Linear regression and correlation
The ASTA team
The regression problem
We want to predict
- We will study the dataset
trees
, which is on the course website (and actually also already available in R).
trees <- read.delim("https://asta.math.aau.dk/datasets?file=trees.txt")
- In this experiment we have measurements of 3 variables for 31 randomly chosen trees:
- [,1]
Girth
numeric. Tree diameter in inches.
- [,2]
Height
numeric. Height in ft.
- [,3]
Volume
numeric. Volume of timber in cubic ft.
- We want to predict the tree volume, if we measure the tree height and/or the tree girth (diameter).
- This type of problem is called regression.
- Relevant terminology:
- We measure a quantitative response \(y\), e.g.Â
Volume
.
- In connection with the response value \(y\) we also measure one (later we will consider several) potential explanatory variable \(x\). Another name for the explanatory variable is predictor.
Initial graphics
- Any analysis starts with relevant graphics.
library(mosaic)
library(GGally)
ggscatmat(trees) # Scatter plot matrix from GGally package
![](data:image/png;base64,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)
- For each combination of the variables we plot the \((x,y)\) values.
- It looks like
Girth
is a good predictor for Volume
.
- If we only are interested in the association between two (and not three or more) variables we use the usual
gf_point
function.
Simple linear regression
- We choose to use
x=Girth
as predictor for y=Volume
. When we only use one predictor we are doing simple regression.
- The simplest model to describe an association between response \(y\) and a predictor \(x\) is simple linear regression.
- I.e. ideally we see the picture \[y(x)=\alpha +\beta x\] where
- \(\alpha\) is called the
Intercept
- the line’s intercept with the \(y\)-axis, corresponding to the response for \(x=0\).
- \(\beta\) is called
Slope
- the line’s slope, corresponding to the change in response, when we increase the predictor by one unit.
gf_point(Volume ~ Girth, data = trees) %>% gf_lm()
## Warning: Using the `size` aesthetic with geom_line was deprecated in ggplot2 3.4.0.
## ℹ Please use the `linewidth` aesthetic instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
![](data:image/png;base64,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Model for linear regression
- Assume we have a sample with joint measurements \((x,y)\) of predictor and response.
- Ideally the model states that \[y(x)=\alpha +\beta x,\] but due to random variation there are deviations from the line.
- What we observe can then be described by \[y=\alpha + \beta x + \varepsilon, \] where \(\varepsilon\) is a random error, which causes deviations from the line.
- We will continue under the following fundamental assumption:
- The errors \(\varepsilon\) are normally distributed with mean zero and standard deviation \(\sigma_{y|x}\).
- We call \(\sigma_{y|x}\) the conditional standard deviation given \(x\), since it describes the variation in \(y\) around the regression line, when we know \(x\).
Least squares
- In summary, we have a model with 3 parameters:
- \((\alpha,\beta)\) which determine the line
- \(\sigma_{y|x}\) which is the standard deviation of the deviations from the line.
- How are these estimated, when we have a sample \((x_1,y_1)\ldots(x_n,y_n)\) of \((x,y)\) values??
- To do this we focus on the errors \[\varepsilon_i=y_i-\alpha-\beta x_i\] which should be as close to 0 as possible in order to fit the data best possible.
- We will choose the line, which minimizes the sum of squares of the errors: \[\sum_{i=1}^n \varepsilon_i^2=\sum_{i=1}^n(y_i-\alpha-\beta x_i)^2.\]
- If we set the partial derivatives to zero we obtain two linear equations for the unknowns \((\alpha,\beta)\), where the solution \((a,b)\) is given by: \[b=\frac{\sum_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i=1}^n(x_i-\bar{x})^2} \quad \mbox{ and } \quad a=\bar{y}-b\bar{x}\]
The prediction equation and residuals
- The equation for the estimates \((\hat{\alpha},\hat{\beta})=(a,b)\), \[\hat{y}=a+bx\] is called the prediction equation, since it can be used to predict \(y\) for any value of \(x\).
- Note: The prediction equation is determined by the current sample. I.e. there is an uncertainty attached to it. A new sample would without any doubt give a different prediction equation.
- Our best estimate of the errors is \[e_i=y_i-\hat{y}=y_i-a-bx_i, \] i.e. the vertical deviations from the prediction line.
- These quantities are called residuals.
- We have that
- The prediction line passes through the point \((\bar{x},\bar{y})\).
- The sum of the residuals is zero.
Estimation of conditional standard deviation
To estimate \(\sigma_{y|x}\) we need Sum of Squared Errors \[
SSE=\sum_{i=1}^n e_i^2=\sum_{i=1}^n(y_i-\hat{y}_i)^2,
\] which is the squared distance between the model and data.
We then estimate \(\sigma_{y|x}\) by the quantity \[
s_{y|x}=\sqrt{\frac{SSE}{n-2}}
\]
Instead of \(n\) we divide \(SSE\) with the degrees of freedom \(df=n-2\). Theory shows, that this is reasonable.
The degrees of freedom \(df\) are determined as the sample size minus the number of parameters in the regression equation.
In the current setup we have 2 parameters: \((\alpha,\beta)\).
Example in R
model <- lm(Volume ~ Girth, data = trees)
summary(model)
##
## Call:
## lm(formula = Volume ~ Girth, data = trees)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.065 -3.107 0.152 3.495 9.587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -36.9435 3.3651 -10.98 7.62e-12 ***
## Girth 5.0659 0.2474 20.48 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.252 on 29 degrees of freedom
## Multiple R-squared: 0.9353, Adjusted R-squared: 0.9331
## F-statistic: 419.4 on 1 and 29 DF, p-value: < 2.2e-16
- The estimated residuals vary from -8.065 to 9.578 with median 0.152.
- The estimate of
Intercept
is \(a=-36.9435\)
- The estimate of slope of
Girth
is \(b=5.0659\)
- The estimate of the conditional standard deviation (called residual standard error in R) is \(s_{y|x}=4.252\) with \(31-2=29\) degrees of freedom.
Test for independence
- We consider the regression model \[y=\alpha+\beta x+\varepsilon\] where we use a sample to obtain estimates \((a,b)\) of \((\alpha,\beta)\), an estimate \(s_{y|x}\) of \(\sigma_{y|x}\) and the degrees of freedom \(df=n-2\).
- We are going to test \[H_0:\, \beta=0 \quad \mbox{ against } \quad H_a:\, \beta\not=0\]
- The null hypothesis specifies, that \(y\) doesn’t depend linearly on \(x\).
- In other words the question is: Is the value of \(b\) far away from zero?
- It can be shown that \(b\) has standard error \[se_b=\frac{s_{y|x}}{\sqrt{\sum_{i=1}^n(x_i-\bar{x})^2}}\] with \(df\) degrees of freedom.
- So, we want to use the test statistic \[t_\text{obs}=\frac{b}{se_b}\] which has to be evaluated in a t-distribution with \(df\) degrees of freedom.
Example
- Recall the summary of our example:
##
## Call:
## lm(formula = Volume ~ Girth, data = trees)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.065 -3.107 0.152 3.495 9.587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -36.9435 3.3651 -10.98 7.62e-12 ***
## Girth 5.0659 0.2474 20.48 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.252 on 29 degrees of freedom
## Multiple R-squared: 0.9353, Adjusted R-squared: 0.9331
## F-statistic: 419.4 on 1 and 29 DF, p-value: < 2.2e-16
- As we noted previously \(b=5.0659\) and \(s_{y|x}=4.252\) with \(df=29\) degrees of freedom.
- In the second column(
Std. Error
) of the Coefficients
table we find \(se_b=0.2474\).
- The observed t-score (test statistic) is then \[t_\text{obs}=\frac{b}{se_b}=\frac{5.0659}{0.2474}=20.48\] which also can be found in the third column(
t value
).
- The corresponding p-value is found in the usual way by using the t-distribution with 29 degrees of freedom.
- In the fourth column(
Pr(>|t|)
) we see that the p-value is less than \(2\times 10^{-16}\). This is no surprise since the t-score was way above 3.
Confidence interval for slope
When we have both the standard error and the reference distribution, we can construct a confidence interval in the usual way: \[b\pm t_{crit} se_b, \] where the t-score is determined by the confidence level and we find this value using qdist
in R.
In our example we have 29 degrees of freedom and with a confidence level of \(95\%\) we get \(t_{crit} =\) qdist("t", 0.975, df = 29)
= 2.045.
If you are lazy (like most statisticians are):
