## ETC3250/5250

Introduction to Machine Learning

### Logistic regression

Lecturer: Emi Tanaka

Department of Econometrics and Business Statistics

# Classification problems

## Classification problems

• In the previous three lectures, our outcome of interest was numeric.
• In classification problems, the response y is a categorical variable:
• Loan approval \in \{\text{successful}, \text{unsuccessful}\}
• Bankruptcy \in\{\text{paid}, \text{default}\}.
• Preferred beverage \in\{\text{Coca cola},\text{Pepsi},\text{Fanta}\}.

## Breast cancer diagnosis

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• We use the Wisconsin breast cancer data set to build a model to predict if the breast mass sample is malignant (M) or benign (B).
• Here the response is categorical with two classes (M and B).
Code
library(tidyverse)
mutate(diagnosis_malignant = ifelse(diagnosis=="M", 1, 0),
diagnosis = factor(diagnosis, levels = c("B", "M"))) %>%
janitor::clean_names()

skimr::skim(cancer, diagnosis, radius_mean, concave_points_mean)
 Name cancer Number of rows 568 Number of columns 34 _______________________ Column type frequency: factor 1 numeric 2 ________________________ Group variables None

Variable type: factor

skim_variable n_missing complete_rate ordered n_unique top_counts
diagnosis 0 1 FALSE 2 B: 356, M: 212

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
radius_mean 0 1 14.14 3.52 6.98 11.71 13.38 15.80 28.11 ▂▇▃▁▁
concave_points_mean 0 1 0.05 0.04 0.00 0.02 0.03 0.07 0.20 ▇▃▂▁▁
Code
cancer %>%
GGally::ggpairs(mapping = aes(color = diagnosis))

## Why not linear regression?

Code
cancer %>%
geom_point(alpha = 0.25, size = 2, aes(color = diagnosis)) +
geom_smooth(method = "lm",
formula = y ~ x,
se = FALSE,
color = "#027EB6",
linewidth = 1.2) +
scale_y_continuous(breaks = c(0, 1)) +
labs(y = "diagnosis") +
scale_color_manual(values = c("forestgreen", "red2")) +
guides(color = "none")
• How would we model this then?

# Concepts

## Propensity score

• Suppose we consider y_i as a binary category: y_i = \begin{cases} 1 & \text{ if $i$-th observation is in class 1}\\ 0 & \text{ if $i$-th observation is in class 2}\\ \end{cases}
• Instead of modelling the outcome directly, we consider the conditional probability, say P(y_i = 1|\boldsymbol{x}_i), also known as the propensity score of class 1.
• The propensity score of class 2 is P(y_i=0|\boldsymbol{x}_i) = 1 - P(y_i=1|\boldsymbol{x}_i).

## Odds of an event

• The odds of an event is defined as \text{odds} = \color{#006DAE}{\frac{p}{1-p}} = \frac{\text{probability that the event will occur}}{\text{probability that the event will not occur}}, where p is the probability of an event occuring.
• The ratio of the propensity scores of the two classes is the odds of being in class 1:

\text{odds} = \frac{P(y_i=1|\boldsymbol{x}_i)}{1-P(y_i=1|\boldsymbol{x}_i)}.

## Logistic function

• The logistic function:

g(z) = \frac{e^z}{1+e^z} = \frac{1}{1+e^{-z}}

• Notice that 0 < g(z) < 1 for all finite values of z.

## Logit function

• The logit function:

f(p) = \log_e \left(\frac{p}{1- p}\right)

• Here -\infty < f(p) < \infty for all p \in (0, 1).
• Note that logit and logistic functions are inverse functions of one another, i.e. f(g(z)) = z and g(f(p)) = p.

# Logistic regression

## Logistic regression for binary response

• Logistic regression is a generalised linear model where it models the log odds as a linear combination of predictors: \text{logit}(p_i) = \log_e \left(\frac{p_i}{1-p_i}\right) = \sum_{j=0}^p\beta_jx_{ij}, \quad p_i = \frac{e^{\sum_{j=0}^p\beta_jx_{ij}}}{1+e^{\sum_{j=0}^p\beta_jx_{ij}}}
• We assume that y_i \sim B(1, p_i) where p_i = P(y_i=1|\boldsymbol{x}_i).
• In generalised linear models, the link function links the predictors to the model parameters.
• In a logistic regression, the link function is the logit function.

## Maximum likelihood estimation

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• We maximise the likelihoood:

L(\boldsymbol{\beta}|\boldsymbol{y}, \mathbf{X}) = \prod_{i=1}^n p_i^{y_i}(1-p_i)^{1-y_i}.

• It is more convenient to maximize the log-likelihood:
\log L(\boldsymbol{\beta}|\boldsymbol{y}, \mathbf{X}) = \sum_{i = 1}^n \left( y_i\log p_i + (1-y_i)\log(1-p_i)\right).
Mathematical details

\begin{align*} \log L(\boldsymbol{\beta}) &= \sum_{i = 1}^n \left(y_i \log\left( \frac{e^{\sum_{j=0}^p x_{ij}\beta_j}}{1 + e^{\sum_{j=0}^p x_{ij}\beta_j}}\right) + (1 - y_i) \log\left( \frac{1}{1 + e^{\sum_{j=0}^p x_{ij}\beta_j}}\right) \right) \\ &= \sum_{i = 1}^n \left(y_i \log\left(e^{\sum_{j=0}^p x_{ij}\beta_j}\right) - y_i \log\left(1 + e^{\sum_{j=0}^p x_{ij}\beta_j}\right) - (1 - y_i) \log\left(1 + e^{\sum_{j=0}^p x_{ij}\beta_j}\right) \right) \\ &= \sum_{i = 1}^n \left(y_i \sum_{j=0}^p x_{ij}\beta_j - \log\left(1 + e^{\sum_{j=0}^p x_{ij}\beta_j}\right) \right) \end{align*}

We then solve the following to find the MLE of \beta_j

\frac{\partial \log L(\boldsymbol{\beta})}{\partial\beta_j} = \sum_{i = 1}^n \left(y_i x_{ij} - \frac{x_{ij}e^{\sum_{j=0}^p x_{ij}\beta_j}}{1 + e^{\sum_{j=0}^p x_{ij}\beta_j}} \right) = 0 assuming function below is concave.

There is no closed-form solution of the above, so we use analytical approaches (e.g. Newton-Raphson method).

## Logistic regression with a binary response

• When response is a binary value (0 or 1):
str(cancerdiagnosis_malignant)  num [1:568] 1 1 1 1 1 1 1 1 1 1 ... table(cancerdiagnosis_malignant)

0   1
356 212 
• Fit the logistic model in R as
cancer_fit <- glm(diagnosis_malignant ~ radius_mean + concave_points_mean,
data = cancer,

coef(cancer_fit)
        (Intercept)         radius_mean concave_points_mean
-13.6987232           0.6389131          84.2228367 

