlqLdmxdDQGvR6/0jWo3ebf/dGos1FlpGJt54KThx/3Q69gae2AWp3Fh0Pnsm7ecLxLlKVKzUacP7aDhJgI/MvWpN1HI9m7cQ5xUWFYWNvTtNPn2Dm6E3zhMKrMNLQaNV/9bw23g0+TnJREyOWjaDXZmFvakJaahEwmo07TD4iPDketzqZ5h34kxkURGx2OXm8sEF6qXA3WLPmNov5BBFVpwPa180hJjicxLpKLp/5mwLAp7NywgLiou7h7F6N81YYolGYA3Lp2lvJ1uyM1MeXsodV06vszq+eOpFO/X4iJukdS7D0AbB60IFta23N01zJM5Qoy01MAqFq/E1tXTEShMCOgVk8UZlbPfct+/9qVlK3ZloMbZ6DOVrFqygAsrO1JSYiiXf/fsLC2Y8PcYaiy1EilJjTpMpQ7V26yf+0kJBIJDT8YRs44/LTkOLYuHI46KxMzS1u6fDUn3/d/3YG0IH1Hq9RpxYZlk6lWry2Jcca54aeP7os6W0XVum1QKs3ZsX4eHt7FOX9yL7UadcZgMLD1r5mE3rpIZkYqnwydSkxkKBdP7ScyPAQrG3uyMjO4ceUUAAumfsPI39Zx+exhNiybhMEAFWu0IDUpBoWZBV5+pbC0tkcmlxMVHkJiXCQ29p6kJsfi6lWc9JQ4zh1ZQ3p6KkGV65DfUAov3xIAKJV5z21+Uw/XbdLh3xUebCs66i5FipYCoGgJY785e0cXZk/6FgsLazTqbACcXL0xMTGleBEPLpy9+8yfyZtAtJIKr4qYZlR4Z0XEq5HJFWg1//Yjy85WIZMZb+95eBVFJpNjZm75yGtTkxOIuBfKzNHdmTP+czLTU4iNuodXkQAAfIvl7aydkhSH0syKQd8v5Jf5J0lJiuX21RO5y61tnTi0fRErZw4lLjoMnV5LSoYORxs5CdGh7PtrAov/15WkuHukJERSq82nrJvxBecPrkEqNcndTlJcBG6+pQFw9SlFUmz4I/t+59px0pJjWTP7G2LCb3HtzD4AHJyNc9mbmVtjYeOMXGGOTqshKf4+Z49uZfXckUTfu0lqUiwAtvb/XniS46NwcvMFoGhAZSrWaILBYEBpZoGltS2Ozh7cuxNMycAqxEaH4+Tqxdo/J7J78yLsHfO/gJmYmKJQmmNj54hcrsTNsyirF44jPDQYmULJf3ODqdKWpPj7eBcpRlLcfQB0WrXxGOL+7Y6Q80vHsX2rqN38Qxq07Y9er0Or1RAdcYuOfX7E3MGPyDvnX6gP6f07l/DwK4tfqercunCQ1KQYOgycRLWmH3P97F4uHduCd1Brmg+YhzYrmZBLhzi4cTofDl+Gb0A1di775d/zGxdO3XZf8vH3qzAYDKQkRD3y/vkF0hmjOhd4/5/Vw62jT+o/6uJehKT4aHQ6LWeP7yYtNYn2Pb/mh8kbuXbhKFmqDNJTk+j91W+07zmUI3vXoFZn4eDsQdU6rVGaWXLh5D4MegO+xcvi6uHH8PFrkDxUFF+ChNBblwm5dpoZKy/QqPXH3LxyAht7F+7fu8nujX9gbetIz4GjkUikhIffJyriJgqZhJCzm1AqzWjR/mMsrWzQ6/VE3AvJ2XCeqUPzk9/Uwwa9AbU6G41GTfjdmwC4exbh9k3jYI67d4xdbpb/MYHBI6fTve8wsrIyH/Qhlby1fUhBBFLh1RItpcI7rXiJkqxbPoOmbXqi1+sJuX6Jjj0elFV6Qj1HKxt73H0CGDlhFWkpCZw8vBV7RzfCQi4TWLEuEaHXKepfPnf95MQYdi4fx2ejliCTK3F09TEOvpFIwGDg4LaFVG/UjaIBVZgyvLXxQvhgmZ2zF1Uaf4STRzGO71yIlZ0zN87to8ewRZzc8yc3L/xNUO2OANg6uhMVdhUHV1+i716lbI1H+77eOH+I9p+MwdHVF71ex6JxvalUrzMg4fKJnVw7uw+fwH8HnNy8fJxSFepRv3VfrpzZj4OLt/H0PDSS3crGgesXj1C7+YfcunICnVZDckIk/kH1cXNx4FbwOeN5OrQNhdKckOBzNGr9IbFRdzmybx0KhRnlqzVm/bIpZKanEnM/DICE2AgyM9KwsXfixpVTmMrklAysSqUaTdmwfBqpyfHcDrlFXGQIUqkJ8VG3uXpqR+4vGhZW9iyZ+iVefo+O6CwaUIUNi0djZm6FhaUd2ap0slUZLJoyGIXSio79Rxfsh4hHA2nU3WukJkbz1/TP0KizUJpbYevkidTEFEtbRxJiwoi+G0Wpml3x9XR6UE3BWNZJYWaJiakcCf/+/FnaOPH3usmYmMpJjAnLM3CrsFpHn2UgU+nytbhx+QRXzh3GytqONYvHIUFCRnoy3n6lMDO3xMLShqp12rBn00LU2SqCL/5j7Ot57xYXTu2jY69vOHZgI8lJscyZ8DkmJqZkpCcDYMCAhaU1GekpDOxcClNTGaYyOeUqNeDq+cOcPrqDjLRkZowZiNLcirULvsPe3oGw28Fkbk5DIjVhy9o/iAy/w/rlM3Bx9wGMLZpzpgzHv1SFxx7b46YertWgDcM/a0uJAOP/A1VqNuXwvk18/1UnpA8GJuZMKWpuaSwHptNpUchebx3Zl0WEUeF1EKFUeKcVKVYaZ1cvvv6kGVKJlAbNPyjQlJf7d6ymar1OjPmmA1lZGXzQeyRlKtTh+MFNjPu2U57ABsaRxMUC6zBpWAvMLW3xLh5EibK1yFKls2nJrzTrMpi180ZibmWHTK4kLTkeJ69SbFv8A236jWPLguFkZabiXiQQSxsnsjJTmf9jW8wt7Wg3YBIA7g5y7Ot0ZPOCkZw7uAZ3v7J4Fgvi/OH1ufuh06pJjAvH0dUXMIYgd99S3L1xJncdE1MZiTGhuDuVRZ2twsTEhPDbl1k561ssbRwIKF/3kfNhaeOAs7sf00Z2wkQmx8HFC3VWOuePbuCyTIFUYhygpFFn4+cfxIEdK9myeiYyuRJ3r2I0bNmDaxeP06rzIGRyOWuXTGTXhgUkJkTz+YhZXL90guDLJylSPBC5Qom1rSO2Tt5ExadhbedMuw+Hoc5WsXX5BNp9/AOb/xz7YM8MfDR4OhqdHjOlEqlUSvjty9y7fZmyVZtQtmqTPMdRvFpXild78VH218/uo3nPHygaWAuAxWN6oNX8e6s7LVOHlZ07phpjq3NKQiTOnv7GGqWqdHRaNarMVLYt/h69XsepPX/ywVdzCLl8iOS4+6ye2p8Og6Zy/cp5woOPIFEnc8LGgY+Hzubyqd3sXjsdN29/AP7ZvZydf01Bq1Gj06rxKlqWL//3bNNgpibFcmDnajyLBhF2/ST9Bn33TK+vUrsVO9bPw8zcEntHNxq16Y2Hd3F2bZhP7cYfEHzxeO66ZSrUIahKQ9JSE2nY6iPOHd+DrYML4aHBeBctzbAxKwDjgClrGweGjVnBsD41cXLxIqBcDYaNWUlKYhz//L2Re/dCKVG2DqYmpoTePM+IX2cx6ZdP+e6X+bi4ez91v1t17Eurjn3zPDfm9/V5Hstkcr74bvIjr237QX/afpB3EOG3v+SdXS2wfA1adf0K+HeE/fT5xoFS5SvVoHylp5eMehOIQCq8LiKUCu+0/Tv/wtOnGB8N/B4wloS6fP4YX42clrtOzkXov3/fjVHTqEWnPNv7fOTcx75XlcYf0bzjJ3meK1etOeUelGIKrNI0z7Isy5I0ame8IPb6bmmeZc16jsrzOGdqUXcHa7p8OTPPstZ9fs39t4mpnI+/XZBneYsexik+g2q15fKJnZSt1oKkmDBs6jTG06805la2WNk4EHHnKhmpSVw8sYtO/X5h+Yxv6Nj3J5zdixBy9STxMfdo1GEQZhbWHNu7CqW5FWUqNcTM2oULRzdy8fQBlGYWnDi0FVcPX5zdfDA1lXPzmjEQW1jZ8Pf25ciVZuh0WoKqNuR++G0AXNx9OXF4GwnJaSiUBiJiUjAYwMunKFKDmh2rp6Iws0Cv1yOTKVCYWZIQE45MrsRUJkeje/IsWg9PHfoyyj7duXqM2q3/7cdbvFxdzh5cQ2SCmvgULbbWFlRr1pt1M7/k9L7lqLMykEil1Gn/BUvH9yIlIRJLG0dqtf6UqLArnN63zBhQdVpcvUtSokIjzh7diYWtKz4+vrTpNYI5o3uQkhjNoe2L+fJ/60mMi2DtvJGUq9YcpbklFWq1ZdyXDSgSULnAxwcPWkZNbKnVaiCamHOkWj77ZcHNqxhhty7RpttX+PmXY+HUYWRmpFKkeFks8pmWs2LN5vwxeQjHD2xCJlfw+ffzGDusA0VLVmDssE64uPvSotNAZo3/lH/2r8feyR2piQm1Gn/AmG86kJGRTqtu35KZkcyh7X8gVyjJSEvh93FDUCiUJCfFFSiUvkoPz9AkbtcLQsGIUCoIbzCdTsvOpb+QGBOGKktN406f4Vm0XIFee/fmOZzc/Dh3ZAPexcvjXdx4m9HFswTB5/YTEZtOTEQIEqkJ/+xeSbdPx+PuU5L1C0dz+uAGsrMzWThhAAbA3MIGjdoY/M4e2UKXgWM5fXAjNy79Q3pqAkoLW0oENeb4nj8pV70NNpYKzp/cR9U6rTCVyZk7cQh6vY4GLXoRHhZMYlwUm1fNIDsrk3XLZ2JiKiclKY70s/soXaE+BzbNICnuPusW/IypTIa5pS2qjFRiIkI4c3gzsfdvs3HJ/6jVrBe7180gJTEWvU5Lm17/tvBFhF7j2N6VZGRk4lm8Ms06DyrweX9aDdK+o1bneVyrVX/8qn8MQPW6zYBmhAWfoEn3kbh4+TNnZAvkCjOKBdahWGAd9qwaR1TYVcpUa0mZai25e/0kfX9az/41E4mNieJ28Dn8/UtjbyfHYOsHgLWdM1qtBolEglxhhqtncWRyJUpzS+4En2b7iomkJEZz7shmjmxfTHZWJhVqteajr2cxZ3QPzC1tiQq/Sef+Y0iKu8/hnSuIvncNvU7L6Bk72L52NrUbf8DV80e4ceUElla2DPpuFtN+6UNmRioGg4FKNZvTsvOnjOhfH3NLG3oOGk2R4mUB+HXW7tzzkVMof97ELxk7rBP37lxl7LBOODi7M2CYsTbuwG9n5DmHH31mbP2u3aRL7nP/m7Un99/JaRpKVWpFqUqt8HIyzZ0ko1OnDwr8ub4ub3v90RwikAqvmwilwnvn93GD8SseSJFipbh8/lieWoOffTuRiT8NJD0tGR1yajVoS/Cl47TvORQnVy/GDuvEyInrWLt4nLFeYmY6/YZM4u8dy/Gt0BaHshVZMvlTOvcfg4WVHSf2/8WpA2vQabUUK1Od1j2HP9O+hl07jpWdM616/8rNkFD2/fkVH49cVqDXXjm5i1oteue7zNreheS4cGQKM6LuGQdq7N8839i1ICUeG3sXSldqyLG9K6nfqi8XTuxEJldy6sA6MtKT2bBoNHqdlozURJzcilC3xUekJscDEHLlH2zsXVGpMjl+aDvZWRnYOrgjNTHl4K5Vxn51ZpZUqteVY7uXkBAThl6nw9bBjfqt+7Fl2XgsrO2xtnPC2s4JMwtrbl05jqdvKcwsrMnOyqDXl1OY8XN33LyKo9dp8SlZheAze7kXcjH3GENDw6jU/EtMZQqObhhf4HP+soriW9u7sX72YPR6He5+ZYkJvwEYZx2LDL2MXGFOWlIsCjNLEmPuEn33GnEx0TTsNYHo86vIfNCfMr8BONmqDFKTY9Fosrl69m9MTGSYWVgTULE+EomUyLBrNOvyNVuXGYNeYtx9Pho6m5iIEA7vWkWr3mMpEtSSOcPr07LzIOQKs9xt2zu58dmIOWxfO5szx3aiUqXz8ZcT8PAuzv+Gtqdl509RqdIZM3f/U2fQygmgOd+bZ/VwsXv4d0pQvV7/zNt6Hd6V1lEQgVQoHCKUCu8dZzdvmrf/iKBKdbh8/lieZWeO76N4QBCden7BuJ+H5Pt6rVaDvZM7nXuP4Ozx3Zw9tosqtVpy+MgeSpY0zlBkYWVH+O3L3Lh4mM9Hr0UqlbJy5lCuntlP6UoNAePAlev3M3Gxe/zFS2luza2LBylSqjoypVduLdIrJ7Zz5u9VSE1kNOsxkui71wCw9anK2gWjqVavDaHBp1BnZ+Lk7sfpA2s4sm0hcqUFJcvXo2jp6pw7vA5Xv8oYwq4jkUpx8ypBo/YDWfjbQOKj73Lp1B50Wi071/6OlY0DGWlJKJQWqLNUZKYnP5jqMZOEmHusW/AzBgxgAD//Crh6FUMqMRAXFYZCYUZqYjQ29i7YO3kQFxWGuaUt926eAvTodVoMBgOZGSk4unojNTEhMz0Jg8FYv7Rdi+9JT0mgc/9fuXJmP4Bx5L+5FRbW9twPC+b29bNkZaQQUL4uqRlq4pJUmFnace2flSjMLNBp1Y85w//KCaNQ8ED6pPqj9i4+fPLLxtzHe1dPYN6oNkgkEoJqd8KzWHn+mj4QM0s7TGRmaBVuZCWFsXNmd6xtnbC0ccytmPCwJh2/4PdRnXH1MraUehUty4rfh2Dv7EVibATqrAxSk2LZtGQ0qUmxrJgxhKzMNGb82J2igXW4efEAG37vQ+sun5OZkcrls4c5sGMFtvYuaNTZ3L97i/HDu5CemkSlWi1QKMyYMqoXWq0GU5mcE4c2I5MpMBj0DOoUyO8rz3HswEYsLG2Ij43g9JHtKM0s6P/NNGzs8p6Xh8Pp2GGd+GToVH7/tR8yuYLyVRtja+/Mwb1bCL5wiC6fjGHlnGFkpkbj4ubFF99NYeQXHfh16hoMwPgf+vLzpJUF+pxeNRFGBeHlEKFUeKfJ5ApUGf/2J8wpCeX6YPRtrgdlYSLD7+TWGCxfvgKpqrzTVxowYGJiSkJsJPMmfUW2KhNP35KUKFOVTSuncfr435R8MFDo0smdVGvULbc1qWO/X5nzSw9Klq+LRCJl/piPsHAtQ3ZKOElx4RQpVZ2Gnb9h8f+6IJFICajclMjQK1Rv1odN878lLTmO4pVak3z/CnGRIXT5ahY29m7sWTUB//L1AWOYOgZY27lQJKAKtVr05vLJnRQpWZkKdTow96cPgHr4+ldi+7KxOHqVxcLOk2Klq3D2yFaiI0Kwd/ZCp9MQHnIZE1MZEkBpZklSfBRFSlRAaWHN9QuHkEpNUJpZEFi5MZdO7kav06E0tyQ26g6pqfHGQVSmsgeDqUxx8y5BbOQdHN18kZqYYG5li0FvQKtTIzWVITOVGwv1m5hSqXZblOaWnDu6FRs7lzyVElSZaayaMxwrawdCr5/BzMKaGs0+4uTeFSSmqABwdXXi4KY5dB88k2xVOiunf/HEn5NnbR3NCaNQ8IL4jbvmHTx04fB6mg1cCBIpm6Z2o2xRZ8pO2PLY1/f4YipgLO01bNKO3OeP7VlB9cbdaN/7JxLj7jNhSGOGjN/M6YMbOL53BVlqPUoLO1p8NJq/V/1CUKW6pCbHs2bRWGxsnegz+Ddi7ocxc0x/UlPisbKxZ/j4vxg9pA0SJISFXKbfkCkUKVGWb3rXoHRQbZbP+YmwkMtY2zpw9/YVblw+Qdd+P3Bo9ypGTdnE7evn2LFuDt0++fGp58XEVMmXo9dx8sBagq+eR5MZx3e/zOfUsb34+/vTqedM1q+YyZnj+yhboSaXLxzD1FSGf+mKBTrvr9K7FEZBBFKh8IlQKryzPB3l3HUpws51c/KUhFKamefOJf/fWoMubt6E3Q6mfJV6hN2+hr17GWQyOWkpCSjNLUhNjufu7askJ8Yw4Jvp7N60gIy0ZKRSKa6efpw/tIZeX04EIC0lARt7l9z9USjN8Q+qQ8iV45jK5PgFVCYmSYVX8Qp0/HQaKyb2ITMtifTkOAaM2U5GagJ3rhyjaGBt1NkqVBkpHNo4g2Y9RnDt1E5O7P4TnSabyLCrOHsUw+6hVrUrl89zJ/gk8dFhqDJS8SlenpiIW1jbuxL4YODV4N92sH7+CDJSEwnNTEEmV9Ko/UDU2SrOHtlCzWY9iY8Ko0nHz5g7pjeW1vaE3TyPraM7BoMBS2sHzCytuXx6LzqdDr1eh16tIz7aOKOTRCLBytYRVWYqer2OG5eOYmIqQ64wIyUhhsiwYJBIsLFzJqB8Pc4e2cyOv6ZRvnpLTh/eiFajRq4wQ/mfOrJm5lZ8/PUMVs8diYtHMf7Zs4qQ4PNoNSrSknZh5+QFleviV7oa075tjo2DGzKFGXqdFqlJ3v/ynudW/fbVM3H1q/ig76jRzmWjad7r6QHsYVkGMzZN74XCxEDbHl8/cd3/dgNJTYqhWZevcXD2Yv/muVha2TNjVGci7wYjNTFh8cSBZGakozC3QavOIjMlDhcLPfaObgDERt/FoDeQnpbEjF/703fIRHQ6LeYW1kSG3+KLbkHodFo6fvgtp45uY83isdjYOSGXK9FostHrtdy6epqm7fsRcv0c2VkZxEXfIyLsOmOHdcKAAUeXxw8oS0pVo9XpSc3Q4ODijY+LnBAbU47fOY+ltS0mpqZEht/myP7NnD91kOzsLMwtrKhRvzU7Ny7BxFRG3SYdn+l8v0zvWhgFEUiFN4MIpcI7zcev1CMloW4FX8hd/t9ag1VrN2Py6M/44avO6HQaHL2CqNGwIwunfYO7d3EcnDxwcfclKiKE0UPaYGPnjLWtAwBVarUkZNEkrG2NLWfWds4kx0fi6lkcgMTYCMpWacrxfSsxMZVRo3EP9uxcj9LROAuMi3dJkuLCsbBxRK4wIwNIS47h9L4VWNo4ojSzwtrRh8unD3Hv2klKVmxI3W7fsf3PX7h2ejfl63bEYDCQkXSfa8fv4uxTjqYdB3L6wFpi79/C5cF+5MjOyiRblU6f7+Zx924EZ/cvYcuycTT7YDAA0eG3SE9NwFQmx9zCBq1WTeV6HVCYWXD72ikkSNBpNVSo2Zq0lHiunNmPwaDHysYJU1MZ1nZOtP1oJLNHf4irZ3Gq1u9I8PlDWNo4oM5WoTSzRKfTEnn3Oh6+JYm8ex1HF29uXDrCl6NXs2f9bCLvGouQdx1o7BtZ5kHXB4BaHUaSqoFGPcfg5ORAyMUD/LNzCVY2jngXL4+1nQuXjm+nWqMeuUE8x4vcqgdwdbLNs+xZAmlO3dHmzdvQvHmbp66fbzeQs3/TrIsxyI6adQQwtph6+pWhTscRABzcOJ2aNWpzZO8azMtWA8i9rT5/0mDa9xzK1J8/5qufFqLKTKdYQCVio+7ywcfDqd2kC9NH90UileDjV5qaDTtSsmx1xnzTAVt7F2o16sylMwcZ/NNCxn7bmcCKdXFw9qR4qcp8OnwW9+/d4u7tK7nHoNXpjf1DpaaER0RjLUtFKZfi4SjHyvzfy1CrTn2Jigjj4J4NuLr70KxtL5q3+4iTR3dj7+iKt28JYqMjMJXJ8PAqWuBz/rKIMCoIr5YIpcI7L6ccVK72//7zv7UGw25fo1XHvpQuV5U5k4djY+eCf5mqjJmzL88mfpq27ZH30Wq1lKrcnIRUNQ7WcspWacreDbMoUbY2EomEnX9NpmzV5iTERmAqk+PiWQxHKxmJUTegfCWi7wVTs9WA3FZcU1M55hZ2JMaEcWL3IpTm1ngVr0CJ2n1wcXXlxJ4/ibp7jQ4DJqIwt2L+jx0IvXYCTVYmpgoFcjNrFo3vi5m5JR5+gSwa15uMtEQ2/PE9UXeDkSvM8ClRkXVzvyP0+mksrOxJS45j/cJf0euMwclgMDB1ZEf0Oh1Obr4Enz9IQkxE7ghwmcKM5IQoMjOM03gqlBbUatKdg9sXYW3nhEymQALUaNwVF3c//tmzgvA7l8EAbt7+FClZEVsHV3xLVGD/pvkkxd1Hna1iydQv0aqzMZUpWD13JF0GjEGv07LxzzGUqtGNcweWotNq8C5amgYdvuD0gXWcO7wOE1NT0lLi0Ot1bFo4Cr1ez+kDa7h8cidxkbeRm9viU7oOMWGXUCrkxEbcosPAScRF3ubcwTWkJsVg5+SJOtsY2F28/FHYeGLQ64kNu0CXr2Zia23BsR1/cGDdZPzK1KJeh6/448f2OHoUxcrWhbDrJ7B38SE7Mx0339LYOHpQvk4nVv3+NZVafE56YiSX9vzOLoOBNh+OxO8pJZzy6wai1WrYumwcSXH3qVinPXVafMzmpeMwGPQc27sKD69iOLl5s3zuPlKT47G0sc932xaWNsyfNJi0lAQ+/mI8Op2WeRO/5OCuVcgVSlKTjIPXjuxZw7o/J9C4TR+kUimlg2oREXYDucIMExMTSpevja29M77FAhnzTQeys1V07jc2z0AlHxc5bTr0ZMGEDynmXw4LK5t896ljj8/5/quOjJm+nrlThnN430ZkcgXf/jIfAL8SZfKdJvRVehfDKIhAKrx5RCgVhIc4OLnxx/RRZGVl4uNXkkYN63IvVoOtleyJrzt7fDfb18zim/8tJzLN+JynXxmKla7K9JHtMRj0+JerTWCVJoTfvpT7Or1ez+kdMzm2YQIW1vbER97OXWZl54zC3JLEmDCKlKpB0cDa2Dp6sGvZUJAqqNywB5GhV1g1dRC12wzE1bsk3YbMZf+aKcRE3KRy3dYkRN7AxFROaPAprB604Lr7lsbRzZfr5w4gN7NArrIAjLNFmVnakBwficLcHm//6tw8uwP7ByEtKSEKn2Jl0Wk1OLn7EXr9DK4uJdBkq3ByL4KJqZywG+c4eXAdWZnphN+5wqxfemJl48jutTOwsLIlW5WBpbUDcVFh3Lp6gpBrJ7F38kCrzsa7eDksLG1RZabh7l2CpPgovIoGEnbzHJcuXSRblY6tWwBmch1tP/oeGwc3lk0agMFg4MaFA9Ro+iHxUWFcP/83Ny8ewWAwUKf1J+xePYkytbuRrTH2D67fujeWNo5EhFzg3KF1+AZUIS4yhAG/biQm/Aan968i7n4ICisX6n00g01Tu/HRd4uJCb9OyMWDAJQo34DKDXuwcnJf0h5My6rVZBMTfp1+P63n1N5lZKQmYOPoQWqGNrd1tKirGavWzWHQqGUgkbDot/4M+nH5E3+28usGYmJiQsVabXEuWp3FY7tSslpnuvT5joatPuLs8d1EhAYjVyipUrsVlWu1ZPSQNtg7udP/m2kAuX9/P2nDI+83fv7BPI+r1Xt01rByVRpSroqx1XrUlM2AcaR8jaZ9qdHUWHs3Z6Q8wOS5xgFfNeu3pmb91nm2lVMzuGHzf0tBTfljFwBDfshbNgpAp9VSu+Gj+/QqiDAqCK/XWx9KDQYDmZmZ+S5TqVR5/hYK1+so45LzHrnvZYC0DA0WZiZPeNW/LCxt+HXa2tzHOS0yet2T9718lcaUr9LY+CBVTUKKGjsrU2o2/ZCaTT/Ms39arYYKtdqi1+tJiL1HmfJ1qNDhV9SqdHbN60vfn9bn7n/Hz35/5L0G/G8bl86fwtzGGUe3w5w/vJ69q39DaW7FlkWjsLB2QKNWodcb8A+qQ2J8HGmJkaQmxWBiKsPS1pGkWBUW1g5Ehl1DnZWJhZUdUXevoTS3Rio1ITMtAXQZSKQmZGVlIZHK0GSrSE6IITkxhtSkOPQGPaqMVIKqNefvzfPRG/RgMJCWnIC1vTPpKQlITUxRZaZh5+hOsw++4vCOJdg5e9Du4x/YtmIier0ejVqFiYmMpLj7RN29jlRqitzag4wMNXFJmdh6lCcl+hpZmWlUbdSdrMw0Dm2dj0ymJDM9mYy0JKxsnTBg7DIhkyuJuH0JSxsnktP+veWuUMjxKBJIUmw4BgMc3DiTjp9NRa/Xo9Nq2bxgJBKpCYnRYcgsHDGzcuDw8qGoUmM5vnMBJSs15eyB1ZjKFEgkUjTZKqLCrrJ/rXHGrei719Bqslk6/kNqtOzP+X+24uIbhEQiZd+83kTevc4/u1yJCr/JvDEfAxirGDzle2Fl60Ri7H2c3Y23qxPjIkhJSUFh64tUaoqluYJiruZciLnPvIlfkaXKwNO3JEkJdylXuREGvQFvv1Lo9fqn/hw/i9RM3SPPeTn9e0l5Fd/3lQsnkhAfjZevP2p19it5j4yHBje6O7za43ndqpa2BXjsNfNNJq7nbzeDwZBvebv/eutDqUajITg4+InrhIWFvZ6dEZ7IWgqxmbav5b3U6mwA7C0gPt2ErKynlwR6HL3ehOR0PUrTRy/C+XG3hohkyMp69D/PPWunk5wQib2LD1lZKqRSE0JvniMo7iwmduXo8vViLhzdxJl9SzExldGkx0+kp8Rxdv9yNGrjhaTj53OIvLaXy8e2oNdpaNjpGy4d20j03atcObEdJ/diJMaEkRB9j2undmFmYUNWehImpgokUlPio8IwGAwYDHqUSmtiI25RpVFPzh5cg16vp0hAVYLP7kWVmYZer8XGwQVV+oMKBiYKJEjp+NVidi/5BlVGGhqtFhOZHO8ipYkMC6Z6kx78s2spto4eVKjdjv0bZpKRlsyBrYtITojkXsgl4iLvkhQfRZnKjblz8yKhobfQIcPJpzypCREY9AYsLMywtbXGs2g5tp3bDhhQWNixd9106rQeiJmlLXcm9sNEZkZachwajZqkhCjMrR24HXwWG2cf4y8VBgNmChkJOj2RYdcoVbU1WxePolabzzEYTEhOiOXG+QM07DuHm6c3c/PCIVr3+5SrJ7bQsOtIdv75A/dunaNIYD2yVWmUKN+YlIQI0lIScHAvTvTdYCRSCaZyM6wdPPCr1J5/di0HA9hZmBAffZduX0xj4YS+BJ8/iJt3ST4cOhuDXs8/u/7M9+fkYf7l6nJwy3y8S1QkU23K1mWTuHv9FC5WBhyt9ej1em4FnyMhLpKPv/iN/duWkJmegoOzJ7eCz2Hr4E546HWys7PJynryzFdPk6XN+8udi03e70RWVt66oi9bhx6fA/9+v3P+flEafd5LoaOl8bhe9fG8Ts7myQQHRxX2brwwcT1/e8nlT7/b8NaHUplMRrFixfJdplKpCAsLw9fXFzMzs3zXEV6v1KvJr3T7er0etTobuVyR2wdPmqFFZ5AXuLX0v3yUEB6nRal88i38h0mlalQaKXZWeb9ibXrlLZ7f/fPJXDi2nT1rppIQc5egJp8Rem4LfX5cS0ZKPLtX/I9KDXugUJrRfegfbFv8PUnRt0iJvYeFlS1qdTb71kygYeevyUxLMLYcpsZjMOg5smUWUqkJqvQkzCxtkZiYkpmawJWTezAxkaDVaqjSoCuhwSe5fHwLCjMLkmIjCA0+iUQiJeL2RQx6PbVb9CE+Ooy9a6ZQoWYr9qyZzLppHyGRSJEpLcnI1iORmKDWQnZWBmcObUadnUlC9F1OH9pkDIZSU0rV6sae5aMoVbUdty8dID01gTs3LlChwYeoksI4e+gCaQkRWNo4YiYHrdYUuVyOUqnE0dUHpbkVSqWSEmVrse3PnzGzsMbSxh5tdgaB1Vrxz64lmFnaY2nniiryDi4eftw4uQ4HtyJEhl4k7v4NarUeSELkTeLv3+Lo1pkYDAb8KnUAEyU75vRFlRKDs0cxLCytMbOw4di2WSTF3jNObapQIFeYozS3JPxWJLERN6hQrwshFw+hVWdj7x2Ilb0HF/YtQKtKwsHFmyIlKnD19F6mftsCqYkpZhbWNGo/iMUT+pGlSqduq74olU/+v8nOoxyeJaox+5ceKEwMlC5fGyuzxigUCpRKJVKpFC9ff2Kjwpj0fVds7JywsnWkTdcv+f3Xvhzbb2z5z1n/Wfy3NdTH5c24ZOT3PX9WD7eISiV5W0XfJTmto+BWmLvxwsT1/O0WEhJSoPXe+m+hRCLB3Nz8ieuYmZk9dR3h9ZBKU1/T+0hzL1aeTnIi4tXPffHKkZqpe2rf0hzF3JSERGeRlK7Fwfrxvx1Gh98koHxdKtRqTUpiNFO+70J2ZgrLxvcCMNYJlUhxdC+KVCrFytYFvU5HckIEWZkpWNu7IZWaIrXyxSOgPmQn4FG0LBEhF4m7H4Kjux9hwSdRmFvh5FaUhJgwylRtgWfZllw9uobYyNv4B9XF178SADHhN7l6Zi9Wds6YWVhj0OvZteo3Y6iVmuDuVxpzS1u+GLeF47uXkZIYg6ODAyYmJqQlhGMiNUGnVYEBkIBek4WLZ3ESYyM4vWsOCoWSW+d2kpmRgkyuQC6XcfP0JvyD6lG7ZT9SEqPyTImao0H7T1k5/UtqNO1FUM02BNVsw51rJ0lIzSZdZ4ljsbq0/7I+3l4F6yun06o5vH0RZpYOXDm0jOY9R5AcF0F85B2a9fwBgD0rxxBYoy2+AdU5uH4KRUpVx9bJiwadhmDn7MW9G6cpVrYuwWcPUv/Dyfy97Ds+GTyes75e3Ll+hujwm5hb2aI0t+S7qbvJzEhlxg+dKBlUh5JBdZ66jwmpD1r3JdCt5yd06/lJvut9P3E9AD9Pf3Tw3XfjVz/y3NM8bhalN9HD3/OCeLiPKJJ3q5/of72r/UbF9fztVJBb9/AOhFLh7VK3oiuHzkYXynunZWqwMi94a+fDfFzk3I1Rk5z29EFPOYq5GoNpzmj8/Fy/cBiNJpvGHT7DysYJRycXsjSuNP90EZYmaVw9uf3Bmnm/0PYuvhQNrEOR0tWJvH0J/5IBnNszF5ncDDetDolEQkZaIo1qDyU1MZqsTOMvA1p1FtdO7+bO1WPGW95qNQE1OpKUnk2dRu0IrNachNi7JMZG0KD9Z8iV5uxdMw0zcyusbJ1w8ShGlUbdWDHtc7TqbJp2+4a4+3eo22YAgdWas27ed2CQYG5pQ1xUKOmpCWjUWQz+bXvuvqckRHF0x2Ja9hr57B8E/5ZzUjgH4u4Mnu7OZKmyUJoVrBUwMkFNUrqOwLof0bhdb7JV6ayeOoCUhEjMrexY/L+uACTFRXBi1yLsnL2xdnAnPSU+z3ZsPcsjtTbepSnqasYxU5j1U1dkciW1mn1IdLix9m2pCg2Y/G1rLKzskCst0Om0mJjk/19vbhB9oJjrs7VsPo+3KYQ+jzxBlHc7iMK7G0aF94MIpcJ7wdPR2Fr6InKC6bPICaaPU6vZh6yd/z2ThrVEoTSnVrMP0em0bJrWA606k2bdv8v3dXXbf8mWP77j3IHV1GjZHys7FwyadMLvnEWTnYmlnRtm5tbsWj6W9ORY7F190WqMJZbK1+1ExXofcPPCQaxsnXDzLc29iOjcsFery//wcDS2RFw+uZMun09GIpGyfOpnAFRt2I2qDbvl7ourl3/uv509iuFdvAK+/sbZdtTZKpLj7rN8yqfoDXoq1euMh6+xLqter2Pbn/8jPTUeK1tnWvYayaYFo1BaWBN3/zalqzTh1qWjyCycqN72a5IT41g6bQg6TTYdB44n/OZZAMykZdi9cgJ6nQZX75I06fboOfvvDExJd6xyH2vUKhTmVtSr+xUn9yzBoNfRsvevRIYa62wmx0XgG1CNdTO/oPmnfxIZl865I1soHVgJk6SLdOr9HatmDcNg0BNQvh4N2w8CyJ1OtniZ6jTv+uTi+A+HURFEX8z7FkJziDAqvAtEKBXeKy/SWprjWVpL4d9gml9rqalMTrfPJj7yfKU6xmKq1+8bg2L9Usbi5/U7Ds5dp/+vWzi1dymX/tnE9TO7sbJzwcU7APcigURGhBMTpjE2sEqMRe6zVen0+2kN25b8xNWTOzGVyekw0PjeDxeQfzigxsQlcOjXD7GwtKZm89559nHf+t9p1PHLPM9lpiVjaeOQ+1iuMOPojkW0+fgnLG0cWDHtC9w+NN4ev3nxCI7uRYiJuEVqYiyLxvUmJSGacg0/poRXBUJvnqBO93HsWjAYb09XJOjpNXQOsRE3OLH7TzyKlAEgKTachp2H4ezpx6Jfu7J10Sha9/k1N4ie3zsfV7+KaFNCCarTKXffjm6dw4XD60iIukOTHt9zcvcS+vy4jrSkGHYu/ZmSlZrmrpuUrsHeqxyxdy/hZJZFxar1yMo0Dv5KiL5L32/nI1ea8/v3HXND6dO8zlbR/4ZQeHeC6H9DKLw/QRREGBXeLSKUCq9dYd3Cv3xsA5s2rAKDjsDyNejVf0SBXndk/+bcuoiPu40/f9JgoiJCkMmUZGVlUDqoFl36fs/yuT/Sc+DoPC2mT+pj+l8lPcy5fj+TmCQ1LnaPvq5K4w+p0thYcmrzH98RE36d5Lhwunw1lxvFShKfmEbxSq3Q63Uc/2sEaclxtOk75onv+XBA9e70KQHVOuQ+fngmpIC6/bgfn5nbqgpgYe1AWlIsjq6+AKQkRpOdlYH1gzqbMktH7kZEkZmt5d7dMOxc/TA1syGoVhcSo0KQ3DpF4r2LlGzRB31WHN6erphbGOuoOnkUxVQmx9nTn5SEyNxQamnrxD/b56E0tyAjLZnMbH1uIPX1dCLU2gJXJ1uK1M0bFmu1HkT5Op3QqLOZ9V0jXL1LYWJiiq2jB1mZqaRmaAHIyNJhAzRs0pYLx3cQnZ5Cow6fcupv4wAiazsX/po7HDNza7Sap7ekv65W0Xe1NTQtUwMG0BtM0al073zf0McRYVR4F4lQKrwXbl6/xOkTh5izaCORiVoW//4tZ47vo1L1Rk997a7NS/MU635cMP10+BycXI3zz08Y0ZXsrEx6Dhydu7wgfUzz83AwBfINpwBhwSdp1msU/uX/nYrT0d4KX08nwiLicAtoyKVzJ3H1q8jJjb+g12rwr9CQqk0+ZMnYnphb2qHRZFMkoCrXTu/GN6AqnkXLcfbgGgKrteT21WNkpiZibm1P+/4TWD6xLz2HLeTY35u5dMhYAD6gWgcO7ljKoR3L0D2YIz0x6jbzx/TGwtqJqDvnqdawCxbmZvgU9Scp9h5KhRxdRhQ+fiWIDT2DwWCsB3n/ziWWTviY+Mg7pKcmEBl2lXWzBpOSEJUb/o7tXIyFvReVWw3h6Npf0Ov1ZCbe5dDSwUhNTHB+qM7rxnnfUK/DYDLTEjm8aQZ6vQ4rWyeKla2LraMnqYnR6HRaQsPC0UsUALjZyVFoZHg7KvEqWpbda6djMBhwcPbK3e72lb/x1Zj1uQOZ8iOC6PPLryXU3cGUrCwVSqX8hQcwvm1EGBXeZSKUCoXidbeWHv57By3bdc+9gHXr/zP21haEhlxl7pQR6PV6WnfuR9WaTRj3Qz+yVBmULleNEqUqEBpylQ2rZuPq5sOOjUtQqdJp3ekTipRrle+tfLU6C1VmOhKJhLHDOjFy4jounNzHxuVTAGjU81fuZav4Z+vvaLJVlK3a7Km3fEt6GFsjHxdOI0LOU6R0da4c35onlObw9XRCm+RNdNg1Lh9aSun6A3DxLcfexYMpXbUF6Snx9Pp2MfvWTMbCxoF67T9nz+rfKF6uDl4PRsLbOrjTvv8EVk0dRFpybO62wy7soM/IpWSkJhB+6xxOrl4kRochlZmQlpxIn1Gr+HNsLxRyOeXrdCAs+AQA/uUbsGXRD0SGXiE+KhSFmSWZaYl8+N0SEmPukhx3n0FjtrBwdFdO7v4TU1M5MeE3UFq7YePoR3h4BFqdAa+A2hxaPoz05FisHdxBIuHDEcu5enI75w48Ovr86NY5VG78Iaf3LWf7kp+wsnPGI6A+ZpYOzPupExgM9B06jbs3zz/yWid3P8wt8k6P+biBTK/j9vy7FkILeiv+XShk/6xEGBXeByKUCu+F5KR4HJ2Mt5CNg54gU21g1aJJfPPTbOwdXBnxRXu8fIrj4OTGp9/8xpH9m6laqylFipWmQ7dP2b5hMb9MWY0qM53ffurP6CYdcltMAWaPH4RGnY1Go6bzx8ORK/6tpbdr4x+MnLiOlKQ4blw5SVKKhvaDZiFXmLF8QrcC90N8XDi9dmon5et0Zv+aiaizMvnjp3botBrKVGvF6mkDUaUno0pPxr1oOTITQrn693wuG3SYyK0JuR2GKiOVlTOGEnfvCu5FynDl5A7SkmJJirvPzfMH8CtTg9Crx4m6e424yNtoslVkq9JZMbk/0XevcfbAaqo3642dkydWtk5cOLoJhZkler0OV++SuBctS69hC7l74zR3b5yhdWfjwJ+HW1wTY++xYc43WNu7os5WodNqWDi2D5iaER8fT9mGAzCVKyhStjHxN/ZiZmVL8v1LNGrXlxpNurF2Wj/aDZjEse3zkEgkuHoHEBZ8AgtrxzznMCszjRrN+1K0Wq9Hzm3bDt1zH7t6Fn/k/Lf98Pvcf+cMXvrvQCZjGDV+NiKIPl5+ARTez1vxTyLCqPA+eb/uewhvlNf5n62DowuxMZG5j001Mdy9c43U1BScXDwxMTXF2dUTG1tHvH1L8PM33bh7+1ruNKNgnIJ02pgvWP7H+NzpGnMCgVqj59Phc/hx6hYsreywd3y0ULVCaY6zmw+1G3+Av58Xh/76kR3LfiIr+9lnpSnpYZ4bUGOS1Ny5fhbPYuUpGlibG+f2kZ2VQa02g8jKTMPDrxwfjVyBKiMZZ88SpCbFUK15X3r/8BdxYRfwLxmAXqfl4+8W4uxTjuuXT+FVri1KS3vSs03QaI3nQGoqo/vX85ArLYiNuIlGk03HQZNx8ijOjbP7SU+OY9+ayRzcOJPWvX+lTttP0WQbZyt6WoW6yAQ1WSau+FVsx841s1BJHXDwCqT5gLl0Gvgb5ao1wdHeCkNGFL6eTkSFXcHBtQimMjkZqQkkRN3O3VZM+A0MBgORoZexd/HN8z7xKWr0Ejl3wiLQqrM4t+nHPOfyeSWkqnP/FHNV5v55WZLTNLl/wPhzl/PnbZCWqXnkDxgD6H//CEZ1K7qKQCq8d0RLqfBeqFW3GSuWzKBilTpIJBIWz5tEnfotUJpZEhoWhrenJ1H3w0hJjsfOwZlfp65h/KhPiI+9n7uNjatmM33xPkJDrvLH9FG5z/u4yLE0MyE1Q4PMwpSPvxjHwqnf8NNDxcx1Wg3qbBWZ6ansWD+Xm1dO8f2kDWRmpPLzkPa5t3qfpa8pGMNp+O1LpCdFsWjsh2jVWVhZ22Dr6IFEIuXKia1Y2jpz4/w+/ErXwszCBlOZnM1/DMOg1yNTmGEqU2AqU2BiYoqdnT0Ark62mJqa4ORgg1xuSrpKj6nS3jiASConPjkbA6ZsWDgag1RJzP1gVs8cStW235KtV/DH6O4ozG2QmJoREZtJtsZAZIKa+BQtaZm6PCWasjXG0Ovr6YRXh0+YP6o17k6fUaxURf5e/BkadRat+4wlJvw6YcEnWPTrBzh7+uPqHUCFel1Y8dvHOHsHoLSwBsCg1/PnuB7IZEo6fjadfRvnk5SuISvb+ItE54++Yf2CIRgMepp3HfpM5/thr/r2/NvaIipaQJ+fCKHC+06EUqFQva6+pcVLBlKuQnU+79sGg15Pxap1qFm3Kc4u7vw29gu0Gg0duw/C3bMIS2b/ys5NS3H18MHJxRM7B2dWL5lCUf9AhvZvjs1DJY8e5uEoJwuwciyGp29JTh7ekrusVZfPGffdB0ilUj78bAxKM0t+/qolltZ2WFlaUsTJlNA47XOF0wvHd9DjswmUqlAfgDGDW6DVZuMe2IaWCjOS4+9Ts2V/ti02Bmknj+L0+XEdSnNrjmyeiZmlLa4+xtqhQXU6ERZ8AokEgmp3xLNYeVx9ShFUszlhwSfw9XSibLUW+PoVJeSUOT2HzCArM5XFv3bh0zGbAahYpSbwfZ59HPSrcdYhX89mULdZvssATExMGTR2JwA1W/anZsv+uctiwq9Tvl4Xyj9U1ql01ZYEVG6OSqXCzMwMqVRKqy9X5i5PyYbKLb6gpIc5DevVz31+8LiNBT6/D3uVQfRtDKEigL4cIowKgpEIpUKhe13BtP0HvWn/Qd5am8VLBvLH0m25hfUVShm/TMk7OOabn+Y8ddtfjZyW+++7MWo6fTIegGp1jaP2y1VuQLnKDXLX8Slahg698rbSFXM1fh2fdYT+9fOHaN5lSO7jSjWacHTXMgDsitbj7JGhXD3TFVOJDq/iFajb/kvWTDfe2i9dtQVSqckj27Rz9mbHnz9TIqjBI8tyFC9Xnz9+aoeZ5aMzFZ0/vI5dy0fz7Zxzuc/N/LYRNVsNzBMqARb/ryu9fyj4dJi3Lh568P51AYhL0aLXm5Cu1uau86K34x8mgqiRCKAvlwiigvAoieHhTnNvmcuXLwMQGBiY7/LMzEyCg4MJCAgQc+W+BV5GMNXr9Q9KxZg9c6mYnGD6osX1c+TM/vQshfYf9vBMUM96Wz/H/bBgsjJTKVqqKvOmDKNoUDM8/asDjy8t9TKcP7yOw5tm0PaTCfgGVCMx9h5L/teV+p2+fuFQmjPA62Hedobn+swf530Pom96AH2R73lhEkH0+Ynr+dvtaXkth2gpFYQHci64LyucPlzPFJ49nOYEoZyWU3j2cGrr4MqihT+SnZWJu09JGtZvgERiHHaUM1vUw15mUC0eVJ9bFw/iG1CNm+f2U6J8Q7SabJZN+BCNOgtXn1K0+PDn3PX3/TWRyNCLZKvSadNvAjtWTKBx76mEXtpHxPVjNOg5jp3zP6V6nWZIJFKqNvgA+DegvKj3OYi+77MivWoijApCwYhQKrwxCmump/8yloxSv5QpSXPCx8sOp1CwgGphZccXv67Nd1l+t7jzC6oPe5bQ6uZbhivHtwIQGXqJIqVqoM7OpGXv/2Hn5MWc79sSk