## 2.5 % 97.5 %
## (Intercept) -43.825953 -30.060965
## Girth 4.559914 5.571799
- i.e. \((4.56, 5.57)\) is a \(95\%\) confidence interval for the slope of
Girth
.
Correlation
- The estimated slope \(b\) in a linear regression doesn’t say anything about the strength of association between \(y\) and \(x\).
Girth
was measured in inches, but if we rather measured it in kilometers the slope is much larger: An increase of 1km in Girth
yield an enormous increase in Volume
.
- Let \(s_y\) and \(s_x\) denote the sample standard deviation of \(y\) and \(x\), respectively.
- The corresponding t-scores \[y_t=\frac{y}{s_y} \quad \mbox{ and } \quad x_t=\frac{x}{s_x}\] are independent of the chosen measurement scale.
- The corresponding prediction equation is then \[\hat{y}_t=\frac{a}{s_y}+\frac{s_x}{s_y}b x_t\]
- i.e. the standardized regression coefficient (slope) is \[r=\frac{s_x}{s_y}b\] which also is called the correlation between \(y\) and \(x\).
- It can be shown that:
- \(-1\leq r\leq 1\)
- The absolute value of \(r\) measures the (linear) strength of dependence between \(y\) and \(x\).
- When \(r=1\) all the points are on the prediction line, which has positive slope.
- When \(r=-1\) all the points are on the prediction line, which has negative slope.
- To calculate the correlation in R:
## Girth Height Volume
## Girth 1.0000000 0.5192801 0.9671194
## Height 0.5192801 1.0000000 0.5982497
## Volume 0.9671194 0.5982497 1.0000000
- There is a strong positive correlation between
Volume
and Girth
(r=0.967).
- Note, calling
cor
on a data.frame
(like trees
) only works when all columns are numeric. Otherwise the relevant numeric columns should be extracted like this:
cor(trees[,c("Height", "Girth", "Volume")])
which produces the same output as above.
- Alternatively, one can calculate the correlation between two variables of interest like:
cor(trees$Height, trees$Volume)
## [1] 0.5982497
R-squared: Reduction in prediction error
R-squared: Reduction in prediction error
- We want to compare two different models used to predict the response \(y\).
- Model 1: We do not use the knowledge of \(x\), and use \(\bar{y}\) to predict any \(y\)-measurement. The corresponding prediction error is defined as \[TSS=\sum_{i=1}^n(y_i-\bar{y})^2\] and is called the Total Sum of Squares.
- Model 2: We use the prediction equation \(\hat{y}=a+bx\) to predict \(y_i\). The corresponding prediction error is then the Sum of Squared Errors \[SSE=\sum_{i=1}^n(y_i-\hat{y}_i)^2.\]
- We then define \[ r^2=\frac{TSS-SSE}{TSS} \] which can be interpreted as the relative reduction in the prediction error, when we include \(x\) as explanatory variable.
- This is also called the fraction of explained variation, coefficient of determination or simply r-squared.
- For example if \(r^2 = 0.65\), the interpretation is that \(x\) explains about \(65\%\) of the variation in \(y\), whereas the rest is due to other sources of random variation.
Graphical illustration of sums of squares
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.
## `geom_smooth()` using formula = 'y ~ x'
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tjYmIOHz68e/furVu3RkRE7Nu3T19fX4FpK0goFM6ePfvYsWMlmzQ1NXft2tWvX7/aT1UO3sto/otnRCRq2Ub5C2AyxsbGRkZGHz9+3LhxY+EZYJ8wjMi6ZVkDk5KSiKhBgwbyTggAACA/OAMMAMrGsipXL6pcvSi4e6s60zC5/21kIRHXQCoAAAAAAIAvSXx8vLu7e2xsrJub2+3btydMmFC0+kVElpaWixYtunHjRrt27W7evOnp6SkUChWVtoJSU1OHDRtWavXLzMzs9OnTylb9qrssLCzEYvHz588rNSoqKoqILC0t5ZIJAACgVqAABgDlEdwOF9wO5z9+UJHOvBfPVYPPqQaf4yZ9kHcwAAAAAACAL4FUKh0/fvyHDx9Gjx69e/dudXX1sno2bNjw7NmzHTp0iIiIWL58eS1mrLSoqKhevXrdvHmzZJODg8OlS5fatm1b+6nqqz59+hDRuXPnKjUqICCAiHr37i2XTAAAALUCBTAAqDHcD/H8yPv8yPtMepqis5QhJ1v6Mlr6MprSUhUdBQAAAAAA4PNOnDhx7949W1vbtWvXMgxTfmc1NbV9+/bp6Ojs3bv333//rZ2ElRUSEuLq6hoXF1eyadSoUcePHy+2vg2qydXVlcvl/vHHHxkZGRUc8vTp0/PnzxsaGvbs2VOu2QAAAOQKBTAAICISN/1K1M5O1M6OePzPdpaaNswdMzF3zMQC+69rIVsN4sS8Fu3ZLtqznYm8r+gsdYDg2iV1/0Pq/oeYnOzP964kbmwMP/opP/op878bY+a6e+a6e+b1danxOwIAAAAA1EV+fn5EtGLFCj7/8x/WiMjExGTWrFlisXjnzp1yjlZpLMtu3brV09MzKyurWBOXy126dOnmzZsFAoFCstVjVlZWI0eOTE1N9fHxqUj//Px8Ly8vqVQ6d+5cFRUVeccDAACQH56iAwCAUhC160BSCRGxFfiwwaqoSIxN5R8KFEMikdy9ezckJGSEOMdWQ42IVi1f3sy+U58+ffT09GrqLirhV7mxMUSUPW0OaWh+usowEkurmroFAAAAAEBdFxsb+/TpU2tr66+/rsTTh56enqtXr75w4cL69es5HGV59FkoFM6ePbvUQ780NTV37dqFQ7/kZ/HixWFhYf7+/qampkuWLClnKWF+fv6UKVMePHjQuXPn77//vjZDAgAA1Dhl+WcQABSSWDbN7+uS39dF0si8ypOwDIdVVWNV1Vh+hercaif+1vRbr+m3nsnNqfJNyyJV/6+8wUXRvYYxIhGTn8fk55FUWv3ZpFLp8ePHO3Xq5OLismXLlg8fPp3ldurUqR9//LF169Y+Pj4pKSnVvxEAAAAAAFTErVu3iKhXr16VGqWnp2dra5ucnPz27Vv55Kq0xMTEQYMGlVr9srS0DAwMRPVLrgwNDQ8ePKilpbV169YxY8bExsaW2i0yMtLFxSUgIKBx48b79u2r4KJDAAAApYUvowGUjqSBkaSBUcX7c5MSiWWJy5UY/v8oqVnD7Bnz5ZCuStTVKT2NiFgut+qTqKlLdXSJqIIlvS+EyvlT/BfPiChn3BSpYSX+2JSUk5MzZcqUwMBAIuratauLi4s9R0QpyUS0fv3601evnTp1as+ePSdPnty/f3/nzp1rJD8AAAAAAJRD9lCauXmlH45s3LhxREREQkJCkyZN5JCrch49euTu7v7+/fuSTZ07d96/fz8O/aoFbdq0uXDhgqenZ2Bg4KVLlwYNGtS3b99mzZrp6OgkJSU9f/48ICDg0qVLLMs6ODjs27cPPxQAAKgH8D0yQJ2nduhPRiKWauvkTJ6l6CxyVPB194Kvuys6Rb2Vk5MzePDgyMjIZs2abdy4sUuXLkSkdvywrADm6OjY81u3JUuW/PLLLwcPHhwyZMjBgwcr+xQqAAAAAABUVl5eHhGpqamVbNqTkvZ3eiYRLTdp0E1DvVirbIhsuGL5+/uPHTs2Nze3ZNPo0aPXrl2LZUa1xtra+vLly9u3b9+xY8fx48ePHz9erIOxsbG3t7eHhwePhy8MAQCgPsD/zwAAgH788cfIyEgHB4eDBw/q6uqW2kdfX3/Tpk2tW7deuHDhxIkTg4KCmjVrVss5AQAAAAC+KEZGRkSUnJxcsumDWBKZl09EGRJJKa0fPhCRsbGxnAOWh2XZtWvXLlq0SFpiw3Yul7to0aKZM2cqJNiXTENDw9vbe/r06ZcuXbp+/XpcXFxGRoaBgYGFhUWvXr26dOmCeiQAANQnKIApKfWjB7jvYogoe9ocVkPzc91Lp3LtkuDWdSLKGzxc3LxFDcYDgPokICAgICCgSZMmBw4cKKv6VWj8+PEJCQmbN2/28fHx9/evnYQAAAAAAF8mKysrIrp3716lRkml0ocPH/J4PAsLC/nk+ryCgoJp06aV+pFBV1d3z549PXv2rP1U1cTq6kmMTYmI+AJFZ6kWdXV1FxcXFxcXRQcBAACQLxTA4BNGIlEJOElErK5eQQ8nRceBeoUVqLCqsi07GAVHgdKsXr2aiNauXaunp1eR/t7e3mfPnr18+XJ4eHjXrl3lnA4AAAAA4MvVuXNnbW3tK1eupKenf/ZhtUK3bt1KSkrq3r27tra2XOOVJSEhYcyYMQ8fPizZ1KRJk0OHDjVv3rz2U1VfQc/eio4AAAAAlcBRdABQGlIpP/opP/opN+a1oqOAEpHq6Ep1dFmtan1qynX3zJ4xP3vGfFZFpaaCQU2Jiop68eKFra2to6NjBYfw+fxZs2YR0YkTJ+QZDQAAAADgSycQCIYMGZKfn79169aKj1qzZg0RDR8+XG65ynP37t3evXuXWv365ptvgoOD62j1CwAAAOocFMAAoGwMkzNpZs6kmbnDRlWku1RDU2JsKjE2ZVVV5R0NakpoaCgRDRw4sFKj+vXrx+PxZGMBAAAAAEB+5s2bp66uvmvXruvXr1ek/86dO2/dumVjY+Pu7i7vbCWdOnXKzc0tKSmpZNOYMWMOHz5c8XVsAAAAANWEAhgA1BiRXafcMRNzx0yUWFgqOgtU1Lt374ioTZs2lRqlr69vZmaWkJAgFArlkwsAAAAAAIiIjI2NV61aJRKJJkyYcOfOnfI7Hz58eMWKFaqqqlu3buVyubWTUIZl2XXr1k2aNCk/P79YE4/HW7NmzcaNG/l8fm1GAgAAgC8czgADgErjZGbwnkURkcTYRGLZVNFxKkHaopXK8l+JKFcoIpFI0XGUwsePH4nIwMCgZJOkoQXLFxARW9rHVCMjo3fv3n38+NHMzKzG0rAs/9EDIiJVVZF1yxqbFgAAAACgLvP09Hzz5s3WrVvd3Nzmzp07depUNTW1Yn0SExNXr1595MgRPp+/bdu29u3b12bCnJycadOmnT9/vmSTvr7+oUOH7O3tazMPAAAAAKEABgAynKRE2QsmN4fV0Cy/M5OaonL1IhGJ7DrVrQIYcbmkpk5ExOaiACYjOxY7KyurZJPQoVs5AzMyMgqHV0HekBEklRARq/I/G2aqBp8jIqlhAxTAAAAAAAAKLV26tFGjRkuWLFmzZs1vv/3Wv3//5MFDqIExEV26dOmf06dCQ0Pz8/MNDAz++OOPrl271ma2+Pj40aNHP3r0qNh19xZfHXTtT0RSVpRTm4EAAAAAiAhbIAIoISY3h/shgfshgcnLq7Wbsjr/7cOuolLjkzNZWZyMdE5GOrFsjU8O1WRqakpEb968qdQooVD4/v17bW1tTc3PlEvLwgoErKoaq6pGDFO1GQAAAAAAvijjxo0LDw93c3PLzMz866+/goODZdcPHDhw7tw5Ho83Y8aM27dv13L1KyIionfv3iWrX0TUunXr2kwCAAAAUAxWgAEoHf6TRyqXQ4gov98gUVvbqk3C+ZikGhZMRGLLpkL7rz/bv3AVDsut+f8sqJ85xomPI6Lsmd7FlvtANQk7OkhatCIiVkunajN06dJl8+bNISEhY8aMqfio8PDwvLw8R0fHqt0UAAAAAAAKvX37NiAg4Pr16+/fv8/OztbX1zc3N3dycurfv7+hoWHRnpaWlr/99ltGRkZoaOifHL7sQDA3N7fvfpzWvXt3gUBQy8mPHDkyb968Ug8GnjZt2uxRI+i0fy1HAgAAACiEAhhAnZfnOZ5Ylv73fGOmoIAb85qIpFWtiygbQcRN2cFj+U79pQ3NFR1HWUgbmkurN0PXrl319PQuXrz46tWrpk0ruqHlrl27iMjZ2bl6NwcAAAAA+KLFxcWtWbPG399fKv3/f9fHxsZGRkaeO3fOx8dn0qRJs2bNKrbxuI6OztChQ1Uzs1pk5xLROHf31qo1v5NH+SQSyerVq7du3VqySSAQrF+/3sPDg/NvdC2nAgAAACgKWyAC1HkSIxOJsanE0EjRQeSLycqU7QzJKe3pQqgygUAwffp0kUi0ePHiop+6y3H+/PlLly41adLEzc1N3vEAAAAAAOqra9euOTo6Hj16VF9f38vL68KFC9HR0UlJSU+ePPnnn3/Gjx/PMMzWrVv79u3777//lhzurK210cx4o5lx7Ve/srKyPD09S61+GRoanjhxwsPDo5YjAQAAAJSEFWBKStjRgWnRmqhaBzKJm1lLtXWJSGpiWlPBAKD+mTRp0uHDhy9evPjzzz8vX768/M5RUVHTp09nGOaXX37h8/m1EhAAAAAAoL65fPmyh4eHSCSaNGmSj49P0bN1jYyMjIyMevbsOXv27Pnz5wcGBjo7O1+4cMHKykqBgQu9ffvW09Pz+fPnJZtsbGwOHTpkYWFR+6kAAAAASsIKMCUlbtpc1M5O1M6O5VX9+2WJaUPZJFLtCmyCx2EkllYSSyupacMq3xEA6iJVVdVDhw7p6Ohs37592rRpWVlZZfU8c+bMoEGDsrKy5s+f37dv39oMCQAAAABQb8TExPzwww9isXjDhg2rVq0qWv0qysTEZP/+/T/88ENqaqqnp2dOTk4t5ywpPDy8b9++pVa/BgwYcOHChfpd/VK5Eqp+4Hf1A79zMtIVnQUAAAA+DwUw+ITl8nLdPXPdPfP7DFR0FqhvmKyMTy/EIsUmgbI0a9bs1KlTjRo18vf3t7e337Jly5s3bwpbc3Jyzp49++23306YMCEnJ8fHx2fevHkKTAsAAAAAUKctX748IyNj+vTp33//ffk9ORzOqlWrnJycXr58uWPHjtqJV5aDBw8OHz48NTW1ZNPEiRP37dunoaFR+6lqgVAoDAsL8/HxiQgOku3M/9Minz179rx//17R0QAAAKA8KIABQNlYVt3/kLr/IdXAs9WZhiko+PSqYkdMgUK0bt06ODh4xIgRaWlpv/zyS6dOnaysrBwcHFq3bm1lZTV+/Pjw8HBra+ujR4/OmTOHYRhF5wUAAAAAqJMeP34cEBDQqFGjBQsWVKQ/h8NZv369QCDYvn17ZmamvOOVSiKRrFy5cs6cOcISRzILBAI/P7/Vq1dzOPXwKyaJRHL48GF7e/vhw4fv2bMnKSlJdv3SpUs+Pj4dOnSYOnVqbGysYkMCAABAWXAGGACUhxvzmogYwwYV6Sy4c4P/8C4R5fdxljRpKt9kIAcNGjTw8/ObPn36iRMnQkNDX79+/erVKz6fb2Zm5uDg4OzsPGDAAC6Xq+iYAAAAAAB12JkzZ4ho4sSJKhU+89vc3NzNze3o0aMXL150c3OTZ7pSZGVlTZkyJTg4uGSTvr7+/v37HRwcajlS7cjKypo0aVJoaCjDME5OTq6urj2l+ZTwnoi2bNly+ubto0eP/vPPP4GBgTt37uzfv7+i8wIAAEBxKIABQOVxuayqGhGxvP/5bwhTkC/bCZ0RKelWh8yHRPH1MCJizBuTCY67K521tbWPj4+Pjw8R5ebmqqmpYb0XAAAAAEBNuXz5MhENGDCgUqP69+9/9OjRy5cv13IB7M2bN56eni9evCjZ1KpVq4MHD5qbm9dmnlqTk5Pj6uoaFRVlbW29efPmjh07EpHqaX9KICKys7Nr37f/vHnzfH19t27d+v333+/YsWPo0KEKDg0AAAD/CwUwACAiEto7MDatiYgq8BCixLxx9oz5cs8kB8zHJMnlUCKinr1RAKsIdXV1Oc3Mj7zPyUgjIqFDd1Yg+HSVYbLmL5PTHQEAAAAAlEFcXJxAILC0tKzUqBYtWhBRLR86dfny5YkTJ6anp5dsGjRo0LZt28r/vMCaNeINGUFEwortKaJUpk2bFhUV1bVr14MHD2ppaZXaR0NDY8mSJW3btp08efKsWbOaNWvWrl27Ws4JAAAA5UABDACIiFhNLZbLIyKWqYf7toNSSU9Pv3LlSveXTxqzYiL66/W79t26N2vWTNG5AAAAAABqQ1pamoGBQcldFlgiv+QUIjLg8Ubp6RRr1dfXJ6KUlJTaCUlEe/bsWbp0qVgsLnadYZi5c+d6e3t/dqMIVk+fa9GYiNjcXMrNlVdQOTh//vz58+etrKz27dtXVvWrkKura3x8/NKlS729vQMDA7F/BgAAgPJAAQxA6YhatZVYWBKRVFu3ypOwauoi65ZEJDExrUh/lbAQbmwMEWVPm8NqaFb5vqWH0dFjkpOIiOXxa3Zm4MTFcrOziEhs2ZSt8BECivL06dPVq1dfvHhRLBYHjxjS2KIhES1fvvxDTq61tfXs2bPd3Nzq5dHZAAAAAACFdHV109LSWJYtVilhWVr54SMRWauqlCyApaWlEZGBgUEtJBSLxUuXLt2zZ0/JJhUVFV9fX3d391qIoUC//vorEa1evVpXt0KfyidPnvzPP//cv38/MDCwsptbAgAAgPzge0YApcOqa0iMTSXGpqyaWkX68x8/4Efe5z+LKnpRqm+Q7zos33WYqH1H+cSsBJb/X92rGrUNaUNzUTs7UTs76eeev/uiCO7eUj3zj+qZf5isDEVnKY9UKv3ll18cHR2DgoJ0dXU9PT2trKxkTRMnTmzVqlV0dPSUKVMGDRqUlJSk2KgAAAAAAHLVsGFDoVD47t27So2Kjo6WjZVPqP+Xmprq7u5eavXL1NQ0ICCg3le/nj9//uzZszZt2jg5OVVwCMMwXl5eRHTy5El5RgMAAIDKQQEMoM5TCbmgGnxOcPWiooPIl8i6ZX5fl/y+LlJDI0VngcqRSCQTJkzYsmWLtrb2mjVrIiMjfX19TU0/rU308vK6fPnymTNn2rVrd+fOnT59+rx580axgQEAAAAA5Oebb74hosDAwEqNkvWXjZVZ9eFjg6joBlHRAZlZNZXt9evXzs7O169fL9nUpk2bCxcufAlnXF26dImIBg4cWKlRvXr1UlVVDQsLk08oAAAAqAoUwJQU90MCN+Y1N+Y1I5FUeRJOeuqnSXJzajAbAECl/PTTT+fOnbOysgoMDPzhhx8EAkHJPl9//fX58+eHDx8eHx/v6emZlVVjn+EBAAAAAJSKi4sLEe3evVsoFFZwyPv370+cOKGurl7xNUlVcPHixT59+vz7778lm4YMGXL+/PlaWH+mDGJjY4nIxsamUqPU1dUtLS3T09MzMpR6cw4AAIAvCs4AU1Iql0O472KIKHvaHKrqgUz8xw8Ft64TUd7g4eLmLWowHgBABd28eXP37t36+vp///13kyZNyukpEAj8/PzS09ODg4NXr169Zs2aWgsJAAAAAFBr2rdv369fv6CgoA0bNixatOiz/aVS6cKFCwsKCubMmaOjU/xssKKeP38eGhoaFxeXlJSkpaVlZmbWtWtXBwcHLpf72bscOHBgwYIFYrFY9svOZiatGxgSUfCbt25jxy1ZsqTYiWX1WEpKChEZGhqWbJJYWpGaGhGxqqUcWCAbkpKSUv6PCQAAAGoNCmDwCSMWq/+5g4ikDYzz3L5TdByoV0QWTThaOkREFfjcBfXMihUriGjNmjXlV79kOByOn5+fvb39/v37J02aVJEhAAAAAAB1zooVK27cuLF582YrK6sRI0aU05Nl2RUrVgQFBVlZWc2YMaOsboGBgatXr3727Fmx6+vXrzcwMPDy8ho/fnypOzEQkVAonD9//uHDh4teHNbiqxkd2xPRAVbgOGnKl1P9IiJdXV0iKnUhl6hdB1HZA9PT0wuHAwAAgDLAFojwH5blZKRzMtKZrExFRwElImpnJ2pnJ2resjqTCLv3yncdlu86jOXxayoY1AnR0dH37t2zsbFxc3Or4BB9ff0pU6aIRCJ/f3+5ZgMAAAAAUJSmTZv+9ttvHA5n5syZK1asyMvLK7Xbx48fx48fv2PHDh0dnYMHD2pqlr49zPbt20ePHv3s2bPWrVsvXLjw0KFDgYGBf//999q1a3v16pWenr506VInJ6eYmJiSY1NTU4cPH16s+lXUP//8Y2NjM2TIkJCQkCq917rHzMyMiF69elWpUSKR6O3bt2pqanp6evLJBQAAAJWGAhgAlI1h8vu65Pd1EXbtWZHukkaNhZ27Cjt3lerryzsa1AlBQUFE5OrqWqknRgcPHlw4FgAAAACgXurdu/eRI0e0tbW3bdvWqVOnTZs2RUVFyZqkUumtW7eWLVtmb29/7ty5xo0bnzt3rnnz5mVNFRER0bixJA3cAAAgAElEQVRx48OHD4eFhc2dO7dfv34dOnRwcnIaP3780aNHr1y50qNHj+fPn/fr16/YErFnz5716dMnPDy85Jxqap+2+OvWrZuent61a9c8PDyGDh2anJxcc78HSqpbt25U+c8jN2/ezMrK6t69+xe1Wg4AAEDJoQAGADVG3KRpQQ+ngh5OUkMjRWcpg4oKo2/A6BuQqqqio3wRXr58SUT29vaVGtW8eXM9PT3ZWAAAAACA+srR0fHSpUvffvvthw8f1qxZ4+TkJLv+8uXLQYMG7dy5UygUTp48OTQ0tEWLUk71ZllW9uKrr74KDg7u06dPqXextrY+duzYxIkTU1NTPT09U1NTZdcvXrzo4uLy7t27kkPc3NxGjRolez1jxoyoqKiDBw9aW1tfvXq1T58+0dHR1XzjSs7Ozs7MzOzGjRuRkZEVH7Vjxw4icnFxkVsuAAAAqDScAQYARESMSPjplVT62c7cj0n8G1eJSNKkmahNe7kGq1nSZtYC245ElJubS7m5io5T/yUlJRGRkVEpBVGppiajo0tExCnyKAbLqoYEENFPPbp4nQ7IzMzU1taunagAAAAAALXPwsLi999/9/b2DggIuHrt+jUiIhIIBD379OnVq5ezs7OpqWlZY1+8eEH6hkTk5eWlr69PRImJiWFhYe/evUtOTtbW1jYzM+vatauNjQ2Xy121alVSUtLp06d/+eWXTZs2/fbbb0uXLpWW+PTHMMy8efO8vb25l/5//ROHw+nfv7+jo+OcOXOOHTvm4eEREhKiX5FtP3KypYnxRETqGqRSZ55B5HA4c+bMmTdvno+Pz6lTp8o6O62ogICAixcvWlpaDh06tBYSAgAAQAWhAAYARERM2qfHAJn8PFbrcyWH7Gx+9FMiIg3Nck4ABlBRUSEioVBYsinfZUjRX7Is+/Dhw2tXry4WZhCRo5E+wzDv379v2bJa588BAAAAACi/r776ysvLa+YsL+vn/xJRs6ZNyzmUS0Yikdy4cYNcXIlIQ0Pjzp07q1evvnHjRuGysEJWVlZz5sxxd3ffuHHj1atXDx8+nJKScv78+ZJzamho7NixY+DAgaXeUUVFZdu2bQUFBadPn547d+7evXs/+744Ma9FJ48SEdOzN3Xq8tn+ymPUqFGHDh2KiIiYO3fu5s2buVxuOZ0jIyOnT5/OMMzq1asrUi0DAACAWoMtEAGUDjchTnA7XHA7nJucVGs3Ldy0kFVTr/HJeS+f8yPv8yPvk0RS45ODMjMxMSGi2NjYcvqIxeKDBw/a2dn17dt31apVsotSqZRl2Z49e37zzTdfzmnbAAAAAPAl4zD00qbZS5tmF6wsPtv57t27GRkZstf79+93dnYODw9v1KjRpEmT/Pz8jhw5snPnzoULF9ra2r5+/Xr69OkuLi75+fljxoyRSCSlVr/MzMzOnj1bVvVLhmEYPz+/Ro0anTt3LiIiompvs07g8XgHDhwwNjb++++/R40aJdvZoiSWZf39/V1dXbOzsxcsWFDWLpQAAACgKFgBBqB0uO/fqVy9SET5auqSBhU4TEtVlZVI2P/dUIITH6d+/DARiVq2LnAa8PlJCrehk8OBvSp3wjnxcUQkbtGSLffROaisgoHfFvRzISJWoKLoLKWws7Pbu3fv5cuXy9oKPzExccyYMQ8ePGAY5uuvv+7bpw/lp8marKysVFVVnzx54uHhMWjQoG3btqmr13x1FgAAAACgLir6lFhYWJiRkdGyZcvc3d05nP950Hnu3LkRERGLFi2KiIhwdHQsa7b27dsfPny4QYMGn72vmpra/PnzZ82atXfv3sqe9Vu3mJqanjt3ztPT8+LFi506dRo3bpyrq2vbtm1lq8FSUlJCQkL2799/9+5dDoezdOnSmTNnKjoyAAAAFIcCGECdlz1tTsmLDCtl8vOIiBGJaz2RXKhcChLcu01EecNGiZs0VXQcZcHy+cTnKzpFmfr27cvj8c6ePbts2bKSp3m9ffvWxcUlMTHR3t5+1apVtra2xLK0YaWsdfr06aNHjw4KClq8ePHZs2ffvXt36tQpTU3NWn8TAAAAAABK582bN/TiXxs93WfPnjVnGP+QEDMzs1J72tvbBwQEjBgx4tq1a6V2MDExCQgIqPjefa6urvPnzw8NDRWLxTxeff5aydLS8sKFCxs2bNizZ8+2bdu2bdvG5XINDQ2zsrJy/ztSuk2bNitXruzatatiowIAAECpsAUiAADIi76+/vDhw1NTUzdu3FisKSsra9SoUYmJiSNGjDh16pStrW3RVh6PJzs+ul+/fsHBwQ4ODpGRkVOnTi15TDcAAAAAwBcoKSmJnj99tn6tyd07/2zzK1r9epCXfyU750p2jphliYhl2V27doWHh5ecRLZcbMKECZU6uUpTU9PW1jYtLS0uLq7a70PZaWlprVixIiIi4ueff+7Ro4eRkVFqaiqPx2vRosWYMWOOHj0aGhqK6hcAAIDSqs+P6tRpeS5DGLGYqncgk7Dj16K2dkTEqmvUWDIAgMpYsGDBmTNndu7c2bFjx0GDBhVeX7duXXR0tKOjo6+vb+Fzox8+fNAiIiJDQ0Pefxse6uvrHz58eMCAAYGBgf7+/t99911tvwcAAAAAACWjofHpY76vr6+pqWnRJp+EpHu5eUT0yuYrFbFwzpw5x44dKzmDpqamk5PT6dOnZQf3Voqs3paYmNi4ceOqpK9rzMzMpk6dOnXqVEUHAQAAgMrBCjAlxWpoSnV0pTq6xKn6z4hVU5NNwlZghzSWwyno4VTQw0lo16nKdwQAKMbMzGzXrl0Mw0yePPnPP/+UXYyPj//zzz81NDS2bdtWWP168uSJs7Oz7LWOjk7RSbS0tDZt2kREv/76q0gkqsX4AAAAAADKiM/nE1HTpk179+5dVp+kpCRXV9dSq1+WlpaBgYFWVlZljS3o1S9r/rKs+cuw/zwAAADUXSiAwX+4XGHnrsLOXcWt2yk6CtQ3nJSPsheMUKjYJKAQ/fr127p1K8MwCxYscHV1vXr16smTJ4VC4bhx44yMjIjo9evXPj4+ffr0iY2NLWuSTp06OTo6vn///saNG7WYHQAAAABAeenr65fTOnTo0Pv375e8zuPxAgMDra2tjY2NiSgxMbGy95Vtflhs5RkAAACAssEWiABQNpbV2rCSiKSGDXLGfX63B0YsJrGIiFi+gLjcIvMUntvEyiEl1AHfffedlZXV3Llzb968OXToUNnzqlFRUR4eHq9evXr9+jURaWtre8+fT1lJZU3i6uoaFhYWHBzcs2fP2osOAAAAAKB8ZMd3PX36NC0tTU9Pr9Q+8fHxpV5XVVU1MDAgotatWxPR9evXvby8Kn7r7Ozshw8f6unpFT14DAAAAEAJYQUYANQYwc2rmn7rNf3W8169VHQWUDr29vZhYWHbt293dHQUi8VEdPny5ZCQkNevX9vY2MybNy8iImLy5MnlzGBnZ0dEsmoZAAAAAMCXLC0tjYhycnLWrFlT9DrLsu+T/nuk7H+PVJDVzPh8fnZ2dkFBARF17NjR0NDwxo0b79+/r/itT58+LRQK+/TpU7iZOQAAAIBywj9WAKDy1NQkllZEJNHTJ6I3b978/fffQUFBHkZ6c+1tiWjSpElxOnoDBgz47rvvynoaUSGYt69Ft64TEdOqHX3VQtFxvjhcLnf48OHDhw83NTXV1tbet2+frq6usbHx/+/cwrKyP1pSLZ2Sw2U7tHz48KEWIwMAAAAAKCNVVVUi0tHR2bt3b7t27UaNGkVEBQUFs2bN+jBhyn+d1CgrU/ZSS0tLIpHk5eVpampmZ2fLtmTgcrljxozZtGnTmjVrtm/fXpH75ubmrlu3jmGYsWPHyuFtAQAAANQkFMAAgIgoz8WNkUiIiFVT/2xnibFprrsnEWVnZ69csODgwYMikYiIBI16yTrweLwbN27cuHFjw4YNs2fPXijP5JXCZGdLX0YTEZmZKzrLF01DQ6OgoODrr78u3sAwsj9apcrNzSUidfXP/xEFAAAAAKjfTExMiGjGjBlr166dPXt2YmLid999N27cuIcPH1JhAew/xsbGOTk5ubm5c+bM2bJli4mJCee/xWHTp08/cODAsWPHunXrNnLkyPJvyrLsjBkz4uPjBw0aZG9v/9mQbPMWggU/EVE+EUmxHz4AAADUNmyBCKB0WC6XVVVjVdXYosdoyRnv1Ut+5D1+5D1GLK7gkHfv3g0cOPDPP/9UU1NbsGDBrVu3Cvev2759e2Bg4Pfff5+bm7t8+XLZ9hoAhUxMTHJyclJTUys1KiYmhnDUNgAAAADUUyzRsJj3w2Lee8UlfrazrP6UmJj4559/amho/Prrr/b29g8fPiQi2rqJdu+g3TsoI42IDAwMPnz4kJOTM3v27Hbt2kkkkqK1Ky0trb179woEgjlz5vz+++/l3FEoFM6YMePMmTPm5ubr16+v0DviCxh9A0bfgFVVq0h/AAAAgJqFFWAASkdk10lk16mak0i1dQt6OBGR1Mi4Iv35z6K4sTFEJOzQmQSCz/ZPTU11c3N79+6do6Pjrl27Pm1hF/9W1sowTIcOHTp06DBx4sTvv//+UWKSvakJEbEClSq+HygD7+kj7sdkIhJ2dGDVNRQdp6I6deoUHR0dGho6fPjwio+6ePEiETk4OMgtFwAAAACAwrAsXcnOISJr1U+fm/Lz869evXr//v2EhASRSGRkZNS8efM+ffo0aNCgX79+HA7n5MmTixYtmjdv3s8//ywufJYx8ELRaVNSUiwsLFauXDlw4EAPDw8iGjBgQNEODg4OW7ZsmTVr1qJFi65cubJ48WIbG5uiHSQSSWBg4KpVq16+fGlubv73338bGBjI7bcBAAAAoMagAAZQ56meO0lSCalr5Pf+/48xrJaWsHNX+d104sSJ7969Gzx48O7du7llr1SztrYODAzMWL+y+ncUt24vbWhORJKKlfS+ELyX0fwXz4hI1LJNHSqADRw48ODBg/v27at4ASwnJ8ff35/D4fTr10+u2QAAAL5wMTExp06devz4cXp6uoGBgYWFxdChQ4t9G05E+fn5hw4dunXrVmZmZtOmTdu3bz9s2LBy/lkIAJWSlpa2ZcuWvXv3yrYBL4rD4fTu3XvJkiUDfpgYcO/ewKXLos+fZ6XSkpPw+fyePXu6uLi4u7sLBIKwsLCQkJDGjRu7uLgU6zls2DALC4spU6YEBQUFBQVZW1t36tTJxMREKBTGxsZeuXIlJSWFiBwdHXfs2GFoaCindw0AAABQs1AAA6jzeC+eMRKxVFuHeg/4fO+acP78+atXr9rY2Gzbtu2zX3Po6uoaNm1KKR+JKC4uzsyqadVuKjEyRumr3ujVq1fLli0jIiJOnDgxZMiQigzZtGlTUlLSsGHDGjVqJO94AAAAX6zr169v3LhRIpEQkZGRUWpqamJiYkRExHfffSdbOCLz8ePHlStXvnnzhoh0dHSePHny5MmTyMhIHx8fLS0thaUHUKjU1NSCggJDQ0M+n1/NqXJzc7926Z+SkqKmpjZo0KBevXqZmZmpqaklJCREREQEBAQEBwdfvHix7dbtNHL0cyJ6946uXS06g7a2tp+f38CBAwuvxMTETJkyhYiWL18uKG3Pj06dOt26dWvv3r1//fXXs2fPoqOjC5tkhbRp06b16tWrmm8NAAAAoDahAKak+M+imMwMIhLZ2bP8z+9HVypu7Ftu/HsiEjdvIdXDBgVQY7Zs2UJEy5cvV1VVrUh/FZVPO3js2bNn2eo1ckwGdQSHw/n555+HDx8+Z86cr776qk2bNuX3P3v2rJ+fn6am5qJFi2onIQAAwBcoIyNj8+bNEomke/fuEyZM0NfXl0gkZ8+e3bt379GjR1u3bt22bVtZT19f3zdv3rRq1Wru3LmGhobx8fGrVq2Kior6448/vLy8FPsuAGpTRkbG33//feHChYiICKFQSEQMwzRp0qRv377fffdd69atqzbt+/fv2ZQUDw+PRYsWGRv/z1OAQ4YMWbFixb59+3755ZcHDx5Qy1Ju0bRp00OHDjVr1qzwyu3bt8eNG5eamjplypSSy78KCQSCyZMnT548OTY2Njo6Ojk5mcfjmZqatmnTRkdHp2rvBQAAAECBOIoOAKXjP7qvcvWiytWLJBRWeRJezCvZJJzk5M/3ZllORjonI53JyqryHeFLkJCQ8ODBA0tLyyo8/RccHMyyrDxSQZ3Ts2dPHx+fnJycwYMHBwUFldWNZdndu3dPmjSJYZidO3eam5vXZkgAAIAvSkhIiFAotLGxmTNnjuyEVy6X++233w4ePJhl2XPnzsm6PX/+/PHjx7IHU2Q7oZmZmS1btozL5YaFhSVX5KMHQN3HsuyePXs6deq0ZMmS8PBwDQ0NGxsbe3v7hg0bvnnzZteuXb169ZoyZUrV/kawLLtp06YtW7YUq37JCAQCW1vbsh5G/Oabb4KDgwurX48fP54xY4arq2tycvK4ceOWL19ekQDm5ua9e/ceOXKku7t7t27dUP0CAACAOgorwOATRizW+G0rEUmMTXPHTFR0HFBeN2/eZFm2d+/eFR9S0N6e06zFH3/8EfM+7t27d40bN5ZfPKhDZs2aVVBQsHHjRk9Pz379+k2bNq1z586Fm2rm5+dfunRp8+bNDx48UFFR2bZtW//+/RUbGAAAoH77999/ieibb74ptsd1ly5dTp06JWslohs3bhBRx44di+52aGxsbGNjExUVdevWrUGDBtViagAFyM/Pnzlz5smTJ7lcroeHx5gxY2xtbTmcT08YJyQknDlzZuvWrcePH799+/ahQ4datWpVkWml/53j1aBBg9HOZR58e/z4cdk/pOnNa7ocRkSU/LGw9f79+yNGjDAyMkpLS4uJiYmPjyciQ0PDZcuWjRw5sqrvGAAAAKBOQgEMAMqT39eFiKjI04WJiYlEZGlpWfFJxK3aEtH1Pw8USCQJCQkogIEMwzALFixo27bt4sWLZadt6+joWFpa6urqJiUlxcTE5OXlEZGtre26devat2+v6LwAAAD1nFgsNjQ0LHncpuxAI9nBYET06tUrIrKzsyvWzc7OLioqStYKUI+xLPvjjz+eOXPG3Nz8wIEDJfc5NDU1nTx58ujRo+fOnfvPP/8MGTIkNDS0IjsZnDlzhr6yISLZEsySJBLJzz//vGPHjk+/vhhCF0NkLwUCwciRIz98+HD58uWIiAjZRQ6H07FjR2dn57Fjx2pqalbp7QIAAADUYSiAAUDZGEbUrvhXG9nZ2URU6scnsU1rqZEJEUlMG5ZslQ2RDQcoNGDAACcnp2PHjp09e/b69euRkZGy61paWoMHD/7222+dnZ0ZhlFsSAAAgC/BkiVLSr1++/ZtImratKnsl4ULSop1k12Ji4uTY0QAJbB9+/YzZ840btw4MDCw5F+EQurq6jt27NDV1d2zZ8+YMWNCQkJ4vM98A+Pv70+LlpXVmp2dPXXq1MDAwJJNDMMcOHDAycmJiEQiUXJycnJyspaWlqmpqZqaWoXfGQAAAEB9gwIYAFROgwYNiKjUvewlhkYSQ6OyBsqGGBmV2aE26BtwO3chIqlZKSU6UBSBQODp6enp6cmybHJyckZGhoGBQVnPvQIAAEBtioyMPH78OBG5ubnJruTk5BBR0f0PZWRPO+Xm5pac5NGjR15eXiWvHz9+XFdXt5oJZQ/KcLlcAwODak4FykNpf5rJycm+vr4CgeDcuXPW1taf7b9jx47o6Ohr166dOnVq8uTJ5fTMy8u7fv267HXJP8+vXr0aPHjw06dPSw7U1dVNT09XUVEpHGJiYlLR91Nb1NTUUIqrHxiG4XK5Kioqig4CNaDwSdPq/78YlIe2traiI0BN4vP5SvuPoroCBTAAICJicnM+vRCJ2HJ7WlpadjdvODs/XcNvvaitbUHPCh0GxrJsZGQkl8utyNYf8iM1bchr3oKIhLm5VNq3M6BYDMMYGRkpuEoKAAAARERUUFBw9OjREydOSKXSUaNGtWnTRnZdJBIRUcnvstXV1WWjSk4lkUgyMzNLXudwODW4zhtLxusTpf1p7tixIzMzc+bMmSV3PiwVn8/39fW1t7dfu3bt5MmTy3lfcXFx+fn5hb8s2vP69etDhw5NSkoqOWrgwIE9evRYuHDhv//+q4S/aWzyB8mTx0TEWFpxLK0UHQdqhhL+SYNqws+0PsFPs/7Bz7SaUAADACIiJu+/apBEXH7PLl267FNX1+RyKD+PEX+mc6H79+/Hx8d37txZT0+vOjkBAAAAoBaEh4f/8ccfHz9+VFVVnTBhQr9+/QqbtLS00tPTZUd1FiVb+1VyZRgRcbncUp9HlkqlLFv+w1efV/ilQPWnAiXBMIzS/jRPnjxJRFOnTq14Qjs7OwcHh5s3bz548MDW1rasbgkJCUSsxetXnTt3bqQiKJx/9+7dMxcvETVpQuYWlJREse9k1xmGWbhw4cqVK/39/YkoMTFR2X7THj9+nHL5Ype4N0QUqW8s6dGrU6dOHA5H0bmgWpT5rydUFv4HWv/gb2h9gr+h5ahUURAFMAClw3v1gvfkERGJ2neQWDSp2iSMSMhJTSEiqaoaq/P5xexSgwbc3BwiYlU/szGFioqKg4NDpcIIbl/PO/7P9n6OQqcBlRoIn6ehKZX9fLn47zkAAADUgMzMzJ07d4aHhxNRt27dxo4dW2xxtr6+fnp6esmDXWVXSn3aqW3btpcuXSp5PSUlJSUlpZqBDQwMGIaRSCRpaWnVnAqUgZqamoaGRvX/YMhDVlbWo0ePLC0tDQ0NK5Xwm2++uXnzZlBQkIWFRVl9xGIxsWxL/yM7XAcSUUpKikQiWb169datW6lDR9qwmYjo5HHa6ktEAoFg06ZN3333XVpammxlGMMwSvKbJhQK9+7d+/vvv799+9a9xVddXPsT0dmzZ39ZuKRBgwaenp7Tp0/HDl11l66urlgsxtne9YO2trZAICCi9PR0iUSi6DhQXTweT1dXNzMzU7ZYH+o0DocjOxlEJBJlZGQoOo7SKecQ1pLwhSmA0uGkpvCjnxKRxLKppMzPR/9P0tiSkUql6hr/M0nSB/XDe4lI1MY2v/+gmk04fPhwuhJMRB8/ftSsQP+MW+EDGuhTA/0092FVviknLYXJyCAiibEJqalXeZ56Jr/3ACKUFQEAAKBmJCUlLViwICUlxcLCYvr06S1atCjZR3ZSSGpqarHrsvoTTimAeiwxMZGIGjduXNmBsiEJCQnl9JEd3PX27VvZL7OysiZPnhwSEkJEFPmQXAcQEQlFRGRgYLBv377CpxJjYmKIyNTUtLKp5OHJkydjx46NiYlhGMbW1tbF6RsiMRF17969O0dw8+ZNX1/f/fv379q1y9HRUdFhAQAAoP7D2nOAOi9vqEeuu2e+s1ut3bHwKeCQkJBnz56V3/n8+fPv3n3apoPP51f5pvwHd9X9D6n7H+Illve5EQAAAACqJjc396effkpJSendu7evr2+p1S8iki1hefjwYbHrkZGRRNSkSRU3MABQfjk5OUSkoaFRsul5fsGwmPfDYt7v+Fi8NkxEmpqa9N8qybIYGRlZWVk9f/48Li7uzZs3/fv3/1T9IiKxmLKyKCuLCvJbtWoVEhJSdE+O0NBQIqrsLh3ycPnyZWdn55iYGCcnp6tXrwYHBw8dOlTW1L179xMnTty7d2/EiBFpaWkjR448ePCgYtMCAADAlwAFMCUl1dCS6uhKdXSpGsfcsSqqsknYalQdAMqRk5MzYMCAvXv3iks7DCwzM3P58uXjxo3DZrUAAAAAyi80NDQuLq5jx44zZ84s57mlTp06EdHdu3cLCgoKL2ZmZj5+/FggEPTs2bM2sgLUOrFY/Pr1ayK6ffu2h4fHjBkz1q5dGxERIZVKiShTKr2SnXMlO+dFgbDkWNkuhcV2Ey1pwIABLMv+/PPPffv2ffHiRckOgwYNOn/+vLm5eeGVe/fuRUVFNW3atHnz5tV5d9UXHR09fvz43NzcxYsXHzlypNQKupmZmZ+f365du3g8nre3d1hYWO3nBAAAgC8KtkBUUvkuNbCaR9ipi7BTl+rPA1CWDh065F265u3tvW3btsGDB3fu3NnU1LSgoCA+Pv7y5csBAQFpaWmamppNmzal3BxFhwUAAACA8gQHBxPRt99+K/tCvyQOh0NErVu3tra2jo6O3rp165w5c7hcbkFBwa+//ioSiXr37l3q4hiAOk12qJWvr6/skK2UlJTCtVkbNmxo1KiRt7e3pUt5284/ePCAiKysrMq/0cSJE3fv3n3ixImSTQzDzJgxY/HixbK/hjJisXjp0qUsy86aNauyb6pmSaXSadOmZWVlzZs3z8vLq/zOQ4YMkfX/8ccf79y5I1seBwAAACAPKIDBJyyXm+vuSUSkoqLoLFBn2NrahoaGrly5MiwszM/Pz8/Pr2grj8cbNWrUggULdINPfyqAlfFlCgAAAAAolkQief/+PREtWbKk1A6mpqa7d++WvZ4zZ463t/e1a9fu3btnYWHx+vVroVBoZmY2bty42ksMUCtiY2NHjx795MkTLpfbu3fvxMTEqKioX375xcbG5vnz5xcuXAgPD585c2abm7do0rRSZxAKhUFBQTwer/xTr0Qika+vb6lba6ipqfn5+Q0ePLjoRZZlFy9eHBER0a5du+HDh1fnPVbfqVOnHj161KFDB29v74r0HzZsWFhY2LFjx7Zv375gwQJ5xwMAAIAvFgpg8B8OR2L5mefR4IvDsty3b4iI5fOlDc1L7dKmTZtjx47FxsYGBQW9ePEiPj6ez+ebmpra2tr27t1bT0+PiDjpabLOjFiEzRABAAAAlFBycnJZC79KMjU13bJly+HDh+/du/fvv//q6+t36dJlxIgR6urqcg0JUMtev37t4uKSnJzcpUuXX3/91cbG5ty5c67vsjgAACAASURBVOPGjfP39w8JCenRo8ekSZPu3r3r7e39+PHjsibZt29fUlJS//79ZR+OSpWWljZhwoRr166VbDIxMTlw4ICtrW3Ri7m5ubNnzz5x4oShoeHevXu5XG513mb1/fXXX0Tk4+PDVPgQh4ULFx4/fvzw4cPe3t4VHwUAAABQKSiAAUCZUlJSLP0PEVGelna6x3htbe2yepqbm//www+1GA0AAAAAapKJicmZM2cq3l9fX3/69OnyywOgcJmZmZ6ensnJyaNHj163bh2PxyMiZ2dnW1vbBw8ebNmyRbbXX8eOHQMCAob/vPIWEREVKyS/ePFi7dq1XC530aJFZd0oOjra09MzJiamZJORkdGOHTuKVr+Sk5NPnz69efPmDx8+mJubHzp0qOiRYAqRkZFx8+bNBg0adO/eveKjzM3NO3bsePv27UePHrVr105+8QAAAOBLxvl8FwD4wqSlpa1bt65Hjx4tW7aUXYmJifnqq6+cnZ337NlT9LRzAAAAAACAemnjxo0vX77s27fvhg0bZNUvImIYxtfXV11dfc2aNQcOHJBdVFNTK9zH78WLF4UzvHr1ysPDIzMz08vLy8bGptS7hIWFOTs7l1r94vF4SUlJQ4YMadWq1cCBA11dXR0cHFq3bu3j4yO7HhISUviRTYFev34tEons7e2Lnk9WEQ4ODkQUHR0tn1wAAAAAWAEGAERExAoErKoaEf11+PCytesyMjKIyLp5c1mrhoaGsbHxnTt37ty5s2PHjm2/rPymhxMRSYxNFJi5CjhPHhWcPEpETM/e1KmLouMAAAAAAIAySkhI+OOPPzQ0NHx9fYvVdVq1arVz586JEyfOnTv37t27S5YsMTIyEggEstaoqKgcB3tVVdUjR44sX748IyNj8ODBZZ2MtXPnzhUrVkgkkmLXORzOwoULPT09//rrr/Pnz0dGRiYlJcmazM3N+/XrN3LkyLZt29b0m64iWTYTk9I+G6qoMPoGRESqqiUbZUMSExPlGg8AAAC+ZCiAAQARUd6QEWKxeN68eX/9tY7P548dO3bq1KlWTZrQhpVE1KhRo8jIyIcPH/r6+l64cMFt3Phly5b9+OOPik4NAAAAAABQ886dO1dQUDB+/HgjI6OSrQMHDjx+/PjYsWOPHDly+vTpfv36WboMIqvmRFRQUDBt2rSnT5/GxMQwDDNr1qxFixaVXBqVl5fn5eV14sSJkpOrq6tv377dxcWFiLy8vLy8vMRicXJyckFBgYmJiWpplSTF4vP5RCQSiUo2SZtZC2w7ElFubi7l5hZrFYvFhcMBAAAA5AEFMAClw2rrSCytiIjV0qq1m6pcDom/GT5KnHPPwmLrnj2fdpln2cIODMPY2toeOHDg7Nmz06dPX758uZ6enoeHR0UmZ/kqjFBERMRg21UAAAAAAFB2ISEhRDRo0KCyOjg4ONy8eXPLli1//vnnyZMn6eW/5LdT1nT+/Hki6tat29KlS+3s7IqOunPnzvHjx4ODg9+/f1/qtKampgcPHix2JhaPxzM1Na3mO5IfY2NjIoqLi6vswNjYWCpr6RgAAABATUABDEDpiKxbiqyru5O71Mg4d8xEIpKqqlWkf/qTKGsex7qx+dGZ88yaW5fTc9CgQfr6+u7u7vPnz7ezs2vRosVnJ2d1dJicbCJi8XBfTVO5Esp9+4aI8ge7S3V0FR0HAAAAAKA+kB3KVf42g3p6esuXL1+wYEFYWNiZ12+O/3e9SZMmx48fNzc3Lzahj49PaGhoORM2a9bs9OnTpa45U2ZfffWVpqbmzZs38/Ly1NQq9PFT5sqVK0RUrEYIAAAAUIOwGgOgztPcsUnTb736vt1FL7J8gcTYVGJsylagKCIUCgtPXW7YsOFn+3ft2nXRokVCoXDlypVVilwVBV93z5k0M2fSTIm5Ra3dVGmJRKKrV68uWbLkbkgw90MC90PCz0uX7N27Nz4+XtHRAAAAAADqvOTkZG1tbRUVlZJN5zKyzmRmhWblyH6ppqY2cODAeRMnumprOWuoU/RzDodTrPp1/fr1vn37hoaGGhkZyfYw1BII9FRV9FRVOAxT2O3Vq1e///47W2QfjjpBIBA4Ojrm5eWdPn264qPu3bsXHR1tY2PTuHFj+WUDAACALxwKYAB1X34+k5/HFORXeYKgoKD8/MoNnzRpkoWFRXBw8KtXr6p838pRU5fq6Ep1dFneF72MTCqV/v333506dRo6dOju3bs/fPggux4SEuLt7W1razt9+vSyNlQBAAAAAICK0NTUzM3NlUqlJZumvE+Y8C7eOz6x6MVmKoI/LMzWaajQmVNa/7uV/f3790eOHJmWltatW7ePHz/KPnkdH+KSMHNSwsxJDdTVGIaZP3/+4cOHtbW1N2/e/Ouvv8r1rcnD5MmTiWjdunU5OTkV6S+VSn/66ScimjJlinyTAQAAwJcNBTAlpXI5RN3/kLr/ISYvr8qT8B8/kE3CjYutwWxQ/8g2qa8UgUDg7u5ORBcuXJBDIihddnb26NGjZ8yY8f79e0dHx02bNvXo0UPW5OvrO3XqVH19/aNHj/bo0UN2aAEAAAAAAFSBqampWCyu7LlWsn01ip7XlZ6ePmbMmPz8/Pbt21+/fr1kRU1dXX3//v3e3t59+vQ5e/bs/7F3nwFRXN/fwO8WduldARELRUTEioiIIhaa3dhBUBAsWBJrEFsQ0dgVSyJEBMEuNkCq2GPEgkpsP6OoqCC9rbDs7jwvJuHPwyIudUG/n1dwzy1nRJHhzNyrrKy8c+fOuLi4Bl9Bs+rfv/+oUaPevXvn7e1dY9WwGn9//7/