## Logistic regression with a factor response

• When response is a factor:
str(cancer$diagnosis)  Factor w/ 2 levels "B","M": 2 2 2 2 2 2 2 2 2 2 ... • Watch out for the order of the levels! cancer_fit2 <- glm(diagnosis ~ radius_mean + concave_points_mean, data = cancer, family = binomial(link = "logit")) coef(cancer_fit2)  (Intercept) radius_mean concave_points_mean -13.6987232 0.6389131 84.2228367  cancer_fit3 <- glm(diagnosis ~ radius_mean + concave_points_mean, data = cancer %>% mutate(diagnosis = factor(diagnosis, levels = c("M", "B"))), family = binomial(link = "logit")) coef(cancer_fit3)  (Intercept) radius_mean concave_points_mean 13.6987232 -0.6389131 -84.2228367  ## Interpretation of logistic models library(broom) tidy(cancer_fit) # coefficients # A tibble: 3 × 5 term estimate std.error statistic p.value <chr> <dbl> <dbl> <dbl> <dbl> 1 (Intercept) -13.7 1.57 -8.70 3.20e-18 2 radius_mean 0.639 0.108 5.94 2.91e- 9 3 concave_points_mean 84.2 9.96 8.46 2.75e-17 • Increasing radius_mean by one unit changes the log odds by \hat{\beta}_1, 0.639, or equivalently it multiplies the odds by e^{\hat\beta_1}, 1.894, provided concave_points_mean is held fixed. ## Threshold • We choose the threshold q such that P(y_i=1|\boldsymbol{x}_i) \ge q is considered to be in class 1. • This gives us the decision boundary: \text{log} \left(\frac{q}{1-q}\right) =\sum_{j = 0}^p\beta_jx_{ij}. • E.g., if p = 2, the boundary corresponds to: x_{i2} = \underbrace{\frac{1}{\beta_2}\left[\text{log} \left(\frac{q}{1-q}\right)-\beta_0\right]}_{\text{intercept}}\underbrace{-\frac{\beta_1}{\beta_2}}_{\text{slope}}x_{i1}. ## Linear classifier • Logistic regression is a linear classifier. • The separation in class is a point for one variable, line for two variables and a hyperplane for more than two variables. ## Out-of-sample prediction scroll data splitting code library(rsample) set.seed(2023) cancer_split <- initial_split(cancer, prop = 3/4) cancer_train <- training(cancer_split) cancer_test <- testing(cancer_split) • Using threshold q = 0.5: cancer_logistic <- glm(diagnosis ~ radius_mean + concave_points_mean, data = cancer_train, family = binomial(link = "logit")) cancer_pred <- cancer_test %>% mutate(propensity = predict(cancer_logistic, ., type = 'response'), pred50 = factor(as.numeric(propensity > 0.5), labels = c("B", "M"), levels = c(0, 1)), index = 1:n()) cancer_pred %>% select(propensity, pred50, diagnosis) # A tibble: 142 × 3 propensity pred50 diagnosis <dbl> <fct> <fct> 1 0.890 M M 2 0.694 M M 3 0.486 B M 4 0.897 M M 5 0.331 B M 6 0.999 M M 7 0.829 M M 8 0.496 B M 9 0.246 B B 10 0.999 M M # … with 132 more rows ## Assessing prediction results • We see some observations are wrongly classified – how do we summarise how well a model is in classifying? # Metrics for classification problems ## Confusion matrix • The confusion matrix, also known as classification table, tabulates the number of correct/incorrect predictions by classes of the response variable. library(yardstick) cancer_pred %>% # get the confusion matrix conf_mat(diagnosis, pred50) %>% # get the table pluck("table") %>% # add the total for each group addmargins()  Truth Prediction B M Sum B 76 11 87 M 5 50 55 Sum 81 61 142 ## What is a good classification metric? cancer_pred %>% conf_mat(diagnosis, pred50) %>% autoplot(type = "heatmap") • We want higher numbers along the diagonal entries of the confusion matrix. • But what is a single number that can summarise how good the classification is? ## Classification metrics • Note that these metrics depend on the chosen threshold q. ## Sensitivity and specificity \text{sensitivity} = \frac{\text{TP}}{\text{TP} + \text{FN}}, \quad \text{specificity} = \frac{\text{TN}}{\text{TN} + \text{FP}} cancer_pred %>% metric_set(sensitivity, specificity)(., truth = diagnosis, estimate = pred50) # A tibble: 2 × 3 .metric .estimator .estimate <chr> <chr> <dbl> 1 sensitivity binary 0.938 2 specificity binary 0.820 • Often used in the context of medical diagnostics. • Wrongful negative diagnosis could be costly for the patient! E.g. undetected cancer, missing out on early treatment. ## Precision and recall \text{precision} = \frac{\text{TP}}{\text{TP} + \text{FP}}, \quad \text{recall} = \frac{\text{TP}}{\text{TP} + \text{FN}} cancer_pred %>% metric_set(precision, recall)(., truth = diagnosis, estimate = pred50) # A tibble: 2 × 3 .metric .estimator .estimate <chr> <chr> <dbl> 1 precision binary 0.874 2 recall binary 0.938 • Terminology used more often in the context of information retrieval. • Note : recall is the same sensitivity. • E.g. search engine retrieves documents – precision measures proportion of retrieved documents that are relevant. ## Precision-recall curve cancer_pred %>% pr_curve(truth = diagnosis, propensity, event_level = "second") %>% ggplot(aes(recall, precision)) + geom_path() + geom_point(color = "pink", size = 1.3, data = ~filter(., .threshold >= 0.2) %>% arrange(.threshold) %>% slice(1)) + geom_point(color = "red", size = 1.3, data = ~filter(., .threshold >= 0.5) %>% arrange(.threshold) %>% slice(1)) + geom_point(color = "maroon", size = 1.3, data = ~filter(., .threshold >= 0.8) %>% arrange(.threshold) %>% slice(1)) + coord_equal() ## Area under the precision-recall curve cancer_pred %>% pr_auc(truth = diagnosis, propensity, event_level = "second") # A tibble: 1 × 3 .metric .estimator .estimate <chr> <chr> <dbl> 1 pr_auc binary 0.968 ## Receiver operating characteristic (ROC) curve cancer_pred %>% roc_curve(truth = diagnosis, propensity, event_level = "second") %>% ggplot(aes(1 - specificity, sensitivity)) + geom_path() + geom_point(color = "pink", size = 1.3, data = ~filter(., .threshold >= 0.2) %>% arrange(.threshold) %>% slice(1)) + geom_point(color = "red", size = 1.3, data = ~filter(., .threshold >= 0.5) %>% arrange(.threshold) %>% slice(1)) + geom_point(color = "maroon", size = 1.3, data = ~filter(., .threshold >= 0.8) %>% arrange(.threshold) %>% slice(1)) + geom_abline(linetype = "dashed") + coord_equal() ## Area under the ROC curve cancer_pred %>% roc_auc(truth = diagnosis, propensity, event_level = "second") # A tibble: 1 × 3 .metric .estimator .estimate <chr> <chr> <dbl> 1 roc_auc binary 0.976 ## F1 Score F_{\beta} = (1 + \beta^2) \times \frac{\text{precision} \times \text{recall}}{\beta^2\times\text{precision} + \text{recall}} F_1 = 2 \times \frac{\text{precision} \times \text{recall}}{\text{precision} + \text{recall}} cancer_pred %>% f_meas(truth = diagnosis, estimate = pred50, beta = 1) # A tibble: 1 × 3 .metric .estimator .estimate <chr> <chr> <dbl> 1 f_meas binary 0.905 ## Detection prevalence \text{detection prevalence} = \frac{\text{TP} + \text{FP}}{\text{TP} + \text{FN} + \text{FP} + \text{TN}} cancer_pred %>% detection_prevalence(truth = diagnosis, estimate = pred50, event_level = "second") # A tibble: 1 × 3 .metric .estimator .estimate <chr> <chr> <dbl> 1 detection_prevalence binary 0.387 • Note: this is not a measure of how good a classification is! ## Prevalence • Prevalence is the proportion of a particular population with the condition. • Assuming we have a representative sample, then we can estimate the prevalence as: \text{prevalence} = \frac{\text{TP} + \text{FN}}{\text{TP} + \text{FN} + \text{FP} + \text{TN}} table(cancer_pred$diagnosis)[["M"]]/nrow(cancer_pred)
[1] 0.4295775
• This is clearly not a representative sample of the population!

## Accuracy

\text{accuracy} = \frac{\text{TP} + \text{TN}}{\text{TP} + \text{TN} + \text{FN} + \text{FP}}

cancer_pred %>%
accuracy(truth = diagnosis, estimate = pred50)
# A tibble: 1 × 3
.metric  .estimator .estimate
<chr>    <chr>          <dbl>
1 accuracy binary         0.887
• Accuracy is the proportion of the data that are predicted correctly.

## Balanced accuracy

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\text{balanced accuracy} = \frac{1}{2}(\text{sensitivity} + \text{specificity})

cancer_pred %>%
bal_accuracy(truth = diagnosis, estimate = pred50)
# A tibble: 1 × 3
.metric      .estimator .estimate
<chr>        <chr>          <dbl>
1 bal_accuracy binary         0.879
• This metric works better if there is an imbalance in the response class.
Prediction \ Truth Positive Negative
Positive 20 70
Negative 30 5000
TP <- 20; FP <- 30; TN <- 5000; FN <- 70
(accuracy <- (TP + TN) / (TP + TN + FP + FN))
[1] 0.9804688
(sensitivity <- TP / (TP + FN))
[1] 0.2222222
(specificity <- TN / (TN + FP))
[1] 0.9940358
(balanced_accuracy <- 1/2 * (sensitivity + specificity))
[1] 0.608129

## Cohen’s kappa coefficient

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\kappa = \frac{2\times (\text{TP}\times \text{TN} - \text{FN}\times \text{FP})}{(\text{TP} + \text{FP})(\text{TN} + \text{FP}) + (\text{TP} + \text{FN})(\text{TN} + \text{FN})}

cancer_pred %>%
kap(truth = diagnosis, estimate = pred50)
# A tibble: 1 × 3
.metric .estimator .estimate
<chr>   <chr>          <dbl>
1 kap     binary         0.767
• Cohen’s kappa coefficient is similar to accuracy but takes into account that some true positives and true negatives are by chance.

Case A

Prediction \ Truth Positive Negative
Positive 45 15
Negative 25 15

Case B

Prediction \ Truth Positive Negative
Positive 25 35
Negative 5 35
# Case A
TP <- 45; FP <- 25; TN <- 15; FN <- 15
(accuracy <- (TP + TN) / (TP + TN + FP + FN))
[1] 0.6
(kappa <- 2 * (TP * TN - FN * FP) / ((TP + FP) * (TN + FP) + (TP + FN) * (TN + FN)))
[1] 0.1304348
# Case B
TP <- 25; FP <- 5; TN <- 35; FN <- 35
(accuracy <- (TP + TN) / (TP + TN + FP + FN))
[1] 0.6
(kappa <- 2 * (TP * TN - FN * FP) / ((TP + FP) * (TN + FP) + (TP + FN) * (TN + FN)))
[1] 0.2592593

## Matthew’s correlation coefficient

• Also called the phi coefficient.

\phi = \frac{\text{TP}\times\text{TN} - \text{FP}\times\text{FN}}{\sqrt{(\text{TP} + \text{FP})(\text{TN} + \text{FN})(\text{TP} + \text{FN})(\text{FP} + \text{TN})}}

cancer_pred %>%
mcc(truth = diagnosis, estimate = pred50)
# A tibble: 1 × 3
.metric .estimator .estimate
<chr>   <chr>          <dbl>
1 mcc     binary         0.770

## Postive and negative predictive values

• Positive/negative predictive value (PPV/NPV) is the proportion of cases with a positive/negative classification that are actually correct.

