nonlinear_visualisation/explanation.html at master · biometrician/nonlinear_visualisation · GitHub

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      <meta name="author" content="Daniela Dunkler" />


      <title>Visualisation of non-linear modeling</title>
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<div id="visualisation-of-non-linear-modelling" class="section level1">
<h1><strong>Visualisation of non-linear modelling</strong></h1>
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<em>by Daniela Dunkler and Georg Heinze</em>
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<p><br></p>
<div id="modelling-non-linear-effects" class="section level2">
<h2><strong>Modelling non-linear effects</strong></h2>
<p><br></p>
<div id="the-linearity-assumption" class="section level3">
<h3>1. The linearity assumption</h3>
<p>Recall the definition of a linear regression model <span class="math display">\[y = \beta_0 + \beta_1 x + \epsilon,\]</span></p>
<p>where <span class="math inline">\(y\)</span> is the outcome, <span class="math inline">\(\beta_0\)</span> the intercept, <span class="math inline">\(\beta_1\)</span> the regression coefficient of the explanatory variable <span class="math inline">\(x\)</span> and <span class="math inline">\(\epsilon\)</span> as the error term of the model. The linear regression model is equivalent to <span class="math display">\[E(Y) = \beta_0 + \beta_1 x\]</span> with <span class="math inline">\(E(Y)\)</span> being the expected value of <span class="math inline">\(y\)</span>.</p>
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The linearity assumption states that with each one-unit difference in <span class="math inline">\(x\)</span>, there should be a <span class="math inline">\(\beta_1\)</span> difference in <span class="math inline">\(y\)</span>.
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<p>Put mathematically, <span class="math inline">\(\partial E(Y) / \partial x = \partial (\beta_0 + \beta_1 x)/\partial x = \beta_1\)</span>.</p>
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<p><em>But what actually happens if this assumption is violated?</em></p>
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A violation of the linearity assumption would imply that in different regions of <span class="math inline">\(x\)</span> the impact of <span class="math inline">\(x\)</span> is not <span class="math inline">\(\beta_1\)</span>, but larger or smaller than on average. This means that inclusion of <span class="math inline">\(x\)</span> as a single explanatory variable is not sufficient to model the association with <span class="math inline">\(y\)</span>.
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<p>In medical applications, the linearity assumption is frequently violated. To illustrate this possibility, let us consider a data set with age and body-mass-index (BMI) of 9377 NHANES participants. Below, is a plot of BMI values against age with the mean BMI values computed at each age (blue line). Additionally, the model assuming a linear association is added in red.</p>
<p><img 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" width="672" /> <br><br></p>
<!---<center><div class = "figure">![](www/age_bmi_1.png)</div></center>-->
<p>The association between BMI and age is obviously not linear. The question is are differences in BMI between adjacent age groups due to a trend in the population or just due to random variation.</p>
<p>A popular nonparametric method to ‘smooth’ the blue curve by ‘local regression’ is the method of ‘locally estimated scatterplot smoothing’ (LOESS) (green line). In our case, it gives:</p>
<p><img 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" width="672" /> <br><br></p>
<!---<center><div class = "figure">![](www/age_bmi_2.png)</div></center>-->
<p>In estimating the LOESS line, R automates some of the decisions, e.g., how complex the underlying model should be and how ‘wiggly’ the resulting curve may be. These decisions are not transparent and therefore, the use of LOESS is more or less restricted to graphical, explorative analyses where trends should be discovered.</p>
<p><strong>For modelling purposes, it is advisable that the analyst takes full control over the complexity of the model.</strong> In this way, the analyst can find the right balance between <em>flexibility</em> and <em>stability</em> of a model.</p>
<ul>
<li><p>Flexibility of a model makes sure that important features of the data are not overlooked. However, if a model is too flexible, it may follow each little ‘hub’ or ‘bump’ and lead to increased variance. See the mean-by-age plot above.</p></li>
<li><p>Stability of a model guarantees that the main conclusions from the analysis do not change if the data are slightly changed (e.g., some observations are removed or added). Simpler models, i.e., models with fewer parameters, are usually more stable than more complex models. However, simpler models bear the risk of <em>misspecification</em>, meaning that there are systematic trends in the residuals which, if not corrected, lead to misconclusions.</p></li>
</ul>
<p>With very large data sets, one can usually reach stability also with a highly flexible modelling approach. In small-to-moderately sized data sets, a data analyst must find the right balance between a flexible and a stable model. Instability can also pose a problem with big data sets, as with the number of observations usually also the number of variables and the number of research questions increases.</p>
<p>In the example above, we see a lot of sudden differences in expected BMI with age changing by one year. Many of these changes are not plausibly explained by underlying population trends. Therefore, the task of the analyst is to separate <em>systematic</em> from <em>random</em> variation in BMI according to age.</p>
<p><br></p>
</div>
<div id="relaxing-the-linearity-assumption" class="section level3">
<h3>2. Relaxing the linearity assumption</h3>
<p>If the association between the explanatory variable <span class="math inline">\(x\)</span> and the outcome <span class="math inline">\(y\)</span> is obviously not linear, one can relax the linearity assumption. The above mentioned model can be extended to accommodate non-linear effects using polynomials. A polynomial of a continuous variable <span class="math inline">\(x\)</span> of degree <span class="math inline">\(k\)</span> is defined as <span class="math inline">\(x, x^2, \ldots, x^k\)</span>. If such a polynomial of degree <span class="math inline">\(k\)</span> is used to represent the variable in a regression model, then for each term of the polynomial a separate regression coefficient is estimated. The dependent variable is modeled by <span class="math display">\[E(Y) = \beta_0 + \beta_1 x + \beta_2 x^2 + \ldots + \beta_k x^k.\]</span> <span class="math inline">\(x\)</span> (=<span class="math inline">\(x^1\)</span>), <span class="math inline">\(x^2\)</span> to <span class="math inline">\(x^k\)</span> are called base functions of <span class="math inline">\(x\)</span>. For a raw polynomial of order <span class="math inline">\(3\)</span> of a variable <span class="math inline">\(x\)</span>, the base functions can be computed by, e.g.:</p>