++svU1HTKlCnNkB4AAAB8t1AAa6FYWR9Z6a9Y6a+ISFjvSZgF+fQkDEkewhKJZJ4/kXn+hJX+qt4rQiv14MGDeoyytbUlhNy/f7+x04Ga8Xi8sWPHxsfHGxkZxcTEnDx5csaMGcrKynTU3Nzcz88vJSVlwYIFdJ3s7Nmz0k0YAAAAAKCVGjBgACEkPj6+TqPop9AGDhxY2bJ79+6srKw2bdqkpqbWOCQsLMzR0ZH+2MTEZN++fRRFrV27tqKiop6pS8mOHTv09fWjo6NnzpxZy3tgAoFg1apVgYGBampqhw4dYrFYzZkkAAAAfG9QAIN/MYRC2QunZS+c5l5LknYu0NyysrLYbHZdR9GnhWVmZn6152fHsTxXT56rJyXDqU9+QAghxNvb+9GjRwMGDLh06VK/fv1q7KOoqLhu3bqDBw8SQhYtWvT48ePmzREAAAAA4Fvg5ORECAkNDRUKJX0mlcfjHTt2jMFgODg40C0lJSVBQUEMBiM7O/tLo0xMTKp+6uDgYGtr++rVqwsXLtQ3d+lQU1M7fvy4gYHBpUuXrKysjh49yuPxqnbg8/kxMTG2trZBQUEaGhoRERH6+vrSyhYAAAC+EyiAAQDh8/mMKmcv/x8Go9RrUanXIt5EZ/EgfSI0n8//6vwidU2hlo5QS4cw8T2nnmJjY6Oiojp16hQaGqqiolJ753Hjxq1Zs6asrGzFihWt7gxtAAAAAACp69+//4ABA54+fRoSEiLhkO3bt2dlZU2YMKFjx450y9atW8vLy2v8gVxLS+tL83h4eJB6bVMvdZ07d46NjR07duzHjx8XL15sbGw8atQoNzc3d3f3cePGmZiYuLm5PXv2zMrKKiEh4UuP9AEAAAA0IvwyGgCIlpbWl3bYEKmoilRUKSVl8RD97lctd27QiDZt2kQICQgIUFNTk6T/vHnzzMzM7t692+rODwAAAAAAaAl++eUXDoezbt26GzdufLXz2bNnAwMDlZSUfH19CSEURe3Zs+fAgQPiPVks1po1awwNDb80lY2NDYfD+fPPPxuSvLSoqqoGBwfHxMT88MMPXC732rVrYWFhISEhCQkJfD7f3t4+PDz8/Pnzenp60s4UAAAAvgt13vQMAL49RkZGderPEAgYpSXP/rylISdnbGzcRFk1Bapde/aEqYQQvmYbaedSB8+fP3/y5En37t1HjBgh4RAmk/nTTz+5u7ufO3eucg8WAAAAAACQUO/evTdv3rxkyZIpU6Zs2bJl+vTpNW6bIRQK9+7dGxAQwGAwfv/9dz09vfLy8p9++unUqVPinRUVFX/77Td7e3vmvu10C6PsM6WgWLWPrKyslpbW+/fv+Xw+h9Mq95A3Nzc3NzevqKh4//59UVERn8/X1NTU0tKSk5OTdmoAAADwfUEBDACIvb29fvoz+mNGWVm1GzBxzIy38qfC3QkpH2hhZG/f9Ak2GkpNndWhIyGE4vHI/78lfUt2+fJl8t85BJIbNmwYl8tNSsKpfgAAAAAA9TFjxoyKigpfX98ff/wxIiJi/vz5Q4cOrYwWFBQkJCQEBgY+ffpUTk5u7969I0aMyMzMdHNzu3//vvhsnTp1Cg8Pp58gpBSVGLxSQgiRkRHvqaioKBKJeDxeKy2A0WRkZIyNjZWUlAghPB6P13ruvwAAAOCbgS0QAYCMHTtWIPpvY/q6HNOlqqqKrdubwdu3bwkh3bp1q9MoeXn5zp07FxQUFBUVNU1eAAAAAADfOHpPBTMzs5SUlFmzZhkZGdGnIH/8+NHExGT+/PlPnz4dMGBAbGzsmDFj0tLSHB0da6x+WVpaxsbGVu6fQXFl//2AVcNzydnZ2RwO56tH/wIAAABA7fAGGECLI3P/DvfmVUJI2VB7gWmP+k3CKC1hv3xBCBGpawj1OtbeWUNDI1dFlRAhIaSckBoeQfz/5efnyxNCCOnXrx9TgoKZ3PmTzKxMQghv5lyqNT/DKC25ubmEEE1NTfGQsJM+kZMjhFCyNWwnQg/JyclRVq7hFDcAAAAAAPiq/v37JyYmXrp0KSoq6tq1a58oihAiEAjatW1ra2s7duxYW1tbQsiFCxcWLFjw+fNn8RlcXV03b94sU9PLXuIyMjJyc3O7dOlS446LAAAAACA5FMAAWhyGUMgo+0x/IEl//iBbIhJRXG7VRmZBvmx8FCGkwqz3VwtghBBdXV3y/i0hZOHChVv2H6ilXvL27dvADRt+G9CHENKxY8eyL8+Zl5cXFxeXkJDwi65GN2UlQoj7rJm9LAeMHDlSX19fkkurivXmNSvzAyFE0NVUpKJa1+GtGv3sZ2FhoXioomffii8PLCgoIISoqn5ff1wAAAAAAI2LyWSOHDly5MiRhJD2f78opyg9Pb37Dx/SUYqiAgMD/f39KYoSH9u+ffvt27dLvlZ0dDRFUZKf/gsAAAAAX4ItEAFaPX6/Afz+Ayt6mTdkksoXuW7cuDF8+PCYmBjxPgKBICQkZMSIEfSOfLUoLS3dtGlT7969Fy1adPHixdLSUrr96tWrfn5+lpaWXl5eX52k6rq3bt16cfEc91oS91rStcgzz549k/jKvgXt2rUjhPzzzz91GiUQCN6+fSsrK6umptY0eQEAAAAAfHf+7mrwPxPDK4ad6U95PJ67u/uG02eo8zHkwiWy8MfKnqqqqu3atcvIyEhOTpZwch6PFxgYyGAwfvjhh8ZPHQAAAOA7gzfAWiihXkeRnDwhhLBY9Z5EpNmmwrgbIYRSUmqsxOCbZ2trezwq2s3NrVOnTvb29vr6+urq6tnZ2U+ePImNjc3JyWEymaOmTallhjdv3ri4uDx79ozL5bq6uo4aNarHm+ck+xMhJDIy8lLylSNHjpw9ezYpKengwYPDhg2rZarc3Nzt27efOnWqoKBg69BBvcx7EUIOHDgQv+Lnzp07z5s3z8XFRcKNRFo1a2trQkh8fPy8efMkH/Xnn38WFRWNGDECe6cAAAAAADQWlSo36R8/fnR1dU1NTSUGhuTjB0IIKSygQ507d46IiHj+/PmsWbOWL18eHx+vrq7+1clXrVqVlZU1fvz47t27N036AAAAAN8RFMBaqHIrm4ZPUmFiVmFi1vB54Luyd+/ecS4ztm3bdu/evd9//71qiM1mjxgxwsfHp5eSAjkVXuPwd+/eOTo6Zmdn29ra7tixo3379oQQmYhXdLRnz549LPovXLhw27Zte/fudXZ2Pnz4sIODQ41TnTt37qeffiopKeFyucOHD+/XtwehKggh48aNy7p85dGjRytWrAgODj58+LCRkVFj/hG0PH379tXR0bl169ajR4969JD0WLgDBw4QQkaNGtWUqQEAAAAAfKdSUlJmzpz56dMnQgj55yWZ41EZsrW1DQoKUlFRMTQ0HD169MWLF11cXMLDw2upgVEU9euvv0ZERGhra/v5+TVD/gAAAADfPBTA4F+UjEzx8rXSzgJahGHDhg0bNuzjx4/Xr1//8OFDUVGRhoaGnp7e4MGD/z1NKv1VjQPLy8tdXFyys7OdnZ23b9/O+u/RSPpIM0IIEQoJIfLy8mvXru3ateuCBQvmzZsXFxfXpUuXalMFBgZu2LCByWR6enouXbpUQ0ODezmO3PuLEDJt2rRJq1Y/fvx43bp1169fd3R0PHr0qIWFRZP8WbQMTCbzp59+WrFihY+Pz7lz5yR56S02NjYhIaFjx44TJ05shgwBAAAAAL4rZ8+eXbRoUVlZDWciu7q6bt68mf6hncFg7Nu378OHDykpKcOHD//1119rPNzrzZs3q1evjo2NVVRUPHz4sLa2dpNfAAAAAMB3AAUwAKiZjo7O5MmT6zQkKCjoyZMngwYN2rZtG139EolEDx8+tCoooL/XpPx5y9TKWk5OjhAyefLkN2/ebNmyZfXq1SdPnqw6z7lz5zZs2KCgoBAUFDR8+PAa1zIzMzt9+vSmTZt27drl6uqakJCgp6dXrwttHegnRu/cubN8+fIdO3ZUntlWo7S0tPnz5zMYDH9/fw6H02xJAgAAAAB880Qi0caNG/fs2SMekpGR+fXXX2fMmFG1UU5Ojq6WnTt3bvr06b169Ro1atRcDtEkhBBy5syZi8lX4uPj+Xx+x44djxw5YmJi0izXAQAAAPDtq+1XqAAAkisrK9u9ezebzd6yZQubzc7KyvLx8TE1NbWzsysv//e5SC8vry5duri5uaWmphJCfvzxR319/eTk5Dt37lTOk52d/dNPPzGZzODg4C9Vv2hMJtPX19fT0zM3N3fRokVNenVSJyMjExYW1rZt24iICBcXl5ycnC/1jIyMHDVqVHFx8bJly760vSQAAAAAANRDaWnprFmzaqx+qampnTx5slr1iyYnJxcUFHTkyJGuXbumpqb6+/s/efKEDq1duzYqKkpWVtbHx+fatWuofgEAAAA0IhTAAKBxXLt2raCgwMHBwdDQMDg42MLCIjg4uLCw0MbGpnLLvuHDhnE4nJiYGDs7u8WLF4tEonnz5hFCzp8/XznPjh07SkpKZs+ePWzYMEnW9fPz69Kly40bN5KSkr7eu7RE9L/nov89J/l59blIqdLV1b148aKRkVFCQkK/fv38/f0fPnxIURQdzc/PP3XqlJOT05w5cz5//uzr67t8+XLpJgwAAAAA8C358OHDmDFjYmJixEMGBgYxMTHW1ta1DHdwcLh+/fqVK1dWr179Wkn1dFbuxYISl1nux44de/LkyZIlS+Tl5ZssdwAAAIDvEbZABABCCBHodRTRt1usr39bEOno8lw9CSEiuf+7Q0tOTiaEODo6rly58tChQxwOZ8GCBQsXLlRXV+fs3kT4FYSQbdu3+3Pljh8/vmXLlqNHjz5//px+dvLKlSv0JHw+/+TJk7KyskuWLJEwczab/fPPP7u7u4eHh3+1ZsZMf1Vx9gQhhGEznFhYSbhEy6Gvrx8bG7tly5aQkJDdu3fv3r1bRkZGU1OztLS0qKiI7mNqaurn5zd48GDppgoAAAAA8C1JSUlxc3PLzs4WDw0dOjQoKEhZWVmSeUxNTU1NTSs/HdJY+QEAAACAGBTAAIAQQvgDbSTvTHG5Qi2dao3v378nhNy7d+/QoUNt27YNDQ01NzcXH8vhcFxdXR0dHd3c3FJSUnx9fVVUVDIyMujon3/+WVRU5ODgoK6uLnk+dnZ2CgoKycnJfD7/mz/ySllZ2d/ff+7cuefOnUtISPjnn38+ffrE5XKNjIz69+/v6Og4fPjw2k8IAwAAAAAAGp/PT09Pz8nJYTAYmpqanTt3ZrNr+D3J0aNHly9fzufzxUOenp4bNmygj0AGAAAAgBYFBTCAFkfYvkP54GGEEJGObr0noRhMSlaOEELJSPTPXP54GOtdOiGkZP4SSkGxHivm5eURQg4fPqygoHDq1Klu3br9XzLyCgx+ASGE/Hdb2KZNG3q/vitXrqirqxcWFpaVlcnKyr548YIQYmFhUaeluVxur169bt68mZGRoa+vX4/kW5327dsvWLBgwYIF0k4EAAAAAKBVunr1amho6OXLl0tLSysbVVRUhg0b5uHhUXlLIhQKAwICajz0i8PhbNu2bdq0ac2UMQAAAADUEQpgAC2OUEdXWJfSF7OwgBBCMRiUskplo6idbsnCZj0Cin5nSyQS+fv7V61+EboAVlBACKGq7K+ooKDwxx9/DB48OD8/X05OTlZWlhCSlZVFCNHS0qphATl5kYoq+UJJT1tbmx7+nRTAAAAAAACgfj5+/Lh48WJ6C3d5efnBgwdra2tTFPXhw4d79+5FRkZGRkaOHDlyx44dbDbby8urxsOGNTU1Q0ND6/roHgAAAAA0JxTAAFo9+T/2M4QCkbJK6ZzFUkxDQUGBEKKlpSX5I5CGhobjx48/efKkouK/75zJyMgQQgQCgXjn8gGDygcM+tJUFRUVhJAatysBAAAAAACgPXr0yNnZOTMzU19f/+eff3ZycuJyuZVRHo934cKFLVu2REdHp6amysjIpKeni09iYmISERGhp6fXfHkDAAAAQN3hnBgAaBz0rveqqqp12v6eftmr8uAu+lP6OLE6oU8R09GpfjIZAAAAAAAALSMjY+rUqZmZmc7OztevXx8/fnzV6hchRF5efurUqTdv3hw4cOD79+9rrH45OTldunQJ1S8AAACAlg8FsBZKLvK4YuBWxcCtDF7p13t/AffWNXoS9qv/NWJuADWiT4R++fLlq1evJBwiEAguXbpECKncdr9Pnz6EEHo3Esnl5+c/evRIS0tLV7f+p6YBAAAAAMA3jKIoT0/P7OzsWbNm7dq1q/IhPHGnT5++c+dOjSFPT8+QkBB69wsAAAAAaOFQAGuhGBV8RtlnRtlnQlH1n0Uo+HcSgfDrKwqFsvFRsvFR3Ns36r8ifMdycnIIIUKhcOXKlULh1//KEUL27t378uVLWVnZoqIieg9DMzMzXV3de/fuvXjxQvKlT5w4IRAIHBwcGAxG/ZIHAAAAAIBv2/nz5+/evduzZ8+AgIAv9REIBD4+PkuWLKFvT6ricrm//fZbQEAAk4lfpAAAAAC0Dvi5Df4jEsk8vC/z8D7rxVNppwKtEl180tfXv3Llio+Pj0gkqgyVOnsUL19bvHwtxZWtbDx//vymTZvk5eVVVFSqTuLl5SUSidavX09JVv3Ny8vbuXMni8WaPXt2410NAAAAAAB8U37//XdCyNq1a790cnBxcbGrq2twcLB4SEtL6/z58z/88EPTpggAAAAAjQoFMABoHPTxXcuXL1dXVw8JCXF1dc3MzKyxZ3l5+ebNmz09PQkhe/bsyc/P19TUlJGRoaMeHh4dO3ZMSEjYvXv3VxetqKjw8PDIy8tzdnbu2rVr410NAAAAAAB8O7Kzs+/fv6+npzdo0KAaO7x+/drBwSEhIUE8xGAwIiMj+/bt28Q5AgAAAEAjQwEMABqHmZkZIeTFixcxMTGGhoZxcXH9+/f39fW9detWUVERIaSsrOzJkye7du2ytLTcvn27goLC4cOHNTU1+Xw+PZbG5XJDQ0MVFBQCAgI2btxY9U2yavLy8iZPnnzjxg0zMzN/f/9muEYAAAAAAGiNHjx4IBKJbGxsatw1/cqVK3Z2djVuw66jo0NRVGFhYePmwygpZhYWMAsLyJfvdwAAAACggVAAA4A6YxQX/7th5vt3lY0ODg6EkMjIyA4dOsTFxS1YsEAoFB48eHDs2LEGBga6urp6eno2NjYbN27MyMgYOXJkUlKSo6PjiRMnCCGOjo5V5zc1NQ0NDVVWVt61a9fw4cMTEhIEAkHVDoWFhUFBQQMGDKCrXxEREXJycpJkTnXpylm5jrNyHbEc2Ah/EAAAAAAA0BpkZWURQnR1dcVDYWFh06dPLygoqNbOYDAWLVo0evRoQsiXNreoN+6FMwoH9ygc3MP4zGvcmQEAAACgUs07XwPA94aZ84n+gPGZRyko1tIzLy/vw/WrA148JoS81NAqsRluYGBACOncubOtrW1ycnJoaOjs2bPXrVs3b968mJiYxMTEN2/efPr0SVVVVUdHx9raeuTIkSYmJoSQJ0+enDx5Ul1dfdy4cdVWsbGxiY2NXbhw4d27d6dPn66qqtq7d28tLS2BQPDmzZvU1NSKigomk+ni4hIQECBh9YsQQslwGEpKhBCKxyM83GoCAAAAAHwX+Hw+IaRy33WaQCBYs2ZN8McsEhpBCCEHfyNXLtMhLpe7c+fOSZMm+fn5VQ5vuKtXr0ZGRiYkJEQMGzS4gy4hpHfv3oa9eo8cOXLKlCmysrJfnQEAAAAAJNcKCmDp6ennzp17/PhxQUGBhoZGhw4dfvjhB/q351WVlZWFh4ffvn27qKjIwMCgV69eEydOZLFYUskZoCEY5WWMsjJCCCUnT3E4zbMopaD477OH//89YVWxsbG//fbb7du3bdq3i5kyjhCSkJDw08rVhoaG06dP9/T0XLt27bVr13755Ze+ffv27t27bdu2M2fOnDlzZo2zFRYWenh4CIXCpUuXqqioiHcwNDSMiYmJjo4+evTotWvXkpOTK0MaGhr29vZz584V/1YAAAAAAABQDX1iMf0eGC0/P9/Dw+P69etkyjSi044QQhQU6JC2tnZYWFjv3r3Jf+9+0cMbFYHJkwAAIABJREFU4sWLFytXrrxx4wYhREZGpvIZPllZ2eTk5OTk5B07dqxbt27ChAkNXAgAAAAAKrX0AtiNGze2b98uFAoJIW3bts3Ly8vMzExJSZkyZcr06dMru+Xk5GzYsOH169eEEBUVlb///vvvv/9++PChj4+PkpKS1LIHqBeZRw+4VxIIIWX2oyt69K7fJMy8XM6NZEKIsEOnil7mX+1Pycn/+wG7hgJYVlbWnDlzbt68SQjR0tKysbGh27t169Y9MzctLc3Pzy84OHjfvn3r169fs2bNlClTgoKCKruJ+/Dhg5ub28uXL4cNG+bh4fGlbgwGY9SoUaNGjeLxeG/fvs3MzJSVldXS0urQoQPK2wAAAAAAICFjY2NCyF9//UV/+s8//7i4uLx8+ZIQQs6eITFRhBBSVkYIMTMzO3LkSOVmibdv32YymV26dGnI6pcvX/b09CwqKjIyMvrxxx/t7e11Lp0n79IJITdu3Lid9ndQUFB0dPScOXNSU1PXrVuHmx0AAACARtGizwArLCzctWuXUCgcNGjQ4cOHg4ODT5w44e7uTgg5ceLEo0ePKnvu3Lnz9evXpqamhw4dOnLkyG+//aanp5eWlvbHH39IL32AZvJ54jTeJJeyUf8+Ksjj8aKiog7tDZR5/kTm+ZMHUReDgoLevn1b7/mfP39uZ2d38+ZNExOTo0ePPnr0aOHChXTIysoqOTn51q1bo0eP/vDhw+TJk1VVVRcvXpyfnz916tSlS5e+f/++2mylpaV79+61sbFJTU21trYODg6W5O5OXl6+a9euQ4YMsbS07Ny5M24IAQAAAABAckZGRvr6+o8fP3758mVycrK9vf2/1S9CCJ9PiotJcTGpqBg7dmx0dHRl9evu3bvv3r3r06dP27Zt6730nTt3ZsyYUVxcvGTJkmvXrk2ePLnqBhgsFsvKyiokJOT06dPq6uoHDhzw9/dvwIUCAAAAwP9p0QWwhIQEPp9vYmKyZMkSdXV1QgiLxRo3btzYsWMpioqKiqK7PXv27PHjx4qKiqtWrdLU1CSEtGvXbu3atSwWKzk5OTs7W5rXAND0hB06CzvpC3X18vLy1qxZ06VLl1mzZkVGRtLR58+fr1q1qm/fvmPHjr17925dJ8/NzZ02bdqHDx+mTJmSmJg4YsQIJrP69w0jI6NDhw7t2bOHwWD89NNP1tbW+/btU1JSorcNsbOzW7JkSUBAgI+Pz+TJk42NjX/55ZeSkpJ58+adOnVKUbG288YAAAAAAAAahbOzM0VRc+bMmT59emFhYbUog8FYvnx5UFBQ1QOGN27cSA+s96J5eXlubm58Pn/Tpk0+Pj5s9he34Rk8eHB0dLSamtrevXsrf90BAAAAAA3RordApB/IGjJkSLW3PaysrM6dO1f5uNatW7cIIebm5lV3O9TS0jIxMUlLS7t9+/bo0aObMevGwTe3ZHTtTgghXG69JxEYGouUVQkhIm2dxkoMWqxbt27NmjUrLy9PQUFh1KhRU60sSdZbQoiNjc1i4+4XLly4deuWk5OTt7f3mjVrxItYX7J06dJ3796NHz8+MDCQwWDU0nPatGlsNnv+/Plz5sxJSUmxs7Pbv39/ZGTkgwcPHjx4UNlNVVV13LhxixcvNjIyasj1AgAAAAAASG7WrFnbt2+vupdMJXl5+f37948cObJq4759+27cuNGlS5epU6fWe9EdO3bk5OQ4OzvXsvF7JUNDw99++23KlCnr16+3s7PjNNeB0AAAAADfqhZdABMIBJqamu3bt6/WLiMjQwihDwYjhPzzzz+EkD59+lTr1qdPn7S0NDra6ggMGrTDOE2ooyvU0ZW0N4Mh1NIhhFAabRq+NDSz6OhoT0/PiooKFxeXVatWtWnThvX+HTkaQghp37796tnzfHx8Tp06tXbt2r179759+zYoKEiSGlhKSkp0dLSenh79dtdX+0+aNOn69evHjh3bs2fP6tWrV61atWrVqpcvX6anp2dnZ6uqquro6HTv3r2Wxx4BAAAAAAAaXV5enru7O4/HEw/p6OgcOXKkZ8+eVRuDg4M3bNggJyd34MCBet+/FBcXh4SEKCoqrl69WsIhQ4cOHTFiREJCwrlz5yZPnly/dQEAAACA1qJ/Df2lnxHpc2sNDAzoTz98+EAIoTc/rIpuET+CCGpEsdk8V09pZwH1kZaWNn/+fKFQuHPnThcXlxr7sFisqVOnWlhYTJky5cKFC4aGhj4+Pl+d+fDhw4SQZcuWycrKSpiMj4/PmTNnjhw58vPPP9M3ioaGhoaGhpJeDAAAAAAAQKN6+vSpi4tLjeci9+vX7/Dhw1WP+Hr16pWfn190dDSXyz1w4ECPHj3qvW5iYiKfz58wYYL47ytq4e7unpCQcOnSJRTAAAAAABqoRRfAavTw4cMzZ84QQsaPH0+3lJaWEkKq7n9Io88WqvEJr+fPn9d4rmxgYGDDTySiX5RhMpmqqqoNnApaAvpNqeb8alJyciJCCCHy8vKMr61LUdTy5ct5PF5AQMCCBQv+r70wn56Ew+HI/jdJnz59oqKiBg4cuHv37hkzZnTv3r2yv4jNpgghhCgrKzOUlAkhAoEgMTGRy+XOmDGj2r8vSlFRfHKaqqrqkCFD4uPjnzx5Mnjw4HpcfpOqfI9NVlYWO4p8G1gsFr7ffjMqdzxWVlamKEq6yUDD0d9yFRUV8dX8lrDZbHzLBYDWJSkpydPTs7i4WDzEYDA4HE5oaKiurq5IJMrIyLh+/frdu3dFIlH79u2Dg4P79u3bkKXv3LlDCBk2bFidRg0aNIjD4dy+fbshSwMAAAAAaV0FsPLy8hMnTkRGRopEImdnZzMzM7q9oqKCEFL1oFqavLw8PUp8Kh6P9/TpU/F2BoPRWJuzNeJU0BI051dTyGTS5SUmk8n62rpnzpy5e/euubn5zz//XHWXQhGLVTlJ1eRNTU39/PwWL168du3aCxcuVLZXMBj0ryfZbDaDzSaEvH//Pi8vz8rKSk1NrdqiX5qcNnTo0Pj4+LS0tKFDh0p+1c2MyWRKfhAatHAMBgNfzW9MtbM/oVXDV/Mbgx9xAaB1OXjw4Jo1a0QiUbV2BoMxYMCAly9f3rx58+bNm1VD7dq1c3d3nzNnjuTbYHxJZmYmIaRDhw51GsXlcrW1td+9e8fn8/HQHgAAAEBDtJrb15s3b/7xxx85OTmysrIeHh729vaVISUlpYKCgs+fP1cbQr/7Jf5mGMC3JCIighCydu1aSc7oos2dO3fTpk2XLl3Kzc3V0ND4UrePHz8SQnR1JT5G7j/0uX303qQtDZWdJfr7MSGE0Umf2Ulf2ukAAAAAAECT4PP5S5cuPX78uHhIQUHhwIEDjo6OIpHo/v37T548yczMZDAYOjo6ZmZmPXr0kPzeqnb0djUKCgrioXLbEeTzZ0IIJVv9WV56CEVRPB4PBTAAAACAhmgFBbCioqIDBw7Qz2RZW1vPnDmz6vbchBB1dfWCgoKSkpJqA+kW8ZdXCCE9evS4fPmyeHtFRUVubm4DE1ZXV2cwGCKRKD8/v4FTQUsgJycnLy/f8L8YkuPwePRdTklJiaDWdSsqKuLi4hQVFc3NzatlyCwslCeEEFJeXl4oNomdnV1YWNiZM2d++OEHuoXd25xh1JUQUsrjUfwKQkhhYSE9vIZrV9ckK9b9+7FYlN5dpKysrDn/0CTx7Nkz3l+3Bme9I4SkqrUt7GPRu3dvvDnU2qmoqAiFQvH/AqA1UlJSon/LU1BQIBQKpZ0ONBSbzVZRUSkqKqJf1odWjclk0j9UV1RUFBUVSTudFqeWJ4oAQCo+ffrk5uZ29+5d8VCHDh3Cw8NNTEwIIUwm09zc3NzcvInSoH93kZ2dbWxsXC0k1NKpZeCnT5+4XK6KikoTJQYAAADwnWjpBbBPnz6tXLkyNze3Q4cOCxYs6Nq1q3gf+hyCvLy8au10/anG21EWi6WsrCzenpub21jHVFAUhRMvvg3017E5v5pV16p93aysLB6P169fPxkZmS/1rPGvYq9evcLCwl69elUZEikoEiaLECIiDEJR5L+7tY8fP9b12t+/f08I0dbWbiH/BPh8fmho6MGDB9PT0yd1NRo8xoEQEhUV5e+zRktLy8XFxdvbG6+Ktmr4fvvtwdf021D5Hyi+mt8AyX84AQCQuidPnri4uLx79048ZGFhERoaqqmp2TyZdO7cmRDy4MEDa2tryUe9ffs2NzfXxMSksV5EAwAAAPhutehXH3g83rp163Jzc4cPH75z584aq1/kvw21U1NTq7U/fPiQ/PcTJ0ArUmHag+fqyXP1FBjV/He+UnZ2NiGkTZs24iGKyxV20hd20hdp1HB3Rxe3Pn36VNnCTU6QPxUufyqcUfbvbqLt2rVTV1d/+PBhXR/0vnHjBiGk8pQ+6Xry5Im1tfWqVavevHnTs2dPJycnut3a2nrgwIE5OTnbt2+3sLBITk6Wbp4AAAAAANBwUVFRjo6ONVa/XFxczp4922zVL0LIiBEjCCEXL16s0yi6v52dXZPkBAAAAPA9adEFsMTExPfv35ubmy9atEhGRuZL3SwsLAghd+/eLS8vr2wsKip6/Pgxh8OxsbFpjlwBGg8lryDU0hFq6VByNWwHXxW9m/wgBa7Mw/syT9OqhkSabXmTXHiTXPj9BogPpPeLU1RUrGVyFotlZ2fH5/PPnTsnefIZGRm3bt3S0NBouo1EJHf16lUnJ6fXr1/b2tpevXo1MTFx0qRJdGjw4MHnzp27e/fulClTcnNzp0+fTp+mBgAAAAAArRFFUXv27PHw8KCPA6+KxWKtWbNm586dzXyklpmZWdeuXR88eJCQkCDhkJKSkr179zKZzMrN6gEAAACg3lp0ASw+Pp4QMm7cONEX0N26d+9ubGycn5+/Z88e+siQ8vLyzZs3V1RUDB48uMbzZgG+DfQOn/M7tJONjxLGRaWmpkp4as6bN28IITo6te07TwiZNWsWg8HYtm0bfXqzJDZu3Mjn82fOnMlisSQc0kRevHjh7u7O4/FWrVp14sQJepf/atq3b7937979+/czmcxly5ZdvXq1+fMEAAAAAIAGKisr8/Ly2rBhQ+UvCiopKysfPXp00aJFzZ8Vg8Hw9fUlhKxYsYLeveOrVq5cmZOTM3HixBrvXwAAAACgTlruGWBCoTAjI4MQsnr16ho76Ojo/P777/THS5YsWbFixfXr1+/du9ehQ4dXr17x+fx27drNmjWr+TJuVMz8XAafTwgRarYl9S0kMIqLmbwSQohIRY2SlW3M/EDaXr58uWvXrtjYWPLfURw5OTkjRozQ0NAYO3bs4sWL27VrV8tw+glEKyur2lfp06fPmDFjzp8/7+3tfejQISbzKyXziIiI06dPt2nTZsGCBXW7nsZGUdT8+fOLioqWLFny008/1d554sSJIpHI29t7/vz5d+7cQdUcAAAAAKAVyczMdHV1ffDggXioU6dO4eHhxsbGzZ8VzcHBYeLEiadPn6b3nKD3oq+RSCTy8/M7efKkrq7u+vXrmzFHAAAAgG9Wy30DLDs7W/zRrS/R0dHZvXu3nZ2dnJzcy5cvVVVVx40bt2PHDiUlpSZNsunIxkfLhwXJhwVVHshUD5zUFHoS1tv0xksNpEwoFPr5+Q0aNOjEiRNlZWX6+vp0u5KSko2NTVFR0aFDh/r37793794vzZCamkqXik1NTb+63NatW/X19aOjoz09PT9/ru1vY1hY2PLly2VkZA4ePFj75orN4Ny5cw8fPuzTp8/PP/8sSf/JkydPnDjx06dP+/fvb+rcAAAAAACgsaSlpTk4ONRY/bK0tIyNjZVi9Yu2a9cuS0vL1NTUESNGXLx4kX5+sZoXL15MnTp13759qqqqYWFhNR7zDAAAAAB11XLfANPW1r5w4YLk/dXV1aX+0kmrxhAI5A/tJ4SI2mh9Hj9F2ulAzcrKymbOnJmUlKSiorJo0SIPD4+ysjJycA8hREFB4fTp0/n5+fv37//tt99++eWXZ8+e7d69u9pWhAKBwNfXl6KoxYsXS7Kimpra0aNHJ0+efOHChbS0tNWrVzs5OVWbMy0tbePGjYmJiRwOZ8+ePdbW1o14yfVDH+jl4+PDYDAkHLJq1arIyMjw8PBly5ZJPgoAAAAAAKTl/PnzCxcurPFBPVdX182bN9dymniz4XK5Z86cWbp06fHjx93d3U1MTJycnHr27NmmTZvCwsI3b97ExcVdu3ZNIBAYGRkdOXLEwMBA2ikDAAAAfCNabgEMmhtFMQsLCCGUrJy0U4Ga0VWrpKSkrl27hoeHd+zYkRCioKDAZrMJoXJycsqzs9u0aePr6zt27NgZM2acOHFCU1Oz6u4ZFEWtXr36zp07ZmZm06dPl3BdAwODhISE+fPnJyUlubu7q6urDxo0qH379nJycu/fv09JSXn58iUhpFOnTvv37+/Xr18TXHrdFBUV3bp1S1NTc9CgQZKP0tPTMzc3v3PnzuPHj3v06NF06QEAAAAAQANRFBUYGOjv7y/+QhWbzfbx8ZHKoV9fwuFwAgMDf/jhh40bN6ampj59+rRaB3V19cWLF8+ePZvD4UglQwAAAIBvEgpgAK3GsWPHIiMj9fT0zp49q6mpWdnOYrGIUCAQCOzt7UNCQnr27Nm9e/fIyEh7e/t9+/bZ2NjY2toSQkpLS5csWRIZGamhoREaGspm1+Gfv7q6+vHjx69cuXLgwIEbN26cP3++arR79+7Tp093c3NrIXdrr169qqiosLCwYNXx/LwBAwbcuXPn2bNnKIABAAAAALRYPB7P29s7KipKPKSmphYcHDx48ODmz+qrhgwZMmTIkH/++ScxMTE9PT07O1tBQUFXV9fKysrS0rJON2gAAAAAIAn8gAXQOpSVlW3evJnBYBw8eLBq9auSvLz8u3fv7O3tJ0+e7Orq2qdPn+3bt7u7u/v5+RkZGUVFRe3Zsyc7O1tPTy88PFxPT68eOdA3bMXFxX///ff79+8rKiq0tLS6dOmiq6vb4OtrTFlZWYQQLS2tGmIsNpGTJ4QwZGr47qetrU0IyczMbNr8AAAAAACgvjIyMmbMmJGWliYeMjIyCg8PrzwmuWUyMDDAJocAAAAAzQMFMIDWIS4u7uPHjyNHjjQ3N6+xg4aGxq+//vrrr78eO3bs2LFjqqqqOjo6ioqKaWlpffr0oSiKyWROmjRpw4YNGhoaNYwXVPz7gUhUeyZKSkqWlpYNupgmRj87KRAIxEOirt24/foTQng8HuHxqkXpIS3hnAAAAAAAABB39+5dNze3T58+iYdsbW2DgoJUVFSaPysAAAAAaJmY0k4AACRy6dIlQsjEiRNr6ePu7p6SkrJx40Zra+vPnz8/ffq0pKSEEKKiojJv3rzLly/v37+/xuoXn89n5OTQH/Nyc5og/WZFv8j1/v37ug7MyMioHA4AAAAAAC3KiRMnxo4dW2P1y8vL69ixY6h+AQAAAEBVKIABtDis7E8yD+/LPLzPzPu/WtSTJ08IIdbW1rWPVVZW9vLyOnv2bEZGxvPnz8+cOUMI6d27t5+fn6mpabXOIpEoMjLS2dnZwMDgTvobutHSduiwYcN27NiRn5/fmFfVjIyMjBQVFW/fvl1eXl6ngVevXiWE9OzZs2nyAgAAAACA+qAoasuWLQsWLODz+dVCbDZ78+bNGzdurOsBwAAAAADwzUMBDKDFYaX/IxsfJRsfxcp4V9mYlZUlJyenqqoq+Tzq6up0LafGQ63u3btna2s7Z86c+Ph4Lpcrq6BAt2u3a/fo0aNNmzb169cvODi4YZciHRwOZ8iQITwe7/z585KPun///rNnz0xMTFr4mQEAAAAAAN+VkpKSGTNmbN26VTykrq4eGRnp4eHR/FkBAAAAQMuHAhhAq0FRVI3tJUtWFS9fWzpnseRTnTlzZuzYsU+ePOnXr9+JEyeePn1qZmZGh+Lj42/cuDFz5kwej+fj4+Pt7S3+lGXLN2fOHELI5s2beWIHfdVIJBKtW7eOEOLl5dW0mQEAAAAAgMQ+fPgwZsyYuLg48ZCBgUFMTMyAAQOaPysAAAAAaBVQAANoHbS0tMrKyuq6LeGHDx+I2KFWSUlJ3t7eQqEwICAgJiZm6NChMjIyVTsYGxtv3bo1Li5OV1f35MmTK1asaHj+zczS0tLJyendu3fe3t4ikeir/QMCAm7fvm1iYjJt2rRmSA8AAAAAAL7qzp07w4cPf/z4sXho6NCh8fHxBgYGzZ8VAAAAALQWKIC1UGV2I3munjxXT0pWrt6T8Hv1oycRdujUeKmBdNAneN28ebNOo+j+3bt3r2zJzMz08vISiUT79u3z9PSsZayZmVlMTIy2tnZERMTx48frlbU07dq1S19fPyoqysXFpbi4+EvdhELhhg0bdu/eraSkFBQUhJMDAAAAAABagoiIiPHjx2dnZ4uHPD09jx49qqys3PxZAQAAAEArggJYCyVS0xBq6Qi1dEgDfh1PKSnRk1Cysl/vzGTy+w/k9x8o6N6r3itC03F0dCSEnDp1SvIhFEXR/emxtC1bthQVFc2ZM2fChAlfnaFdu3Z//PEHg8HYuHHj58+f6561NKmpqR07dqxz584JCQmDBw8+fvx4WVlZ1Q4CgSAuLs7W1nbPnj3q6urHjh0zNjaWVrYAAAAAAECjn1H78ccfxTdj53A4gYGBAQEBeHANAAAAAL6KLe0EoMVgscoHD5N2EvBFdnZ2urq6ly5dSklJ6devnyRDLly4cP/+fTMzs759+9IteXl5x44dU1NTW7ZsmYTrWlhYjBkz5vz582fOnHFxcaln9lKir68