\text{PPV} = \frac{\text{TP}}{\text{TP} + \text{FP}}, \quad\text{NPV} = \frac{\text{TN}}{\text{TN} + \text{FN}}

cancer_pred %>%
metric_set(ppv, npv)(., truth = diagnosis, estimate = pred50)
# A tibble: 2 × 3
.metric .estimator .estimate
<chr>   <chr>          <dbl>
1 ppv     binary         0.874
2 npv     binary         0.909

## Youden’s J-index

J = \text{specificity} + \text{sensitivity} - 1

cancer_pred %>%
j_index(truth = diagnosis, estimate = pred50)
# A tibble: 1 × 3
.metric .estimator .estimate
<chr>   <chr>          <dbl>
1 j_index binary         0.758
• J index is between 0 and 1 (inclusive).

## Classification metrics

cancer_pred %>%
metric_set(sensitivity, specificity, precision, recall, pr_auc, roc_auc,
f_meas, accuracy, bal_accuracy, kap, mcc, ppv, npv, j_index)(.,
truth = diagnosis,
propensity,
estimate = pred50,
event_level = "second")
# A tibble: 14 × 3
.metric      .estimator .estimate
<chr>        <chr>          <dbl>
1 sensitivity  binary         0.820
2 specificity  binary         0.938
3 precision    binary         0.909
4 recall       binary         0.820
5 f_meas       binary         0.862
6 accuracy     binary         0.887
7 bal_accuracy binary         0.879
8 kap          binary         0.767
9 mcc          binary         0.770
10 ppv          binary         0.909
11 npv          binary         0.874
12 j_index      binary         0.758
13 pr_auc       binary         0.968
14 roc_auc      binary         0.976

# Modelling for count data of binary category

## Survival on titanic

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• Response does not have to be categorical to fit a logistic regression.
• Observation may be the count for each category as below:
Code
titanic <- datasets::Titanic %>%
as.data.frame() %>%
pivot_wider(c(Class, Sex, Age),
names_from = Survived,
values_from = Freq,
names_prefix = "Survived_")

titanic
# A tibble: 16 × 5
Class Sex    Age   Survived_No Survived_Yes
<fct> <fct>  <fct>       <dbl>        <dbl>
1 1st   Male   Child           0            5
2 2nd   Male   Child           0           11
3 3rd   Male   Child          35           13
4 Crew  Male   Child           0            0
5 1st   Female Child           0            1
6 2nd   Female Child           0           13
7 3rd   Female Child          17           14
8 Crew  Female Child           0            0
9 1st   Male   Adult         118           57
10 2nd   Male   Adult         154           14
11 3rd   Male   Adult         387           75
12 Crew  Male   Adult         670          192
13 1st   Female Adult           4          140
14 2nd   Female Adult          13           80
15 3rd   Female Adult          89           76
16 Crew  Female Adult           3           20
Code
skimr::skim(titanic)
 Name titanic Number of rows 16 Number of columns 5 _______________________ Column type frequency: factor 3 numeric 2 ________________________ Group variables None

Variable type: factor

skim_variable n_missing complete_rate ordered n_unique top_counts
Class 0 1 FALSE 4 1st: 4, 2nd: 4, 3rd: 4, Cre: 4
Sex 0 1 FALSE 2 Mal: 8, Fem: 8
Age 0 1 FALSE 2 Chi: 8, Adu: 8

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
Survived_No 0 1 93.12 183.88 0 0.0 8.5 96.25 670 ▇▁▁▁▁
Survived_Yes 0 1 44.44 56.09 0 9.5 14.0 75.25 192 ▇▂▁▁▁
Code
datasets::Titanic %>%
as.data.frame() %>%
ggplot(aes(Survived, Freq)) +
geom_col(aes(fill = Sex, group = Age), position = "fill") +
facet_grid(Class ~ Age) +
labs(y = "Proportion")

## Logistic regression with count data

titanic_fit <- glm(cbind(Survived_No, Survived_Yes) ~ Class + Age + Sex,
data = titanic,

tidy(titanic_fit)
# A tibble: 6 × 5
term        estimate std.error statistic  p.value
<chr>          <dbl>     <dbl>     <dbl>    <dbl>
1 (Intercept)   -0.685     0.273     -2.51 1.21e- 2
2 Class2nd       1.02      0.196      5.19 2.05e- 7
3 Class3rd       1.78      0.172     10.4  3.69e-25
4 ClassCrew      0.858     0.157      5.45 5.00e- 8
5 AgeAdult       1.06      0.244      4.35 1.36e- 5
6 SexFemale     -2.42      0.140    -17.2  1.43e-66

# Multi-class logistic regression

## Digit recognition with MNIST data

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• Images of single digits are rescaled to 28 \times 28 = 784 pixels.
• Labels are 0, 1, …, 9.
• This is a multi-class classification problem.
Code
dat_mnist <- dslabs::read_mnist()
mnist <- dat_mnist$train$images %>%
as.data.frame() %>%
mutate(label = as.factor(dat_mnist$train$label))