<table>
<thead>
<tr class="header">
<th align="center">Variable value <span class="math inline">\(x\)</span></th>
<th align="center"><span class="math inline">\(x^1\)</span></th>
<th align="center"><span class="math inline">\(x^2\)</span></th>
<th align="center"><span class="math inline">\(x^3\)</span></th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">1</td>
</tr>
<tr class="even">
<td align="center">2</td>
<td align="center">2</td>
<td align="center">4</td>
<td align="center">8</td>
</tr>
<tr class="odd">
<td align="center">3</td>
<td align="center">3</td>
<td align="center">9</td>
<td align="center">27</td>
</tr>
<tr class="even">
<td align="center">…</td>
<td align="center">…</td>
<td align="center">…</td>
<td align="center">…</td>
</tr>
</tbody>
</table>
<p>In R the <code>poly()</code> function is a convenient way to compute polynomial terms.</p>
<p>Even with <span class="math inline">\(k\)</span> chosen as 2 or 3, such a model is flexible enough to relax the linearity assumption, i.e., the assumption that each increase in <span class="math inline">\(x\)</span> is associated with a difference in <span class="math inline">\(y\)</span> of <span class="math inline">\(\beta_1\)</span>. Note, the regression model described above is still a linear model, despite that it provides a non-linear function of the explanatory variable <span class="math inline">\(x\)</span>.</p>
<p>In the last decades, a couple of techniques were developed that allow in very flexible ways to relax the linearity assumption. Among them are <strong>fractional polynomials</strong>, and various types of ‘splines’, like <strong>natural (restricted cubic) splines</strong> or <strong>B-splines</strong>. The use of these methods allow investigation of non-linear effects of continuous variables. In all these proposals, the continuous variable <span class="math inline">\(x\)</span> is first transformed into a few base functions, and the base functions are then used for modelling.</p>
<p><br></p>
<div id="fractional-polynomials" class="section level4">
<h4>2.1. Fractional polynomials</h4>
<p>Fractional polynomials select one or two base functions from a predefined catalogue of eight possible transformations, which is:</p>
<p><span class="math display">\[\{x^{-2}, x^{-1}, x^{-1/2}, log(x), x^{1/2}, x, x^{2}, x^{3}\}.\]</span></p>
<p>The so-called ‘powers’ (<span class="math inline">\(-2, -1, ..., 3\)</span>) in those transformations are selected by using those one or two transformations that yield the best model fit. Models requiring one power are called first-degree (FP1) function and models requiring two powers are second-degree (FP2) functions. If the same power is selected twice (i.e., ‘repeated powers’), e.g. <span class="math inline">\(x^{2}\)</span> is selected twice, the FP2 function is defined as <span class="math inline">\(\beta_1 x^{2} + \beta_2 log(x)\)</span>. This defines 8 FP1 and 36 FP2 models. These 44 models are sufficient for most biomedical applications as they include very different types of non-linear functions.</p>
<p>A suitable pretransformation is applied to make the base functions independent, but for pragmatic reasons the pretransformation of <span class="math inline">\(x\)</span> will only shift the values to the positive range (if necessary) and then divide them by a multiple of 10. In this way, the pretransformation stays simple enough to be written down in a report.</p>
<p>To select the best model among those 44 candidates, a closed testing procedure, called the function selection procedure (FSP) has been introduced:</p>
<ol style="list-style-type: decimal">
<li><em>Test of overall association of the outcome <span class="math inline">\(y\)</span> with <span class="math inline">\(x\)</span></em>: The best-fitting FP2 model for <span class="math inline">\(x\)</span> at the <span class="math inline">\(\alpha\)</span> level is tested against a model without <span class="math inline">\(x\)</span> (using four degrees of freedom). If the test is not significant, stop, concluding that <span class="math inline">\(x\)</span> is not significant at <span class="math inline">\(\alpha\)</span>. <span class="math inline">\(x\)</span> is not included in the final model. Otherwise continue.</li>
<li><em>Test the evidence of non-linearity</em>: The best-fitting FP2 model for <span class="math inline">\(x\)</span> is tested against a straight line (linear function) at the <span class="math inline">\(\alpha\)</span> level (using three degrees of freedom). If the test is not significant, stop, concluding that the linear function of <span class="math inline">\(x\)</span> is sufficient. Otherwise continue.</li>
<li><em>Test between a simple or a more complex non-linear model</em>: The best-fitting FP2 model for <span class="math inline">\(x\)</span> is tested against the best-fitting FP1 model at the <span class="math inline">\(\alpha\)</span> level (using two degrees of freedom). If the test is not significant, the final model includes the best-fitting FP1 function, otherwise the final model includes the best-fitting FP2 function.</li>
</ol>
<p>This procedure preserves the overall (i.e. familywise) type I error probability at a chosen <span class="math inline">\(\alpha\)</span> level. A typical choice for the nominal <span class="math inline">\(p\)</span>-value is <span class="math inline">\(\alpha = 0.05\)</span>.</p>
<p>The approach is implemented in the R package <code>mfp</code>, in which it can be combined with variable selection and used with continuous, binary or time-to-event outcome variables. Using this R package to model the association of BMI on age in our example gives the following fit:</p>
<pre><code>##