fFxe3ZMmSqKiohQsXrlixwtLSsmPHjjIyMm/fvv3rr78KCgoIIf3799+3b1/Hjh2lnS8AAAAAwPeupKRk2rRpFy9eFA+pq6uHhIRYWVk1f1YAAAAA0BrhDTCA1kFWVvbnn3+mKMrLy6vGbUCqefXqFV3lWrduHZP577/0+Ph4gUAwZswYFRUVyZeeMWMGISQmJqZeiUuZmppaSEhIdHT0uHHj2Gx2cnLy4cOHg4KC4uLiPn/+PHz48LCwsKioKFS/AAAAAACkLj09fciQITVWv0xMTBITE1H9AgAAAADJ4Q0wgFZj6tSp165dO3Xq1KhRo8LDw42MjL7U8++//54xY0ZBQcGiRYtsbGwq2+/fv08IGTJkSJ3WtbKy4nK59+7dq2/i0mdhYWFhYcHn8zMyMgoKCioqKjQ1NbW1tRUUFKSdGgAAAAAAEELIX3/95ebmlpubKx4aPnz4wYMHlZSUmj8rAAAAAGi9UAADaE127txZUFCQkJBgb2+/aNGi2bNnKyoqVu2Ql5e3b9++33//vby8fOrUqb6+vlWjWVlZhJD27dvXaVEZGRkdHZ03b96Ul5dzudyGX4W0cDgcExMT+raZx+PxeDxpZwQAAAAAAIQQEhYW9vPPP1dUVIiHPD09/f39K7e1AAAAAACQEApgAK0Jl8s9cuTI5s2b9+3bt3Hjxm3btllbWxsYGGhoaOTk5Dx9+vT27dsCgUBOTm7Dhg1z586tNrysrIwQIisrKz5zmf1IBp9PCKFk5cSjcnJyFEWVlZW16gIYAAAAAAC0NEKhMCAgYM+ePeIhDoezY8eOKVOmNH9WAAAAAPANQAEMoJVhsVi+vr7Tp0/fuXNnbGxsUlJSUlJSZbRNmzZjx45dvHixtra2+Ni2bdsSQrKysrp27Vp92syPjKJCQohIXZNisapFMzMz5eTk6nRyGAAAAAAAQO0KCgpmz5599epV8ZCWllZoaGjfvn2bPysAAAAA+DagAAbQ4vD7DeD3G1B7n86dO+/Zs0cgEDx8+PDjx495eXmamprt27fv3r17LXuDGBoaEkLu3r1b9WAwmszD+6x36YSQiu49iYxM1dDLly/z8/PNzMzqdzkAAAAAAADiXr9+7ezs/L///U88ZGpqGh4eXtfN2wEAAAAAqkIBDKAVY7PZdXoi0t7e3t/f//z580uWLGEwGBKOOn/+PD22PikCAAAAAACIuXLliqenZ0FBgXho4sSJO3bskJOrYW92AAAAAADJ4RRZgO9I165de/Xq9fTpU7qmJYm8vLwDBw6w2exJkyY1aW4AAAAAAPCdCAsLmz59unj1i8FgLFmy5MSJE6h+AQAAAEDDoQDWQsk8TeP8dZPz101GBb/ek7DevaEnYebnNmJu0Kr98ssvhJCVK1e+efPmq51FItGiRYsKCwtdXV319fWbPjsAAAAAAPiWCQQCHx+fpUuXVlRUVAtxudz9+/f7+fnVsqk7AAAAAIDk8GNlCyXz6D73WhL3WhLh178Axk7/h56EmZ399d4UxSj7zCj7zCgvr/eK0PJZWVnNnj07Ly9v2rRp6enptfTk8/k//vhjXFycoaHhqlWrmitBAAAAAAD4NuXn50+ePDk4OFg8pK2tffHixYkTJzZ/VgAAAADwrUIBDP7FEAgUA7cqBm6VOxEm7VygaW3YsMHBweF///ufnZ1dSEiIQCAQ75OSkjJq1Khjx45pa2sfOXJERUWl+fMEAAAAAIBvxvPnz+3s7K5fvy4e6tu3b2JiYu/evZs/KwAAAAD4hqEABvDdYbPZhw8f9vb2LiwsXLFiRe/evZcvX56VlUVH9+3bN2LECCcnpwcPHpibmyckJBgaGko3YQAAAAAAaNWSk5OdnJxq3IJi3LhxZ8+e1dLSavakAAAAAOAbhwIYwPeIxWKtX78+MTFx2LBh2dnZhw8ffvnyJR3av39/amqqvr5+YGBgdHS0tra2dFMFAAAAAIBWbf/+/dOmTSsqKqrWzmQyfX19Dx48KCcnJ5XEAAAAAODbxpZ2AgAgNWZmZsePH8/Ly7t8+XKH188JERJCfH19e1kPMjExkXZ2AAAAAADQuvH5/GXLlh07dkw8JC8vv3///pEjRzZ/VgCPquklAAAgAElEQVQAAADwnUABDOB7p66uPnHiRPnjYeRdOiFk+vTplIKitJMCAAAAAIDWLScnx83N7c6dO+IhPT29I0eOmJqaNn9WAAAAAPD9QAEMAAghhOJwKFk5QghhMKSdCwAAAAAAtG5Pnz51dnZ+9+6deKhfv36hoaFt2rRp/qwAAAAA4LuCAhhAi8NK/0fmxVNCSIVpT6GuXvMs+nnC1OZZCAAAAAAAvm2JiYleXl7FxcXioQkTJuzevVtWVrb5swIAAACA7w0KYAAtSEFBQVJSUtv/PXViiQghF+6llpn2GDp0qKIi9iQEAAAAAIBW4ODBg2vWrBGJRNXaGQzGsmXLVqxYIZWsAAAAAOA7xJR2AgBACCFv376dN29et27d5s6de/36dboxMTHRw8PD2Nh4yZIlmZmZ0s0QAAAAAACgFnw+f8GCBb6+vuLVLwUFhdDQUFS/AAAAAKA5oQDWQlEyHEpWjpKVa9CBTCz2v5OwWY2XGjS+48ePDxgw4PTp00pKSs7OzuPHj6fbp02bNnnyZDk5uSNHjlhaWkZFRUk3TwAAAAAAgBplZWWNGTPmxIkT4qGOHTvGxsY6Ojo2f1YAAAAA8D3DFogtVKMcyFRuNbjcanDD54EmtWPHjk2bNsnIyCxfvtzb21tBQYGT8ie5kkAIsbCw6D17TmFh4c6dOw8cOODu7r5p0yYPDw9ppwwAAAAAAPB/Hj16NGPGjA8fPoiHrKysQkJC1NXVmz8rAAAAAPjOoQAG/6JYrLIxEwkhIi6OI24+Z8+e3bx5s7KycmhoqLW1dY19VFRU1q9fP2DAgNmzZ/v6+urr69va2jZzngAAAAAAADW6ePGit7f358+fxUMuLi6//vorh8Np/qwAAAAAALAFIvyHyaww7lZh3E3YSV/aqXwvCgoKVq5cyWAwDhw48KXqVyV7e/v9+/eLRKJFixbVeG8JAAAAAADQnCiK2rp1q4eHh/gdCpvN3rhx486dO1H9AgAAAABpQQEMQGoCAwPz8/NdXV3t7Owk6T969OhRo0ZlZmYGBwc3dW4AAAAAAAC1KC8v9/b23rJlC0VR1UKKioqhoaFeXl5SSQwAAAAAgIYCGIB0UBR16tQpFou1dOlSyUetXLmSEHLq1KkmywsAAAAAAOArPn78OHLkyBpvTPT19RMSEiR8yA8AAAAAoOmgAAYgHWlpaR8/fuzXr5+2trbko4yNjY2NjZ8+ffru3bumyw0AAAAAAOBLHj9+7Ojo+PDhQ/GQpaVlTEyMoaFh82cFAAAAAFANCmAA0vH69WtCSO/eves6kB7y6tWrxs8JAAAAAACgVufPnx85cuT79+/FQ66urpGRkRoaGs2fFQAAAACAOLa0EwD4Tn369IkQ0qZNG/EQpawi7KRPCKGUlMSjWlpahJCsrKzGzYd7JYGVnUUI+TzqB0pOrnEnBwAAAACA1o6iqMDAQH9/f/FDv9hstp+fn6enp1QSAwAAAACoEQpgANIhLy9PCOHxeOKhCuNuFcbdvjSwtLSUEKKgoNAoaYhEonv37iUkJLgKeCZyHEJIgP+G7pYDhg4d2lhLAAAAAABAa8fj8by9vaOiosRDampqwcHBgwcPbv6sAAAAAABqgS0QAaSDPvrr7du3dR1ID9HR0WlgAhRFRUZGWlhYODk57dy5Mzs7m26PiIhwd3c3MTHx9/cvLCxs4CoAAAAAANDaffz4ccyYMTVWv/T19aOjo1H9AgAAAIAWCAUwAOno27evjIzM5cuXhUKh5KPKyspu3LihoKBgamrakNVLSkpcXFzmzJnz5s2bAQMGbNy40czMjA5t27Zt0qRJhJDdu3cPHjy4xqOtAQAAAADgO5GSkjJ8+PAa7wtsbW3j4+ONjIyaPysAAAAAgK9CAayF4t66KnvhtOyF04yyz/WeRObpY3oS1scaDigG6VJRUbGyssrJyYmOjpZ81IkTJ3g83vDhw7lcbr2XLikpGT16NH2neu7cuQsXLnh5eSkrK9NRR0fH/fv3//XXXxMmTPjw4cPo0aNv375d77UAAAAAAKD1Onv27IQJE+gDjKtxdXU9evSoiopK82cFAAAAACAJFMBaKNa7NzLPn8g8f0Lq8npQNcycbHoSRnHx13uLRHRnVvqreq8IdbJw4UJCiL+/P32s11fl5eVt2bKFwWDQA+uHoqi5c+empaUNHDjw0qVLAwcOrLGbjo7O77//vnr16s+fP8+cOTMjI6PeKwIAAAAAQKtDUdSWLVu8vLzKysqqhdhs9ubNm7dv385m41hxAAAAAGi5UACDfzGEQvp1Me61JGnn8r2wsbGxt7d//fr1vHnzBAJB7Z35fL6Hh8enT5+mTJnSs2fPei967ty5uLg4Q0PD0NDQrz6tuXjx4tmzZ+fm5q5Zs6beKwIAAAAAQOtSWlrq5ua2detW8ZC6uvqpU6c8PDyaPysAAAAAgDpBAQxAmvbu3WtgYHDp0qWpU6fm5eV9qVtmZua4ceNu3LhhZma2ZcuWei8nEokCAgIIIdu2bZNwr5J169bp6upGR0enpqbWe10AAAAAAGgt3r9/P3r06EuXLomHTExMEhISrK2tmz8rAAAAAIC6QgEMQJpUVVVPnTrVrVu3q1evWlhY7Nq16927d1U7vH79etOmTZaWlikpKebm5sePH5eTk6v3cvfv309PT+/fv/+Xdj4UJysru2DBAoqizpw5U+91AQAAAACgVbhz587w4cMfP34sHho6dGhUVFSHDh2aPysAAAAAgHrAht0AUqanpxcTE+Pn53fkyJGNGzdu3LixY8eO2traFEV9+PCBPnyLw+EsWLDAx8eHw+E0ZK2kpCRCyOjRo+s0ysnJadWqVUlJSRs2bGjI6gAAAAAALUpmZmZUVFRiYuLbt29zcnIUFBR0dHSsrKycnJz69Okj4SQlJSVxcXGxsbHPnz/Pzs5msVhaWlq9e/d2dHQcMmQIi8Vq0ktoXBEREStWrODz+eIhT0/PDRs2tK7LAQAAAIDvHApgANKnoKDw66+/enl5RUREXLp06eXLl2/evKFDJiYmDg4OM2bM0NPTa/hC9LTdu3ev06h27dppamq+efOGoigGg9HwNAAAAAAApKuoqGj79u1//PFHeXk53aKgoFBQUJCRkZGSkrJ79+4hQ4asX7/e1NS0lkmEQmFISMi2bdtyc3PpFi6XKxKJsrKyHj16FBoaamxsvHbtWjs7u2qj/vrrr5s3b3748KG4uLhNmzbt27cfNmxY165dm+hiJSEUCgMCAvbs2SMe4nA427dvnzp1avNnBQAAAADQECiAAbQUBgYGa9euXbt2LZ/Pz8rKYjAYbdu2beArX9Xk5OQQQjQ1NcVDAr2OInl5Qghh1fBtoU2bNtnZ2QUFBWpqao2YDwAAAABA83v16pWzs/PLly/l5eXnzp07atSoHj16yMnJCQSCt2/fJiQkhISEXLlyxd7efufOnZMmTapxkqKiIi8vr6SkJCaTOWHChPHjx1taWqqqqlIUlZWVdeXKlWPHjt26dcvZ2dnb23vNmjUsFovP54eEhOzatYv+sbyq9evXd+vWzdfXt1q1rHmUlJTMnTs3Li5OPKSurh4SEmJlZdX8WQEAAAAANBAKYAAtDofDaZT3vcQpKioSQoqLi8VD/IE2tQwsLi5mMpn0cAAAAACA1uvdu3cjR47Mycmxt7ffsWNH27ZtK0NsNltfX3/OnDkeHh6///67v7///PnzBQLBtGnTqk1SVlY2efLke/fuGRsbHzx4sFu3bpUhBoOhra09derUqVOnxsbGLlq0aN++fcXFxYsWLXJxcXn27BmLxbK1tbW3t+/YsaOqqmpOTs7ff/8dFRWVlpbm7Ow8ZsyYvXv3NuTc37pKT093cXF5/vy5eKhbt27h4eFNdG8CAAAAANDUmNJOAACaj46ODiEkPT29TqM+f/6cmZnZpk0bGRmZJkkLAAAAAKBZlJeXOzs75+TkuLm5hYWFVa1+VcVms729vcPDw2VkZJYtW3b//v1qHZYtW3bv3r1+/fpdunSpavWrGgcHh7i4OC0trbCwMBsbm2fPng0aNOjKlSsnT5708PAYPny4ubm5g4PD0qVLk5OTIyIiOnTocOHChbFjx5aWljbmZX/Z9evX7ezsaqx+jRw5MiYmBtUvAAAAAGi9UAAD+I7QW5ckJCTUadTly5crKiqsra2bJikAAAAAgGbyxx9/PH36dNCgQZs3b2Yyv3I7PGzYsA0bNvD5/FWrVlEUVdl+586dEydOtGvXLiwsTElJqfZJOnfuvGfPHgaDUVpa6uzsfOrUqS+d9WVnZ5eQkGBhYfHgwQNvb++qKzaRsLCwKVOm5Ofni4c8PT0PHTqkoKDQ1DkAAAAAADQdFMBaKKGWjrCTvrCTPmGy6j2JSFWNnoTCfQsQQgixtbWVl5ePjo5+//695KOCg4MJIU5OTk2WFwAAAABAk+Pz+bt372az2Zs3b2azJToOYNasWT169Lh3715iYmJl49atWwkhq1atqvFsXXHR0dF0NUtbW5vFqu3+Tl1dPTw8XF9fPzr6/7V334FNlW3jx++Tpkk3XbS0ZcjeFJAqyCylBUG0ZchoraAsHwsoCLLxZYnyIOtFtkLZKLsgS6DIUhCoyFDBwo/RMjrpbtL8/oj2xQZLupL09Pv5K9zrXKGEk6vXOffZt2vXLmMWLx6NRjNhwoSxY8fm5uYW6FKr1StWrJgzZ85zC4QAAACAheMbrYXK7hSY0Tcso2+YrgSbv+c2baFfROvDthUQQgg7O7vhw4dnZ2dPmzbNyCm7d+8+efJk/fr1e/ToUaaxAQAAAGXq1KlTiYmJgYGB9erVM3KKQqF4//33hRB79+7VtyQmJp48edLT07Nv377GrPDnn39u2rTJycnp6UUK4eLi8sUXXwghZs+erdVqjYyzSJKTk/v3779mzRrDLk9Pz927d/fq1assjgsAAACYGAUw/EWnVKaNHJc2clxmv3Bzx4IyFBERUbVq1T179ujz6sL98ssvo0ePVigUM2fOLPxiVQAAAMDCRUdHCyG6detWpFkBAQFKpfLEiRP6P54+fVqj0QQGBhp5g9TOnTs1Gs2IESMaNmz4+++/x8XFPXdK27Zt27Vrd/v27Z9++qlIoRrjxo0bXbt21f9VFODr63v48OEXX3yx1A8KAAAAmAUFMPxNknQ2tjobW51abe5QUIacnJzWr19vZ2f36aefjhs3LjMz899G7tq16/XXX09PT58wYYK/v78pgwQAAABKnX4b8Dp16hRpVqVKlTw9PePj4zUajRDi/v37RVpE//zdnj171q1bVwhx9+5dY2a99tproujP7n2uY8eOdevW7c8//zTs6tmz5969e728vEr3iAAAAIAZUQADKpwmTZp8++23lStXXrt27csvv7xy5cqn8/CMjIyoqKjg4OChQ4dmZmZOmjTpgw8+MGO0AAAAQKlITk4WQjg7Oxt2rU9Kmfng8cwHj9Py8gx7nZ2dtVptamqqECIpKUkI4eLiYjjsaFq6fpHrWdn5jbGxsTY2Ng0aNNBP0cfwXC1atNDPNWawkSIjI0NDQ1NSUgq0S5I0atSo1atX25Zg+30AAADAAhn14F8AMuPn53f48OHp06fv2bNn8uTJkydPdnNz8/DwSElJefTokf5R2PXr1585cyb3fgEAAEAeXF1dhRCJiYmGXTuSU0+mZwghhrk5OxjsbZiYmKhUKitVqiSEcHNzE0IkJCQYLnImPXPxowQhREtbdQMbtRAiNzc3KSmpatWq+VP0MQghtDqd/oiOCquWdjYFlvLw8BBCPHjwoPjv9ikajWbq1KmrV6827FKr1QsXLuzTp0+pHAgAAACwKBTAgArKx8dn9erVly9f3rFjx+HDh2/dupWQkKBQKDw9Pdu0afPaa691796d534BAABANvSFqOvXr7du3dr4WYmJiQ8fPvT29tZ/N/bx8RFC/P7778bMVSqVKpUqIyNDf1whRLVq1fRd2Tpdn1t3hRC+tjZHatcoMDE9PV0I4eDgYHyc/yYpKemdd945efKkYVeVKlUiIyP1d5sBAAAA8kMBDKjQmjZt2rRp0+nTpwshUlNT7ezslEr+WwAAAIAp2NgUvPOpGCRJEkIoFIrn7uDXrVu3xYsXHzp06L333ivQpfj7ri8bGxtba+unu44dO6bVaoOCgvTrd+nSRaVSHT58WKlUWv9zZP4XaZVKlR+Ml5fX7du3r1+/fuPGjWbNmtWo8VetK0+rzT+0YeRxcXFCiKpVq5ZwW8IbN2707dv3jz/+MOzy9fXdunWrvihoUfR/q+zHKA/5Hwpra2t+pvKgUCiUSiU/TXnIv+hZrVbrdDrzBoOS03