glimpse(mnist)
Rows: 60,000
Columns: 785
$V1 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V2    <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V3 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V4    <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V5 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V6    <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V7 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V8    <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V9 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V10   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V11 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V12   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V13 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V14   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V15 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V16   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V17 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V18   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V19 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V20   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V21 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V22   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V23 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V24   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V25 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V26   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V27 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V28   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V29 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V30   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V31 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V32   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V33 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V34   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V35 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V36   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V37 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V38   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V39 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V40   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V41 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V42   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V43 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V44   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V45 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V46   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V47 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V48   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V49 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V50   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V51 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V52   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V53 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V54   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V55 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V56   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V57 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V58   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V59 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V60   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V61 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V62   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V63 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V64   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V65 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V66   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V67 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V68   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V69 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V70   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V71 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V72   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V73 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, …$ V74   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 222, 0, 0, 0, 0, 0, 0, 0,…
$V75 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 225, 0, 0, 0, 0, 0, 0, 0,…$ V76   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V77 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V78   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V79 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V80   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V81 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V82   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V83 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V84   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V85 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V86   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V87 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V88   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V89 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V90   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V91 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V92   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V93 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V94   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V95 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V96   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V97 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V98   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V99 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V100  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 147, 0, 0, 0, 0, 0, 0, 0,…
$V101 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 234, 0, 0, 0, 0, 34, 0, 0…$ V102  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 169, 0, …
$V103 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 250, 0, …$ V104  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, …
$V105 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V106  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V107 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V108  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V109 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V110  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V111 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V112  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V113 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V114  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V115 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V116  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V117 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V118  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V119 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V120  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V121 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V122  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V123 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V124  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$V125 <int> 0, 0, 0, 0, 0, 0, 145, 0, 0, 0, 118, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V126  <int> 0, 0, 0, 0, 0, 0, 255, 0, 0, 0, 219, 0, 0, 23, 0, 0, 0, 0, 0, 0,…
$V127 <int> 0, 0, 0, 0, 0, 0, 211, 0, 0, 0, 166, 0, 0, 197, 0, 0, 0, 0, 0, 0…$ V128  <int> 0, 51, 0, 0, 0, 0, 31, 0, 0, 0, 118, 0, 0, 253, 0, 0, 0, 0, 58, …
$V129 <int> 0, 159, 0, 0, 0, 0, 0, 0, 0, 0, 118, 0, 0, 252, 0, 0, 0, 0, 242,…$ V130  <int> 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 208, 0, 0, 0, 0, 221, 0…
$V131 <int> 0, 159, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 143, 0,…$ V132  <int> 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 25…
$V133 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6…$ V134  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V135 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 189, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V136  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 190, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V137 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V138  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V139 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V140  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V141 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V142  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V143 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V144  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 13,…
$V145 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, 0, 0, 0, 0, 0, 0, 0, 25,…$ V146  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 91, 0, 0, 0, 0, 0, 0, 0, 10,…
$V147 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 142, 0, 0, 0, 0, 0, 0, 0, 0,…$ V148  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 155, 0, 0, 0, 0, 0, 0, 0, 0,…
$V149 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 246, 0, 0, 0, 0, 0, 0, 0, 0,…$ V150  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 182, 0, 0, 0, 0, 0, 0, 0, 0,…
$V151 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 155, 0, 0, 0, 0, 0, 0, 0, …$ V152  <int> 0, 0, 0, 0, 0, 0, 32, 38, 0, 0, 242, 0, 155, 0, 1, 0, 93, 0, 0, …
$V153 <int> 3, 0, 0, 0, 0, 0, 237, 43, 5, 0, 254, 0, 155, 38, 168, 0, 164, 0…$ V154  <int> 18, 0, 0, 0, 0, 0, 253, 105, 63, 0, 254, 0, 155, 178, 242, 0, 21…
$V155 <int> 18, 48, 0, 0, 0, 0, 252, 255, 197, 0, 254, 0, 131, 252, 28, 0, 2…$ V156  <int> 18, 238, 0, 0, 0, 13, 71, 253, 0, 0, 254, 0, 52, 253, 0, 0, 250,…
$V157 <int> 126, 252, 0, 0, 0, 25, 0, 253, 0, 0, 254, 0, 0, 117, 0, 0, 194, …$ V158  <int> 136, 252, 0, 0, 0, 100, 0, 253, 0, 0, 66, 0, 0, 65, 0, 0, 15, 0,…
$V159 <int> 175, 252, 0, 124, 0, 122, 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V160  <int> 26, 237, 0, 253, 0, 7, 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0,…
$V161 <int> 166, 0, 67, 255, 0, 0, 0, 174, 0, 0, 0, 0, 0, 0, 0, 0, 0, 203, 0…$ V162  <int> 255, 0, 232, 63, 0, 0, 0, 6, 0, 143, 0, 0, 0, 0, 0, 0, 0, 229, 0…
$V163 <int> 247, 0, 39, 0, 0, 0, 0, 0, 0, 247, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0…$ V164  <int> 127, 0, 0, 0, 0, 0, 0, 0, 0, 153, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$V165 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V166  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V167 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V168  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V169 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V170  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V171 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V172  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 138, 0, 0, 0, 0, 0, 0, 0, 13…
$V173 <int> 0, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 2…$ V174  <int> 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 1…
$V175 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 0,…$ V176  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 0,…
$V177 <int> 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 0…$ V178  <int> 36, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 254, 0, 0, 0, 20, 0, 0, 0,…
$V179 <int> 94, 0, 0, 0, 0, 0, 0, 139, 0, 0, 18, 0, 254, 0, 0, 0, 176, 0, 0,…$ V180  <int> 154, 0, 0, 0, 0, 0, 11, 224, 0, 0, 232, 0, 254, 0, 10, 0, 253, 0…
$V181 <int> 170, 0, 0, 0, 0, 0, 175, 226, 20, 0, 254, 0, 254, 57, 228, 0, 23…$ V182  <int> 253, 54, 0, 0, 0, 33, 253, 252, 254, 0, 254, 0, 254, 252, 254, 0…
$V183 <int> 253, 227, 0, 0, 0, 151, 252, 253, 230, 0, 254, 0, 254, 252, 100,…$ V184  <int> 253, 253, 0, 0, 0, 208, 71, 252, 24, 0, 254, 0, 252, 253, 0, 0, …
$V185 <int> 253, 252, 0, 0, 0, 252, 0, 252, 0, 0, 254, 0, 210, 89, 0, 0, 254…$ V186  <int> 253, 239, 0, 96, 0, 252, 0, 252, 0, 0, 238, 0, 122, 0, 0, 0, 214…
$V187 <int> 225, 233, 0, 244, 0, 252, 0, 252, 0, 0, 70, 0, 33, 0, 0, 0, 0, 3…$ V188  <int> 172, 252, 0, 251, 0, 146, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 95,…
$V189 <int> 253, 57, 120, 253, 0, 0, 0, 252, 0, 136, 0, 0, 0, 0, 0, 0, 0, 25…$ V190  <int> 242, 6, 180, 62, 0, 0, 0, 158, 0, 247, 0, 0, 0, 0, 0, 0, 0, 215,…
$V191 <int> 195, 0, 39, 0, 0, 0, 0, 14, 0, 242, 0, 0, 0, 0, 0, 0, 0, 13, 0, …$ V192  <int> 64, 0, 0, 0, 0, 0, 0, 0, 0, 86, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V193 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V194  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V195 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V196  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V197 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V198  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V199 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V200  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 220, 0, 0, 0, 0, 0, 0, 0, 13…
$V201 <int> 0, 0, 126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, …$ V202  <int> 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, …
$V203 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 79…$ V204  <int> 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 235, 0, 0, 0, 0, 0, 0, 0, 0…
$V205 <int> 238, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 189, 0, 0, 0, 0, 0, 0, 0, …$ V206  <int> 253, 0, 0, 0, 0, 0, 0, 178, 0, 0, 0, 0, 189, 0, 0, 0, 204, 0, 0,…
$V207 <int> 253, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 189, 0, 0, 0, 236, 0, 0,…$ V208  <int> 253, 10, 0, 0, 0, 40, 0, 252, 0, 0, 104, 0, 189, 38, 0, 0, 135, …
$V209 <int> 253, 60, 0, 0, 55, 152, 144, 252, 20, 0, 244, 0, 150, 222, 190, …$ V210  <int> 253, 224, 0, 0, 148, 244, 253, 252, 254, 0, 254, 0, 189, 253, 25…
$V211 <int> 253, 252, 0, 0, 210, 252, 252, 253, 254, 0, 224, 0, 205, 253, 12…$ V212  <int> 253, 253, 0, 0, 253, 253, 71, 252, 48, 0, 254, 0, 254, 79, 0, 11…
$V213 <int> 253, 252, 0, 0, 253, 224, 0, 252, 0, 0, 254, 0, 254, 0, 0, 121, …$ V214  <int> 251, 202, 0, 127, 113, 211, 0, 252, 0, 0, 254, 0, 254, 0, 0, 162…
$V215 <int> 93, 84, 0, 251, 87, 252, 0, 252, 0, 0, 141, 0, 75, 0, 0, 253, 12…$ V216  <int> 82, 252, 2, 251, 148, 232, 0, 252, 0, 0, 0, 0, 0, 0, 0, 253, 0, …
$V217 <int> 82, 253, 153, 253, 55, 40, 0, 252, 0, 192, 0, 31, 0, 0, 0, 213, …$ V218  <int> 56, 122, 210, 62, 0, 0, 0, 252, 0, 252, 0, 40, 0, 0, 0, 0, 0, 18…
$V219 <int> 39, 0, 40, 0, 0, 0, 0, 59, 0, 187, 0, 129, 0, 0, 0, 0, 0, 19, 0,…$ V220  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 234, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V221 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 234, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V222  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 159, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V223 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V224  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V225 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V226  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V227 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V228  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 132…
$V229 <int> 0, 0, 220, 0, 0, 0, 0, 0, 0, 0, 0, 0, 74, 0, 0, 0, 0, 0, 0, 0, 2…$ V230  <int> 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 2…
$V231 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 238…$ V232  <int> 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 52…
$V233 <int> 219, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 69, 0, 0, 0, 0…$ V234  <int> 253, 0, 0, 0, 0, 15, 0, 109, 0, 0, 0, 0, 0, 0, 0, 0, 253, 0, 0, …
$V235 <int> 253, 0, 0, 0, 0, 152, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0,…$ V236  <int> 253, 163, 0, 0, 87, 239, 16, 252, 0, 0, 0, 0, 0, 131, 0, 0, 0, 1…
$V237 <int> 253, 252, 0, 0, 232, 252, 191, 230, 20, 62, 207, 0, 0, 252, 83, …$ V238  <int> 253, 252, 0, 0, 252, 252, 253, 132, 254, 185, 254, 0, 0, 179, 25…
$V239 <int> 198, 252, 0, 0, 253, 252, 252, 133, 255, 18, 210, 0, 13, 27, 162…$ V240  <int> 182, 253, 0, 0, 189, 216, 71, 132, 48, 0, 254, 0, 224, 0, 0, 251…
$V241 <int> 247, 252, 0, 68, 210, 31, 0, 132, 0, 0, 254, 0, 254, 0, 0, 252, …$ V242  <int> 241, 252, 0, 236, 252, 37, 0, 189, 0, 0, 254, 0, 254, 0, 0, 252,…
$V243 <int> 0, 96, 0, 251, 252, 252, 0, 252, 0, 0, 34, 68, 153, 0, 0, 252, 2…$ V244  <int> 0, 189, 27, 211, 253, 252, 0, 252, 0, 89, 0, 150, 0, 0, 0, 252, …
$V245 <int> 0, 253, 254, 31, 168, 60, 0, 252, 0, 236, 0, 239, 0, 0, 0, 250, …$ V246  <int> 0, 167, 162, 8, 0, 0, 0, 252, 0, 217, 0, 254, 0, 0, 0, 214, 0, 9…
$V247 <int> 0, 0, 0, 0, 0, 0, 0, 59, 0, 47, 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, …$ V248  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V249 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V250  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 215, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V251 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V252  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V253 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V254  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V255 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V256  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, …
$V257 <int> 0, 0, 222, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25…$ V258  <int> 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25…
$V259 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252,…$ V260  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 181,…
$V261 <int> 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 74, 0, 0, 0, 1…$ V262  <int> 156, 0, 0, 0, 4, 96, 0, 4, 0, 0, 0, 0, 0, 0, 0, 192, 217, 0, 0, …
$V263 <int> 107, 51, 0, 0, 57, 252, 0, 29, 0, 0, 0, 0, 0, 198, 0, 226, 79, 1…$ V264  <int> 253, 238, 0, 0, 242, 252, 26, 29, 0, 0, 0, 0, 0, 246, 0, 226, 0,…
$V265 <int> 253, 253, 0, 0, 252, 252, 221, 24, 20, 216, 84, 0, 0, 220, 29, 2…$ V266  <int> 205, 253, 0, 0, 190, 252, 253, 0, 254, 253, 206, 0, 0, 37, 254, …
$V267 <int> 11, 190, 0, 0, 65, 217, 252, 0, 254, 60, 254, 0, 90, 0, 248, 253…$ V268  <int> 0, 114, 0, 60, 5, 29, 124, 0, 57, 0, 254, 0, 254, 0, 25, 202, 0,…
$V269 <int> 43, 253, 0, 228, 12, 0, 31, 0, 0, 0, 254, 156, 254, 0, 0, 252, 4…$ V270  <int> 154, 228, 0, 251, 182, 37, 0, 14, 0, 0, 254, 201, 247, 0, 0, 252…
$V271 <int> 0, 47, 0, 251, 252, 252, 0, 226, 0, 0, 41, 254, 53, 0, 0, 252, 2…$ V272  <int> 0, 79, 183, 94, 253, 252, 0, 252, 0, 212, 0, 254, 0, 0, 0, 252, …
$V273 <int> 0, 255, 254, 0, 116, 60, 0, 252, 0, 255, 0, 254, 0, 0, 0, 252, 0…$ V274  <int> 0, 168, 125, 0, 0, 0, 0, 172, 0, 81, 0, 241, 0, 0, 0, 225, 0, 8,…
$V275 <int> 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 150, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V276  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 98, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$V277 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V278  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V279 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V280  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V281 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V282  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V283 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V284  <int> 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, …
$V285 <int> 0, 0, 245, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12…$ V286  <int> 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25…
$V287 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252,…$ V288  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 68, 0, 0, 0, 0, 252…
$V289 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 223, 8, 0, 0, 0, 10…$ V290  <int> 14, 48, 0, 0, 96, 181, 0, 0, 0, 0, 0, 0, 0, 79, 0, 252, 10, 0, 0…
$V291 <int> 1, 238, 0, 0, 252, 252, 0, 0, 0, 0, 0, 0, 0, 253, 0, 252, 0, 139…$ V292  <int> 154, 252, 0, 0, 252, 252, 0, 0, 0, 0, 0, 0, 0, 252, 0, 252, 0, 2…
$V293 <int> 253, 252, 0, 0, 183, 220, 125, 0, 20, 206, 0, 0, 6, 135, 29, 252…$ V294  <int> 90, 179, 0, 0, 14, 167, 253, 0, 254, 252, 24, 0, 152, 28, 255, 2…
$V295 <int> 0, 12, 0, 0, 0, 30, 252, 0, 254, 68, 209, 19, 246, 0, 254, 39, 0…$ V296  <int> 0, 75, 0, 155, 0, 0, 252, 0, 108, 0, 254, 154, 254, 0, 103, 19, …
$V297 <int> 0, 121, 0, 253, 92, 0, 108, 0, 0, 0, 254, 254, 254, 0, 0, 39, 39…$ V298  <int> 0, 21, 0, 253, 252, 77, 0, 85, 0, 0, 254, 236, 49, 0, 0, 65, 254…
$V299 <int> 0, 0, 0, 189, 252, 252, 0, 243, 0, 48, 171, 203, 0, 0, 0, 224, 2…$ V300  <int> 0, 0, 198, 0, 225, 252, 0, 252, 0, 242, 0, 83, 0, 0, 0, 252, 104…
$V301 <int> 0, 253, 254, 0, 21, 60, 0, 252, 0, 253, 0, 39, 0, 0, 0, 252, 0, …$ V302  <int> 0, 243, 56, 0, 0, 0, 0, 144, 0, 89, 0, 30, 0, 0, 0, 183, 0, 0, 0…
$V303 <int> 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V304  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V305 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V306  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V307 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V308  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V309 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V310  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V311 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V312  <int> 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V313 <int> 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15…$ V314  <int> 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21…