## Call:
## glm(formula = bmi ~ log((age/100)) + I((age/100)^3), family = &quot;gaussian&quot;,
##     data = explanation_data)
##
## Deviance Residuals:
##     Min       1Q   Median       3Q      Max
## -14.981   -3.939   -0.693    3.107   47.821
##
## Coefficients:
##                Estimate Std. Error t value Pr(&gt;|t|)
## (Intercept)     34.2969     0.3911   87.69   &lt;2e-16 ***
## log((age/100))   5.3436     0.3296   16.21   &lt;2e-16 ***
## I((age/100)^3) -10.9008     0.8387  -13.00   &lt;2e-16 ***
## ---
## Signif. codes:  0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1
##
## (Dispersion parameter for gaussian family taken to be 32.72564)
##
##     Null deviance: 315682  on 9376  degrees of freedom
## Residual deviance: 306770  on 9374  degrees of freedom
## AIC: 59324
##
## Number of Fisher Scoring iterations: 2</code></pre>
<p>The pretransformation of age includes a division by 100. The powers 0 and 3 are selected leading to the FP2 functions <span class="math inline">\(log((age/100)) + (age/100)^3\)</span>. The fitted model looks like this:</p>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>For more information on fractional polynomials we refer to the <a href="http://mfp.imbi.uni-freiburg.de/fp">multivariable fractional polynomials website</a>.</p>
<p><br></p>
</div>
<div id="splines" class="section level4">
<h4>2.2. Splines</h4>
<p>Splines are a common method of modelling nonlinear effects of continuous variables. A spline function is defined by a set of piecewise polynomial functions of a continuous variable that are joined smoothly at a set of knots.</p>
<p>In <a href="https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-019-0666-3/">Perperoglou A, Sauerbrei W, Abrahamowicz M, Schmid M. BMC Med Res Methodol. 2019</a> the idea of splines is very eloquently explained as: <em>The term ‘spline’ refers to a craftsman’s tool, a flexible thin strip of wood or metal, used to draft smooth curves. Several weights would be applied on various positions so the strip would bend according to their number and position. This would be forced to pass through a set of fixed points: metal pins, the ribs of a boat, etc. On a flat surface these were often weights with an attached hook and thus easy to manipulate. The shape of the bended material would naturally take the form of a spline curve. Similarly, splines are used in statistics in order to mathematically reproduce flexible shapes. Knots are placed at several places within the data range, to identify the points where adjacent functional pieces join each other. Instead of metal or wood stripes, smooth functional pieces (usually low-order polynomials) are chosen to fit the data between two consecutive knots. The type of polynomial and the number and placement of knots is what then defines the type of spline.</em></p>
<p><a href="https://bmcmedresmethodol.biomedcentral.com/articles/10.1186/s12874-019-0666-3/">The above mentioned paper</a> also includes a simple-to-read review of splines methodology and splines functions procedures in R.</p>
<p><br></p>
<div id="linear-b-splines" class="section level5">
<h5>2.2.1. Linear B-splines</h5>
<p>A B-spline of order <span class="math inline">\(n\)</span> is a piecewise polynomial function of degree <span class="math inline">\(n-1\)</span> in a variable <span class="math inline">\(x\)</span>. It is defined over <span class="math inline">\(n+1\)</span> knots <span class="math inline">\(t_{j}\)</span>, which must be in non-descending order <span class="math inline">\(t_{j}&lt;t_{j+1}\)</span>. B-splines transform the original variable <span class="math inline">\(x\)</span> into base functions which are greater than 0 for specific subranges of <span class="math inline">\(x\)</span> and 0 otherwise. The number of degrees of freedom defines the number of base functions, and the degree defines the type of transformation. Linear B-splines have degree 1. The subranges are defined by the location of knots. These are usually set automatically, but are part of the definition of the spline transformation.</p>
<p>For example, linear B-splines with three base functions (i.e., <code>degree=1</code> and <code>df=3</code>) as functions of age look like this</p>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>In contrast cubic B-splines with three base functions (i.e., <code>degree=3</code> and <code>df=3</code>) as functions of age look like this: <img src="data:image/png;base64,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" width="672" /></p>
<p>The individual spline bases have no simple interpretation and can only be used together as a set of independent variables representing variable <span class="math inline">\(x\)</span> (here age) in a regression model. In our example, by representing age in several transformations, we can estimate a nonlinear association of BMI with age.</p>
<p>Note, different choices of the number of degrees of freedom and the degree will lead to different model fits. Hence, both parameters have to be carefully selected by the analyst.</p>
<p>Let’s see splines in action. We refit the model with BMI and age, now using B-splines to model age. Applying linear B-splines with three base functions (<code>degree=1</code> and <code>df=3</code>) creates the following fit:</p>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>A smoother function can be obtained by using cubic B-splines with three base functions (<code>degree=3</code> and <code>df=3</code>):</p>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>Increasing the number of degrees of freedom leads to a more ’wiggly&quot; fit. The plots below show linear B-splines with 5, 10, 15, and 20 base functions:</p>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>The plots below show cubic B-splines with 5, 10, 15, and 20 base functions:</p>
<p><img src="data:image/png;base64,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" width="672" /> <br><br></p>
</div>
<div id="restricted-natural-cubic-splines" class="section level5">
<h5>2.2.2. Restricted (natural) cubic splines</h5>
<p>Restricted cubic splines (also known as natural splines) are cubic transformations (i.e., third-order polynomials) of the explanatory variable <span class="math inline">\(x\)</span> in the interior of its range (within the outermost knots), and are linear at the edges (outside the outermost knots). Typically, a small number of knots (e.g., 3 to 5) is sufficient to model most data in biomedical applications. Knots are located at various percentiles of <span class="math inline">\(x\)</span>. For example, Frank Harrell recommends in his book<a href="#fn1" class="footnote-ref" id="fnref1"><sup>1</sup></a> the following settings:</p>
<table>
<thead>
<tr class="header">
<th align="center">number of knots</th>
<th align="center">percentiles</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center">3</td>
<td align="center">0.10 0.5 0.90</td>
</tr>
<tr class="even">
<td align="center">4</td>
<td align="center">0.05 0.35 0.65 0.95</td>
</tr>
<tr class="odd">
<td align="center">5</td>
<td align="center">0.05 0.275 0.5 0.725 0.95</td>
</tr>
</tbody>
</table>