+ZUavV/GZPBvTfb4VxX3FROD4PAP7i5ORk7hAAAABQgdjZ2eWn9yUkSZK9vX3hYwIDA728vL7//vvffvutZcuWT3fl/xLQzs7OXqXKb9doNIsWLRJCDBw4UL++vb19165d9+7du3nz5gKFtPx6mI2NTX4wHTp0iIyMnDx5shCiX79+/xfkUwUww8iPHj0qhOjcufNz31Qh9u/fP2DAAP2jywoIDQ1dvXp1qRQgy0hJ3jgskLW1dYGCMcovfQ3M3FGgNNnZ2Zk7BJQaSz65oxisrKz4UlRCnLEAAAAAAGaQmJhY8kvO3dzcJEnSarVJSUnPHTxmzJhx48YNHTp0z549arU6v13/EFx9SNZP/WJ3wYIF165da9euXbNmzR4/fqxv/PDDD/ft2zd16tTWrVvnb2kohMjMzNS/SE1NfSz+el+dO3eOjIw8ceKEu7v7wIED8xfJyMvTv9BoNPmNeklJSZs3b1YqlW3atCnQZbzIyMiPP/5Yo9EUaJck6aOPPho3blxaWlpaWlrxFi9Ttra29vb2xX7jsChqtdrR0VEIkZGRod8LFOWds7OzRqOxzP89UFROTk4qlUoIkZSUpP37sgyUX0ql0tnZOSUlJf9bDcovhUKhf3Bsbm5uSkqKucOxOO7u7sYPLvh0XwAAAAAAZCk0NNTPz+/ChQsRERE5OTmFD96+ffvcuXPt7OzmzJnzdHvTpk3feeedhISEsLCwR48eFb5I1apV9beX9e7d28hnes2dOzc5OTk0NNTNzc2Y8QXk5OSMGjVq7NixhtUve3v7devWjR8/vrRuvAMAAAAsGQUwAAAAAECFYG1tvXbt2mrVqu3atSskJOTmzZvPHJaRkTFjxoz33ntPkqSlS5c2bNiwwICZM2d27Njx6tWrQUFBJ0+efOYieXl5GzZs6Nmzp/6y+o0bN165cuW5EW7atOmrr75ydXUdP358Ed+cEEIkJia++eabmzdvNuzy9vbevXv3q6++WoxlAQAAgPKILRAtlO2OLVb37ggh0t/9j86umBt9qk+fsP75RyFEVo9gTa26pRkfAAAAAJRDHh4e+/fvDw8P/+mnn9q3bx8SEtKjR4/sWvX0vZcuXTp/8ODmzZsfPHjg5OS0YsWKLl26GC6iVCo3btz44YcffvPNNyEhIZ06dQoJCUlq6afvvXv37pfHj23ZsuXatWsKhWLatGnZ2dmfffbZ66+/vmzZsqCgoGcGptVqFy5c+Pnnn1tbW69evdrDw6Oob+3q1athYWF37twx7Hr55ZfXrl1bpO1iAAAAgPKOApiFknJzpKxMIYQoyZ74Ws1fi2iM2MlXq1WfOi6E0Dk45fyduQEAAACAzFSpUmXv3r0rV65ctGjRtm3btm3bJr5YLFq0FEKEhYWJhARJknr16jVlypSnH/FVgFqt/vLLL4OCgmbPnn38+PHjx4+LIcNF6FtCiClTpogfTgghXnrppU8++cTPz0+n0+Xm5i5YsCA0NDQoKGj48OHNW7fOX+rJkyeHDh1auHDh9evX7e3tly1b1r59+6K+qe+//37o0KFPnjwx7Ordu/eiRYuefuYZAAAAUBFQAMNfpLw81Y+nhBBaTy8KYAAAAABkTK1Wjxw5ctCgQd9///3hw4cPODmlCiGE6NSpk3+zZt27d3/hhReMWSc4OLhHjx4nT548dOjQgapV7wohhGjSpEmXF1t27969RYsW+mGSJE2cONHX13fq1KmHDh06dOiQg7u7+GaXEOK3336r336Q/nn1bdq0+fzzzxs0aFDUt7Ny5cqpU6fm5eUVaLeyspo0adKoUaOKuiAAAAAgAxTAAAAAAAAVkaOjY3BwcHBw8Ii7ceczMoUQy/53qbvSqkiLWFtb+/v7+/v7+zxOXJuYLISYNm68v+Mz9rHv3r17ly5dvv3226ioqJPnz+sbs7Ky3CtV6tKlS0hISOfOnYv6FnJycsaOHbtlyxbDLgcHh2XLlnXr1q2oawIAAADyQAEMAAAAAFChLa/qVfJFItxdI9xdCx+jUqkGDhw4cODAjLy8Glf/EEI0bdr06LVrxTtiYmLioEGDzpw5Y9hVo0aNDRs2FONmMgAAAEA2KIABAAAAAGBStgrF+Xq1hBAqSSreClevXg0LC7tz545h18svv7x27Vp3d/cShQgAAACUcwpzBwAAAAAAQMUiCVFDZV1DZe1lXZzLUvfu3fvqq68+s/oVHh6+c+dOql8AAAAABTAAAAAAAMoHnU63ePHiIUOGZGRkFOiysrKaOnXq/Pnzra2tzRIbAAAAYFHYAhEAAAAAgHIgKytr5MiRu3btMuyqVKnSqlWr/P39TR8VAAAAYJkogAEAAAAAYOni4+PDw8MvXrxo2FWzZs0NGzbUq1fP9FEBAAAAFostEAEAAAAAsGgXL14MDAx8ZvWrQ4cOhw4dovoFAAAAFMAdYBYqt1lLzQu1hRBCpSr2IpoXautUaiFEXuXKpRUYAAAAAMCUdu/ePXLkyMzMTMOu8PDwuXPn8tAvAAAAwBAFMAuV27BJyRfRVquhrVbD2NGSpPX0EkLo3KiWAQAAAID56XS6JUuWzJo1S6fTFehSKpUzZswYOnSoWQIDAAAALB8FMPxFp1RmhJM7AQAAAIBFyMjIeP/996Oiogy7XFxcVq9e3aFDB9NHBQAAAJQXFMAAAAAAALAscXFxb731VkxMjGFXrVq1NmzYULduXdNHBQAAAJQjFMAAAAAAABXaR/cfXMrMEkJse6Gqq5VV8RZZnZC0JTlVCPFJlcrt7O1KEs/58+fffvvthw8fGnb5+/uvWrWqUqVKJVkfAAAAqAgogAEAAAAAKrSb2TkxmVlCiFyDR20Z74FGq18kRat97uCcPN1njxKEEF7WyiGuzk93bd26dcyYMTk5OYazhg0bNmPGDKvilugAAACACoUCGAAAAAAAJqURusWPEoQQvrY2+QUwnU43b968efPmGY5XKpWzZs169913TRolAAAAUJ5RAAMAAAAAwMzS0tJGjBhx8OBBwy5XV9e1a9e2adPG9FEBAAAA5RcFMAAAAAAAzOn+/fthYWGXL1827Kpdu/bGjRtr165t+qgAAACAck1h7gAAAAAAAKi4zp4927lz52dWv4KCgo4cOUL1CwAAACgGCmAAAAAAAJhHYmJi7969ExISDLuGDh0aGRnp4OBg+qgAAAAAGWALRAslpadJGo0QIs/RSSiKWaeUMjOlnGwhhM7OXmdtXZrxAQAAAABK7M6dOyInp0CjSqWaP39+//79zRISAAAAIA8UwCyUbdQOq/93SwiR9p8xOvtiXvGnOn9GdfakECLzjTc19RqUYngAAAAAgGJLS0v7ty5XV9evv/76lVdeMWU8AAAAgPywBSL+Imk0dpGr7CJX2e7bZe5YAAAAAEC2bt26FRwc/MyuRo0aHTlyhOoXAAAAUHLcAYa/6XRWD+KEEFpzBwIAAAAAcnX27NlBgwYlpKcbdnXp0mXlypWOjo6mjwoAAACQHwpgAAAAAIAKLcjRoZZaJYSwlYq/S0pzW3W4q7MQooZK9W9jvv7668mTJ+fm5gqFQnz0gRBCpGcIISRJ+uCDDyZMmKAo7hOgAQAAABRAAQwAAAAAUKG95+5S8kV6ODn2cPrXm7e0Wu2cOXMWL17815/z8sTP5/UvVSrVF1980a9fv5LHAAAAACAfBTAAAAAAAMpQcnLykCFDoqOjDbs8PT0jIyNbtmxp+qgAAAAAeaMABgAAAABAWYmNjQ0NDf3jjz8Mu5o0abJ+/fqqVauaPioAAABA9theHAAAAACAMnHs2LHAwMBnVr/eeOON/fv3U/0CAAAAyggFMAAAAAAASl9kZGRoaGhKSkqBdkmSRo0atXLlSltbW7MEBgAAAFQEbIEIAAAAAEBp0mg0U6dOXb16tWGXWq1euHBhnz59TB8VAAAAUKFQAAMAAAAAoNQkJSW9++67P/zwg2FXlSpVIiMjW7RoYfqoAAAAgIqGApiFygrqIeXkCCF0NsXfEyOnuZ+mXkMhRF4ll1KLDAAAAADwL27evBkWFnbjxg3DrqZNm65fv97Hx8f0UQEAAAAVEAUwC5Xn4lbyRXSOjlpHR2NHKxS5vi2FEDon55IfGgAAAAAqmqNHjw4dOjQ1NdWwKzg4eMmSJTY2NqaPCgAAAKiYKIDhLzorq6yg18wdBQAAAACUSytXrpw2bZpWqy3QLknSRx99NG7cOEmSzBIYAAAAUDFRAAMAAAAAoPhycnI++uijzZs3G3bZ29svXbq0R48epo8KAAAAqOAU5g4AAAAAAABzCom9U/nX3yr/+tsDjaaocxMTE/v27bt582YxZLg4dlIcOynad9B3eXt77969m+oXAAAAYBbcAQYAAAAAQHFcu3YtNDT0zp07Qgixfq3YukkIITIzhRB+fn7r1q2rXLmyWQMEAAAAKi7uAAMAAAAAoMiOHDnSo0ePv6pfQojsbPHkiXjyRGg0vXr12rFjB9UvAAAAwIwogAEAAAAAUDQrV64MDQ198uRJgXZJksaNG7dixQobGxuzBAYAAABAjy0QAQAAAAAwVk5OzpgxY7Zu3WrYZW9vvxgv+VsAACAASURBVGzZsldffdX0UQEAAAAogAIYAAAAAABGSUhIGDRo0NmzZw27atSosWHDhgYNGpg+KgAAAACG2AIRAAAAAIDnu3LlSmBg4DOrXy+99NKBAweofgEAAACWgzvALJTy5u9SWpoQQtO4qU5pXbxFrOLuKR4+EEJoa9bOc6pUmvEBAAAAQEWyd+/eiIiIjIwMw66wsLDPPvtMpVKZPioAAAAA/4YCmMXR6XS//vprnR+OeKQ/EUIcS0pp/HJrW1vboq5z69Yt6+gjDR7eF0L8VKuhR6fObm5upR8uAAAAAMiaTqdbsmTJ7Nmz8/LyCnRZWVlNmjRp1KhRZgkMAAAAQCHYAtGCJCYmTp8+3dfXt3PnzteuXdM3Dh48uF69em+//faFCxeMWSQnJ2f58uXt27f38/Pbs2ePvnH+/PmNGzd+7bXXoqKidDrdMydKubmO82Y4zpthF7mqVN4OAAAAAJR32dnZ77///syZMw2rXw4ODpGRkVS/AAAAAMtEAcxSbN68uVWrVl9++eXDhw/btGnj7e2tbw8MDFSpVPv37+/WrdvIkSMzMzMLWeTcuXOtW7eeOnXq9evXGzZs2KxZM317u3btPD09f/zxx8GDB/fo0ePevXv5U/Ly8g4cODBy5Mi2bdvqWy5fvty+fftPPvnk0qVLZfNeAQAAAKAciI+P79mz5zfffGPY9cILLxw8eDAoKMj0UQEAAAAwBgUwizBjxoxRo0ZlZWUNGTLkl19+2bNnT61atfRdCxYsuHbt2oIFCzw9Pbds2dKzZ8/ExMRnLrJz587g4OA7d+507dr1xIkTJ06c6Ny5s75ryJAhly5d2rZtW9OmTc+dOxcUFHT58mUhxOnTpwMCAt56660tW7bcv39fP1iSpOvXry9dujQoKGjw4MF37twp+78AAAAAADCb99xd5nt7zvf2dFJY5Tdevny5W7duFy9eNBzfunXrAwcO1KtXz4QxAgAAACgaCmDmt2LFiiVLlri6un7zzTeffvqph4dHgQEqlSosLCw6OrpNmzYxMTGDBw/Ozc0tMObs2bMRERF5eXmfffbZhg0bGjZsWGCAJEn+/v4HDx4cNGjQw4cPQ0ND58+f36tXr19//bVVq1YrV66MiYnRj2zSpMnFixfnzJnj7e0dFRXVpUuXM2fOlNF7BwAAAACzC3J0CHd1Dnd1tlVI+pbdu3cX2DwjX3h4+I4dO3jEMgAAAGDhKICZ2bVr16ZPn25jY7N58+b8TQifydXVdevWrb6+vqdPn164cOHTXRkZGUOHDs3Jyfnss8/eeeedQhaxtraeN2/ewIED4+Li5s6dq1QqlyxZsn///pCQECcnp/xhVatWHTp06I8//jhs2LDExMQ333zzmZc9AgAAAIDM6HS6xYsXDx061HD/eaVSOWfOnPnz51tbW5slNgAAAADGowBmZjNmzNBqtVOnTm3ZsuVzB9va2n711VcqlWrp0qUPHz7Mb1++fHl8fHxwcHB4eLgxB+3Tp48kSUKIqVOn9u/fX//akFqtnj179vTp07OyssLDw5OSkox7TwAAAABQLmVkZLzzzjszZ87U6XQFulxcXLZu3Tp06FCzBAYAAACgqCiAmdOdO3eOHDlSrVq1QYMGGTmlevXqgwcPTk9P37Ztm75Fp9OtXbvWyspqypQpxqyg0+n+53/+R5/OnT179rnjIyIi3nzzzfj4+AULFhgZJAAAAACUO3Fxca+//npUVJRhV61atfbt29ehQwfTRwUAAACgeCiAmdPBgweFEG+88YZKpTJ+Vt++fYUQ3333nf6PMTExcXFxrVq1qlGjhjHTv//++5iYmObNm9vb2x87diw7O/u5Uz755BN7e/s1a9YkJycbHycAAAAAlBfnz5/v0qVL/qORn+bv73/o0KG6deuaPioAAAAAxUYBzJyuXLkihCj80V+GmjVr5ujoePXqVf0f9S/atWtn5HT99YzDhw/38/NLT0+PjY197pTKlSsHBwfn5OQcPny4SKECAAAAgOXbuXNnSEjI0/vM5wsPD9+0aVOlSpVMHxUAAACAkqAAZk4PHjwQQnh5eRVpliRJXl5eaWlpaWlp+YtUqVLFyOmnT5+WJKlLly7648bHxxszKygoSD+3SKECAAAAgIXLzc1dtGhRVlZWgXaVSrVgwYL58+crlUqzBAYAAACgJPgeb06SJP1bV0a/8EImGj6Q+Zmy23fObt+5QGN8fLyLi4uzs7N+kUJieFrNmjWFEPfv3zdmMAAAAACUF9bW1uvXr+/ateujR4/yG11dXdesWWP8ThsAAAAALA13gJmTp6enKHpVSafTxcXFOTo6Ojg4iL/v/TJykZycnMzMTP3EuLg48dStYzorq6zX+2S93ie7Q4DhRCcnJyHEkydPihQqAAAAAFi+atWqrVu3Lv/ZzA0bNjx8+DDVLwAAAKBcowBmTk2aNBFCnDx5skizLl26lJaWpp8rhGjcuLHxi6hUKmdn58ePH2dlZZ07d87BwUF/a5cQQigUufUb5dZvpH2hluFE/bWQlStXLlKoAAAAAFAu+Pn5ffHFF0KIzp07R0VFVa9e3dwRAQAAACgRtkD8B3t7+5Ivot9UUKFQ6G+0KkSvXr0mTJiwZ8+eOXPmqNVqI9ffuXOnECI4OFi/fps2bapVq/bzzz/Hx8fXqVPnudNfeOGFS5cubdy4MSMjo1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- Note the data points are the same in both plots. Only the prediction rule changes.
- The error of using Rule 1 is the total sum of squares \(E_1 = TSS = \sum_{i=1}^n(y_i-\bar{y})^2\).
- The error of using Rule 2 is the residual sum of squares (sum of squared errors) \(E_2 = SSE = \sum_{i=1}^n(y_i-\hat{y}_i)^2\).
\(r^2\): Reduction in prediction error
- For the simple linear regression we have that \[r^2=\frac{TSS-SSE}{TSS}\] is equal to the square of the correlation between \(y\) and \(x\), so it makes sense to denote it \(r^2\).
- Towards the bottom of the output below we can read off the value \(r^2=0.9353=93.53\%\), which is a large fraction of explained variation.
##
## Call:
## lm(formula = Volume ~ Girth, data = trees)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.065 -3.107 0.152 3.495 9.587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -36.9435 3.3651 -10.98 7.62e-12 ***
## Girth 5.0659 0.2474 20.48 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.252 on 29 degrees of freedom
## Multiple R-squared: 0.9353, Adjusted R-squared: 0.9331
## F-statistic: 419.4 on 1 and 29 DF, p-value: < 2.2e-16