$V315 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252,…$ V316  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 186, 0, 0, 0, 0, 25…
$V317 <int> 0, 38, 0, 0, 132, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 252, 0, 0, 0, 0…$ V318  <int> 0, 165, 0, 0, 253, 26, 0, 0, 0, 0, 0, 0, 0, 140, 0, 252, 0, 0, 0…
$V319 <int> 0, 253, 0, 0, 252, 128, 0, 0, 0, 0, 0, 0, 0, 253, 0, 252, 0, 55,…$ V320  <int> 139, 233, 0, 0, 146, 58, 0, 0, 0, 131, 0, 0, 66, 252, 0, 245, 0,…
$V321 <int> 253, 208, 0, 0, 14, 22, 0, 0, 16, 251, 91, 0, 158, 118, 29, 108,…$ V322  <int> 190, 84, 0, 0, 0, 0, 253, 0, 239, 212, 137, 0, 254, 0, 254, 53, …
$V323 <int> 2, 0, 0, 20, 0, 0, 252, 0, 254, 21, 253, 144, 254, 0, 254, 0, 0,…$ V324  <int> 0, 0, 0, 253, 0, 0, 252, 0, 143, 0, 254, 253, 249, 0, 109, 0, 0,…
$V325 <int> 0, 0, 0, 251, 215, 0, 108, 88, 0, 0, 254, 145, 103, 0, 0, 0, 5, …$ V326  <int> 0, 0, 0, 235, 252, 100, 0, 189, 0, 11, 254, 12, 8, 111, 0, 150, …
$V327 <int> 0, 0, 23, 66, 252, 252, 0, 252, 0, 167, 112, 0, 0, 140, 0, 252, …$ V328  <int> 0, 0, 231, 0, 79, 252, 0, 252, 0, 252, 0, 0, 0, 140, 0, 252, 141…
$V329 <int> 0, 253, 254, 0, 0, 60, 0, 252, 0, 197, 0, 0, 0, 0, 0, 220, 0, 0,…$ V330  <int> 0, 252, 29, 0, 0, 0, 0, 14, 0, 5, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0,…
$V331 <int> 0, 165, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V332  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V333 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V334  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V335 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V336  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V337 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V338  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V339 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V340  <int> 0, 0, 159, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V341 <int> 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V342  <int> 0, 0, 120, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15…
$V343 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 252…$ V344  <int> 0, 7, 0, 0, 126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 242, 0, 0, 0, 0, …
$V345 <int> 0, 178, 0, 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 252, 0, 0, 0, …$ V346  <int> 0, 252, 0, 0, 247, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 252, 0, 0, 0,…
$V347 <int> 0, 240, 0, 0, 176, 0, 0, 0, 0, 29, 40, 0, 54, 255, 0, 222, 0, 7,…$ V348  <int> 11, 71, 0, 0, 9, 0, 0, 0, 0, 232, 214, 10, 251, 253, 0, 59, 0, 1…
$V349 <int> 190, 19, 0, 0, 0, 0, 0, 0, 0, 247, 250, 129, 254, 56, 29, 0, 0, …$ V350  <int> 253, 28, 0, 32, 0, 0, 255, 0, 178, 63, 254, 222, 254, 0, 254, 0,…
$V351 <int> 70, 0, 0, 205, 8, 0, 253, 91, 254, 0, 254, 78, 254, 0, 254, 0, 0…$ V352  <int> 0, 0, 0, 253, 78, 0, 253, 212, 143, 0, 254, 79, 248, 114, 109, 0…
$V353 <int> 0, 0, 0, 251, 245, 0, 108, 247, 0, 0, 254, 8, 74, 113, 0, 0, 0, …$ V354  <int> 0, 0, 0, 126, 253, 157, 0, 252, 0, 153, 254, 0, 5, 222, 0, 178, …
$V355 <int> 0, 0, 163, 0, 129, 252, 0, 252, 0, 252, 34, 0, 0, 253, 0, 252, 2…$ V356  <int> 0, 0, 254, 0, 0, 252, 0, 252, 0, 226, 0, 0, 0, 253, 0, 252, 141,…
$V357 <int> 0, 253, 216, 0, 0, 60, 0, 204, 0, 0, 0, 0, 0, 255, 0, 141, 0, 0,…$ V358  <int> 0, 252, 16, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0, …
$V359 <int> 0, 195, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V360  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V361 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V362  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V363 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V364  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V365 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V366  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V367 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V368  <int> 0, 0, 159, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V369 <int> 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V370  <int> 0, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100…
$V371 <int> 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 185, 0, 0, 0, 0, 2…$ V372  <int> 0, 57, 0, 0, 232, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0,…
$V373 <int> 0, 252, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 252, 0, 0, 0, …$ V374  <int> 0, 252, 0, 0, 176, 0, 0, 32, 0, 45, 0, 0, 0, 252, 0, 194, 0, 0, …
$V375 <int> 0, 63, 0, 0, 0, 0, 0, 125, 0, 219, 81, 0, 140, 253, 0, 67, 0, 0,…$ V376  <int> 0, 0, 0, 0, 0, 0, 0, 193, 0, 252, 247, 134, 254, 223, 0, 0, 0, 1…
$V377 <int> 35, 0, 0, 0, 0, 0, 0, 193, 0, 143, 254, 253, 254, 37, 29, 0, 0, …$ V378  <int> 241, 0, 0, 104, 36, 110, 253, 193, 178, 0, 254, 167, 254, 0, 254…
$V379 <int> 225, 0, 0, 251, 201, 121, 252, 253, 254, 0, 254, 8, 254, 48, 254…$ V380  <int> 160, 0, 14, 253, 252, 122, 252, 252, 143, 0, 254, 0, 254, 174, 1…
$V381 <int> 108, 0, 86, 184, 252, 121, 108, 252, 0, 116, 254, 0, 254, 252, 0…$ V382  <int> 1, 0, 178, 15, 169, 202, 0, 252, 0, 249, 254, 0, 202, 252, 0, 24…
$V383 <int> 0, 0, 248, 0, 11, 252, 0, 238, 0, 252, 146, 0, 125, 242, 0, 252,…$ V384  <int> 0, 0, 254, 0, 0, 194, 0, 102, 0, 103, 0, 0, 45, 214, 0, 194, 128…
$V385 <int> 0, 253, 91, 0, 0, 3, 0, 28, 0, 0, 0, 0, 0, 253, 0, 67, 0, 0, 0, …$ V386  <int> 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 199, 0, 0, 0, 0, 0, 0, …
$V387 <int> 0, 195, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0…$ V388  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V389 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V390  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V391 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V392  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V393 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V394  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V395 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V396  <int> 0, 0, 159, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V397 <int> 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V398  <int> 0, 0, 85, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$V399 <int> 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 16…$ V400  <int> 0, 198, 0, 0, 252, 0, 0, 0, 0, 4, 0, 0, 0, 13, 0, 205, 0, 0, 0, …
$V401 <int> 0, 253, 0, 0, 252, 0, 0, 45, 0, 96, 0, 0, 0, 109, 0, 190, 0, 0, …$ V402  <int> 0, 190, 47, 0, 30, 0, 0, 222, 0, 253, 0, 0, 0, 252, 0, 24, 0, 0,…
$V403 <int> 0, 0, 49, 0, 22, 10, 0, 252, 0, 255, 0, 0, 58, 228, 0, 0, 0, 0, …$ V404  <int> 0, 0, 116, 0, 119, 53, 0, 252, 0, 253, 110, 255, 181, 130, 0, 0,…
$V405 <int> 0, 0, 144, 80, 197, 179, 0, 252, 0, 200, 246, 254, 234, 0, 29, 0…$ V406  <int> 81, 0, 150, 240, 241, 253, 253, 252, 178, 122, 254, 78, 254, 38,…
$V407 <int> 240, 0, 241, 251, 253, 253, 252, 253, 254, 7, 254, 0, 254, 165, …$ V408  <int> 253, 0, 243, 193, 252, 255, 252, 252, 162, 25, 254, 0, 254, 253,…
$V409 <int> 253, 0, 234, 23, 251, 253, 108, 252, 0, 201, 254, 0, 254, 233, 0…$ V410  <int> 119, 0, 179, 0, 77, 253, 0, 252, 0, 250, 254, 0, 254, 164, 0, 25…
$V411 <int> 25, 0, 241, 0, 0, 228, 0, 177, 0, 158, 171, 0, 254, 49, 0, 209, …$ V412  <int> 0, 0, 252, 0, 0, 35, 0, 0, 0, 0, 0, 0, 252, 63, 0, 24, 56, 0, 72…
$V413 <int> 0, 255, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 140, 253, 0, 0, 0, 0, 0, …$ V414  <int> 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 214, 0, 0, 0, 0, 0, 0,…
$V415 <int> 0, 196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 20, 0, 0, 0, …$ V416  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, …
$V417 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 124, 0, 0, 0, 0,…$ V418  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, …
$V419 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V420  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V421 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V422  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V423 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V424  <int> 0, 0, 150, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V425 <int> 0, 0, 253, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V426  <int> 0, 0, 237, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V427 <int> 0, 76, 207, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V428  <int> 0, 246, 207, 0, 231, 0, 0, 0, 0, 92, 0, 0, 0, 73, 0, 0, 0, 0, 0,…
$V429 <int> 0, 252, 207, 0, 252, 5, 0, 45, 0, 252, 0, 0, 0, 252, 0, 0, 0, 0,…$ V430  <int> 0, 112, 253, 0, 253, 54, 0, 223, 0, 252, 0, 0, 0, 252, 0, 0, 0, …
$V431 <int> 0, 0, 254, 0, 252, 227, 0, 253, 0, 253, 0, 0, 0, 126, 0, 0, 0, 3…$ V432  <int> 0, 0, 250, 32, 252, 252, 0, 253, 0, 217, 0, 201, 0, 0, 0, 0, 0, …
$V433 <int> 0, 0, 240, 253, 252, 243, 0, 253, 0, 252, 73, 253, 30, 23, 29, 0…$ V434  <int> 0, 0, 198, 253, 226, 228, 253, 253, 178, 252, 89, 226, 50, 178, …
$V435 <int> 45, 0, 143, 253, 227, 170, 252, 255, 254, 200, 89, 69, 73, 252, …$ V436  <int> 186, 0, 91, 159, 252, 242, 252, 253, 240, 227, 93, 0, 155, 240, …
$V437 <int> 253, 0, 28, 0, 231, 252, 108, 253, 0, 252, 240, 0, 253, 148, 0, …$ V438  <int> 253, 0, 5, 0, 0, 252, 0, 253, 0, 231, 254, 0, 254, 7, 0, 248, 25…
$V439 <int> 150, 0, 233, 0, 0, 231, 0, 253, 0, 0, 171, 0, 254, 44, 0, 106, 2…$ V440  <int> 27, 0, 250, 0, 0, 117, 0, 74, 0, 0, 0, 0, 254, 215, 0, 0, 208, 0…
$V441 <int> 0, 253, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 254, 240, 0, 0, 157, 0, 0,…$ V442  <int> 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 148, 0, 0, 207, 0, 0,…
$V443 <int> 0, 148, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 225, 0, 0, 0, …$ V444  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0,…
$V445 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 241, 0, 0, 0, 0,…$ V446  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 160, 0, 0, 0, 0,…
$V447 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V448  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V449 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V450  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V451 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V452  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V453 <int> 0, 0, 119, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V454  <int> 0, 0, 177, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V455 <int> 0, 85, 177, 0, 0, 0, 0, 0, 0, 87, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V456  <int> 0, 252, 177, 0, 55, 6, 0, 0, 0, 251, 0, 0, 0, 119, 0, 0, 0, 0, 0…