<p>With three degrees of freedom (= three transformations) their basis functions would look as follows: <img src="data:image/png;base64,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" width="672" /></p>
<p>Applying natural splines to model BMI on age results in a fit, which is ‘more linear’ in the tails.</p>
<p><img 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Y9+gO/CT9iL/boXUhtZOsocOxJoS2pmewECLXoN9O1wNabnl2fyX+FqTFfsxX7dCzcv0N6XJ6K1ctmvQGurij/mEtE3kb764ZM+p0uAfvXTJ39+3z3/hEBtcN0LEGiSvE1orVx2KlBiM8aKMI9W8C58huL4Cg/UgLnYF3sBAk2StwmtlYukQKMZoR5fJ9C2C8I8HALViLnYF3vhNgSa2u41I+RlAoFmu3VHqFkQCLT1xDRgLvbFXrh9gdZMI+uSoXtKszW3KFBCoqnt6CvCPBwC1Yi12Jd7AQJNkRbJ3D2l2Rr1Aj0EmB4rFii1HWNFmIdDoBqxFvui/iDQJMl+r91Tmq0RFWgsI4sWIX/OHq0VaNMV4R0OgWrEWuyL8oNAkyT7nbuntHKwLNDV2SihW3+AlivCOxwC1Yi12BfldxsCLfMFgUzHY++UVg7mBRoyKD2dDReEdzwEqhFjsS/LDwJNkul47J7Uag0E2mpBeMdDoBoxFvuy/NIbWTrSDN0Fmul36p7WbIWsQCMZWTQIObJaoIymjBVhHQ+BasRY7Mvqg0BTZPqduqc1W6FRoIvH469zXj1K7TY4QMMVYR0PgWrEVuyr6oNAU2T6nbqnNVthQaDRo1/XC7R0TfiDroFANWIr9vVeuAWBpqZQNY9sx0PvtGYrFAp0+TgE6h8IgXbDVuzrvQCBJsh2XIywQEMZWT7cRaCctowVYR0PgWrEVOzOXoBAE2Q7LkafQFcPUwQaeJyTzXYLwukAAtWIqdidvQCBJsh2XIxtgcYeZ2Wz2YJwOoBANWIqdmcv7EKg7Z4vtkJaoJnfCIFA/QMh0G6ojT27UYwKdN7IVKqG6cFtCjSdZ1ZjxopwOoBANaI19lB5uXsBAs0O0wNtAnUeJQmUeQrKasxaEUYHEKhGlMYerC93L1gU6HUjUyH1Gh2nA7oFmvoc/emS9xYCLSgv0lxSQKAa0Rl7sMC8vZDeyGLBJ1lsZCqkXmPjsEiZ54q4QJN/VtP+hEAh0LaojD1cYt5eMCjQ5UamQus1NhCDjHvm0CHQTHNiF8xuIFCNKIw9VmPeXoBAl71GBmJgUqDuY0SB+k0oq0ZrTu6D1w0EqhF9sceqzN8L9gS62shUiL1GBmIgIFDaiwYuqZnmBRppQlo2WntyH6xuIFCNqIs9WmX+XthUoC36czYyFWK3kZHobC9Q4ogeiYkWCzSR5kwM3LUv7AYC1Yi22ON15u8FCHTdbXgkOpk3sCcg0Fx7eh8QaM3ENKAs9tzOWe2FLQXaor9V8IyJkrsND0Ulfq3MNZoEyu5yFijjOXwuCPbil/UCgWpEV+yZfePsBQjU7TY4FJVmAqVLsVSg0TcWs2fRr+PDktaNdACnE3qXEKhGZGOnVVWEjQVa3eE6eM5Myd2GxyLSSqB0K1JH9IlOM9ehlECZEwsBgWoEAiUH2qKPa/CcmdK7Dd5JpJFAGVKEQDl9QqAagUDJgdIbR7tYBM+ZaTY0tymn8xl7Ao11mTjwKlC6QTNR0GqCNbEgEKhGRGOnVlWY3FPJ1pEyGkd6WAbPmWkuMq8tp/OZNgLlSLFcoNFpkgTKOwXNBEGtCca8wkCgGoFAyYFyWmfn2k2g4c/MUjgQffb6deJ9ogO1l0VjXpgDsVluKlBGiXHmFQEC1Yhk7NSiirC1QMkdhtp6wbOmmovMbcvqfISsvtfxa2ryBMqSrUNslhBo6EAItBsQKD3SmsZe8Kyp5gZzG7M6H2ELNNTwsKFA430mjlsI1GtGT3HuEF4nxA4hUI0Ixk6tqRjbCZTXYai1HzxrqtnBnNaszkf4AvVbXv3ZW6CRSWb7e71o53dJzXDmEGYnxA4hUI1AoPRImfNKzrWRQCPNWZ2PFAjUa7qlQONdpg7TLtBEjxCoRuRip9dUhM0EyuwwEEAgeN5cs2PVwxBoTJPjfVQrSguUZtBMGMyayBLvAwLVCATKiJQ7scRU2wiU10ka8snjUqCrtvM9NCuyzlaJUAXKOAVND8gtoSzxPiBQjYjFTi+pGEoFGgghFDxvroSxFtyXcPcEX6CLxtc7uAJtZ9DNBcr+o5oj3gcEqhEIlBEpf2LRqYZiT+x9ylinQnNe/Tlyn87rKFDvnaTrTYZAy68nkugzAVuguRG5NVTeHwSqEanY6RUVxYJAo59XDMSe3PzpoYhmHP0Yb3a/ahAJZRKoY9DFDSsCdVvmlzNAQVGUdQeBagQC5YRaMLPIVGsFermTeWaZNGhAoBGPvl4/VV9K83Dy/h1HVKDBloTl9CmoibLuIFCNCMXOqKgo2etStg+13cyKBbq4j+LPBgJ1Pfrateb1afvqbDSTgQMEyusOAtUIBMoJtd3M/NjdlxTdufj3bSvQ2aILgV6DXgdPFijr4k158p0lBZq/hEGIdkWR7g0C1QgEygm13cxYAl2dAK7v7iHQlEGfeOm/8unGzhBo01PQfF9rgeZPQQmDtiuKdHcQqEZkYucUVJRtBMrtkRq8d09YoKtzv8hDeYE6Ok20owj03GR9smlQoMTn8JRRmxVFujcIVCMQKCvUZlOLCvS6p9fa8rug+/POuZ1oRxXo3RxTwJ+k5+UQKLM3CFQjIrFz6imOSoGSg/fuuWooqC2vPcmfnhCTAk087ja9tgl+MX5XAm1XFcnOIFCNQKCsUJtNzYv9vJ2T9nIPkBWocwdfoAcVAnUaFy5nq6JIdwaBakQidlY9xbktgWbe49Es0PGeZXBEgc7/aGRQjkBDjQuXs1VRpDuDQDUCgbJCbTa3ZexXCTEESvNnmUDTBg20mO6Yo2MItOUpaK1Asz8kEKFRUaT7gkA1IhA7q5wSSAi02VYZY3e0tJFAA0PMdxcJ1Iszf1rZQ6CEk1kIFAJtSmHsNXJilVMC8wL1tUQ4/2MSesGyr0DvLw6VE2g+78vW6efw5JEbVUWyKwhUI9sLlFVNKbICrTcou0ty8C9DVsp/E4iLb+TwCHd0gdIk772t5HCQFyjhRVDyyI2qItkXBKoRCJQXa5PJPQkmKFDSezgsYm/4xNvRBEoaOCvQxT+bGFROoMm6oPeS7AoC1UipQIvlxKymBCICrT7XGAWTEmhDg4oK9NwqloalvG5WoPTDs109QKA6gUCZsVZMbimYiEBbn4LKCtR5a36JGoE2/D2RRsSKCwLVyNYCbVholgTqCUZWoN4IjkBTERAjXDXzE6JBoI0vpdeKWHFBoBopiz21zoGmfTAi0LBfHIHerQRabND3ycR1lwmAGqDbbJ2UAwQaJVZcEKhGIFBm6Lwjon4JCZTiLwe6MdMuZQqUEFmg3SIvK3W18hjlKTkECoE2BQLlhk4+IOmXGoG2sGaA7gK9vzrUF2gDkVG68QWqzqCx6oJANVIu0Na/psWmt0D5nS5a5fySFmjEUJ3M6au0lUBDDS/pWZtLSqA6T0Fj1QWBagQC5YaeP4Kgl7hAw4baSp0uETFSZphoCIEmiVQXBKoRCJQbeuYIilvuXYHexQRa6buQxIb7inttIdD7ewg0QaS6IFCNVAi09Y/BcMkLNHSBXO4kCX3OULwyEhDo8t/lZ4hZiXnPrVkj0T8lkGp4d7mC6JxSCHRFpLogUI0UxZ5e6EDLLnQWKKPTsT1FKxMxgbbQZkZigTuJ0o71SB979dic0UZv5hQKVJ1BIwUGgWqkr0C71pkigQ4PkL12HxRoS3OmJBYT6PVGMgaWQCNNp4emlEoJVOcpaKQgIVCN1Ai07W/BsJkFevCIBkgJOhd7tCVdbK5Am5sz5TD/zjtHoPONqngIAp0UCoEuiRQkBKqRGxCo7895T4QCYs7RJ9qOZrWBWaA9xOl7Kn3v+h7qa6Rlo/sPnRp5jPR8HAKFQJvSVaB962wQaEiffQV6ijXKGWXJy5Sa3p8/1V5HG4Hep0Jljz4/sniooUBzjSBQCLQpVQJt+lMGbM4CDeszKVCiQRMDR1pkbEYT0vxGTQuDJgSauMhydHjmeXJGoKs7INAFkYqEQDViWqAxfUYFSgk6H3vk4ZzO6B7qK9Dsz3wkn3vTLRr/OxAMoFpkNyPQSIVCoBopiT230n67Lrx2dTnQRqCpgSMPZn12H5fnWiiaBfrEy9g0aMNHX0SorIdigaozaLgkIVCN2BVoWJ8EgZIMGh83epX1nM6i1vFO1Vo9h+8m0DN5iXIFGr9+Pb0gco3cj75BoBBoFXUCbflTMDxi+uws0GG7Jx6KkbJN7l2dUmIezvmaJtALSYfG+gnEdb2nsiRyjSBQCLQpNgUa1+cpZVBC0KnY5+2eftSDf6bWUKCE+3O3nUfu3Kvpx6ZHHd+5q6ooco0gUAi0KSYFmvRnXqBFX6FabvfgsEHjROWylFBEoNUGpZ4B0l9BGPzpCvRCYJrUM2BvyIqiyLWCQCHQplQKNOGijgU26jPyVc4eAl1v9+CwJKnMJ55pgbY5BaW+Bum1KxHofXC6VIF69xUWRbYVBAqBNsWiQMdzjdh34RsIdN2hZ4DgsHmbLB9eSCh0omZSoGfSs453799XVBXZVhAoBNqUgtgJa+01a8pY9GyBEoL2Yw9qIjBqRiOuR1yBhnxSa1AJgd7nHRqcW+i+oqrIEBSoNoOGixIC1UitQKMy6lhf1QIlfwc15ojAqHSBXMgItMkpqJBAz6RSwJkvvyoyeDWjUaDh+oRANWJQoIeNBJrwQ2BUgjmWbCDQ+FlsqUDvyAK9T2SCN19eWWRbQaAQaFN6CbRjdU0l30+g5yZJOQRGTTrDhyRQskEDsdAv5uEPlRToPVGgZ4L54M6XWRZpIFAItCnVAo3IqGN1lQo0H/TcMmsGb9CILKJcJRRRR0agjDwFjvYF6j8cffucIdA7/7vzyUuclE8WAo0DgXbEnkAPvQVK+Va7OybPnveeQIPuWd9dlijvXr/zQAANBXrn/4BdwR8M4mwh0PCBEGg3Ogm0Y3HNFd9FoOcHCWZYj8i15z1LoNWJSjwUCaCtQO/903P2GXc2C0QRQqAQaFP4sZNWu2NxZQUaM2g2aMbvui96KrDnPUmgtTubItDpRk+Bjh1lTtLzr/kWz3ZJWKDaDBreqhCoQswJ9FAq0GzQ82MEM0xNy+x5nxaoP4vyTBEeWtxI2+yOLVCno5RDE+8iOYlhz3aJXzMQKARaQR+Bdqyta703FejiIZIZzg2L7Xm/EOhSHNFZFCcqJdDD8sbq4fT7POUCvU85lCDQlEIh0CgQaEcaCDT048H9aCTQ2AecTlSB1tjz3hVoSA1NBEp4MCTa4T435hYCfbor4lCSQOMKvSmBBg0KgWqki0A7VtahvUDdwwlecB3A+z2kM0uB5q/KVwJLoPHHFzE3EejlnpBCiQKNKRQCjQKBdsSkQId/8gTqNorHmtvAnj0Jx3i8nGQQ3b+17240EugiJaUCDX5I31MoWaBhhUKgUSDQjrQQaOoFxdY0E2jsp+GYV5anu2TNy/x7RYoEemaWIUegya+JrjPJEGhIoRBoFAi0I+zYCcvdsbAOLQUaPjqxbVvZ8/66kRPnmcoEOn/cqZlA3YxyDOoqlHq+HhHodgaljRXcqhCoQiwKdPx3pUBjxHZsI3tOwQdiTUyjgLxAD/F2MYFevgHWUKCeQvmZ5CUrUDObCpQ4WHCrQqAKaSLQ7SgWqNPE3X+rRwK0teeJLtDynZ0+ukag59ipM3Z9Gfi4Z3lmybO9AoFCoE2xJdCVU8oF6m0/77E1Tey5HoYg0LqdndHv/Gi4XejelUAvEGZ9FyKd36KkQqCJPQ6B9sOgQKcbUYGGDLp4NGw099EW29vf5zPbCJTwcKQdSaAXMlOnCNRNcuSw0HHcXKkQaJlBIVCNmBLouvqKBJq02snXQb09wyG+Ds0oMQ02zQU6hxrKe3z6RBEG35MnHcjLlbBADxBow4lpwJ5A51scgY438mpLbGqWNhNDDMGHZhSaRunW7iPQ8z9ieQ9ngCxQikLjSYZAE3scAu0HN/b+NZagUqAUu0U3NMub0e6vwYdmlJ4vD4pAD/F2BQI9hR1K9qd3+WX6kfUC3cigEGjLiWnAkkCd4mMKlGa4+cHK5+65uUgLdH68qUDPsFM1c3Fk+jQ0dihZgqHYtxdofrTQVoVAFWJOoNebLIESLTc9UqVPylxMCPQQOiAn0FOxQ0dJRnKfOXklZgoC7ShQkOe1IJfS4za8RP0yjH/kcP9qB0eOjcKeUXxK5Amze577jrbz7mcGw03bmYsjvQV433kwdmRhpqrSXDQUZbSOWxhnoC0xdAbq/u0mn4FGT4n8I+83OPkcgvcCJcyYQfbIsUG0nfvANZb8GegIM3cr/FVIPocfHiPEJHsGOvnzRs9Ai+MrPFAD1gS6uE0U6Pk/VN/V6ZMzGZJAK7Z2H4Fe/kUW6BleBpe87y5FXqCEFVAi0Oxwoa0KgSrk1gU67Cmq8jay52k/Aj21cyhBoOQ375JT7QddoAGDQqAaYca+QZHF8AqPINBxR9GsV3HyyZ+NDoEethDoqcKhvsNMIOYAACAASURBVELD7RZyTUcSFegmBoVAw/EVHqgBYwJd3pHYyEPbeUPxtyprl5fM5vUcZlagRVs7f+CWAj21cihBoOn1CMZOynILx0Kg4fgKD9TA7Qr07rqdeJu0qz0PHrxJs8YhtEgL9BC6WSbQU7lD84vjvMGUiKFYoE3OUqnLfoJAraBWoG6N+WWXFOh1P52yO7dcnyWz2kSg1K4T7aKhFgv01MahgYe9l0ejAYgK9JD5o7UksFUhUIVoFai3tf2qS2zk5YbK7FrvzV4yFdPaRqDUUJih1gj0VOzQ5CIF3l+KjF4n0EqDjl1AoI0mpoFl7LkV9Jr0wxcMQ6DrDcX4kQ7Gfq6e1m4Feip1aGKlgm/QB4cuFShlsbJAoJH4Cg/UwBg7bQk3E6i/cQP1m7gqEE2g2558BuZF3beFA1FjYcZaL9BToUOjqxX5hFNg3EqB1hl0KdBcT4GtCoEq5DHuxEDrqvJhENi8fs2FN7K3oWi/0sHYxpXTGoPnH1I4UrpNol0s/U0Eeipy6F1kyaIfEfUGjQuU9opx1YynHiDQNhMT55TcyOEDtiDiT4JAAxsqvFEF9GlNoDFaCfTEd6hzqZHl/amLhS6DD8ahUKD+9oNA1XFKb+TgARtwLVWmQIMbKrRLJey53jcQ6AAj+feBC94F1ju9aIUCjdUgi7kDCLTNxMQ5qRToulKj/vQ2srvRpv3j7SgZfVYIlL1rSUepEOiJ59BhYb31Swp0tW7iAr32lmntbT4IVB0njQL1C5Uk0MA+G7ePs53K7HnX6FPUc/BFR8Xb8A8qflbaWqAnhkOnhV0vYvpiy/ehn5NewxBoRRlcD4dAm0xMmvMyJTdD8IjOhMs0VHDLjRzbaB6FJ5+1Jx/zzObgi46iNrEm0BPVoVdVLhcy58/7q0IhUAi0GedlUipQSsvU75NHtlTxc/cGAl130VygB+8eWteFAu1RCpSlWCyso9D8Il6CD46cS8T4eKVBIdBYfIUHSnNeJpZAi0uHDqNGZ4Gm99mVMn0yo0rP7Bo86zDK2VF8LMaBFAaBdimG/GqsFnZlUNJCxvJOEWh1GTgCzXTkbVcIVBvnZUpv5MABfeGU6CjQ/D7zdhtTn00E6vRAfxpMfnrJOWZ5IDmSkVGgnaohsx7OwvLW9FQp0LonIstsQ6AtJibMZZl0CZS1pS8bmbbP6vTZ5EOA3QR6OPjhbSLQxFcwuF2uSa2I934RU6ENBFpaBstjIdAWExPmskyqBMrb0U8bOb3PgruMrk8vriYfYZmCLz4y+Pi6ETHaWoHG6qFBocRXxX9uwVrbl+Hg0omY87SlQD2DQqDKuKxSZiMHjugIrz5fvyZus0p96hboYQHxkPWh5EAmcgJtVCiUlR3voC/vU95LBXr9V2EdQKDR+AoPFOaySpoEyqzOly/jGyXyZm2RPrmfOA819A5nCjR7dnTgbk9OuzVXgUavQcPuM0h8Ze+8O2hLfMl76AsRIgJlPoeHQHUxrJKoQA8BqMc+PRujCLRen1yBBltWCDS9uafAZAQaqIi2hZJaWkeo+WW+BH/p1Bsnvb6LBxsJtORFUAhUF8Mq5Tayf0Q7Qv4kFud5PxAE2kKf3A9Rh1r6d7UWKPc9Xla7NWeBRmuiealkBHoXeq6RWNfpjUd3mFQqvNQWGXR9JATaYGKynOaCoq5iSdmkqPNnXqBN9Fko0Nw3gxoJdDGW+8/KnuOsBBq5Cje70xSBpb0L3kqt9hT81J8zRjbJy3+XC5Q03oi7YSFQXQyrJCjQYn+OWyIl0Ptm+pxqnSUlp3HgWK5AI0PXCTT4cm2WtUBXVdGrVHyDBm2aUOgc/LW71QhUgZYbNCDQdDfuhoVAVbEsKOIyFlRNikJ/znsiKdBm+ly9S8Ob1fq+dTPO98njQ6/GmW+UnyWRiAu0W6mclg5dODNwFZHgqi+CX/a16H5rgRLqyd2xEKgqlgVFXMaCqklQVoiLXZEQaDt91gg09Z5OB4Gu31Bi9M/EEei1LEpKhVFUK4HexQS6WPxg8MueFmueyFn+ryEJCDQeX+GBoiwLiriMBVWToKgQlxslKtCW+gy/zZ2b1tqg3QQa2trbC3Sqi8BdeVhFtTRo1J/L9Q8Ev+hnuew5gTo3C9LLFqhrUAhUE6uCIi4jv2gSlJThep/EBNpSn+4TY/K8FgYNHthDoNyT5UI8gQ6FEa6vHMyiWgk0ehnQU1yh/vUThvsTWmwj0MhapXC2LASqiXVBkZaRXTNJ+GXobpOIQK+bJ3+Bnqw+F3HSAl77Nm5etkBDQ3v3eye/PfAFei6NSH3lYFfVQpxxgZ6iCg1dgOZyF1mghQYNr1XyECelEKgm1gVFWkZuySRhF6G/TYICXeiTcIWzrD4Xu4Uh0MWRMZ2xLkocGdrvulagpDV+EqhfTrH6yg1YUFXTKWjUn8OKhhUavoLXiXGaD4FCoA8cgXb5bB+7CAPbJCDQlT5pAiUHyhVo6O2kK30EGvwQFYNigUbrKzdgUVndXUmtacigY979Q9IC9e/hJhgCTcRXeKAgbkFR1pFZMUmYJRjcJp5Al6990gRKi9P7nCVxYimbNRBosOtdCPRwIAk0pNCYQM8/eiUg0GQvTkohUEW4BUVZR2bFpOBVYMR+jkDXbx1RBEoNNPFmenpmXIHGUhzuJCnQXJxh2gmUWC2FZXWYFJpdWFehcYHehX83MJTOJgLN9+JkFAJVxLxIlDMh95h6WBUY899KoO4773mBsgOlBO1ut6jNWAINDh3pei8CvSiUsrJrhaYEencXGyp0HzPFEGgivsIDBZkXSUSgnPqLG3Ah0MAHlzIGZQTKFqh7R6hhWKDJU9BUbIT7KWwt0NKyGv9KkAS6Nmj0d7TuIgZtJNDAIRBo7cTkuC4SXaCseklDr7+4ARcCDX7uMylQVqBVAj31Emh0E1cJlLLKCgQ6T5K2uguFxn+IcCyY4Eix4ZkBcztZZxQC1cN1jUhvZjjH1NLGn7NAQ/pMCpQX6CF8q3JqobzHkxw7fyG+60GFtsqNBVp+Cnr5F2195xrJCjR4Me3g8LUC5Z6CQqB6uK6RZoEm9TkJNKzPhEC5gR7WN9tMLSZQ8iloagtXnIDSBMorsfSAtQINfSQphPtuUlyglIuMQKAQ6ICAQInFl9HnINCYPqMCrYk0Hzj9zKSnQIuhrTJNoKR6KS+s1eRJa+wYNFkwq3EgUAjUYbFGtM8jOgdVQdz6WX8+CTSuz5hAqyIlCpTUd6VAu/hzc4GSG2YhLfJKoZmCmY6J5Zmb/6hAU52sEwqBqmGxRkICzTXK6/NJoCl/BgVaEunGAo2kuUag0bUPtST0p1GgwUvU+SwUmi2YywHRPDMFGu4HAq2bmBiLNdpcoM38mdRnSKBFkfKsVSVQb228oR1IA3Eu80Fb5dYCbVVZpHW+KjRYMHdOwcTzzDNouDUEWjcxMRZrRPxK4aYnoA30GTmh4Efqv/BYObkRpkCDBiUNxBQoYZ21CjT4Ux0urzmvmkOgEGiIVUHRCmDLE9AW+vS2Q5NQc8EzvBYVKP0UlDTOiSHQzMMTRIESeiI3JJMX6OIkNCvQ+/tEollrkBBooo91PiFQLTgFRWE7gXL0mbpg8mo7FEdaIFBa7xBot5/wTD58yTv5k8OXL8j3EyjvFBQC1YJXUAQaVXlTf6Z+VG65HypCVSNQ36C0cU4dBEqsd3Jg5Jk0YMx7SKFhgd5FE81ZBQg0GV/hgUKECipLmyrPbX2OPtO/ynndDw1DzYVfJdDw+jQgtfx+w3x/2gWa7HDKe8CgEYHeJX9tkBZSrHAg0KqJCREsqBwtqjx36kTQ5/LVT5JAK4MN3Zk5hta9nEDj/RNHby7QxjNOdnnNu6fQqEDrDRprmXthZpVPCFQJkYLqTgN/roqeINDQJ+840ZLudCZI6347gabX32uZ71C5QNOdLvPuKNT/HNP1nmBf9QLNGXSVTwhUCdGC6kvutTuuP/MCZZ9BZpsSBErrPSXQHidk0fX3W2Y7pAo011OnCae7XebdLaiwQId/BociLzgEmo6v8EAZ4gVFhy4Kr1QiD7P1mRVowVNwL9zgveljSL2rFCh1dDMCDXW8Fuj6Ax0pgQYVCoFCoEUC5ZhiXSixxwv8mRZo4eUbMi3Tk6gSaHSFaskUgNcw26Ehgfpdr/K+Kqv3MwKtMWi8HQQKgVIPaHr6mRZoJMiMxQlT3ESgPYWS6J06uCmBJuvdKa33HYF6L4p6YxFXnFp2EKgFEgVFhSvQLv6MCzQaJF2gsYap4+l2PpkWKLne6YFx50TsNtB7QKBrhboCDZXWlUIxUtutpgGBqsBZs3KBMr8IXOPPkD7jAl2OGgyEGjLj/txjHoICjXVPHZxe7+S4CqZF6tfvf513v8KyvwqzHoy25uXPe5aTgEBV4CxZiUAZz4RPLfXpfHMzLND1uKxQ3JaM+3OPeSQF2lIo+RJwWmZ71C3QTCgRgTJ+l3DVAQR6gwJNF5SzZN0FWuvPiD0jAvVG5sSSPHbZA++YIG7ek4tUQ7ZAvJa5Hk0KdBojKtBFpd0tSf2NPhEXHQLNxFd4YCfSNeU8ViFQeklE29L1GbhuiC/QwNChWIinDPHPnTCPCQGBbjff5SAJgQYVGi7Law8Q6A4EulwI94HOAq3zZ0qfvkCDY4eCqXnOVfJIiLRAGxqFWCCM7wW1EeiG812O4uR9XUF3vkFjpTn3QFh25ulGbDYQ6EYkK8u9dxOBRh6s0qcr0MjYobhrThkgUMMCfRonLdA7T6HR6px6oAqUFDwEqoFkcbl31Qi05qlwtT7XAo0OHow7F3iiEQTKEGiqqw3nu+Rx3dopKc+gqQodu8ivOwSai6/wwE6Qa+1MgUDpJ3IpE9XqcynQxOBFgSfaxI+vEmjdIqYgVwh1aE69k+Mqnl6mX49HZ6hU7aVLdKo7CPTGBMootlNngcZbZSqTVMOzQFOjB+Ouec4Ve4z4J2ViK4HSS4Q6tG6B5iJ6dAYrrr5r6WUXHgLNxVd4YB94BVcl0OKnwg30OQs0Pbp/u6dA090uUSzQzNhtBNppuiSBLoerqsCh/CBQCJTFsMo1T4Wb+HMUKH10skCTfxw2EmgrpdBLhDp0F4H2/YOx4NEZLleDFIVmlp7z3CRlUAh0G3gF11Ogkcppo89BoPk4vdv5ek42uFWBkodm1Ts5rqpJJvp1mWOfDqivw/s7gkCJ4UOg8vAKrk6gJWdyrfx5FighTj+aBgINPFol0OpljEIuEfLQNyLQacR8JeZLMfHbnScIlBBf4YEO2cUndsOiWKBED7ktGunzEnou9vX48606gUYe5TxPO5MVaCOlkEuEPPKtCHQcs0U1Dr9+vOYaEgSaja/wQIc2AmUWHF+gU30UCbSRPy8CHfKeC8C/lQs848KEQBOduogKNNQ3eeQmAu00W55AL4M2Kci7kEKncoBAs/EVHuhgSaAnwjmX/3grfZ79mch7OIC1QMtfszIlUHqRUEfm1Ts5rtqJRjt2cGJvVJPDt5Z8hdJeMloAgVaQX31aLyzKBcp/87GZP+8vmYrn3Y3UuWVDoE2cQi8S6sidBNr1hHuBGzv9egx5gYYVmj3RWAKBlkNZflo3HLYTaDt9Dv5kCnQRTjpw0gmq93iVQJusZBB6kVBHZtY7Oa76uYb7dfBj38Sg1Pgh0HIoy0/rhkOtQMnvVjf3Z4lAw6FF5sdpwNsmJ30CJY98cwJlXBSMVJwDECgnvsID15DWn9YNgwqBcj7u07ZCh5kWC7Tsg57JBlx/UgTawinknskDNxFon8mGO14TEmjlZRUjCmV8dXiB23oZOgSahLT+pF44sAW6KAi6h9r5c5ElCDQPuWfywLco0MYnoe71liHQXHyFB64hrT+pFw5lAl38M1Iby8eIxUkuzXGqfQSaL/gbEKjfNXngXgLt+qmDKxGBNri6YtigQ2nQJ5B4Dg+BJiEWAK0bOjUCTWlj4SFiZZLrcpoqS6CH6I3E/LJTYxzlsMx7q7UMQO6aPDC33slhNZhtjUC7nYTygEBLIRYArRs6nQR6lQyxLBk1OU2VL9DgJBLzI6TAnS4VikDrnULvmTpwMu/kOXSZbGq+M3GB6lAoBFoKtQJI3dCpF2jQG/MjzUrSL6msQL2XG4KTiAROTEGuvxi7FmifyabmOxOIfXF8U4MWKRQCLYVcAqRuyFQJNC6ODfxZLdBk4OQUkI9ao0yg5IGTeafOoc9kU/OdSQtU/iQUAi2FXAKUXuhwBXogCXRq1V6fJIEGnsM7kUKgyYbJHm9ZoOInoRBoIfQSIHVDpkig61sBcwz3tyrFVdfXuXIE6gZaL9CDd0/mqDWLvDdcTRdyz+SB03knzqHTbJsIVFihEGghjBogdUOlTqCpL4an/Vl4+lkl0Pg0nMiZSSh4D4km0GqnkHsmj5vOO3EOfSabnO8EQaCNDcpTKARaCKMGSN1Q6SfQ5E/CFp5+npoKNHbqzE1CwQnorgXaabLJ+U5QBCp6EurW0iJ0CDQBowZI3VBpIdDglTVS/izXJ/GbGV6w1CfdtyVQes/kgdN5p82hz2TT852gCVTwJBQCLYNVBZRuiFQKNPa1nLu7hEAr/FkoUOqrlsTn4vsVaCbvtDn0mWx6vhOh2IN9SSk0/hweAk3AqwJKN0T6CPQuIdAafa6SwxWoP4/gqTPBhO7BVQJtu54r6D1TB87knTaHPpNNz3eCLNDWBqUqFAItglcFlG6IMAXqeScgokb+DI6/nGyVQMPSo5rwEIBw2AKaQCulQu6YPG4m77Q59Jlser4TdIEKnYRCoEUwy4DSDY0SgWbuGS4tW1t04fGXk9UlUMJRS3Ys0E6TTc93giNQkZNQCLQIZhlQuqHRXqD3cX++X3f66aQmL9A5uJhACffF02BaoA/phqke9yNQCYVCoEUwy4DSDY02Al3cdR8/Aa3VZ7FAg4qjnpVG0wCB0iBHVTfZzHxHmAJtbtCsQiHQErhlQOqHRLVA13fd30cFSj79jI++nmwq7+vYqE/X6Sas9ec1781X9Aq9Y/K4ubxTptBlrvkJD3AFuvlJKARaArsOKN2QaCTQkem3tVL+rCiw9WwlBVrNjgRKp2ayufmOBGNPd0s1aKOzULcIr6FDoFH4hUDohgRPoKGzrYA+fYG20GcPgfqfDYVAE+Nm815HzWRz8x0pEGjjSzTlyhwCLYBfCIRuSBQINHhnG3+mR3dmWylQ8reTuqBKoORxs3mvo2ayufmOlAi0x0lovNQh0AIKKoHQDYV2Ar2LCrSNPssFGjmzhEATDRM97lCgPU5CY+UefREUAo1SUgmUfgg0EOjJ1ec2/mQKNDIZD1Y+ypny3mNNJ8gdk4fN5r2Oirnm5ztQKNANFQqB8impBEo/BFoI9JQqr1b6bC/QBt8nKgcCJQ/aaL4DxQLtYtBQ1UOgfIpKgdANgSYCbVBWhME5eV/Fu1OB0jsmj5vNeyXlkyVMeAi+fNisDdsoFALlU1QKhG4IsAQacQyhpur16eeEKtCoGSHQRMt4l1oFShohHDtxhC4GdYsfAuVTVgv5bgjwBerdW19QpMG96RIEekqLUcKfU/A9F3U1EqFj8rjZvFdSPtn8fAeqBNrpJHRd/xAom9JiIPSTpV6g+Woq02d2uvUClWAKvuuqLkfK90seNp/3SornSpjvGHzluH0MutwDOgX6qx8ej8+//9lw46unG8fpBgRKJ6Ci+lKKDZadbjLvy4gh0HS/5GEJea+jeK6E+Y7B146bdWH1Sahbr3PoggL99Hjh+c/ON758sbgBgTLwVVRdR9Gx8tM1KdA5+K6ruhoq2zF5WELe6yieK2W+Q/DV43Yy6HUnKBTo2+PzHz2deH5y/M4vHh/ffXL87mfnG9/9Qq9ASwxaVHWzQClvqHj35quoUJ8QaN2yLofKdkwelpD3JvSZ74V6gXZXqD6BPinzx+f/f/3x+f9fvjhr9OmGdwpaHF/hgRPF1ZDvJsvrU+wT5QHruHfWVlAiLsJ8OQItyk0HrsF3XlfO+/vkYQl570j1hM9EYueltpdBhw2hT6Bff3xR5uPjq+NH59PRD5dWlRdoeTUQ+skQdWdIO86d+fop1iftI30QKGmobL/kYQl570nlfC80EShDoQUG9Qp2Cl3+XfiLQNWdgdbUQ76fBGl7+t4h+rP+9PNmBboIvuO6umPl+iUPS8h7Tyrne6GRQHuehOoV6ODM+TXQD6f7vzVS3HEdr4O06idO3p+HwAHTjZcx5sqJtjiTDq1ZUsMTEaNmKs3HyjRsFX5D2ueW1HOQZHWvNkK+5RqvYBtlb6JcoG/GJ+/De/I/mN9DgkADjkkLtLZsMqE1S6ougVZNpflgmYatwm9Ih+RSeo6QNSHtVMLj7k6pQN9OH2P684tAP/A+CFp8hlx44EjVU5JsN3Fiz9SXj/p3pZ/A0J645CKjTZjxFJ6dmz4sg++5su5g6X7Jo06hSz2FTyeC1kWrp/BnOj2NvzsbtGXeGwn07Yvnl3eNvnxxPvl8Og1V8hpoXUHk+4kxnpqlHw/fk62YdIXkIiNOmCLQdleZr71U0Gk9Lwi0hLr5nmkp0F4KPV8RMvA2vLBA30zCvLyTdPn/h06T4vgKDxyoK4h8PzEGszAEOrmoslrykREnnM67E3Q1uxNo9AoNtyhQVQYdrqnbLu9NBDqfcL77ZPzHly/cT9IXx1d44ABtpVr1c4Uk0IN3QKU/m0x1YFOBVl+s0plXd4HS+yUPO4UuJ9BUKmgdNBZoF4VOFyVvlfcGAn336vjBLx4tC7T9dc9yAvVOQYfb2UJJ1kaTmZLyvgwaAk31Sx52Cl2lQIkdNBdoB4POv+rQKO8NBPpq8b1NK0/huQXCXPdDkUADv1fMqJI2E52gC5SZmnBQDbpYBk+eZuHQ9G7Jo06hQ6BrWit0+bM4LfJeL9A3y++9vz2qehOJukqt+pkYzZIT6GF1O/SD76sSSRZGk3lS876eZi0lGQ50sQiePs/OAqWPOoUuKNB4KojH9xBoa4Ouf1dsnpvkVzmPEx9edDrwkduuOL7CAy+QV6lVPyN5gbryufxyXHl9tJkmOe/hORRSlOHkvNoKNP6Web5f8qhz6BCoR1OFuj/MKC7Qt8eVQB//x/l6oH+m5Hqg5DVq1c8IW6CH4C++y/mTJtBTsxNQxQINNSH3Sx51Dl1SoLUfWukk0KYG9TbaMDnpz4HmKY6v8MAL5CVq1c/AgSrQWT9ZfzbQZweBNqG+Ry94xkSzQ4dakLsljzqHfosCJaxupkk7hfoCvUwPAg2SXzhahZD7GZjcmLyg8kKggWVllEWrSa7YTqANevSC58yUchmNzHjxbsmjzqFDoEGaGTQk0KfhIdAQ+XUjlgijozNMgYaWdVUUTfTJ+/KAWoFSzgch0FISOSDQUaB5g1IV6r0IeuE1BBogv260GmH0c4Eu0MNYGkGBtvWnUoFyuww09YNnTZUSXmbAaLfkUefQ9ylQSptGBoVA6WTXhFgjjH7OHEgCXX35KCRQQjlwomqad2ZGCGFx2ucm1l6gD8E7s93SR51Dh0CjZA1KUigESie/JrQi4fRzWjw5Jwg0sqotTj8rEredQNk9+q0DwfPmyg6P3C190Dl0WYGGc0E9uLNA2xgUAqVDWBNSkXD6ObEEOi7lnSfQBqefFYlTL9AH745V8Ly5UsLLKDvSLS+OM/sUKKnRiWLQvEIhUDKEFaEVCasjskAXH55X58+tBMru0W8fCp43V0p4exFoMBnUY+OxU1aVtP71Bg2/DQ+BBiCtCKVIWB0tPuGZE+hdTKB5f1bNh8DmAiV26bUPBs+bKym89DlvpFteHGcg0Axpe57yCoVAydBWJF8lvH4Wn09KC3TxxH29qE3ePSpP2wX9Ak28z91KoJFm9G55cZzRKFDysXUCbWHQ02oDBXcQBEqGtiD5MuH1QxXoci1Xi9rg9LPanxsJlN+lG0U4eOZkaTmM3Z/olRnHgwKBln3taqBUoKRGM3mBJhUKgZIhLki2Tnj9EAW6WsvFohLeR6yaDBETAn3YVKAPsfujvTLDOKNPoIxDtxFoSqGnAoNeuoRAfcjrkasUXjcHikAXS3m3ehM+78+6uVDZRKD8LonBMydLHIsXxFN7Zhhn5AVa8qWBkUqBNjDo4qHoToJAiZCXI1cqvG4W33GPCtRZy3lJG+mz3p8QaGgsZnZvQaCsIwsFSmu1Ir47rjdimwkCJUJfjkyt8LohCNRdy2lJ9fhzE4EW9EkMnjtb6lC89N6AQHlHJmInLSqtbC7Et8fiZng/QaBEGMuRLBZmN3mBOmt5Ny5pm1c/ExPhkMs7MymUONtNra9A6b1yw3hQIVD+B7YmagVabVD3geCWgkCJMFYjWS68Tg45gQb+Gl7+2+r0EwJtItB4Q3qv3DAelAmUe+CWAg0a1L8/sKkgUBqcxUjWC6+T5XWSQwJdr+8s0Gann238uYVAC7qkBs+dLXkoVn6tCpT7Wu9MmUBprQJQBBo4CYVAafAWI1EwvE4yAnWW926k3elnG3/uXqCJltzOWSgSKP+4aoFWGjR8r7u1gh8EhUA9eGuRKBlWF4e0QD0vEvXZ67rJUfoLtKRLavDs6dJH2o1AC47bWqDudgre6Z2EQqA0mGsRrxlWF6tfOnIFGhCjUn9KCJTQJzV49nTpA+1BoKXn2anYaWvKLSKSQB2DbirQb/7iT//pL8//XfJ0z44EyusiJdCQGRf+bKHPZru7u0CL+qQGz50t5+s3+xBo0WH1Aq0zaOi+tUKDBj0f00ugv/nes9/6T+f/Lnm6BwKNkBBoWI5NTz8h0CF47mzdodnHN0OHQAsREOgpsFFy2wwCJcFeisjGYXVwiAo0IsdpXYO/aczWZ7ud31ugRX2Sg+fNVRO7EyixWQJvp6R32rYCbUdxfIUHFqxEK4HOtxYCzfkzKtDq+MuAQGXYu0Br1jxYwwAAIABJREFUDOrejuy19yFQCgUL0VGgWX/GBFodfiESAs12Sg6eNVVVQKAFuHuFYlAINEPJQhS+MrcgLNC8PiP+rI++lGzeg+NXhtpqfoYlBIEWQRJo7ITlfEh/gf5/1wH/bwvvwpctRGU/h6BACf4MC7Q6+HI6C5TeZ8kEDUvoZgXKveQVE5pAFyehGwv0//22tTeRytahsp+1P0eBZtYy+JvwBfq8fYHSg6fPUxsQKLmG1qz2S9ygwd97OHUX6K/tvQtftgyV3QQEml/IiEDrY6+hTKDkdNH7LJmgYQlBoNQSciEKNPS5wVNvgX7zk2fv/eV/m/nvBf40ItDKT1X4AqX8HVToTwhUiJ0JlNyQUlPXf6YEGjDoqbdAf/O9Z/+8RJqCAi1ehZpeDp5AKf4MUR15LSUCpSeM0WnJDA1LCAKt2LrzP5MC9RV66i/Qomft5gXKPdjx5+mlWX9CoEJAoDVbd/53WqDu1SdO/Z/C70ag5VcnPHkCvQ8LNPAiTLU+m3/5sFCgxJwxOi2ZomEJQaBVr75N/84I1LmAz6n7m0if7+YpfOHlsQdWAn1amKBAe5x+QqDr4OlNtXG7Ao1VDKkhvaaGG1mBXg36/hYC/c333vt3exNo8NGDQ+DB03UJQwK14c++AuV0WjJHwxKCQGs/QDPcygp0+Rtkp/6fA/377z37bVOXsytbhFNGoK4/1wp1/RkSaI+n7z2uHpTPeySIunDbTNKwhCDQcEtGUV1uEQR6Nej7/QX619Y+B1q0BsuFCD4WEOhCoYtb92GB9jn9hEDd4OlNtbErgdJbsorqfIsi0KVCu78GakygRUuwXIjwY0GBzgqd/z0tlCtQO/5UKFBO8Iy2yoBAgy2ZRUUV6EKh/T9IX/K83axAI49FBHpYPHhaLJ4j0D5P3/tc/renQDmdFs3SsIQg0HBTZlGlDbr87t/1JLRwzhSBNngPyY5AEx9n9N84WirU86cj0F7+1CVQQuo5nRbN0rCEINBwU25RkU9B531ZOmeaQK19DrRgBRZLEXvEf+N9qdDx0cU6LQXKePrOjL4ws2kgUBluWKDe4tJbEnC7oAt02Jv4IP2KghW4LkX0kZBAnef1q3V6uV4j6uknL/rCxGbgC5ScelavRfM0LCEINNSSgN8HXaD3vQX6+PmzP9qPQOOEBbo06PqqIC+XK0R/+g6BVs7TsIQg0GDTPIEu6ALt/jGmb37y3j+DQGMCvSrUuarSJNDclze9WmDEVJjXHOUCzQbP6rVonoYltCOBctoWbINTwqBbC/Sbv/iTZ8/e+307H6Tnpp9IVKDDQ95l6V6u/RlbTr8Y6CEVpjULBCoDBBpsW7APzvdqEai5nzXmpp+G/yb86lH/usgvC/150wLl9Vo0UcMSgkDDjQv2weV+CFSbQKOPBq6L/JLgz3AtUEMqzGoeQt6jkdSE3GSmhiV0ywJlQd0B8fIYHlAh0BYUx1dyFDP7RJICDa3Ty6IPfzImUJhUAlICjR7MCp7TWBcQ6ARxC8TLY3wEAi2Al3wqCYGG7fiSf/p5gkDrZ2pYQhDoBHELJMpjepBi0E0E+s1/MyvQ1HNvMnGBRvz4ssSfye+Shpp2oZtAeb2WzdSwhCDQGdoWSJTH/KgKgf7Xf3J5/fMP/qNFgaZfvaQS7SXix6LzT45AC3NKoUagVddUajFVwxKCQGdIWyBVHteH5QX6zU/mt5D+sOyqIsXxFRzk5beJQKNvwjfVJ+OiRpoEGn+EGXOLqRqWEAR6hbQHEuWxeFxaoGd/vvf7//b+P/zJk0F/d88C9e+O+LHUn/SvlPf0p5xAIwfzgme1VgUEeoWwBdLlsWwhK9BfP5u+y/nN3zwr+32k4vgKDnLTe4iePHII91Hmz3wtEAIqTCmJXgLNj9xgqoYlBIEuIOyBZHms2kgK9OkE9Ppd+J+XnYIWx1dwkJvfjgJt7s9bEGjVN9obTNWwhCDQBYQ9kCyPdSNBga6uB/o/v63+g/RufrsJtEyf6St/xiYRbdgFCFQGCHRJdg9kymPdSlKgC2cWXhy0OL6Cg9z8HpoY1O8i58/w78Jnrpwcm0S0YRcgUBkg0BXZTZAuD7edlEC/+cnqDPR3tF9MxM1bJ4Fmzz+DAqXWQi6cwoQSoeQ9EUxF0A0ma1hCEOiK3CbIlIfXUEigj58vXvcsvDZocXz8Y9ysHZoI1Osi68+gQOm1QG7YAzmBBo9lBs9rrgkIdE1uu3DK49wyZtDOAv3N9579r7+c/Fl2dfri+PjHuOltKNDrzbw+gwJl1AK5YQ90CZQbPLO9IiDQNdn9wimPc9uNBfrNXwyXAP2T4XOg/9effvvZs9/Xfj1QN7+HJgZdd0DxZ0CgnGKgtutCH4GShq6frGEJQaAO+R3DE+hpW4E6F7KzcTk7N78dBErypydQZjFQ2/WgUqA1H4evn6xhCUGgDsw9Q+gLAs3hpPfQXqA0f7oCJQ0Tn0esWRd4Ak09xo66fraGJQSBuvD2DKmrDQXajuL4+Mc46R3MV23Q6/FEfboCJY2SmEe0XQ8EBRo4lhc7BCqEFYGeINAkTnpH81UK9Cpgsj9XAiUOk5pIrFkPugiUOHb1bA1LCAL14O0ZWk+DQBcGhUCvuPltKNBL7sn+XAqUOkxyJpFmPagVaM2Hkapna1hCEKgHb88Qe3JPQSHQK25+mwo0p8/VtzevAiUPk5xJpFkPIFAZIFAf1p6hdgSBRnHSe1gKtNygw9GM08+lQOnDJKcSadUDUt5T4VSEXT1dwxKCQH14e4bY0QECjeGkd/ZmvUDdX93M+HMSKGeY5FQirXpQLdCKt4Kqp2tYQhBoANaeIfZz3s6L/fwSAp1x0ttOoN7PFmf8OQqUM0p6KpFWPZAUqHso+bgJwxKCQLNU7Ib1fl5uaAj0ipPftUBLDXpwTvkJ+hwFyhomM5dIqw5AoDJAoASKy2O9o5dPKSHQK+v0LrRZJdACf14EyhsmPZdYqw5AoDJAoBRKy2O1o89AoD7O7ltYs0Kg3gdvKf58Eih3nMxkwo16UC/QiqdatfM1LCEIlEZZeSyrav2uMAQ64+y+JgL1v7lA8ef9S/ZAudmEG3WAI9D0owVh187XsIQgUCJF5bGsqsPKoBDojLP7XIEWGPSc4LBAMz/d8Zo9VG42wTY9EBVoLYYlBIFSKSmrVT1ONoBA1zjbdinNMoHeRwWa++kjtkCzswk36kADgcphWEIQKB1+9a320eq7hRDozMnPUo1A76/+dAWa9ufTsQ0EWn9ljTIgUBkgUAbs6lvto9XVgSDQmVMkS6ei5/D3C4Fy/dlHoIWJZAKBygCBsmBW32ojLWQAgS44xbLk3SIw6dAXaO7p+5lbFyj/FGAbDEsIAuVRK9DJoBDohKObOoHOPvQESvFnE4FWvyVdBgQqAwTalagbINCJk5+jQ+xmhoUQXYGS/AmBCqF/I0eBQLviy2HaqhDoyCmao9DtFEsjOgKl+ZMt0MIc9QAClQEC7QoEmqWZQD1/XgVK0ycEKoX+jRwFAu2KL4cDBLqmlUBXTizz5z4E2juSAvRv5CgQaFeidoBAJwgCJRjUkeJSoMSn7xCoHPo3chQItCsQaBY/Q4dIzuj+XAqU4U8IVAj9GzkKBNoVCDRHNEMcgXpavAqU48+VQFNh6vMnBCoEBNoVCDQHSaBpgwa8OAuU5c+rQHNxQqBN0b+Ro0CgXQno4QCBLskJNH8KGhLjJFCWPieBEuKEQJuifyNHgUC74uw4CNQj9heGLNCoP++Yp5+DQGmBWhUo85t0W6F/I0eBQPsCgWbIyjIt0LAaC/15SsUOgfbDwEaOAYH2BQLNQBNozKARN14EyvXnQ7qgINB+GNjIMSDQvsRkAIGOZAWaOAWNqHEQKPv88yFTUKr9CYEKAYH2JSYDCHSA4MqoQKP+vM/qM/T8/QEClcLARo4BgfYFAk3jZycs0IBB4/68559+7kagncMow8BGjgGB9gUCTRPOTiRpRH0W+zNTUBBoLwxs5BgQaF8g0DSlAk35s+DtdwhUFAMbOQYE2peQCw4Q6EyZQGv0GfEnBCqIgY0cAwLtS0wGEOhA8K9L7K9OT38SBPrgH6AHCFQGCLQvEGiaUG7CBmX60/tNeII/dyBQnRiOHXnvDASaIuXJ2AM0f4YFGtMnBCqK4diR986YFegmvF5yyc3rAIcFw9fc716GmfUZbhHqfIQfbufUAACcPTe5oN3228UZ6MnzZ/gE8/2FP3nnn7Qz0Af/CDXgTEgG5L0zQRdYOAMtjo/T2rdkWqB3KYEu/Rl6POtPCFQIw7Ej752BQFMEMpMS6F1KoPPb75HHU/4kCvTBO0IN2MgyIO+dgUBTEAV6cvUZMOT140thgSb9CYGKYjh25L0zQRUcINABqkDPXF0YMuTi05+hh9P6hEBlMRw78t4Zb6tCoFcCf1kI/gwZ0vWn8zDNn4SCgkB7YDh25L0zEGgCPy8EfQYUufr2UYE/IVBZDMeOvHcGAk1AFqjzhNxx5Prbm75As/6EQGUxHDvy3hkINAFRoPcua0c63373BJr3J12gD84RasBGlgF5701QoAcI9AxNoJ4/18/h3auHuAKl+xMCFcJw7Mh7b7zdCoHOeH9XSPpcS9K7+NJaoAR9QqDSGI4dee8NBBrHzQrVnwtJhv05C5TkT45AH5xDtICNLAPy3hsI9ErCYWGBhvV5tWTg4p8F/oRAhTEcO/Lem7AqDhAoQaAxf06aDF08eSlQpj8hUCEMx4689ybiCgg0K9C4PkdNBi8+vxAo0Z88gT6o9Cc2shDIe28g0Cssgab8eR/150KgVH9CoNIYjh157w0EeiXjT/LvHl08Gfnto1mgZH9CoNIYjh157w0EeiUjUIY/72P+nARK1+dChrRJQ6CtMRw78t6biCwOhd3tQ6BZf0Z/e3N8f57hTwhUHMOxI+/didiisLc9CDSrz8RvF/P9CYGKYzh25L07EOgMTaB0fwauO38RKMufbIE+KPQnNrIQyHt3INCJhMSuAs3rc/njR0GBpi7LnPInBCqE4diR9+5EbFFo0FsXKN2f4V/uOPsTAjWG4diR9+7EdFHW220KdP4UE92fkZ8+usv8MEgLgT5AoG0xHDvy3h0IdCIjUNbT98hvx91lfhgEAtWI4diR9+5AoBM5gbL8Gfzto/sqfxopqCDYyDIg792BQCfSAg28pZ7yZ/jHjyBQixiOHXnvTkygZQa9WYEGXs9M+zP040fRyzJDoJoxHDvy3p2IMCDQVT5CbwhF/Dnd9J7D538bGQJVieHYkff+BIWxx+/Cxy0Wfkc97U/vFLTan1YKKgQ2sgzIe39C+3aPV6TP+DMj0NzF58v8CYFqwHDsyHt/INCBmMMin0jK+nP9HH7yJwRqD8OxI+/9gUAHov4kCDR38eRSf0KgGjAcO/LeHwh0IOrPvEAjV19aXX2+3p9WCioENrIMyHt/INCBmD7zAs1c/LPcnxCoCgzHjrz3BwIdiPozI9D4xT8Xl5+P+TMTghN84aQVgI0sA/LeHwh0IKbPjEAT/rxePjn6AmgmCCf4wkkrABtZBuS9PxDoQNqfMYGm/DkceUicgPqX/Ug9aqSgQmAjy4C89wcCHYjoM30CmvTnfPnP+Aug6Tjc4AsnrQBsZBmQ9w2AQP0s+E/EC/R5PvQszsQbSOlI3OALJ60AbGQZkPcNgEDdLASeiBf5c7z+J1OgD7FHrRRUAGxkGZD3DYBAnSz4z8ODAs37c7r+UvwTTMlgvOALJ60AbGQZkPcNgEBXWQg8Dw8KlOLPU5k/x2i84AsnrQBsZBmQ9w2AQJdZCDwPDwmUoM/F55din6BPRAqBqsFw7Mj7BkCg1ywENBj8FBPRn7lvIKVChUC1YDh25H0DINA5CyEPVvmzQqCB4AsnrQBsZBmQ9w2AQMcshEUYECjdn5lfQWIGXzhpBWAjy4C8bwAEOmQhYkJfoAR93s+pTF5ChBl84aQVgI0sA/K+ARDoOQlRFboCpZx+3gdyWu1PMwUVABtZBuR9CyDQh4e4Cx2BNvQnBGoDw7Ej71sAgUafv3sCZbz8CYFewUaWAXnfgt0L9JQQ6PpTTE39CYHawHDsyPsW7FyglxnTTkAbPn2HQM1gOHbkfQv2LdATXaCN/QmB2sBw7Mj7FuxZoNOMCQJt+fYRBGoIw7Ej71uwX4FeZ5wX6MqfsfY9/WmnoHywkWVA3rdgtwJdzDgr0PX5Z6Q9y58QqBEMx468b8FeBUrx5yRQ5/l7+ACePyFQIxiOHXnfgn0KdDXhtD/v3LePwkcw/QmBGsFw7Mj7FuxSoOsJZ05A3bePgkdw/QmBGsFw7Mj7JuxPoO6EkwL1334PHcH2JwRqBMOxI++bsDuBehNOCTTw8aXAEf39aaigPLCRZUDeN2FvAvVllhBo2J/uIXx/QqBWMBw78r4J+xJoSGZxgYY+Pu8fUuBPCNQKhmNH3jdhVwINyiwq0OC3j7xDSvwJgVrBcOzI+ybsSKCvwzJj+dMTaJE/IVArGI4ded+E3Qs0rc+gPxcHlfkTArWC4diR902AQDn+dAW6lT8NFZQHNrIMyPsmQKApf7q/aewItNCfEKgZDMeOvG8CBJryZ1qgpf6EQM1gOHbkfRsg0Jg//R+Fv18dVexPCNQMhmNH3rcBAk34MyXQcn9CoGYwHDvyvg0QaMKfCYFW+BMCNYPh2JH3bYBAgy9/ur8J7wq0xp8QqBkMx468bwMEGvRnUKALBW7rT0sF5YKNLAPyvg07F2jMn2mBhr9VD4GGwEaWAXnfBgg06M+kQANpg0BjYCPLgLxvAwTq+nO4kRBoMG8QaARsZBmQ922AQIP+DAl0pT8IlAg2sgzI+zZAoP7T9/v5F+Ug0GqwkWVA3jcCAg34M/4MPpK2vv40VVAO2MgyIO8bAYEG/BkVaDRvEGgEbGQZkPeNgEBDV6+LPIOP5w0CjYCNLAPyvhHO9q74yQyzAg1c/DMs0ETeINAI2MgyIO8b4ezufQk05s+wQBN5g0BjYCPLgLxvhLO5dyfQ8MXnQwJNJQ4CjYGNLAPyvhE7F2jCn3dJf0KgNLCRZUDeN8LZ2zsTaOTHjwInoMnEdfanqYJywEaWAXnfCGdv70ugsR+PI5yAQqA0sJFlQN43wtnauxJoRJ8BgYbEB4FSwEaWAXnfivXO3pNAo/70BBr0HgRKARtZBuR9K/Yq0NjT94BAw96DQClgI8uAvG/FemPvRqApfzoCjXgPAqWAjSwD8r4V6329F4Hm/Xm39GfQe5v501ZBrcFGlgF534r1vr5dgb4k+/Oe5k8IlAI2sgzI+1ast/U+BJrU51qgCe9BoASwkWVA3rdihwId/en/KLwv0KT3INA82MgyIO9bsd7VNyzQSYbT03fvR+EDAk17DwLNg40sA/K+FetNffsCvfozL9CM9iDQPNjIMiDvW7He0zcv0IU/swLNaW8rf9oqqDXYyDIg7zLcskDvHX/GBDp9iinvPQg0CzayDMi7DDcu0KU+0wJd+hMCLQcbWQbkXYbbFijJn6NAKdqDQLNgI8uAvMtwywJ9f+3PtEBJ2oNAs2Ajy4C8y3DDAnX9mRTogaY9CDQHNrIMyLsMogL91Q+Px+ff/2y48e7TF8fjP/5RM4F6/kwJ9ACBNgIbWQbkXQZJgX56vPD8Z+cbX3083PpBI4H6/kwI9LASaKLXbfy5y4LSgOHYkXcZBAX69vj86Xzzq0+O3/nF0/nnJ8cPPnt8959HndYL9NHVZ+JN+AME2gxsZBmQdxnkBPqkzB+f///1x+f/v71o9PHxzfHDhgK9X+ksJlDHn0ntQaAZsJFlQN5lkBPo1x8Pynx8dfxotmmA0vhenq++FBbo3YoD/QQUAs2CjSwD8i6DgnfhzwKdbdpQoBdXhgQa8CcE2gpsZBmQdxnkBfr1x89/9vjli+9+8Xf/4nj84K/m+781Utrvywuvr7ycCPjzsGjHGON1htLYAQC7olygl1c9nwT60+Fd+I+m+7cR6KFKoBmDloYOANgXxQJ9e3nf/e35A0xfPL77tN278MNT+MVz+NBLoJM/S59393kGv8unNBowHDvyLoP0U/i3L57/+KLR8dTzVbN34TMC9V4hLdMeBOqAjSwD8i6DsEDfjGecX74YzzzPL4Z2Fuj1NzgbaA8CdcBGlgF5l0FWoPMz9i9fjO/Cz/9oJdCrJb0T0Bbag0AdsJFlQN5lkBTou1fHD0ZbvvtkNOnbY+Mz0LhA21gPAl2DjSwD8i6DpEBfLWQ5vfb56vo2fGeBNrIeBLoGG1kG5F0GQYG+WZ5sfvni+P3PHju8C3815VqgrazXw5+7LCgNGI4deZdB8qucx4nzyefbF8OlmbxvdJbG5wp0/SZ8O+1BoCuwkWVA3mWQE+jb40qgj1/99Emhf/aZ1640vqRAD+20B4GuwEaWAXmXQfpzoHlK45sFeu8L9NBQoHGDFkb+sM+C0oDh2JF3GXYp0AME2g1sZBmQdxn2J1Dv+sm11oNAl2Ajy4C8y7BDgSb9WWK95v7cZUFpwHDsyLsMexDo/Uqg3sVDINCWYCPLgLzLsDuBniDQrmAjy4C8y7A3gZ46CDRi0MLAL8FXHCsMNrIMyLsMuxDo/cKfEGhfsJFlQN5l2JdATxBob7CRZUDeZdiVQE95gZYN1tifuywoDRiOHXmXYR8Cvb8I9ASB9gcbWQbkXYYdCXThz9YCDRi0sKMx+KqjRcFGlgF5l2E/Aj1RTkCbCbSwnyn4usMlwUaWAXmXYScCvV7+cxuBFnYzB195vCDYyDIg7zLsRaCz4voI1DVoaTdT8JXHC4KNLAPyLgME2kOgpb3Mwdd2IAc2sgzIuww7EejVbVsItLSTa/DVPYiBjSwD8i7DPgS6kFuXN+EfVgYt72QOvr4LKbCRZUDeZdiFQJeK7C/Q8j6uwTfoQwhsZBmQdxn2INCVInsJ9KFFH3PwDfoQAhtZBuRdhh0I1PdnV4FWdHENvkUnMmAjy4C8y3D7Al0bstN7SA+zQCt6WATfpBcRsJFlQN5luHmBOobsJ9CHdv7cZUFpwHDsyLsMty5Q15AQaGewkWVA3mW4cYF6huz2Eugg0KoOFsE36kcAbGQZkHcZblugviI7CvShmT93WVAaMBw78i7DTQs0oMiuAq07fMEeC0oDhmNH3mW4ZYGGFNlToO3YY0FpwHDsyLsMNyzQoCIh0M5gI8uAvMtwuwJ9HfUnBNoRbGQZkHcZ9ijQqD8h0HqwkWVA3mWAQBX6c5cFpQHDsSPvMkCgEGhTsJFlQN5lgEAh0KZgI8uAvMsAgUKgTcFGlgF5lwEChUCbgo0sA/IuAwQKgTYFG1kG5F2GfQnUyMdAd1lQGjAcO/Iuww4Fqt+fuywoDRiOHXmXAQKFQJuCjSwD8i4DBAqBNgUbWQbkXQYIFAJtCjayDMi7DBAoBNoUbGQZkHcZIFAItCnYyDIg7zJAoBBoU7CRZUDeZYBAIdCmYCPLgLzLsCuBpj9HXzhQD/ZYUBowHDvyLsP+BGrgBHSXBaUBw7Ej7zJAoBBoU7CRZUDeZYBAIdCmYCPLgLzLAIFCoE3BRpYBeZcBAoVAm4KNLAPyLgMECoE2BRtZBuRdBghUoT93WVAaMBw78i4DBAqBNgUbWQbkXYY9CdTM5+h3WVAaMBw78i7D7gQa8ycE2gZsZBmQdxkgUAi0KdjIMiDvMkCgEGhTsJFlQN5lgEAh0KZgI8uAvMsAgSr05y4LSgOGY0feZYBAIdCmYCPLgLzLAIFCoE3BRpYBeZcBAoVAm4KNLAPyLsOOBGrnc/S7LCgNGI4deZdhbwKN+RMCbQQ2sgzIuwwQKATaFGxkGZB3GSBQCLQp2MgyIO8yQKAK/bnLgtKA4diRdxkgUAi0KdjIMiDvMkCgEGhTsJFlQN5luF2BeraEQLcAG1kG5F2GWxWo/6FPQx8D3WVBacBw7Mi7DLcq0IewQGP+hEBbgY0sA/IuAwQKgTYFG1kG5F2G2xbogSrQwkF6sceC0oDh2JF3GW5WoI8QqAjYyDIg7zJAoBBoU7CRZUDeZbhxgR4g0I3BRpYBeZfhdgX6GgKVABtZBuRdBggUAm0KNrIMyLsMty7Qw8qfEGh3sJFlQN5luGGBnnyBGvHnLgtKA4ZjR95lgEAh0KZgI8uAvMtw8wI9QKCbgo0sA/Iuwy0L9ASBbg82sgzIuwwQKATaFGxkGZB3GW5foAcIdEuwkWVA3mW4aYGeINDNwUaWAXmXYZ8CLexzM/ZYUBowHDvyLsMOBHo4ndzP0Rf2uRl7LCgNGI4deZfhtgV6WgtU7VN2lz0WlAYMx468ywCBamSPBaUBw7Ej7zLsQaAHCHQ7sJFlQN5luHGBniDQjcFGlgF5lwEC1cgeC0oDhmNH3mXYhUAPEOhmYCPLgLzLcOsCPUGg24KNLAPyLsMuBVrY5XbssaA0YDh25F2GfQj0YOtz9LssKA0Yjh15l+HmBXry/QmBdgQbWQbkXQYIVCN7LCgNGI4deZdBv0BLeT1yFeh0z2vp0AAAYIneM9ATzkC3BGdCMiDvMug/Ay2NDwIVARtZBuRdBghUI3ssKA0Yjh15l2EHAj25Ai3scUP2WFAaMBw78i4DBKqRPRaUBgzHjrzLAIFqZI8FpQHDsSPvMuxBoCdrL4HusqA0YDh25F0GCFQjeywoDRiOHXmXAQLVyB4LSgOGY0feZdiFQI1dzG6fBaUBw7Ej7zJAoBrZY0FpwHDsyLsM+xDoaelPCLQn2MgyIO8y7ESgSwo73JI9FpQGDMeOvMsAgWpkjwWlAcOxI+8yQKAa2WNBacBw7Mi7DBCoRvZYUBowHDvyLgMEqpE9FpQGDMeOvMsAgWpkjwWlAcOxI+8yQKAa2WNBacBw7Mi7DBCoRvZYUBowHDvyLsP+BFrY36bssaA0YDh25F0GCFQjeywoDRg2ecFmAAAMyUlEQVSOHXmXAQLVyB4LSgOGY0feZYBANbLHgtKA4diRdxkgUI3ssaA0YDh25F0GCFQjeywoDRiOHXmXAQLVyB4LSgOGY0feZYBANbLHgtKA4diRdxkgUI3ssaA0YDh25F2G3Qm0sLtt2WNBacBw7Mi7DBCoRvZYUBowHDvyLgMEqpE9FpQGDMeOvMsAgWpkjwWlAcOxI+8yQKAa2WNBacBw7Mi7DBCoRvZYUBowHDvyLgMEqpE9FpQGDMeOvMsAgWpkjwWlAcOxI+8y7E2ghb1tzB4LSgOGY0feZYBANbLHgtKA4diRdxkgUI3ssaA0YDh25F0GCFQjeywoDRiOHXmXAQLVyB4LSgOGY0feZYBANbLHgtKA4diRdxkgUI3ssaA0YDh25F0GCFQjeywoDRiOHXmXAQLVyB4LSgOGY0feZdiZQAs725o9FpQGDMeOvMsAgWpkjwWlAcOxI+8yQKAa2WNBacBw7Mi7DBCoRvZYUBowHDvyLgMEqpE9FpQGDMeOvMsAgWpkjwWlAcOxI+8yQKAa2WNBacBw7Mi7DBCoRvZYUBowHDvyLsO+BFrY1+bssaA0YDh25F0GCFQjeywoDRiOHXmXAQLVyB4LSgOGY0feZYBANbLHgtKA4diRdxkgUI3ssaA0YDh25F0GCFQjeywoDRiOHXmXAQLVyB4LSgOGY0feZYBANbLHgtKA4diRdxkgUI3ssaA0YDh25F2GXQm0sKvt2WNBacBw7Mi7DBCoRvZYUBowHDvyLgMEqpE9FpQGDMeOvMsAgWpkjwWlAcOxI+8yQKAa2WNBacBw7Mi7DBCoRvZYUBowHDvyLsPtCvQRApUAG1kG5F0GCFQjeywoDRiOHXmX4YYF+mDWn7ssKA0Yjh15lwEC1cgeC0oDhmNH3mWAQDWyx4LSgOHYkXcZblmgrkELexJgjwWlAcOxI+8yQKAa2WNBacBw7Mi7DDct0AcIdHOwkWVA3mWAQDWyx4LSgOHYkXcZIFCN7LGgNGA4duRdhtsW6AMEujXYyDIg7zLsSKCFHUmwx4LSgOHYkXcZIFCN7LGgNGA4duRdhhsX6AMEujHYyDIg7zJAoBrZY0FpwHDsyLsMty7QBwh0W7CRZUDeZYBANbLHgtKA4diRdxkgUI3ssaA0YDh25F2GmxfoAwS6KdjIMiDvMuxHoIX9iLDHgtKA4diRdxkgUI3ssaA0YDh25F2G2xfoAwS6JdjIMiDvMkCgGtljQWnAcOzIuww7EOgDBLoh2MgyIO8yQKAa2WNBacBw7Mi7DBCoRvZYUBowHDvyLsMeBPoAgW4HNrIMyLsMEKhG9lhQGjAcO/Iuw24EWtiNDHssKA0Yjh15l2EXAn2AQDcDG1kG5F0GCFQjeywoDRiOHXmXYR8CfYBAtwIbWQbkXQYIVCN7LCgNGI4deZcBAtXIHgtKA4ZjR95l2IlAHyDQjcBGlgF5lwEC1cgeC0oDhmNH3mUQFeivfng8Pv/+Z9c7vnzx3S/6CNQWhmNH3mVA3mWQFOinxwvPfzbd8e6TIwR6xnDsyLsMyLsMggJ9e3z+o8fHrz45fucX4z1vjhDoBcOxI+8yIO8yyAn06XTzx+f/f/3x8P/zE3gIdMBw7Mi7DMi7DHIC/frj8czz1fGjyaj/Eq+BXjAcO/IuA/Iug4J34SeBvjp+iDeRBgzHjrzLgLzLIC/Qrz8e3kV6+/T0fSnQb40UdwwAADYoF+ib44fn/108CoECAHZIsUDfjh9jujyRx1P4AcOxI+8yIO8ySD+Ff/vi+eU9+DeX998h0AHDsSPvMiDvMggL9M14/vnli8v/IdABw7Ej7zIg7zLICvTT6WtIb44z88fqIVCLIO8yIO8ySAr03avjB6MtIdAVhmNH3mVA3mWQFOgr73tHeAo/YDh25F0G5F0GQYG+8b+3CYEOGI4deZcBeZdB8quc87P2DyHQNYZjR95lQN5lkBPo2yMEGsNw7Mi7DMi7DNKfA82z9cQ0YDh25F0G5F0GCFQjhmNH3mVA3mWAQDViOHbkXQbkXQYIVCOGY0feZUDeZYBANWI4duRdBuRdBghUI4ZjR95lQN5lgEA1Yjh25F0G5F0GCFQjhmNH3mVA3mWAQDViOHbkXQbkXQYIVCOGY0feZUDeZYBANWI4duRdBuRdBghUI4ZjR95lQN5lgEA1Yjh25F0G5F0GCFQjhmNH3mVA3mWAQDViOHbkXQbkXQYIVCOGY0feZUDeZYBANWI4duRdBuRdBghUI4ZjR95lQN5lgEA1Yjh25F0G5F0GCFQjhmNH3mVA3mWAQDViOHbkXQbkXQYIVCOGY0feZUDeZdAv0EK+9S3pCPYJ8i4D8i5Dq7xDoOAC8i4D8i4DBAqagrzLgLzLAIGCpiDvMiDvMkCgoCnIuwzIuwwQKGgK8i4D8i4DBAqagrzLgLzLAIGCpiDvMiDvMtysQAEAwAoQKAAAFAKBAgBAIRAoAAAUAoECAEAhECgAABQCgQIAQCEQKAAAFKJFoL/64fH4/PufDTfe/fTF8TjdAL358sV3v7j8A3nfjHefPqX6H/9ovIG8b8VXT545tvSMEoF+erzw/GfnG19/fLnxnV9IR7UP3n1yHASKvG/GV0Oqjz8430DeN+PLF609o0Ogb4/Pn/4Yf/XJMJlXx+9+dr4xnheBvrw5jplG3rfi6W/WB589vvvPw05G3rfifK5wTXWTvKsQ6NO8fnz+/9OfhB+f/0pcNPr1x8PfCdCX8x/lSwkh75vxdjzteXP8EHnfkFWq2+RdhUC//ng8jX51/Gisqsfz/z+SDGonPP3x+pfDa6DI+1ZMJwwDyPtmvB1SPeS/Td5VCHTmItBXY3WNswVdeXX8cHwTCXnfivmE4QLyvhmrk842eVcl0MvE3n0ynlLPbw6Dfrx9evo+JBp534xzhv/uXxyPH/zVI/K+JfNroB82y7sqgb5pODFA4fInCwLdmKcM/3R4F/4j5H1T3g0f9/lBu3rXJNC3lzclFxPDBzt6c3nNxBMo8t6Xt8MeftrN62dcyHtvvvzzi0A/+KxZvSsS6NsXz88vSuAv8na8ubz/jjPQjXl7HN+3ePX0lAt5344vXwT/cN3GGeib8eOtKKjN+PLFJdUQ6MaMeR9Sjbxvx6v2f7jUCPTT4/RxLLwruRVvjjNPz2KQ962YnzRe/oG8b8XamTf1Lvy7V8cPphcips9l4XNxvVkLFHnfinkjnz8DgbxvxlqgbfKuRKCvFt+nwjczNmZ8DoO8b8ar8aRnfA8Ped+I5VP4W/om0vhmxsjwRWF8N3gzRoEi75vx5YvzRYCGNzOQ9+14u/j0Q6O8qxDoeFmUM+e/zF/h6jSbMr2KjrxvxtvxqkCXV+GQ982YXrS6nIg2ybsKgb49rgT6+NX5Y8bfx9/jjZjfhkTeN+Or86Uo/+yz6QbyvhH/43w90JZ5VyFQAACwCAQKAACFQKAAAFAIBAoAAIVAoAAAUAgECgAAhUCgAABQCAQKAACFQKAAAFAIBAoAAIVAoAAAUAgECgAAhUCgAABQCAQKAACFQKAAAFAIBAoAAIVAoAAAUAgECgAAhUCgAABQCAQKbPG3/+bbz549+0f/2y/H2//1nzx79t4f/vLzZ7/1ny63//78+Ht/8B/lIgQ7AgIFlvjmr5+N/PbFl9/8ZLj1W/9mFOjn0+N/KBso2AcQKLDEkx//8Onc8+//+Nmz3z3f/vnl9kWrF4E+PX4++fyHv4ZBwRZAoMAQv/ne4M3zP37nSaT/89vP/uhy+/NBoE+3h8ef7njv30lFCfYDBAoM8etJi09P3c/CnF/5fBLq6va5we9KRQn2AwQKTPLzsyoXlnRvP93xO7+MHAtAKyBQYI1/+Nv7v/i9y1P2p/POPxrv/Hy8vWA6GQWgGxAoMMV/+b2FHyFQIAwECgwxfGrpH/3pv/3vPx+FOT1l/9y5DcAWQKDAEOOnmB7jr4HihU+wJRAosMNVkO677uPtn88fXoJLwRZAoMAOVyteP/fpfg50bPDrZ8/+uVicYDdAoMAQ41P4v/3jZ8+Gc83P/W8i/fZfPpn2b57hBBRsAAQKDPGbPx7fYf+DvxnOML/5+fjN+P/D/S48/Ak2AAIFlvjm3//e+VpL/8/1DXf/akznDzr9L38pGSXYDRAouAnwxSMgAQQKDPPz6bwTX30HIkCgwDCfT++1z2/HA7AlECgwzJM33/tnT+ef/+Xb+OImkAACBZb59benC9TjNzyAABAoMM0//PXwpjveQQISQKAAAFAIBAoAAIVAoAAAUAgECgAAhUCgAABQCAQKAACFQKAAAFAIBAoAAIVAoAAAUAgECgAAhUCgAABQCAQKAACFQKAAAFAIBAoAAIX8/0HQPsn9oJW7AAAAAElFTkSuQmCC" width="672" /></p>
<p>For comparison, natural splines with 5 transformations.</p>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>B-splines and restricted (natural) cubic splines are implemented in the R package <code>splines</code>.</p>
<p><br></p>
</div>
</div>
</div>
</div>
</div>
<div class="footnotes">
<hr />
<ol>
<li id="fn1"><p>Harrell Jr. FE. Regression modeling strategies. With applications to linear models, logistic regression, and survival analysis. Springer 2015, chapter 2.4.6<a href="#fnref1" class="footnote-back">↩︎</a></p></li>
</ol>
</div>


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