6RGozUQGZ+BxMyJpgMWEXppH2eP7sS9WBUU6dfRxF3FRJuCn6MEB1srJBLRGvoiRAB9PUQQFYRnJ0Kp8EZ5E4MpvJxWU3g54RSeL6AWxNP6Yj4ttObImaJTYe3GtatX0EnMSM3UkZ2ZxY7lv2EqV6JKT6Skhzl7FVJKeVlzRxvPmfXfk52Vgbt3SQKr1ufyqT1kZ2VgY+/CldN7KVqq6nMf239DKLwfQVSE0NdHBFFBeDEilApvnDcpmAIvrdUUXk44hdcTUPNT0AFEKQ9aVIt6NeHozonUavYhmekpbNg4i2+n7MbS2oExn9fNrQN7P/QqqUkx9PxyKge3LSQzPRkP31JsWzEBZzc/PIqUYu/6mfT97g9uXztZoH141SEU3rwgKgLo6yVCqCC8XCKUCm+kNyWYwstvNYWXF07hyQEVXm1IfRr/crVZMeNr+n5Xh/P/bKXdR6OYP+ZjLKxssbZzIi05DgBHN19iIm4zdUQ7rG2dsLRxRCKRoFBa4FMiCK+i5di9djqOrj6PDaVJadpHqvSLECq8bCKICsKrI0bfC2+0Zw2mr3pUbs4gKHh5o/Rz5IzWh+cPqP/18Aj+HIUZUl+WPMHbYPzcpVIpxdze7Wk9RQg1ep2j70UIfTOI6/nbTYy+F94Jb1KLKTx6Sx9eXjjNr/UUXiyg5tdSmF9QhTcvrOZ3+z3Hw8el1+nJyspCqXw5+/8mh9D3MYAWBhFEBaFwiFAqvPFyLhDvWziFlxtQczzulvbjwup/vWh4fVLY/K+Xffs9P/8NoVB4QVSE0MIhQqggvBlEKBXeGm9aqym82nAKrz6gPqygAbCg4fVlvNerIELo+00EUEF4c4lQKrxV3sRgCq8+nMKjwenhPqjw8kPq4xRmoHxW+QVQECH0fSJCqCC8PUQoFd46b+Lt/ByvI5zmeFpIhdcXVN8EqZk6QPfI86JP6PtDBFBBeLuJUCq8td7UVlPIGz5e5Yj9h+UXUvNrKXzbg2p+x6TXmyCVvnklmkQIfXWczZMJCHATI7EF4R0iQqnwVnuTW01z5Nd6Cq82oEL+Ae1xQTXHmxJYn7SPkPfY/i0P9PoDoAihr15+rZ/G8kBRhbA3giC8SiKUCu+EN7nVNMd/W09fZ0DN8bSWxPy6ABSGwm7xfBwRQl8tcftdEN5vIpQK74y6FV3JzMzk0FlVYe/KU70JATU/b2oYLAyiUP2rI8KnIAj5EaFUeOfk9DU7HZxa2LtSIP8NOg/3QYXCDanvExFCXy4RPAVBeFYilArvrLehv2l+ntSKCiKkvgz5BVAQIfR5iPApCMLLIkKp8M57W8Mp5B+S/tuSCiKoPokIoC+HCJ+CILxqIpQK7423OZw+LL/b/fkFr/ctqGaodCB5tE4piAD6LET4FAShsIhQKrx33pVwmuNxgSu/FtUcb2tgzbfV0wB6gylSiQifz0KET0EQ3jQilArvrXctnP7XkwLakwLrw15XeH3cLfb8/Pe4CrNO6dtCBFBBEN4GIpQK772HL9jvakD9r4K2KBY0vL4o0cL5cojwKQjC20yEUkF4yPsYUJ9EhMU3lwiggiC8a0QoFYTHEAFVeFOIACoIwvtAhFJBKAARUIXXRQRQQRDeVyKUCsIzEgFVeFlEABUEQfiXCKWC8AJEQBWehQihgiAIjydCqSC8JP8NHCKkvt9EABUEQXg2IpQKwisiQur7QwRQQRCEFydCqSC8JiKkvhtEABUEQXg1RCgVhEKSX7gRQfXNIgKoIAjC6yNCqSC8QURQLRwifAqCIBQ+EUoF4Q33uMAkwuqzE+FTEAThzSVCqSC8pZ4UsN7nwCqCpyAIwttJhFJBeAcVJJi9jcE1v+PKzMwkODiKgAA3zM3NC2GvBEEQhJdBhFJBeE+9aIvi84Ra0YopCIIgPI4IpYIgPBcRMAVBEISXSVrYOyAIgiAIgiAIIpQKgiAIgiAIhU6EUkEQBEEQBKHQiVAqCIIgCIIgFDoRSgVBEARBEIRCJ0KpIAiCIAiCUOhEKBUEQRAEQRAKnQilgiAIgiAIQqEToVQQBEEQBEEodCKUCoIgCIIgCIVOhFJBEARBEASh0IlQKgiCIAiCIBQ6EUoFQRAEQRCEQidCqSAIgiAIglDoRCgVBEEQBEEQCp0IpYIgCIIgCEKhE6FUEARBEARBKHSmhb0DL8pgMJCZmZnvMpVKledv4d0nPvP3j/jM3z/iM3//iM/87WYwGJBIJE9dT2IwGAyvYX9eicuXL6NWqwt7NwRBEARBEIQnkMvlBAYGPnGdt76lVCaTUaxYsXyXqVQqwsLC8PX1xczM7DXvmVAYxGf+/hGf+ftHfObvH/GZv91CQkIKtN5bH0olEgnm5uZPXMfMzOyp6wjvFvGZv3/EZ/7+EZ/5+0d85m+ngty6BzHQSRAEQRAEQXgDiFAqCIIgCIIgFDoRSgVBEARBEIRCJ0KpIAiCIAiCUOhEKBUEQRAEQRAKnQilgiAIgiAIQqEToVQQBEEQBEEodCKUCoIgCIIgCIVOhFJBEARBEASh0EkMBoOhsHfieZ07dw6DwYBcLs93ucFgQKPRIJPJCjybgPB2E5/5+0d85u8f8Zm/f8Rn/nZTq9VIJBIqVKjwxPXe6mlGn/aDKZFIHhtYhXeT+MzfP+Izf/+Iz/z9Iz7zt5tEIinQLxNvdUupIAiCIAiC8G4QfUoFQRAEQRCEQidCqSAIgiAIglDoRCgVBEEQBEEQCp0IpYIgCIIgCEKhE6FUEARBEARBKHQilAqCIAiCIAiFToRSQRAEQRAEodCJUCoIgiAIgiAUOhFKBUEQBEEQhEInQqkgCIIgCIJQ6EQoFQRBEARBEAqdCKWCIAiCIAhCoROhVBAEQRAEQSh0IpQKgiAIgiAIhU6EUkEQBEEQBKHQiVAqCIIgCIIgFDoRSgVBEARBEIRCJ0KpIAiCIAiCUOhEKBUEQRAEQRAKnQilgiAIgiAIQqEzLewdEATh7dKrVy9OnTqV5zmZTIajoyP169dn8ODB2NjY5Fl++fJlli5dyunTp0lMTMTJyYnq1aszYMAAvLy8CvS+UVFRtG7dmlmzZlG1atUCvWbRokVcu3aNSZMmFezggAYNGlClShXGjx9f4Ne8ad6kY3jc52YwGFizZg3Lly8nIiICe3t7GjRowFdffYWlpeVjt6dSqahQoQJ6vT7P83K5nMuXLxd4naFDhxIQEEC/fv1e1qEKgvCCRCgVBOGZlSpVip9++in3sUaj4erVq0yZMoXg4GBWrVqFRCIBYMWKFYwdO5aqVasydOhQnJ2duXfvHgsWLGDPnj0sXryY0qVLP/H97t+/T9++fUlLSyvwPt6+fZu5c+eydevWZzq2mTNnPjEUCQX3pM9twYIFTJ06lb59+1K9enXu3r3L9OnTuXXrFosXL879+fmvGzduoNfrmTJlCh4eHrnPS6XSZ1rn22+/pXXr1tSvX5+iRYu+jMMVBOEFiVAqCMIzs7S0JCgoKM9zlStXJiMjg99//52LFy8SFBTE2bNnGTNmDD169OD777/PXbdq1ao0bNiQDh06MGLECLZs2ZLv++j1ejZu3Mhvv/32zPs4ceJEWrRogYuLyzO9rlSpUs/8XkJeT/vc9Ho98+fPp0uXLgwdOhSAGjVqYGtry+DBg7ly5QqBgYH5vjY4OBiZTEaTJk2QyWTPvY6LiwstWrRg0qRJzJkz5zmOUhCEl030KRWEt9TevXtZsmRJYe9GHmXKlAEgMjISgIULF2JlZcXXX3/9yLr29vYMHz6cJk2akJ6enu/2bty4wc8//0y7du2eKZjevHmTgwcP0rp160eWrV27lpYtW1KmTBnq1avHjBkz0Gq1ucsbNGjA8OHDcx9rNBomTZpEnTp1KFu2LH379mXTpk34+/sTERHxTNv9/fffmTBhAjVq1MjdVmhoaO46o0aNolq1anleB8aAXaVKFdRqNVlZWUyePJkmTZpQpkwZKlSoQO/evQkODn7s+fjvMQFs2LDhmY9hxowZj7wmP0/73NLT02nTpg2tWrXK83yRIkUACA8Pf+y2g4ODKVas2GPDZkHXAWjTpg0HDhzg5s2bT1zvVViyZAn79u177e8rCG8yEUoF4S20d+9ehgwZwpUrVwp7V/LICVheXl4YDAaOHj1K9erVMTMzy3f9Zs2a8fnnnz/2drmbmxt79+5lxIgRKJXKAu/H1q1bcXJyokKFCnmenzdvHqNGjaJ69erMnTuXHj168Mcff/Djjz8+dls//vgjf/75Jz179mTWrFk4OjoyatSo59ru0qVLuXPnDuPGjeN///sfV65cyRMW27ZtS1JSEsePH899zmAwsGPHDpo1a4ZcLufbb79l3bp19O/fn0WLFjF8+HBu3rzJkCFDMBgMBT5H/1WQY+jcuTN//fUXzs7OT9zW0z43a2trRo0aRcWKFfM8v2fPHgCKFy/+2G1fv34dqVRK7969CQoKokqVKvz44495frEpyDoA5cuXx8XFhW3btj3xeF6Fy5cvM3jwYBFMBeEh4va9ILxlcgJp06ZNmTBhQqHsg8FgyNOClpKSwqlTp5gzZw5BQUGUKVOGpKQksrOz8fT0fO73sbW1fa7XnThxgsDAwDz9EtPS0pgzZw5dunThhx9+AKBWrVrY2tryww8/0Lt370fC0L1799i4cSPfffcdvXv3BqB27drEx8dz9OjRZ96utbU1s2fPxsTEJHf7M2bMICkpCTs7OypWrIinpyc7duygdu3aAJw9e5bIyEjatm2LWq0mIyODUaNG0aJFCwCqVKlCRkYG48ePJy4u7qmBMT8FPQZXV1dcXV2fur3n+dzOnTvHH3/8QaNGjR4bSvV6PTdv3kQqlfLNN9/w6aefcvnyZWbOnElISAjLly8HeOo6OX1LJRIJZcqUyfNLwOuS04I8ePBgpk2bRqNGjV77PgjCm0aEUkF4i8THxzNkyBA0Gg3btm17qS08N27cKPC6p0+ffmRwklQqpXr16vz6669IJJLcC79Op3tp+1hQ4eHhlC9fPs9z58+fR6VS0aBBg0duqwP8888/j4ShkydPYjAYaNasWZ7nW7VqlRtKn2W7gYGBuYEUyA14KpUKOzs7JBIJbdq0YdmyZfzyyy/I5XK2bduGl5dXbqviwoULAYiNjeXu3bvcuXOHAwcOAMauBs/jec7Ny3TmzBkGDhyIt7c3Y8aMeex6BoOBefPm4ejomDs4qXLlyjg6OjJs2DCOHDlCrVq1nrpO3bp1c7fp4eHBuXPnCryv/v7+z3mUjzd48GAOHjyIo6PjS9+2ILxNRCgVhLeIra0tDRo0YPfu3TRt2jS3Ne11K126NL/88gtgbG1SKBS4ubnluQ1va2uLhYVFbv/S/GRmZqJWq5+7RfRx0tPTH+kykJycDED//v3zfU1sbOwjzyUmJgLg4OCQ5/mHw8OzbPe/+5QT3B8uXdSuXTtmz57N4cOHqVevHrt27aJ79+65y48cOcLYsWO5c+cOFhYW+Pv7Y2FhAfDct++f59y8LNu3b2f48OEUKVKEhQsXPvFnwcTEJN9yYPXq1QOMv1jVrVu3QOvkMDMze6aqDv/73/8KvO7THDlyhN27d9OgQYOX/h0QhLeRCKWC8BYxNTVlypQpfP311xw4cICOHTvmucC+LhYWFo8dHf2wWrVqcfLkSbKzs1EoFI8s37BhA2PGjGHlypWPtGy+CFtb20eChrW1NQCTJk3C19f3kdfk10qVM3I/ISEBNze33OcTEhJeaLtP4uPjQ1BQEDt37kQmk5GUlESbNm0A4+3+zz77jIYNGzJv3jy8vb0BY9mtI0eOPHG7/22xzszMfGXHUFALFixg0qRJVK5cmdmzZ2NlZfXE9WNiYjh06BB16tTJ040gKysLADs7uwKt87DU1NRHnnuSzp07F3jdJzl48CAHDhygadOmTJkyBVNTcTkWBDHQSRDeMjnBtH79+ixYsKCwd+eJ+vTpQ3JyMlOnTn1kWUJCAgsWLMgNYS+Th4cHUVFReZ4rV64cMpmMmJgYAgMDc//IZDImT56c74jyihUrYmJikjsAJ8fDj59nu0/Tpk0bDh8+zLZt2wgKCsoNileuXCE7O5sBAwbkBlIgN5A+rqXU0tKS6OjoPM89fMv6VRzD06xevZqJEyfSrFmz3CoNT6NWqxk1ahR//fVXnud37NiBVCqlYsWKBVrnYVFRUXlqmb4uCxcupH79+iKQCsJDxDdBEN5COcE0p/XnTRUUFMRXX33FtGnTuH37Nu3bt8fOzo5bt26xaNEiMjIymD9//mMLpT+vmjVrsnLlSgwGQ+627ezs6NevH9OnTyc9PZ2qVasSExPD9OnTkUgklCxZ8pHteHl50bFjR6ZMmYJGo6FkyZLs3bs3tw+nVCp9ru0+TcuWLRk3bhzbt2/PU9+1dOnSmJqaMnHiRPr06YNarWbDhg0cPHgQyNv6+bD69eszb9485s6dS1BQEAcPHswzuKegxxAdHU10dDSlSpVCLpc/83HliIuLY9y4cXh4eNCzZ0+uXbuWZ7m3tzf29vaPvJ+Xlxdt27bljz/+QC6X59bCnTt3Lt27d8fPzw+gQOuAMcSfP3+eXr16PfexPK85c+agVCpFIBWEh4hvgyC8pUxNTd+KmYcGDRpEqVKlWLFiBePGjSM5ORlXV1fq1KnDwIEDcXd3f+nv2aRJE2bNmsXly5cpW7Zs7vODBw/GycmJlStXsmDBAmxsbKhevTpff/31Y1vqRo0ahbm5OYsWLSI9PZ3q1aszaNAgZs2ahbm5+XNv90lsbW2pW7cuhw4dyh1lD8Zb+5MnT2bmzJkMGjQIGxsbgoKCWLZsGb169eLMmTP5DsQZMGAAiYmJLFq0CI1GQ7169RgzZgyDBg16pnOzdu1aZs6cyf79+1+oqsKhQ4fIysri/v379OjR45Hl48aNo0OHDvm+36+//oqPjw+bNm1i9uzZuLi48OWXX9K3b9/c1xdkHYBLly6RnJz8yEC21+Ft+O4KwusmMbxIYTtBEIQ31MCBA7G3t2fs2LHPvY3k5GQOHz5M7dq18/Q7nDBhAhs2bODkyZMvY1eFQjJixAhSUlKYPXt2Ye+KIAiIllJBEN5RQ4YMoXv37nz++efP3RprZmbGmDFjCAgI4KOPPsLc3Jxz586xbNkyBg4c+JL3WHidIiMj2bNnDytXrizsXREE4QHRUioIwjtr/vz5XL9+nSlTpjz3NoKDg5k2bRoXLlxApVLh7e1N165d6dGjx0vvCyu8Pl9//TX+/v4MGDCgsHdFEIQHRCgVBEEQBEEQCp0oCSUIgiAIgiAUOhFKBUEQBEEQhEInQqkgCIIgCIJQ6EQoFQRBEARBEAqdCKWCIAiCIAhCoROhVBAEQRAEQSh0IpQKgiAIgiAIhU6EUkEQBEEQBKHQiVAqCIIgCIIgFDoRSgVBEARBEIRC939XXVLS80MsgAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_theme(style='whitegrid')\n",