$V457 <int> 0, 230, 177, 0, 235, 78, 0, 0, 0, 247, 0, 55, 0, 252, 0, 0, 9, 0…$ V458  <int> 0, 25, 177, 0, 253, 252, 0, 31, 0, 231, 0, 6, 0, 252, 0, 0, 31, …
$V459 <int> 0, 0, 98, 0, 217, 252, 0, 123, 0, 65, 0, 0, 0, 0, 0, 0, 82, 171,…$ V460  <int> 0, 0, 56, 151, 138, 125, 0, 52, 0, 48, 0, 18, 0, 0, 0, 0, 137, 2…
$V461 <int> 0, 0, 0, 251, 42, 59, 0, 44, 0, 189, 0, 128, 0, 197, 29, 0, 203,…$ V462  <int> 0, 0, 0, 251, 24, 0, 255, 44, 113, 252, 0, 253, 0, 252, 254, 0, …
$V463 <int> 0, 0, 0, 251, 192, 18, 253, 44, 254, 252, 0, 241, 0, 252, 254, 2…$ V464  <int> 16, 0, 0, 39, 252, 208, 253, 44, 240, 253, 1, 41, 0, 63, 63, 252…
$V465 <int> 93, 0, 0, 0, 143, 252, 170, 143, 0, 252, 128, 0, 91, 0, 0, 252, …$ V466  <int> 252, 0, 102, 0, 0, 252, 0, 252, 0, 251, 254, 0, 200, 57, 0, 102,…
$V467 <int> 253, 7, 254, 0, 0, 252, 0, 252, 0, 227, 219, 0, 254, 252, 0, 0, …$ V468  <int> 187, 135, 220, 0, 0, 252, 0, 74, 0, 35, 31, 0, 254, 252, 0, 0, 2…
$V469 <int> 0, 253, 0, 0, 0, 87, 0, 0, 0, 0, 0, 0, 254, 140, 0, 0, 223, 0, 0…$ V470  <int> 0, 186, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 223, 0, 0, 0…
$V471 <int> 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 118, 0, 0, 0, 127, 0, 0, 0,…$ V472  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, …
$V473 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, …$ V474  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V475 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V476  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V477 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V478  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V479 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V480  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V481 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V482  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1…
$V483 <int> 0, 85, 0, 0, 0, 5, 0, 0, 0, 190, 0, 25, 0, 0, 0, 0, 9, 0, 0, 0, …$ V484  <int> 0, 252, 0, 0, 0, 135, 0, 0, 0, 221, 0, 205, 0, 135, 0, 0, 137, 0…
$V485 <int> 0, 223, 0, 0, 0, 252, 0, 0, 0, 98, 0, 235, 0, 253, 0, 0, 214, 26…$ V486  <int> 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 92, 0, 174, 0, 0, 254, 123, 6…
$V487 <int> 0, 0, 0, 48, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 254, 254…$ V488  <int> 0, 0, 0, 221, 0, 16, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 254, 253, 13…
$V489 <int> 0, 0, 0, 251, 0, 0, 0, 0, 0, 42, 0, 20, 0, 229, 29, 0, 254, 203,…$ V490  <int> 0, 0, 0, 251, 62, 21, 253, 0, 83, 196, 0, 253, 0, 253, 254, 134,…
$V491 <int> 0, 0, 0, 172, 255, 203, 252, 0, 254, 252, 0, 253, 0, 112, 254, 2…$ V492  <int> 0, 0, 0, 0, 253, 253, 252, 0, 245, 253, 7, 58, 0, 0, 28, 253, 25…
$V493 <int> 0, 0, 0, 0, 109, 247, 252, 15, 31, 252, 254, 0, 0, 38, 0, 253, 2…$ V494  <int> 249, 7, 169, 0, 0, 129, 42, 252, 0, 252, 254, 0, 4, 222, 0, 39, …
$V495 <int> 253, 131, 254, 0, 0, 173, 0, 252, 0, 162, 214, 0, 192, 253, 0, 0…$ V496  <int> 249, 252, 137, 0, 0, 252, 0, 74, 0, 0, 28, 0, 254, 112, 0, 0, 50…
$V497 <int> 64, 225, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, …$ V498  <int> 0, 71, 0, 0, 0, 184, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0,…
$V499 <int> 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 154, 0, 0, 0, 0, 0, 0, 0, 0…$ V500  <int> 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$V501 <int> 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V502  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V503 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V504  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V505 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V506  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V507 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V508  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V509 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V510  <int> 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1…
$V511 <int> 0, 85, 0, 0, 0, 136, 0, 0, 0, 111, 0, 231, 0, 0, 0, 0, 185, 0, 0…$ V512  <int> 0, 252, 0, 0, 0, 252, 0, 0, 0, 29, 0, 245, 0, 135, 0, 0, 254, 0,…
$V513 <int> 0, 145, 0, 0, 0, 241, 0, 0, 0, 0, 0, 108, 0, 252, 0, 0, 247, 93,…$ V514  <int> 0, 0, 0, 0, 0, 106, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 179, 253, 68…
$V515 <int> 0, 0, 0, 234, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 146, 254, 255…$ V516  <int> 0, 0, 0, 251, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 67, 121, 13, …
$V517 <int> 0, 0, 0, 251, 0, 53, 0, 0, 0, 62, 0, 132, 0, 227, 29, 6, 60, 13,…$ V518  <int> 0, 0, 0, 196, 71, 200, 149, 0, 79, 239, 0, 253, 0, 252, 254, 183…
$V519 <int> 46, 0, 0, 12, 253, 252, 252, 0, 254, 252, 0, 185, 0, 158, 254, 2…$ V520  <int> 130, 0, 0, 0, 252, 216, 252, 0, 246, 86, 138, 14, 0, 226, 28, 25…
$V521 <int> 183, 48, 0, 0, 21, 65, 252, 86, 38, 42, 254, 0, 0, 234, 0, 107, …$ V522  <int> 253, 165, 169, 0, 0, 0, 144, 252, 0, 42, 254, 0, 0, 201, 0, 2, 2…
$V523 <int> 253, 252, 254, 0, 0, 14, 0, 252, 0, 14, 116, 0, 141, 27, 0, 0, 1…$ V524  <int> 207, 173, 57, 0, 0, 72, 0, 74, 0, 0, 0, 0, 254, 12, 0, 0, 0, 0, …
$V525 <int> 2, 0, 0, 0, 0, 163, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, …$ V526  <int> 0, 0, 0, 0, 0, 241, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, …
$V527 <int> 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 116, 0, 0, 0, 0, 0, 0, 0, …$ V528  <int> 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V529 <int> 0, 0, 0, 0, 0, 223, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V530  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V531 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V532  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V533 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V534  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V535 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V536  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V537 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V538  <int> 0, 0, 0, 0, 0, 105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V539 <int> 0, 86, 0, 0, 0, 252, 0, 5, 0, 0, 19, 121, 0, 0, 0, 0, 255, 0, 0,…$ V540  <int> 0, 253, 0, 0, 0, 242, 0, 75, 0, 0, 177, 245, 0, 57, 0, 0, 222, 6…
$V541 <int> 0, 225, 0, 0, 0, 88, 0, 9, 0, 0, 90, 254, 25, 252, 0, 0, 49, 239…$ V542  <int> 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 254, 126, 252, 0, 0, 0, 253, 6…
$V543 <int> 0, 0, 0, 253, 0, 73, 0, 0, 0, 0, 0, 254, 86, 57, 0, 0, 0, 76, 25…$ V544  <int> 0, 0, 0, 251, 0, 170, 0, 0, 0, 15, 0, 217, 0, 104, 0, 10, 0, 8, …
$V545 <int> 39, 0, 0, 251, 0, 244, 0, 0, 0, 148, 0, 254, 0, 240, 29, 102, 0,…$ V546  <int> 148, 0, 0, 89, 0, 252, 109, 0, 0, 253, 0, 223, 0, 252, 254, 252,…
$V547 <int> 229, 0, 0, 0, 253, 126, 252, 0, 214, 218, 25, 50, 0, 252, 254, 2…$ V548  <int> 253, 114, 0, 0, 252, 29, 252, 98, 254, 0, 240, 0, 0, 253, 35, 16…
$V549 <int> 253, 238, 0, 0, 21, 0, 252, 242, 150, 0, 254, 0, 0, 233, 0, 16, …$ V550  <int> 253, 253, 169, 0, 0, 0, 144, 252, 0, 0, 254, 0, 3, 74, 0, 0, 50,…
$V551 <int> 250, 162, 254, 0, 0, 0, 0, 252, 0, 0, 34, 0, 188, 0, 0, 0, 0, 0,…$ V552  <int> 182, 0, 57, 0, 0, 0, 0, 74, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 147,…
$V553 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 25…$ V554  <int> 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 250, 0, 0, 0, 0, 0, 0, 0, 2…
$V555 <int> 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0…$ V556  <int> 0, 0, 0, 0, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V557 <int> 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V558  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V559 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V560  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V561 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V562  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V563 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V564  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V565 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V566  <int> 0, 0, 0, 0, 0, 231, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V567 <int> 0, 85, 0, 0, 0, 252, 0, 183, 0, 0, 164, 0, 0, 0, 0, 0, 254, 0, 0…$ V568  <int> 0, 252, 0, 0, 0, 245, 0, 252, 0, 0, 254, 116, 24, 51, 0, 0, 206,…
$V569 <int> 0, 249, 0, 0, 0, 205, 0, 29, 0, 0, 215, 165, 209, 242, 0, 0, 4, …$ V570  <int> 0, 146, 0, 159, 0, 216, 0, 0, 0, 0, 63, 233, 254, 252, 0, 0, 0, …
$V571 <int> 24, 48, 0, 255, 0, 252, 0, 0, 0, 0, 36, 233, 15, 253, 0, 13, 0, …$ V572  <int> 114, 29, 0, 253, 0, 252, 0, 0, 0, 121, 0, 234, 0, 252, 0, 168, 0…
$V573 <int> 221, 85, 0, 253, 0, 252, 0, 0, 0, 252, 51, 180, 0, 252, 29, 252,…$ V574  <int> 253, 178, 0, 31, 71, 124, 0, 18, 0, 231, 89, 39, 0, 252, 254, 25…
$V575 <int> 253, 225, 0, 0, 253, 3, 218, 92, 144, 28, 206, 3, 0, 252, 254, 1…$ V576  <int> 253, 253, 0, 0, 252, 0, 253, 239, 241, 0, 254, 0, 0, 240, 109, 2…
$V577 <int> 253, 223, 0, 0, 21, 0, 253, 252, 8, 0, 254, 0, 23, 148, 0, 0, 64…$ V578  <int> 201, 167, 169, 0, 0, 0, 255, 252, 0, 0, 139, 0, 137, 0, 0, 0, 0,…
$V579 <int> 78, 56, 255, 0, 0, 0, 35, 243, 0, 0, 8, 0, 254, 0, 0, 0, 0, 0, 2…$ V580  <int> 0, 0, 94, 0, 0, 0, 0, 65, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 20, 0,…
$V581 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 25…$ V582  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 209, 0, 0, 0, 0, 0, 0, 0, 15…
$V583 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0…$ V584  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V585 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V586  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V587 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V588  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V589 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V590  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V591 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V592  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V593 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V594  <int> 0, 0, 0, 0, 0, 207, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
$V595 <int> 0, 85, 0, 0, 0, 252, 0, 252, 0, 0, 57, 0, 0, 0, 0, 0, 216, 0, 0,…$ V596  <int> 0, 252, 0, 0, 0, 252, 0, 252, 0, 0, 197, 0, 168, 0, 0, 0, 254, 1…
$V597 <int> 23, 252, 0, 48, 0, 252, 0, 147, 0, 0, 254, 0, 254, 75, 0, 0, 158…$ V598  <int> 66, 252, 0, 228, 0, 252, 0, 134, 0, 0, 254, 0, 254, 189, 0, 0, 1…
$V599 <int> 213, 229, 0, 253, 0, 178, 0, 134, 0, 31, 222, 0, 48, 253, 0, 41,…$ V600  <int> 253, 215, 0, 247, 0, 116, 0, 134, 0, 221, 180, 0, 9, 252, 0, 252…