    "plt.figure(figsize=[8, 6])\n",
    "ax = sns.kdeplot(data=vdem_pca, x='PC 1', y='PC 2', alpha=.8, fill=True)\n",
    "for i, country in enumerate(vdem_pca.index):\n",
    "    ax.text(\n",
    "        x = vdem_pca['PC 1'][i], \n",
    "        y = vdem_pca['PC 2'][i], \n",
    "        s = country, \n",
    "        horizontalalignment = 'center', \n",
    "        verticalalignment = 'center', \n",
    "        size = 6, \n",
    "        color = 'black', \n",
    "        weight = 'normal'\n",
    "    )\n",
    "ax.set(xticklabels=[], yticklabels=[])\n",
    "ax.set(\n",
    "    xlabel = f'$\\longleftarrow$ PC 1 (eigenvalue: {np.round(eigenvalues[0], 2)}) $\\longrightarrow$', \n",
    "    ylabel = f'$\\longleftarrow$ PC 2 (eigenvalue: {np.round(eigenvalues[1], 2)}) $\\longrightarrow$'\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2edf5ab4",
   "metadata": {},
   "source": [
    "Two reagions are visible in the plot. But which countries belong to those regions? This is where clustering, the other family of algorithms in unsupervised ML, can help."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "bddc982a",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'lax' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[48], line 1\u001b[0m\n\u001b[1;32m----> 1\u001b[0m \u001b[43mlax\u001b[49m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'lax' is not defined"
     ]
    }
   ],
   "source": [
    "lax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c58e405",
   "metadata": {},
   "source": [
    "## D3.3. Clustering\n",
    "\n",
    "Clustering analysis is used to group similar objects or data points together based on their characteristics or features.\n",
    "\n",
    "The goal of clustering is to divide a dataset into groups, or clusters, where each group contains data points that are similar to each other and dissimilar to data points in other groups. The similarity between data points is typically measured using a distance metric, such as Euclidean distance or cosine similarity.\n",
    "\n",
    "There are many different algorithms used for clustering analysis, including k-means, hierarchical clustering, and density-based clustering. Each algorithm has its own strengths and weaknesses, and the choice of algorithm depends on the characteristics of the dataset and the goals of the analysis.\n",
    "\n",
    "Clustering analysis has many practical applications, such as customer segmentation, image segmentation and anomaly detection. By identifying groups of similar data points, clustering can help to identify patterns and relationships in the data, and can be used to make predictions or inform decision-making.\n",
    "\n",
    "\n",
    "### D.3.3.1. K-Means\n",
    "\n",
    "K-means is an algorithm used for grouping similar data points together based on their features. The algorithm works as follows. First, the number of clusters ($k$) is specified. Second, the algorithm randomly selects k initial points as the centroids of the clusters. Third, each data point is assigned to the cluster whose centroid is closest to it. Fourth, the centroids of the clusters are updated by calculating the mean of all the data points in each cluster. Then, the last two steps are repeated iteratively until the centroids no longer change, or until a maximum number of iterations is reached.\n",
    "\n",
    "The final result of the k-means algorithm is a set of $k$ clusters, where each data point belongs to the cluster with the closest centroid.\n",
    "\n",
    "K-means can be used in a variety of applications, such as image segmentation and data compression. It is particularly useful when the number of clusters in the data is not known in advance, and the goal is to discover the underlying structure of the data.\n",
    "\n",
    "However, it is important to note that k-means has some limitations. For example, the algorithm is sensitive to the initial choice of centroids, and may converge to a local optimum instead of the global optimum. Additionally, k-means assumes that the clusters are spherical and equally sized, which may not be appropriate for all datasets."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edd1a6fa",
   "metadata": {},
   "source": [
    "First, we will import appropriate library package. Second, we will define the number of clusters (4 in our case) and random state for reproducability reasons. Third, we will fit the model to our transformed 4 principal components that we derived in previous subsection. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "49d847d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "# create instance of class\n",
    "kmeans = KMeans(n_clusters=4, random_state=42)\n",
    "\n",
    "# cluster countries based on first four components\n",
    "y_kmeans = kmeans.fit(X=X_pca[:, :4])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "875ce7f5",
   "metadata": {},
   "source": [
    "Now, we can add derived labels from the clustering to our DataFrame and name this column \"label_kmeans\". The labels are digits between 0 and 3, where are digit corresponds to cluster it was assigned to. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c9f90536",
   "metadata": {},
   "outputs": [],
   "source": [
    "# add cluster labels\n",
    "vdem_pca.loc[:, 'label_kmeans'] = y_kmeans.labels_\n",
    "vdem_pca.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "949c1ae9",
   "metadata": {},
   "source": [
    "Let's check how many countries have been assigned to each cluster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d367253",
   "metadata": {},
   "outputs": [],
   "source": [
    "vdem_pca[\"label_kmeans\"].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab677d83",
   "metadata": {},
   "source": [
    "Cluster $1$ has the most counties - 78, whereas cluster $0$ includes only 5 countries. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6ea2745",
   "metadata": {},
   "source": [
    "To see the resulting clusters, we can plot each cluster area with different colour. Since our data is 4-dimentional, we will plot clusters only on the first two dimentions. However, you can add yourself plots on other dimentions by modifing the folowing code: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c29f6516",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# acknowledgement: https://gist.github.com/nicoguaro/1cc7474bc2331e48fb64\n",
    "from matplotlib.patches import Polygon\n",
    "from scipy.spatial import ConvexHull, convex_hull_plot_2d\n",
    "\n",
    "def plot_clusters(df_model,label_column,number_clusters):\n",
    "    plt.figure(figsize=[8, 6])\n",
    "    ax = sns.kdeplot(data=df_model, x='PC 0', y='PC 1', alpha=.0, fill=False)\n",
    "    for i, country in enumerate(df_model.index):\n",
    "        ax.text(\n",
    "            x = df_model['PC 0'][i], \n",
    "            y = df_model['PC 1'][i], \n",
    "            s = country, \n",
    "            horizontalalignment = 'center', \n",
    "            verticalalignment = 'center', \n",
    "            size = 6, \n",
    "            color = 'black', \n",
    "            weight = 'normal'\n",
    "        )\n",
    "    for label in range(number_clusters):\n",
    "        df = df_model[df_model[label_column] == label]\n",
    "        points = df[['PC 0', 'PC 1']].to_numpy()\n",
    "        hull = ConvexHull(points)\n",
    "        color = plt.cm.Set1(label)\n",
    "        poly = Polygon(points[hull.vertices], closed=True, capstyle='round', facecolor=color, alpha=.25)\n",
    "        plt.gca().add_patch(poly)\n",
    "    ax.set(xticklabels=[], yticklabels=[])\n",
    "    ax.set(\n",
    "        xlabel = f'$\\longleftarrow$ PC 0 (eigenvalue: {np.round(eigenvalues.loc[0], 2)}) $\\longrightarrow$', \n",
    "        ylabel = f'$\\longleftarrow$ PC 1 (eigenvalue: {np.round(eigenvalues.loc[1], 2)}) $\\longrightarrow$'\n",
    "    )\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "plot_clusters(df_model=vdem_pca,label_column='label_kmeans',number_clusters=len(vdem_pca[\"label_kmeans\"].unique() ) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce1132de",
   "metadata": {},
   "source": [
    "**But is this number of clusters is optimal?**\n",
    "\n",
    "Identifying the optimal number of clusters is an important step in clustering analysis, as it helps to ensure that the clusters are meaningful and useful for the intended application. There are several methods that can be used to identify the optimal number of clusters:\n",
    "\n",
    "1. Elbow method: Plot the sum of squared distances between each data point and its closest centroid (also known as the inertia) as a function of the number of clusters. The optimal number of clusters is often the point where the curve begins to flatten out, or where the rate of decrease in inertia decreases significantly. This point is known as the \"elbow\" of the curve.\n",
    "\n",
    "2. Silhouette method: Calculate the silhouette score for each data point, which measures how well the data point fits into its assigned cluster compared to other clusters. The optimal number of clusters is often the point where the average silhouette score across all data points is highest.\n",
    "\n",
    "3. Gap statistic method: Compare the observed sum of squared distances between each data point and its closest centroid to the expected sum of squared distances for a null reference distribution. The optimal number of clusters is often the point where the gap between the observed and expected sum of squared distances is highest.\n",
    "\n",
    "4. Information criterion methods: Use statistical information criteria, such as Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC), to compare models with different numbers of clusters. The optimal number of clusters is often the model with the lowest information criterion value.\n",
    "\n",
    "It's important to note that there is no one \"correct\" method for identifying the optimal number of clusters, and different methods may produce different results depending on the dataset and the clustering algorithm used. Therefore, it's recommended to try multiple methods and evaluate the results to make an informed decision about the optimal number of clusters for the specific application.\n",
    "\n",
    "The above mentioned method are applicable for cases with no groundtruth, which will be the most common case in clustering analysis. For some other evaluation methods you can further read [here](https://scikit-learn.org/stable/modules/clustering.html#clustering-performance-evaluation)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c05fe4ad",
   "metadata": {},
   "source": [
    "**Silhouette method**\n",
    "\n",
    " The silhouette score $s$ is defined as following \n",
    " \n",
    " $s = \\frac{b - a}{max(a, b)}$, \n",
    " \n",
    " where $a$ - is the mean distance between a data point and all other points in the same class, $b$ - is the mean distance between a data point  and all other points in the next nearest cluster.\n",
    "\n",
    "In the following we will calculate average silhouette score for all clusters in each model. Function *silhouette_score()* returns the mean Silhouette coefficient over all samples; as parameters we would pass in feature matrix and predicted cluster labels. \n",
    "\n",
    "The mean Silhouette coefficient over all data points of an individual cluster is a measure of how tightly grouped all the points in the cluster are. Thus the mean Silhouette coefficient over all data of the entire dataset is a measure of how appropriately the data have been clustered. The highest value is 1 which would indicate the pefrect fit and the worst value is -1. Values near 0 indicate overlapping clusters. Negative values generally indicate that a sample has been assigned to the wrong cluster, as a different cluster is more similar.\n",
    "\n",
    "To find the optimal number of clusters , we will try models with 2-25 clusters and plot those values:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c1023b8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "\n",
    "range_n_clusters = range(2, 26)\n",
    "silhouette_scores = []\n",
    "\n",
    "for n_clusters in range_n_clusters:\n",
    "    clusterer = KMeans(n_clusters=n_clusters,  random_state=42)\n",
    "    cluster_labels = clusterer.fit_predict(X_pca[:, :4])\n",
    "    # The silhouette_score gives the average value for all the samples.\n",
    "    # This gives a perspective into the density and separation of the formed clusters\n",
    "    silhouette_avg = silhouette_score(X_pca[:, :4], cluster_labels)\n",
    "    silhouette_scores.append(silhouette_avg)\n",
    "    \n",
    "plt.plot(range_n_clusters,silhouette_scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7967ee8",
   "metadata": {},
   "source": [