$V601 <int> 253, 252, 0, 140, 0, 36, 0, 134, 0, 251, 241, 0, 0, 252, 6, 252,…$ V602  <int> 253, 252, 0, 8, 106, 4, 0, 203, 0, 129, 254, 0, 0, 157, 212, 217…
$V603 <int> 253, 252, 0, 0, 253, 0, 175, 253, 144, 0, 254, 0, 9, 112, 254, 0…$ V604  <int> 198, 196, 0, 0, 252, 0, 252, 252, 240, 0, 253, 0, 127, 63, 109, …
$V605 <int> 81, 130, 0, 0, 21, 0, 252, 252, 2, 0, 213, 0, 241, 0, 0, 0, 0, 0…$ V606  <int> 2, 0, 169, 0, 0, 0, 253, 188, 0, 0, 11, 0, 254, 0, 0, 0, 0, 0, 2…
$V607 <int> 0, 0, 254, 0, 0, 0, 35, 83, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 27, …$ V608  <int> 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, 0, 0, 255, 0, 0, 0, 0, 0, 0, 0, 2…
$V609 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 242, 0, 0, 0, 0, 0, 0, 0, 25…$ V610  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, 0, 0, 0, 0, 0, 0, 0, 252…
$V611 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, …$ V612  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V613 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V614  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V615 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V616  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V617 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V618  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V619 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V620  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V621 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V622  <int> 0, 0, 0, 0, 0, 13, 0, 208, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V623 <int> 18, 28, 0, 0, 0, 93, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V624  <int> 171, 199, 0, 0, 0, 143, 0, 252, 0, 0, 140, 0, 101, 0, 0, 0, 131,…
$V625 <int> 219, 252, 0, 64, 0, 121, 0, 252, 0, 0, 105, 0, 254, 0, 0, 0, 247…$ V626  <int> 253, 252, 0, 251, 0, 23, 0, 252, 0, 0, 254, 0, 254, 0, 0, 40, 24…
$V627 <int> 253, 253, 0, 253, 0, 6, 0, 252, 0, 218, 254, 0, 254, 0, 0, 155, …$ V628  <int> 253, 252, 0, 220, 0, 0, 0, 252, 0, 252, 254, 0, 205, 0, 0, 252, …
$V629 <int> 253, 252, 0, 0, 0, 0, 0, 252, 0, 160, 254, 0, 190, 0, 0, 214, 17…$ V630  <int> 195, 233, 0, 0, 45, 0, 0, 252, 0, 0, 254, 0, 190, 0, 203, 31, 72…
$V631 <int> 80, 145, 0, 0, 255, 0, 73, 253, 144, 0, 254, 0, 205, 0, 254, 0, …$ V632  <int> 9, 0, 0, 0, 253, 0, 252, 230, 254, 0, 236, 0, 254, 0, 178, 0, 0,…
$V633 <int> 0, 0, 0, 0, 21, 0, 252, 153, 82, 0, 0, 0, 254, 0, 0, 0, 0, 0, 13…$ V634  <int> 0, 0, 169, 0, 0, 0, 253, 8, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 6, 0…
$V635 <int> 0, 0, 254, 0, 0, 0, 35, 0, 0, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0,…$ V636  <int> 0, 0, 153, 0, 0, 0, 0, 0, 0, 0, 0, 0, 242, 0, 0, 0, 0, 0, 0, 0, …
$V637 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 0, 0, 252…$ V638  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252,…
$V639 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, …$ V640  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V641 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V642  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V643 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V644  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V645 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V646  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V647 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V648  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V649 <int> 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V650  <int> 172, 0, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V651 <int> 226, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V652  <int> 253, 25, 0, 0, 0, 0, 0, 252, 0, 0, 0, 0, 33, 0, 0, 0, 0, 112, 0,…
$V653 <int> 253, 128, 0, 64, 0, 0, 0, 252, 0, 0, 7, 0, 166, 0, 0, 0, 0, 253,…$ V654  <int> 253, 252, 0, 251, 0, 0, 0, 252, 0, 0, 117, 0, 254, 0, 0, 165, 0,…
$V655 <int> 253, 253, 0, 253, 0, 0, 0, 252, 0, 122, 117, 0, 254, 0, 0, 252, …$ V656  <int> 244, 252, 0, 220, 0, 0, 0, 252, 0, 252, 165, 0, 254, 0, 0, 252, …
$V657 <int> 133, 141, 0, 0, 0, 0, 0, 217, 0, 82, 254, 0, 254, 0, 0, 106, 0, …$ V658  <int> 11, 37, 0, 0, 0, 0, 0, 207, 0, 0, 254, 0, 254, 0, 155, 0, 0, 9, …
$V659 <int> 0, 0, 0, 0, 218, 0, 31, 146, 230, 0, 239, 0, 254, 0, 254, 0, 0, …$ V660  <int> 0, 0, 0, 0, 252, 0, 211, 45, 247, 0, 50, 0, 254, 0, 190, 0, 0, 0…
$V661 <int> 0, 0, 0, 0, 56, 0, 252, 0, 40, 0, 0, 0, 254, 0, 0, 0, 0, 0, 0, 0…$ V662  <int> 0, 0, 169, 0, 0, 0, 253, 0, 0, 0, 0, 0, 250, 0, 0, 0, 0, 0, 0, 0…
$V663 <int> 0, 0, 255, 0, 0, 0, 35, 0, 0, 0, 0, 0, 138, 0, 0, 0, 0, 0, 0, 0,…$ V664  <int> 0, 0, 153, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 0, 0, 0, 0, 0, 0, 0, 9…
$V665 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 206,…$ V666  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131,…
$V667 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, …$ V668  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V669 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V670  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V671 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V672  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V673 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V674  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V675 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V676  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V677 <int> 136, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V678  <int> 253, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V679 <int> 253, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V680  <int> 253, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0,…
$V681 <int> 212, 0, 0, 24, 0, 0, 0, 235, 0, 0, 0, 0, 7, 0, 0, 43, 0, 118, 0,…$ V682  <int> 135, 0, 0, 193, 0, 0, 0, 252, 0, 0, 0, 0, 88, 0, 0, 179, 0, 243,…
$V683 <int> 132, 0, 0, 253, 0, 0, 0, 172, 0, 0, 0, 0, 154, 0, 0, 252, 0, 191…$ V684  <int> 16, 0, 0, 220, 0, 0, 0, 103, 0, 0, 0, 0, 116, 0, 0, 150, 0, 113,…
$V685 <int> 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 194, 0, 0, 39, 0, 0, 0, 0, …$ V686  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 194, 0, 32, 0, 0, 0, 0, 0, 0…
$V687 <int> 0, 0, 0, 0, 96, 0, 0, 0, 168, 0, 0, 0, 154, 0, 199, 0, 0, 0, 0, …$ V688  <int> 0, 0, 0, 0, 252, 0, 0, 0, 209, 0, 0, 0, 154, 0, 104, 0, 0, 0, 0,…
$V689 <int> 0, 0, 0, 0, 189, 0, 0, 0, 31, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, …$ V690  <int> 0, 0, 96, 0, 42, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0…
$V691 <int> 0, 0, 254, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V692  <int> 0, 0, 153, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
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$V725 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V726  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
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$V729 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V730  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V731 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V732  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V733 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V734  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V735 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V736  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, …
$V737 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 228, 0…$ V738  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 252, 0, 0, 0, 129, …
$V739 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 28, 0,…$ V740  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V741 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V742  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
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$V745 <int> 0, 0, 0, 0, 147, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…$ V746  <int> 0, 0, 0, 0, 252, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
$V747 <int> 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …$ V748  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
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$V755 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V756  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V757 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V758  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V759 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V760  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
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$V775 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V776  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V777 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V778  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V779 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V780  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V781 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V782  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$V783 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…$ V784  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$label <fct> 5, 0, 4, 1, 9, 2, 1, 3, 1, 4, 3, 5, 3, 6, 1, 7, 2, 8, 6, 9, 4, 0… Code mnist %>% mutate(id = 1:n()) %>% filter(id %in% 1:10) %>% pivot_longer(starts_with("V")) %>% mutate(row = rep(rep(1:28, each = 28), max(id)), col = rep(rep(1:28, times = 28), max(id))) %>% ggplot(aes(col, row)) + geom_tile(aes(fill = value)) + facet_wrap(~id, nrow = 2) + scale_y_reverse() + theme_void(base_size = 18) + guides(fill = "none") ## Multi-class logistic regression • For multi-class problems, we can fit a logistic model for every class. mnist_digit_preds <- map_dfc(0:9, function(digit) { mnist_data <- mnist %>% mutate(target_digit = as.numeric(label == digit)) %>% select(-label) mnist_fit <- glm(target_digit ~ ., data = mnist_data, family = binomial()) predict(mnist_fit, mnist_data, type = "response") }) %>% mutate(id = 1:n(), label = mnist$label) %>%
pivot_longer(-c(id, label), names_to = "name", values_to = "pred") 
• The predicted class then can be determined by the highest probability out of all classes.

# Takeaways

• Logistic regression allows us to predict binary categorical variables.
• It is estimated via maximum likelihood methods.
• Logistic regression is a linear classifier and such, it cannot deal with complex classification patterns.
• In problems with multiple predictors, logistic regression separates the points using a hyper-plane.
• Variable selection approaches such as lasso and ridge regression can still be considered (covered in tutorial).