    "According to average Silhouette score, the best separation is achived by 2 clusters. Though, according to the plot above, 4 closters will be a good separation choice too.   \n",
    "\n",
    "However, this judgment is questionable while there is no ground trooth of the best separation of countries. You can try other methods (provided above) in order to justify the number of clusters in the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f09897ab",
   "metadata": {},
   "source": [
    "### D3.3.2. DBSCAN\n",
    "\n",
    "Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is an algorithm used to identify clusters of data points in a dataset based on their density. Unlike k-means, DBSCAN does not require specifying the number of clusters in advance and can discover clusters of arbitrary shapes.\n",
    "\n",
    "DBSCAN works by defining a notion of density around each data point. It groups data points that are close to each other and have a sufficient number of neighboring points within a specified distance, known as the epsilon radius. The algorithm distinguishes between three types of data points:\n",
    "1. Core points: These are data points within the epsilon radius of at least a minimum number of neighboring points (specified as the minimum number of points required for a cluster).\n",
    "2. Border points: These are data points within the epsilon radius of a core point but do not have enough neighboring points to be considered core points themselves.\n",
    "3. Noise points: These are data points that are not within the epsilon radius of any core point.\n",
    "\n",
    "DBSCAN starts by randomly selecting an unvisited data point and expands a cluster around it by iteratively adding reachable core and border points. This process continues until no more reachable points can be added to the cluster. Then, another unvisited data point is selected, and the process repeats until all data points have been visited.\n",
    "\n",
    "The result of DBSCAN is a set of clusters, where each cluster consists of a group of connected core and border points. Noise points are not assigned to any cluster.\n",
    "\n",
    "DBSCAN has the advantage of being able to discover clusters of various shapes and handle noise points effectively. However, it requires careful selection of the parameters, such as the epsilon radius and the minimum number of points, which can impact the results. Additionally, the performance of DBSCAN may be affected by the density variations in the dataset.\n",
    "\n",
    "In summary, DBSCAN is a density-based clustering algorithm that groups data points based on their density and proximity. It can automatically discover clusters of arbitrary shapes and is effective in handling noise points. However, parameter selection is important, and the algorithm's performance can be influenced by the density variations in the dataset.\n",
    "\n",
    "In the following we will import appropriate library, create instance of the model class, fit the model to our data and then plot these clusters. As an example, we will specify the epsilon radius *eps* as 1.2 and the minimum number of points *min_samples* -- 4."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7364dc61",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import DBSCAN\n",
    "\n",
    "# create instance of class\n",
    "DBSCAN_model = DBSCAN(eps=1.2, min_samples=4)\n",
    "\n",
    "# cluster countries based on first four components\n",
    "y_DBSCAN = DBSCAN_model.fit(X=X_pca[:, :4])\n",
    "\n",
    "# add cluster labels\n",
    "vdem_pca.loc[:, 'label_DBSCAN'] = y_DBSCAN.labels_\n",
    "print (vdem_pca[\"label_DBSCAN\"].value_counts())\n",
    "\n",
    "plot_clusters(df_model=vdem_pca,label_column='label_DBSCAN',number_clusters=len(vdem_pca[\"label_DBSCAN\"].unique())-1 )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "228b79e5",
   "metadata": {},
   "source": [
    "The noise points are labeled as *-1*, other clusters are labeled from *0* to *2*. So using the current parameters, the model estimated 50 points as noise and other points were divided into 3 clusters. \n",
    "Let us check which countries were assigned to class *2*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5faf9618",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in [2]:\n",
    "    print (\"Countries in cluster %d:\"% i)\n",
    "    print (vdem_pca[vdem_pca[\"label_DBSCAN\"]==i].index.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e7ebc97",
   "metadata": {},
   "source": [
    "If you return back to the density plot in PCA subsection, you will find out that two dense areas on the left side of the plot were identified by DBSCAN. The first dense area that includes countries like Denamrk, Switzerland and Netherlands and the second -- Costa Rica, Cuprys, Argentina, etc. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef37f8a3",
   "metadata": {},
   "source": [
    "Let us find out how whould clusters change if we tune parameter *eps*. \n",
    "\n",
    "Here, we will define sliding bar that with different eps values would draw appropriate clustering models. Move sliding bar to the left or right in order to change eps parameter and have a new plot. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2c427e21",
   "metadata": {},
   "outputs": [],
   "source": [
    "import ipywidgets\n",
    "\n",
    "def define_eps(df_model, label_column, min_samples, slider_value, slider_min, slider_max, slider_step):\n",
    "    '''\n",
    "    Draws clusters with a slider that allows to select eps parameter of the model. \n",
    "        Eps controls the local neighborhood of the points. Smaller eps would indicate higher density necessary to form \n",
    "        a cluster and a higher value would merge close clusters into one cluster, and eventually \n",
    "        the entire data set to be returned as a single cluster.        \n",
    "    \n",
    "    Parameters:\n",
    "        df_model : DataFrame object\n",
    "            DatFrame with data that has to be modeled and clustered.\n",
    "        label_column : string\n",
    "            Label name to store our clustering results.\n",
    "        min_samples : integer\n",
    "            The number of points in a neighborhood for a point to be considered as a core point.\n",
    "\n",
    "        slider_value : integer or float\n",
    "            Initial filter value.\n",
    "        slider_min : integer or float\n",
    "            Minimum filter value.\n",
    "        slider_max : integer or float\n",
    "            Maximum filter value.\n",
    "        slider_step : integer or float\n",
    "            Size of steps with which filter value is slided.\n",
    "    '''\n",
    "    def draw_filtered_graph(eps_value):\n",
    "        y_DBSCAN = DBSCAN(eps=eps_value, min_samples=min_samples).fit(X=df_model.iloc[:, :4].to_numpy()).labels_\n",
    "        df_model.loc[:, label_column] = y_DBSCAN\n",
    "        number_clusters=len(set(y_DBSCAN))-1\n",
    "        plot_clusters(df_model=df_model,label_column=label_column,number_clusters=number_clusters)\n",
    "    \n",
    "    ipywidgets.interact(\n",
    "        draw_filtered_graph, \n",
    "        eps_value = ipywidgets.FloatSlider(value=slider_value, min=slider_min, max=slider_max, step=slider_step)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6e205231",
   "metadata": {},
   "outputs": [],
   "source": [
    "define_eps(\n",
    "    df_model = vdem_pca, \n",
    "    label_column = \"label_DBSCAN\",\n",
    "    min_samples = 4,\n",
    "    slider_value = 1.4, \n",
    "    slider_min = 0.6, \n",
    "    slider_max = 3, \n",
    "    slider_step = 0.2\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53123b2f",
   "metadata": {},
   "source": [
    "### D3.3.3. Agglomarative clustering\n",
    "\n",
    "Agglomerative clustering, also known as hierarchical clustering, is a popular method used to group similar data points into clusters based on their distances or similarities. It starts with each data point considered as a separate cluster and then merges clusters iteratively until a stopping criterion is met.\n",
    "\n",
    "The agglomerative clustering process can be summarized as follows:\n",
    "1. Initially, each data point is assigned to its own individual cluster.\n",
    "2. The algorithm calculates the distance or similarity between each pair of clusters.\n",
    "3. The two closest clusters, based on a chosen linkage criterion (e.g., minimum distance, maximum distance, average distance), are merged together into a single cluster.\n",
    "4. Steps 2 and 3 are repeated iteratively until a stopping criterion is met. This can be a pre-defined number of clusters, a specific level of similarity or distance, or any other criterion chosen by the user.\n",
    "\n",
    "As the algorithm progresses, a tree-like structure called a dendrogram is formed, where the branches represent the merging of clusters at different levels of similarity. The dendrogram can be visualized to understand the hierarchical relationships between the clusters.\n",
    "\n",
    "Agglomerative clustering does not require specifying the number of clusters in advance, as the algorithm dynamically determines the number of clusters based on the merging process. By considering the entire dataset and capturing hierarchical relationships, agglomerative clustering can reveal nested clusters and provide insights into the data structure.\n",
    "\n",
    "\n",
    "Agglomerative clustering is flexible and can handle various types of data, including numerical and categorical variables. However, it can be computationally expensive, especially for large datasets, as the distance or similarity matrix needs to be updated at each iteration.\n",
    "\n",
    "In summary, agglomerative clustering is a hierarchical clustering technique that iteratively merges similar clusters based on a chosen linkage criterion. It does not require the number of clusters to be specified in advance and provides a hierarchical structure of the data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc6cb36b",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "for n_clusters in [2,3,4,5,6,7]:  \n",
    "    y_Aggl = AgglomerativeClustering(n_clusters=n_clusters).fit(X_pca[:, :4])\n",
    "    cluster_labels=y_Aggl.labels_\n",
    "    \n",
    "    vdem_pca.loc[:, 'label_Aggl'] = y_Aggl.labels_\n",
    "    plot_clusters(df_model=vdem_pca,label_column='label_Aggl',number_clusters=len(vdem_pca[\"label_Aggl\"].unique()) )\n",
    "    ilhouette_avg = silhouette_score(X_pca[:, :4], cluster_labels)\n",
    "    print(\"For\", n_clusters,\"clusters the average silhouette score is :\",silhouette_avg)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b98d082a",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "### Recommended readings\n",
    "\n",
    "<a id='bacher_unsupervised_2022'></a>\n",
    "Bacher, J., Pöge, A., & Wenzig, K. (2022). \"Unsupervised methods: Clustering methods.\" In: Engel, U. & Quan-Haase, A. (eds). *Handbook of Computational Social Science*, vol. 2, p. 334–351. Abingdon: Routledge. https://doi.org/10.4324/9781003025245.\n",
    "\n",
    "<a id='mclevey_doing_2022'></a>\n",
    "McLevey, J. (2022). *Doing Computational Social Science: A Practical Introduction*. SAGE. https://us.sagepub.com/en-us/nam/doing-computational-social-science/book266031. *A rather complete introduction to the field with well-structured and insightful chapters also on unsupervised Machine Learning. The [website](https://github.com/UWNETLAB/dcss_supplementary) offers the code used in the book. For this session, read **chs. 8 and 19** on dimensionality reduction and the unsupervised and supervised types of Machine Learning.*\n",
    "\n",
    "### Complementary readings\n",
    "\n",
    "<a id='efron_computer_2016'></a>\n",
    "Efron, B. & Hastie, T. (2016). *Computer Age Statistical Inference: Algorithms, Evidence, and Data Science*. Cambridge University Press. http://www.cambridge.org/9781107149892.\n",
    "\n",
    "<a id='ghani_machine_2016'></a>\n",
    "Ghani, R. & Schierholz, M. (2016). \"Machine Learning.\" In: Foster, I. *et al.* (Eds.). *Big Data and Social Science: A Practical Guide to Methods and Tools*, p. 147–186. CRC Press. *Overview article about types and algorithms of Machine Learning.*\n",
    "\n",
    "<a id='hofman_integrating_2021'></a>\n",
    "Hofman, J. M., Watts, D. J., *et al.* (2021). \"Integrating explanation and prediction in computational social science.\" *Nature* 595:181–188. https://doi.org/10.1038/s41586-021-03659-0.\n",
    "\n",
    "<a id='kitchin_big_2014'></a>\n",
    "Kitchin, R. (2014). \"Big Data, new epistemologies and paradigm shifts.\" *Big Data & Society* 1:1–12. https://doi.org/10.1177/2053951714528481.\n",
    "\n",
    "<a id='poge_principel_2022'></a>\n",
    "Pöge, A. & Reinecke, J. (2022). \"Principal Component Analysis.\" In: Engel, U. & Quan-Haase, A. (eds). *Handbook of Computational Social Science*, vol. 2, p. 322–333. Abingdon: Routledge. https://doi.org/10.4324/9781003025245."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "758d9eec",
   "metadata": {},
   "source": [
    "<div class='alert alert-block alert-success'>\n",
    "<b>Document information</b>\n",
    "\n",
    "Contact and main author: Haiko Lietz & Olga Zagovora\n",
    "\n",
    "Version date: 18 August 2023\n",
    "\n",
    "License: Creative Commons Attribution 4.0 International (CC BY 4.0)\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "726e55c1",
   "metadata": {},
   "outputs": [],
   "source": []
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